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Thaddeus Steven Robinson

Spinoza and the Metaphysics of Mechanism

Doctor of Philosophy

Jan A. Cover

Michael Jacovides

Jeffrey Brower

Daniel Frank

July 25, 2007

Jan A. Cover

Rod Bertolet

Graduate School ETD Form 9(01/07)

SPINOZA AND THE METAPHYSICS OF MECHANISM

A Dissertation

Submitted to the Faculty

of

Purdue University

by

Thaddeus Steven Robinson

In Partial Fulfillment of the

Requirements for the Degree

of

Doctor of Philosophy

August 2007

Purdue University

West Lafayette, Indiana

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ii

For my wonderful wife Katie whom I love very much

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ACKNOWLEDGMENTS

I would like to thank my committee members Jeff Brower, Jan Cover, and Mike Jacovides for all their helpful comments. In addition, I would like to thank Chris Martin, Kevin Sharpe, and Winship Varner for their valuable input on various parts of this dissertation.

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TABLE OF CONTENTS

ABSTRACT.........................................................................................................................v CHAPTER 1: INTRODUCTION........................................................................................1

The Mechanical Hypothesis.....................................................................................1 Descartes’ Mechanism.............................................................................................8 Spinoza’s Mechanism and the Plan of the Dissertation.........................................23

CHAPTER 2: SPINOZA AND THE REJECTION OF DESCARTES’ ACCOUNT OF MATTER ...........................................................................................................................29

Spinoza’s Project in E1P15s ..................................................................................31 The Vacuum Argument..........................................................................................32 E1P12 and the Divisibility Argument....................................................................51 Spinoza on Corporeal Substance and Body...........................................................61

CHAPTER 3: SPINOZA’S IMMEDIATE INFINITE MODE OF EXTENSION............65

Reconstructing Spinoza’s Account of Motion-and-Rest .......................................68 Spinoza’s Account of Motion-and-Rest.................................................................84

CHAPTER 4: THE MODE-SUBSTANCE RELATION................................................107

The Relation of p-part to Whole and the Potential Parts Doctrine ......................110 The Relation between Bodies and Corporeal Substance .....................................117 Curley’s Challenge...............................................................................................128

CHAPTER 5: SPINOZA’S NATURALISTIC CONCURRENTISM ............................135

God and Finite Modes..........................................................................................136 Spinoza’s Concurrentism.....................................................................................148

BIBLIOGRAPHY............................................................................................................168 VITA................................................................................................................................176

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ABSTRACT

Robinson, Thaddeus Steven. Ph.D., Purdue University, August 2007. Spinoza and the Metaphysics of Mechanism. Major Professor: Jan. A. Cover.

Descartes, Gassendi, Galileo, Boyle, Spinoza, and Hobbes, among many others,

were adherents of what Boyle called “the mechanical philosophy”. According to the

mechanical philosophy, the explanation for all natural phenomena is found in the various

motions and collisions of insensible particles of matter. The first half of the 17th Century

saw a number of efforts to systematize the mechanical philosophy by providing it with a

solid metaphysical foundation. In his Principles of Philosophy Descartes put forth

perhaps the most successful and influential of these early efforts. Spinoza, like many of

his contemporaries, was impressed with Descartes’ system; nevertheless, he was

convinced of the inadequacy of the underlying metaphysics. The basic tools of

mechanistic explanation are matter and motion, and any attempt to systematize the

mechanical philosophy must offer accounts of each of these tools. It was with Descartes’

account of precisely these tools that Spinoza took issue. In my dissertation I argue that

much of what is distinctive about Spinoza’s metaphysics arose, at least partially, as the

result of Spinoza’s efforts to replace Descartes’ suspect metaphysics of matter and the

relation between matter and motion, with philosophically adequate accounts.

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I begin in chapter one by offering a characterization of 17th Century mechanism in

general. I then turn to Descartes’ specific interpretation of mechanism and metaphysics

which underlie it by taking a close look at the first two books of Descartes’ Principles of

Philosophy. Last, I show Spinoza’s commitment to Descartes’ account of mechanism. In

chapter two I present and critically evaluate Spinoza’s criticisms of Descartes’ account of

matter. I show that Spinoza offers two arguments for the conclusion that Descartes’

account can’t be right, and that the lesson he draws is that no corporeal substance is i)

composed of really distinct parts, ii) a body, despite the fact that it is extended and iii) as

such, Descartes is wrong to think that the essence of body is extension. In chapter three I

argue that these considerations lead Spinoza to maintain that regions of extension, as

opposed to bodies, are the subjects of motion and that the essence of body is extension in

motion. I make this case by offering a novel interpretation of what Spinoza refers to as

“the immediate infinite mode of extension”.

Perhaps the chief obstacle to understanding Spinoza’s substance monism is

accounting for the relation between bodies and the one extended substance. I argue in

chapter four that Spinoza avoids the problems with Descartes’ account of matter by

adopting the Scholastic-Aristotelian idea of a posterior part to account for the relation

between bodies and extension. In the final chapter I turn to Spinoza’s resolution of the

tension between mechanical and theological explanation. The explanations the

mechanical philosophy seeks to offer take the form of showing that any particular

observable phenomenon is the effect of a series of causal relations obtaining between

particles of matter. However, on its face, this view conflicts with the traditional

theological commitment that God is the sole cause and author of all things, a view to

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which Spinoza adheres. In chapter five, I argue that Spinoza is a concurrentist, and as a

result resolves this problem by maintaining that instances of secondary causation are

instances in which God and finite modes concur in causing an effect. In making this case

I outline Spinoza’s unique account of force and show how, according to Spinoza, it

grounds the laws of nature.

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CHAPTER1: INTRODUCTION

Introduction

In this dissertation I will be concerned primarily with Spinoza’s reaction to the

mechanism of his day. Ultimately I argue that much of what is distinctive about

Spinoza’s metaphysics arose, at least partially, as the result of his efforts to replace

Descartes’ account of the metaphysical foundations of mechanism, with a philosophically

adequate one. Before I turn to Spinoza’s reaction to the mechanism of his day we need to

have both a general sense of the mechanical worldview and its assumptions, and an

acquaintance with Descartes’ particular interpretation of this worldview. To this end, this

chapter is divided into three parts. I begin in section 1 by laying out a general sketch of

early modern mechanism. In section 2, I turn to a perhaps the most influential account of

the mechanical worldview, Descartes’. Last, in section 3, I show that Spinoza is a

mechanist, but takes the metaphysical foundations of Descartes’ mechanism to be deeply

problematic. I conclude section 3 with an outline of the rest of the dissertation.

Section 1: The Mechanical Hypothesis

In order to determine the nature of early modern mechanism, there is no better

place to begin than with Robert Boyle, the originator of the term ‘mechanical

hypothesis’. This is an appropriate choice not only because of Boyle’s place as a

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paradigm mechanist and as a representative of the state of mechanism at the time Spinoza

was formulating his ideas, but also because of Spinoza’s familiarity with Boyle’s work,

especially his 1661 Certain Physiological Essays. In fact, Spinoza commented on this

work and briefly corresponded with Boyle through the future president of the Royal

Society, Henry Oldenburg.1 The following passage (taken from Certain Physiological

Essays) is particularly illuminating for the purposes of this chapter.

And as for the last of the three Discouragements above mention’d, I consider’d, that the Atomical and Cartesian Hypotheses, though they differ’d in some material points from one another, yet in opposition to the Peripatetick and other vulgar Doctrines they might be look’d upon as one Philosophy: For they agree with one another, and differ from the Schools in this grand and fundamental point, that not only they take care to explicate things intelligibly; but that whereas those other Philosophers give only a general and superficial account of the Phaenomena of Nature / from certain substantial Forms, which the most ingenious among themselves confess to be Incomprehensible, and certain real Qualities, which knowing men of other Perswasions think to be likewise Unintelligible; both the Cartesians and the Atomists explicate the same Phaenomena by little Bodies variously figur’d and mov’d. I know that these two Sects of Modern Naturalists disagree about the notion of Body in general, and consequently about the Possibility of a true Vacuum, as also about the Origine of Motion, the indefinite Divisibleness of Matter, and some other points of less Importance than these: But in regard that some of them seem to be rather Metaphysical than Physiological Notions, and that some others seem rather to be requisite to the Explication of the first Origine of the Universe, than of the Phaenomena of it wherein we now find it; in regard of these, I say, and some other Considerations, and especially for this

1 See Ep. 6, 7, 11, and 13. Unless otherwise noted, all translations are those of Edwin Curley as presented in The Collected Works of Spinoza, Volume 1 (Princeton: Princeton University Press, 1985); hereafter, ‘C’. References to Samuel Shirley’s Spinoza: Complete Works (Indianapolis: Hackett, 2002) are abbreviated ‘S’, and will be referred to by page. ‘G’ in a footnote refers to Spinoza Opera, 4 vols., ed. Carl Gebhardt (Heidelberg: Carl Winters, 1925), cited by volume and page. Quotations from the Ethics will be abbrivated ‘E’ and included in the text. If the location of the citation within the Ethics is not otherwise noted, I will include this in the text accompanying references to Curley, Shirley, and Gebhardt. I will use the following standard abbreviations for the subdivisions of the Ethics and Descartes’ “Principles of Philosophy”: anumber immediately following an ‘E’ refers to the corresponding book of the Ethics. ‘P’ refers to proposition, ‘a’ to axiom, ‘d’ to definition, ‘p’ to proof, ‘s’ to scholium, ‘L’ to lemma. For example, ‘E2P13Lp1’ refers to the first proof of the lemma following proposition 13 of book 2 of the Ethics. With respect to texts besides the Ethics, I will use the abbreviations ‘ST’, ‘TEI’, ‘DPP’, ‘MT’, ‘TPT’, and ‘Ep’ to stand for the Short Treatise, Treatise on the Emendation of the Intellect, Descartes’ “Principles of Philosophy”, Appendix Containing Metaphysical Thoughts, Theological-Political Treatise, and the correspondence, respectively.

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Reason, That both parties agree in deducing all the Phaenomena of Nature from Matter and local Motion; I esteem’d that notwithstanding these things wherein the Atomists and the Cartesians differ’d, they might be thought to agree in the main, and their Hypotheses might by a Person of a reconciling Disposition be look’d on as, upon the matter, one Philosophy. Which because it explicates things by Corpuscles, or minute Bodies, may (not very unfitly) be call’d Corpuscular…I sometimes also term it the Mechanical Hypothesis on Philosophy.2

In this passage Boyle sketches the three competing philosophical systems of the day:

Cartesianism, the atomism of Gassendi and Walter Charleton, and Scholastic-

Aristotelianism. Despite their metaphysical differences, the Cartesian and the atomist are

united against the scholastic-Aristotelian on one “grand and fundamental point”: rather

than explaining natural phenomena in terms of substantial forms and real qualities as the

Scholastic-Aristotelians do, both the Cartesian and the atomist explain these phenomena

in terms of “little Bodies variously figur’d and mov’d” and deduce “all the Phaenomena

of Nature from Matter and local Motion.” In this respect, the two views constitute “one

philosophy” which Boyle calls the “Mechanical Hypothesis.” At bottom, then,

mechanism is an explanatory strategy that is distinctive in that it accounts for all

phenomena from only two fundamental principles: matter and local motion.

How do we move from these two principles to the explanation of some interesting

natural occurrence, that is, how do we “deduce” phenomena from matter and local

motion? In order to offer a rough answer to this question we’ll need to get clear about

mechanism’s two fundamental principles. However, as Boyle indicates in the passage

above, the competing philosophical systems spelled out these principles in different

ways. In what follows, I aim to lay out a basic account of these principles to which both

2 Robert Boyle, The Works of Robert Boyle [Works], 14 volumes, ed. Michael Hunter and Edward B. Davis (London: Pickering and Chatto, 1991), vol. 2, 87. This passage is taken from the preface to the 1661 Certain Physiological Essays.

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the atomist and the Cartesian would agree. This will give us a starting point when we

turn to Descartes’ attempt to systematize the mechanical philosophy. Let’s start with

matter.

Matter

Boyle explains: “I agree with the generality of philosophers, so far as to allow that

there is one catholic or universal matter common to all bodies, by which I mean a

substance extended, divisible, and impenetrable.”3 In general, the term ‘matter’ refers to

the three-dimensional stuff out of which bodies are made. Nevertheless, among the early

modern mechanists the term is used ambiguously. Sometimes ‘matter’ is used to refer to

the sum whole of the three-dimensional universe, as Boyle (among others) does when he

refers to finite bodies as the “parts of matter.”4 In other cases, the term is used as a

synonym for ‘finite body’. According to the mechanical hypothesis, there is only one

fundamental kind of matter which is by nature extended (in three-dimensions), divisible,

and impenetrable; and insofar as ‘matter’ is synonymous with ‘finite body’ this applies to

bodies as well. Thus, it follows from this that no two bodies can be in the same place at

the same time. But the existence of matter as such is not sufficient for explaining natural

phenomena. The world of experience contains cold bodies and hot bodies, sticky bodies

3 Ibid. vol. 5, 305. Quotation is taken from the 1666 The Origin of Forms and Qualities According to the Corpuscluar Philosophy.4 For Boyle see, eg. Ibid, 307; for Spinoza see E1P15s (C 423, S 225-226, G II 58-59); for Descartes see e.g. CSM III, 154: AT III, 191, and CSM III, 242-243: AT IV, 166. References to Descartes are given to The Philosophical Writings of Descartes, Vol. 1, 2: Cottingham, Stoothoff, and Murdoch, trans., and Vol. 3: Cottingham, Stoothoff, Murdoch, and Kenny, trans. (Cambridge: Cambridge University Press, 1984, 1985, 1991); henceforth ‘CSM’ (citations are by volume and page) and to Oeuvres de Descartes [AT], 13 volumes, ed. Charles Adam and Paul Tannery (Paris: J. Vrin, 1964-76). With the exception of those taken from Descartes’ Principles and Meteorology, all translations are those of CSM. Translations of the Principles are from Rene Descartes’ Principles of Philosophy [MM] trans. Valentine Rodger Miller and Reese P. Miller. (Dordrecht, Holland: D. Reidel Publishing Co., 1983). Translations taken from the Meteorology are taken from Discourse on Method, Optics, Geometry, and Meteorology [O]. trans. Paul J. Olscamp, (New York: Bobbs-Merrill Company, Inc., 1965).

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and smooth bodies; if there is only one kind of matter how do we account for the wide

variety of bodies and properties in the world? This is the role of local motion.

Local Motion

By ‘local motion’ Boyle intends to include rest as well. Local motion and rest are

properties of bodies: in general a body has the property of motion when its spatial

relations are changing and a body has the property of rest when its spatial relations are

remaining the same.5 It is the presence of local motion that accounts for the diversity of

bodies and their qualities. Boyle explains:

…to discriminate the catholic matter into [a] variety of natural bodies, it must have motion in some or all its designable parts; and that motion must have various tendencies…as we plainly see in the universe or general mass of matter there is really a great quantity of motion, and that variously determined, and that yet diverse portions of matter are at rest.6

So motion divides the whole of the material universe into parts of different sizes and

shapes, i.e. into finite bodies. The vast majority of these bodies are insensible. Insensible

parts of all different shapes and sizes come together to form composites and indeed all

the bodies of everyday experience are composed from insensible bits of matter.

Composite bodies have varying structures (or “textures” as Boyle calls them) which are a

function of the shapes and sizes of the particles of which they are composed. In addition

to supposing particular accounts of both matter and motion, the early modern mechanists

made a number of other assumptions: I will draw attention to three.

5 That Boyle takes motion and rest to be properties see Ibid. Descartes takes motion to be a mode of bodies: see Principles II.27; MM, 52: AT VIIIA, 55. 6 Robert Boyle, Works, vol. 5, 305.

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Contact Action and the Laws of Nature

Bodies are only capable of producing changes in the motion of other bodies or

their parts, and they do so only through contact.7 Boyle writes:

It is not easy to conceive either how one [body] can act upon the other [body], but by local motion (of the whole body or its corporeal effluvia); or how by motion it can do any more than put the parts of the other body into motion too, and thereby produce in them a change of situation and texture….8

Moreover, although bodies are causally efficacious, they can never initiate change: they

are not self-movers. The motion of a body is always the direct result of a collision with

another body.

Boyle is much less explicit about his commitment to the existence of the laws of

nature than he is about the other features of the mechanism here discussed. Nevertheless,

he and all other mechanists are committed to the idea that the causal interactions of

bodies are something more than random.9 Rather, the interactions of bodies follow

regular patterns. Our explanations of natural phenomena are all ultimately based on our

knowledge of these regularities. Further, given that all natural phenomena are reduced to

matter and motion, the base laws of nature are the laws of motion.

Primary and Secondary Affections

Last, and most importantly, there is a distinction between what Boyle calls the

primary and secondary affections of matter. It is this distinction that allows for

mechanical explanation. The insensible particles of matter have only four properties:

7 Two notes: First, I am prescinding from the problematic case of body-to-mind causation. Second, Malebranche would certainly not agree even in the case of body-to-body causation. Nevertheless, he is committed to there being something significant about contact since body-to-body contact is an occasion for God’s causal activity. 8 Ibid., 321. 9 In Boyle see, e.g. Ibid., 306-307.

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motion or rest, impenetrability, shape, and size. These are the primary affections of

matter. All the other affections found in the world—taste, smell, color, etc.—arise as the

result of minute particles colliding with our respective sensory structures. Thus Boyle

writes:

…I consider that, when one inanimate body works upon another, there is nothing really produced by the agent in the patient, save some local motion of its parts or some change of texture consequent upon that motion; and so, if the patient come[s] to have any sensible quality that it had not before…it is but a consequent to this mechanical change of texture that, by means of its effects upon our organs of sense, we are induced to attribute this or that sensible quality to it.10

Bodies are in motion or at rest, they have a size and shape, but they do not have colors or

tastes or smells; they are not cold or hot, firm or fluid.11 Thus there is nothing in the

material world itself that exactly matches our experiences of secondary affections.

Rather, the objects in the world which cause us to experience color and the like are

nothing more than particles of matter.

From all of this we can offer a general answer to original question: how do we

move from the principles of matter and motion to an explanation of some particular

phenomenon? Given the basic account of mechanism here offered we get an explanatory

scheme. A mechanical explanation of a phenomenon consists in showing how it arises

from the regular interactions of various insensible particles of matter each possessing

only motion or rest, shape, and size. Thus for example the explanation of the fact that

fire burns wood lies in the interactions between the parts of fire and wood. This, then,

gives a general sense of early modern mechanism. This account, however, ignores a

whole set of deep metaphysical issues, issues Boyle feels justified in abstracting from

10 Ibid., 320. 11 Although bodies certainly have the capacity to produce these sensations within us: see Ibid., 319.

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because he doesn’t take them to immediately bear on physiological issues. Not everyone,

however, was so willing to put aside the metaphysics. As we will see, Descartes takes

the metaphysics underlying the mechanical hypothesis to be of the utmost importance.

Section 2: Descartes’ Mechanism

By the 1660s what Boyle dubbed the “Mechanical Hypothesis” was already old

news; at least 30 years prior, Descartes had begun writing Le Monde, his earliest attempt

to account for all natural phenomena from matter and local motion alone. Nor was

Descartes the first to account for natural phenomena using only mechanistic principles.

He was one of many so-called “innovators” who rejected the scholastic-Aristotelian

philosophy of nature (either in whole or part) in favor of some form of mechanism.12

Richard Westfall explains:

No one man created the mechanical philosophy. Throughout the scientific circles of western Europe during the first half of the 17th century we can observe what appears to be a spontaneous movement toward a mechanical conception of nature in reaction against Renaissance Naturalism. Suggested in Galileo and Kepler, it assumed full proportions in the writings of such men as Mersenne, Gassendi, and Hobbes, not to mention less well known philosophers. Nevertheless, Rene Descartes…exerted a greater influence toward a mechanical philosophy of nature than any other man, and for all his excesses, he gave to its statement a degree of philosophic rigor it sorely needed, and obtained nowhere else.13

Descartes gave mechanism a degree of philosophic rigor in that he systematized it. First

in Le Monde, and then much more successfully in the Principles of Philosophy, Descartes

formulated a full account of reality in which he attempted to render consistent (amongst

12 This is Descartes’ own term. See CSM, III 27: AT I, 158. Not every innovator rejected scholastic-Aristotelianism whole hog; some tried to render Aristotle and mechanism consistent. For an interesting discussion of some of these thinkers see Marjorie Grene, “Aristotelico-Cartesian Themes in Natural Philosophy: Some Seventeenth-Century Cases” Perspectives on Science 1 (1993): 66-87. 13 Richard Westfall, The Construction of Modern Science: Mechanisms and Mechanics, (Cambridge: Cambridge University Press, 1999), 31.

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other things): Christian theological commitments, the mechanical worldview, and the

foundations of knowledge. According to Descartes, the mechanical worldview and its

principles (which he refers to as his “physics”) are dependent on a series of deep

metaphysical theses. Descartes laid out these theses and his justification for them first in

the Meditations and later in book I of the Principles. Thus Descartes confided to

Mersenne: “…I may tell you, between ourselves, that these six Meditations contain all

the foundations of my physics.”14 In what follows I want to examine the foundations of

Descartes’ physics as presented in part I of the Principles. I will then turn to part II of the

Principles and an examination of Descartes’ account of the principles of mechanism and

how they flow from the foundations laid in part I.

Principles I: The Foundations of Physics

Part I of the Principles begins in the same way that the Meditations does: with

Descartes’ methodological doubt. After regarding as false everything that we can, in

principle, doubt, Descartes uncovers in the Cogito that which is indubitable: “That it is

not possible for us to doubt that, while we are doubting, we exist.”15 Descartes concludes

that we are essentially thinking things. As he surveys the contents of our minds he

discovers the ideas of many things, including the idea of a perfect being. Descartes puts

forth two arguments for God’s existence on the basis of our possession of the idea of

God: a version of the ontological argument and a version of the causal argument

originally offered in Meditation 3. Descartes then turns to the (other) divine attributes.

Given our concept of God as a perfect being it follows that God is a being who, in

14 CSM III, 173: AT III, 298. 15 Principles I.7: MM, 4: AT VIIIA, 6.

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addition to having created all things and being the source of all goodness and truth, is

eternal, omniscient, and omnipotent. Likewise God is “veracious in the highest degree”

and so God is no deceiver. From this Descartes obtains his most powerful epistemic

principle: if p is clearly and distinctly perceived, then p is true: “it follows that the natural

enlightenment or the faculty of knowing given to us by God, can never attain any object

which is not true, insofar as it is clearly and distinctly perceived.”16 Thus, God

guarantees that our clear and distinct perceptions correspond to reality.

Descartes is careful to point out, however, that extension is not among God’s

perfections. Descartes argues that “divisibility is incorporated together with local

extension in the nature of corporeal things, and because it is an imperfection to be

divisible, it is certain that God is not corporeal.”17 Descartes, following a long line of

thinkers, takes divisibility to be an imperfection since everything divisible is

corruptible.18 The last thing to say about God is that He is a substance. While there are

other substances in the universe, they are not substances in the same way as God.

‘Substance’ is an equivocal term. God is a substance in the sense that His existence is

absolutely independent of everything else. Finite substances are worthy of the name

16 Principles I.30: MM, 15: AT VIIIA, 17. Likewise Descartes explains in Meditation 4 that “from this contemplation of the true God, in whom all the treasures of wisdom and the sciences lie hidden, I think I can see a way forward to the knowledge of other things.” CSM II.37: AT VII, 53. 17 Principles I. 23: MM, 12: AT VIIIA, 13. 18 I am not aware of any text in which Descartes explicitly asserts that divisibility entails corruptibility, but he comes close at CSM III, 189; AT III, 422. The principle that divisibility entails corruptibility has a long history going back at least to Plato. See for example, Plato, Five Dialogues, 2nd ed., trans. G.M.A. Grube, (Indianapolis: Hackett Publishing), 116 (Phaedo 78c); See also St. Thomas Aquinas, Summa Contra Gentiles, God, trans. Anton C. Pegis, (South Bend, Indiana: University of Notre Dame Press, 1955), 103 (SCG I.18); Malebranche, a prominent Cartesian, is especially clear on this point. He says: “All material things, being extended, are capable of division and hence of corruption; a little reflection on the nature of bodies clearly shows them to be corruptible.” See Nicholas Malebranche, The Search After Truth, eds. Thomas M. Lennon and Paul J. Olscamp, (Cambridge, Cambridge University Press, 1997), 255 (3.2.10).

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‘substance’ insofar as they are independent of all other things except God.19 Thus, the

existence of any finite substance is independent both of all other finite substances and all

the properties of substance.

According to Descartes, there are two kinds of finite substance: extended

substance and thinking substance. These two kinds of substance are distinguished from

one another insofar as each is uniquely characterized by one principle attribute which

Descartes says “constitutes its nature and essence.”20 Likewise, these principle attributes

are that through which (i) substance becomes knowable and (ii) all other possible

properties, or “modes” as Descartes calls them, exist and are understood.21 The principle

attribute of corporeal substance is extension in length, breadth, and depth and so all

corporeal substance’s properties exist through extension. According to Descartes, if we

search our minds we will uncover clear and distinct ideas of corporeal substance, thinking

substance, and God. Having a clear and distinct idea of corporeal substance entails

having a clear and distinct idea of its nature or essence, that is, extension. These, then,

are the relevant metaphysical foundations for Descartes physics. I now turn to Principles

II to examine how the principles of mechanical explanation rest on these foundations.

Principles II: The Metaphysics of Mechanism

In section 1, I offered a general sketch of the principles of mechanistic

explanation, matter and local motion, along with contact action, the laws of nature, and a

distinction between primary and secondary affections. In what follows, we’ll see how

Descartes develops and justifies these principles. 19 Principles I.52: MM, 23: AT VIIIA, 24-25. 20 Principles I.3: MM, 2: AT VIIIA, 25. 21 There are exceptions to this claim since the modes of existence and duration are not attribute-specific: see Principles I.56: MM, 25: AT VIIIA, 26.

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Matter

Descartes’ account of the nature of matter falls right out of his argument for its

very existence. This argument, the first of part II of the Principles, infers the existence of

matter on the basis of our possession of a clear and distinct idea of matter, or corporeal

substance, as existing independent of our own minds. Given that God isn’t a deceiver,

this clear and distinct perception must be true and so matter exists. Not only do we have

a clear and distinct perception of matter as existing, but as existing in a particular way.

When we inspect our idea of matter Descartes claims that we will find that it corresponds

perfectly with the subject matter of geometry. He writes, “…I know of no kind of

material substance other than that which…Geometers call quantity and take as the object

of their demonstrations.”22 In the Discourse on Method Descartes makes explicit exactly

what he takes the subject matter of geometry to be:

After that, wishing to seek other truths, I considered the object studied by geometers. I conceived of this as a continuous body, or a space indefinitely extended in length, breadth and height or depth, and divisible into different parts which may have various shapes and sizes, and may be moved or transposed in every way: for all this is assumed by geometers in their object of study.23

Given that we do indeed clearly and distinctly conceive of matter in this way, again it

follows from God’s nature that we cannot be deceived, and so matter exists as such.

Matter, or corporeal substance, has all and only geometrical properties.24 Descartes

writes “there is absolutely nothing to investigate about this substance except those

22 Principles II.64: MM, 77: AT VIIIA, 78-79. For a brief discussion of the correspondence between matter and geometry see E.A. Burtt, The Metaphysical Foundations of Modern Science, (Mineola, New York: Dover Publications, Inc., 2003), 106 23 CSM I, 129: AT VI, 36. 24 Descartes seems to treat motion as a geometrical property, and commentators typically follow Descartes in defining motion as such. E.g. Garber, Metaphysical Physics, 293.

13

divisions, shapes, and movements”.25 This, then, is Descartes’ account of matter.

However, before moving to a discussion of local motion I want to discuss five features of

Descartes’ metaphysics of matter.

First, given Descartes’ claim that the essence or nature of corporeal substance is

extension, one might wonder what Descartes takes the difference between corporeal

substance and space to be. Descartes asserts in Principles II.11, “space does not in fact

differ from material substance.”26 Descartes explains that if you closely look at our idea

of body and focus only on those essential features of the idea—extension—you will come

to see that it is the same idea we have of space. Descartes makes this especially clear in a

letter to Mersenne. He writes:

If you wish to conceive that God removes all the air in a room without putting any other body in its place, you will have to conceive accordingly that the walls of the room touch each other; otherwise your thought will contain a contradiction. Just as we could not imagine him flattening all the mountains in the world while leaving all the valleys, so we cannot think that he removes every kind of body and yet leaves space behind. For the idea that we have of body, or matter in general, is contained in the idea that we have of space, i.e. of something which has length and breadth and depth, just as the idea of a mountain is contained in the idea of a valley.27

In the same way that the concept of a valley is the same as that of a mountain, so the

concept of space is the same as our concept of matter.28 Given that we have a clear and

distinct perception of matter or corporeal substance, so too do we have clear knowledge

of the nature of space.

25 Principles II.64: MM, 77: AT VIIIA, 78-79. Descartes seems to take motion to be a geometrical property. Thus in the passages cited above, Descartes claims that it is part of the nature of the object of geometer’s study that its parts are movable. 26 MM, 44: AT VIIIA, 46. 27 CSM III, 132: AT II, 482. 28 In Principles II.12 Descartes discusses the apparent difference between space and extension in that we think of space as immovable whereas we think of bodies as capable of moving. He claims that space conceived of as immovable is a case of conceiving of extension “in a general way.”

14

Second, it follows that the existence of vacua is impossible. A vacuum, according

to Descartes, is an extension—a space—in the absence of a substance. Descartes thinks it

is obvious that “no properties or qualities belong to nothingness.”29 It follows that

extension cannot exist without corporeal substance and so a vacuum cannot exist.30 The

extended universe, then, is “full” of bodies—there is no space without body; the extended

universe is a plenum. Third, the extended universe—the plenum—is unlimited. To

conceive of a limit to the extended universe is to conceive of a space beyond which there

is no extension, but given that space is identical with extension, it isn’t really to conceive

of an edge or limit to the plenum.31 Fourth, the existence of atoms is impossible.

Descartes maintains that being extended entails being divisible; it falls out of the very

nature of corporeal substance that it is divisible.32 Given that atoms would be indivisible

bodies, there can be no atoms. Thus, all bodies are, at least in principle, divisible.

Further, the parts into which corporeal substance is divisible are extended and so are

themselves corporeal substances.33

Last, Descartes makes explicit in later letters to Henry More that matter is

impenetrable, that is, no two bodies may occupy the same place at the same time. He

writes: “it is impossible to conceive of one part of an extended thing penetrating another

equal part without thereby understanding that half the total extension is taken away or

29 Principles I.11: MM, 6: AT VIIIA, 8. 30 Descartes denial of vacua is found in Principles II.16; MM, 46-47; AT VIIIA, 49. 31 Principles II.21: MM, 49: AT VIIIA, 59. 32 CSM II, 59: AT VII, 86; CSM II, 115: AT VII, 163. 33 Descartes makes this explicit at Principles I.60; MM, 27; AT VIIIA, 28-29. Descartes writes “from the sole fact that we now have the idea of an extended or corporeal substance…we are however certain that…each part of it {which can be} delimited by our mind is really distinct from the other parts of the same substance.”

15

annihilated; but what is annihilated does not penetrate anything else….”34 So according

to Descartes, if two bodies were to become wholly interpenetrated, then the extension of

the two would be reduced to one. Given that the essence of body is extension, we can’t

say that there are two bodies there and as such where there were once two bodies there is

only one.35

In light of all these consequences it seems worthwhile to briefly summarize

Descartes’ account of matter. According to Descartes, the essence or nature of corporeal

substance (or body, matter, or material substance, each of which Descartes uses

interchangeably) is extension in length, breath, and depth. Being extended entails being

divisible into parts, and so all corporeal substances are divisible into parts. Each one of

these parts is itself an impenetrable corporeal substance and has a shape, size, and is

subject to motion. We know all of this with certainty because we have a clear and

distinct idea of corporeal substance which is guaranteed to correspond to reality given

God’s honest nature.36

Local Motion

All matter is essentially the same. We have one clear and distinct idea of matter

and so there is only one kind of matter.37 It is the presence of motion in matter that

accounts for the vast diversity we find in the natural world. Descartes claims: “all the

properties which we clearly perceive in it are reducible to the sole fact that it is divisible

34 CSM III, 372: AT V, 342. 35 Likewise Descartes seems to deny that bodies can be rarefied and condensed on the grounds that it would require co-location. See Principles II.5-7: MM, 41-42: AT VIIIA, 42-44. 36 Descartes’ argument that this is indeed our concept of matter is more complicated than I have represented here. See Garber, Metaphysical Physics, chapter 3 for a more detailed discussion of this argument and a number of others. 37 In later sections of the Principles Descartes distinguishes between three kinds of matter: subtle, spherical, and terrestrial. The difference between these kinds of matter is one of size and shape, not essence.

16

and its parts movable; and that it is therefore capable of all the dispositions which we

perceive can result from the movement of its parts…all the variation of matter, or all the

diversity of its forms, depends on motion.”38 Two terminological notes: throughout his

works Descartes consistently uses the term ‘motion’ as shorthand for both motion and

rest. Second, for his scholastic predecessors the term ‘motion’ referred to change in

general: this is not what Descartes has in mind. For Descartes, all change in the material

universe is ultimately reducible to the only sense of motion he allows, local motion. In

general, local motion is merely a change in spatial relations. Descartes, however,

tightens this definition, offering an account of motion “properly speaking”. He defines

local motion as follows:

…it is the transference of one part of matter or of one body, from the vicinity of those immediately contiguous to it and considered as at rest into the vicinity of [some] others.39

A part of matter is in local motion when its spatial relations are changing relative to its

immediately contiguous environment which is simultaneously considered at rest. This is

an account of motion according to which it is relative: the same body or part of matter

can be considered both in motion and at rest (although not simultaneously) relative to our

consideration of the body’s immediately contiguous environment. Descartes pauses to

emphasize a number of features of his definition of motion, of which I will mention two.

First, by “one part of matter or one body” he does not mean that only simple (divisible

but undivided) bodies move. Rather he makes clear that by ‘one part of matter’ he means

everything that is transferred together. Thus, although a body might have many moving

38 Principles II.23: MM, 50: AT VIIIA, 52. 39 Principles II.25: MM, 51: AT VIIIA, 53. Descartes’ italics.

17

parts, this does not exclude it from motion so long as the body and its parts are all moved

simultaneously with respect to its contiguous environment. Second, he adds that motion

and rest are modes of bodies in the same way that shape is a mode of body.

Many of the parts of matter are in motion. However, this might seem an

impossible event. First, Descartes identifies extension or matter (taken as a whole) with

space, but space doesn’t move. In response to this concern we need merely note that

Descartes does not share our post-Newtonian intuitions about space. According to

Descartes, the parts of space are movable. Indeed, in his De Gravitatione, Newton

singles this feature of Descartes metaphysics out as unacceptable.40 Second, if bodies are

impenetrable and the material universe is a plenum, there is no empty space into which

bodies may move. Descartes’ surprising solution to this puzzle is that all motion is

circular:

No body can move except in a {complete} circle {of matter or ring of bodies which all move at the same time}; in such a way that it drives another body out of the place which it enters, and that other takes the place of still another, and so on until the last, which enters the place left by the first one at the moment at which the first one leaves it.41

A further question has to do with the origins of motion. Motion is a mode of body and so

requires matter for its existence. Further, it follows from the nature of extension that its

parts are moveable, not that they are moved. Given the presence of motion in the world,

and that its existence doesn’t follow from the existence of matter itself, from where does

motion come? Descartes answer is God: “it seems obvious to me that this is none other

40 Isaac Newton, Philosophical Writings, ed. Andrew Janiak (Cambridge: Cambridge University Press, 2004), 25. 41 Principles II.33: MM, 56: AT VIIIA, 58.

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than God Himself, who {being all-powerful} in the beginning created matter with both

movement and rest.”42

Contact Action and the Laws of Nature

In addition to claiming that God accounts for the existence of motion in the

universe, Descartes adds that God “maintains in the sum total of matter, by His normal

participation, the same quantity of motion and rest as He placed in it at that time.”43 Thus

the material universe contains the same quantity of matter now, and indeed at any given

time, as it did at the first moment after creation. According to Descartes, a body’s

quantity of motion is equal to the product of its size or volume and its speed.44 So we can

interpret the quotation above as asserting that if we were to figure the quantity of motion

for every individual body in the universe and add them, we would find that this number

never changes. Why does God maintain this quantity? Descartes answers, saying “it is

one of God’s perfections to be not only immutable in His nature, but also immutable and

completely constant in the way that he acts.”45 Thus, according to Descartes it follows

from God’s immutability that He preserves the same quantity of motion.

This is not all that Descartes draws out of God’s immutability. In fact he

maintains that “from this same immutability of God, we can obtain knowledge of the

rules or laws of nature, which are the secondary and particular causes of the diverse

42 Principles II.36: MM, 58: AT VIIIA, 61. 43 Ibid. 44 The quantity of motion of a particular body will always be relative to some other body (or bodies) because a body’s speed is always relative some other body (or bodies). Thus the quantity of motion of a train moving at 10 mph relative to a train on the next track over will moving at 15 mph will be different from the quantity of motion of the first train relative to an stationary (relative to both trains) observer. 45 Principles II.36: MM, 58: AT VIIIA, 61.

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movements which we notice in individual bodies.”46 Descartes derives the laws of nature

from God’s immutability and in addition seems to maintain that that the laws themselves

are secondary causes of motion. This is a mysterious claim in that (i) Descartes seems to

speak as if bodies are the secondary causes of motion and (ii) it isn’t really clear what the

laws of nature are such that they can be causally efficacious since they aren’t substances

or modes of substance. I will have more to say about this presently, but before doing so I

want to turn to the laws themselves. The first law of nature is that “each thing, as far as is

in its power, always remains in the same state; and that consequently, when it is once

moved, it always continues to move.”47 This is Descartes’ account of inertia: bodies

naturally stay in the same state of motion. Thus if a body is in motion it tends to stay in

motion and likewise with rest. What require explanation are changes in motion and rest

as opposed to the maintenance of motion or rest in a body. Descartes’ second law is that

all motion is by nature rectilinear. His third law concerns collisions: “a body, upon

coming in contact with a stronger one, loses none of its motion; but that, upon coming in

contact with a weaker one, it loses as much as it transfers to that weaker body”.

Descartes maintains that from these three laws we can obtain (at least) seven rules of

motion which explain the outcome of bodily collisions given different initial conditions,

as well as rules covering the motions of fluids.

As we’ve seen, Descartes claims that the laws of motion are the secondary causes

of motion. However, in many cases Descartes treats bodies as if they were secondary

causes as well. For example, in his discussion of the third law Descartes writes “when

46 Principles II.37: MM, 59: AT VIIIA, 62. 47 Ibid.

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any hard bodies which have been set in motion…strike a yielding body to which they can

easily transfer all their motion, they immediately come to rest.”48 Elsewhere Descartes

writes “when one body makes another body move, it loses as much of its own motion as

it gives to the other.”49 Despite this evidence, there are reasons to think that bodies are

not causally efficacious for Descartes. As we’ve seen matter has only geometric

properties, e.g. size, shape, and motion. However, some commentators have argued

bodies cannot, in addition, be causally efficacious because causal efficacy (force) is not a

geometric property. If this is right, and bodies are not causally efficacious, then it is not

too far a step to claim that Descartes is an occasionalist (at least with respect to body-to-

body causation).50 To call Descartes an occasionalist in this sense is to say that in

instances of body-to-body causation, God, and not a finite body, is the cause of changes

in motion. A proponent of this view need only interpret Descartes’ claim that the laws of

nature are secondary causes as claiming that God’s causal interactions with the world

follow certain regularities. Nevertheless, even if Descartes is an occasionalist, it is

contact between two bodies that is the occasion for God’s action. Indeed, Descartes lays

out seven rules covering the behavior of bodies in collisions. As such contact action is

the foundation for accounting for natural phenomena.

Primary and Secondary Affections

As we’ve seen, Descartes’ matter possesses only geometric properties.

Nevertheless we perceive in nature colors, smells, heat, moisture and the like. These

certainly aren’t geometric properties. How then does Descartes account for them?

48 Principles II.40: MM, 61-62: AT VIIIA, 65. 49 CSM III, 330: AT V, 135. 50 For a summary see Garber, Metaphysical Physics, 293-299.

21

Descartes again asks us to look to our own minds: “size, in a body which has been

observed, or figure, or motion…are known by him in a manner very unlike that in which

he knows, in the same body, what color is, or pain, or odor, or flavor….”51 The problem

with color et al. is that although we have clear and distinct ideas of these properties, they

are only ideas of perception. That is, we can be certain that we experience color and that

this experience is caused by something outside of us, but unlike size, figure, and motion,

we cannot be certain that they exist outside our mind as genuine properties of substances.

Descartes maintains that our sensation of these properties is ultimately the result of

particles of matter interacting with our senses in various ways. Thus Descartes says

it must certainly be concluded regarding those things which, in external objects, we call by the names of light, color, odor, taste, sound, heat, cold, and of other tactile qualities…that we are not aware of their being anything other than various arrangements {of the size, figure, and motions of the parts} of these objects which make it possible for our nerves to move in various ways, {and to excite in our soul all the various feelings which they produce there}.52

Thus despite our natural propensity to ascribe color et al. to the objects of experience a

close look at our ideas reveals that we are ignorant of the causes of our experiences.

Nevertheless, Descartes maintains that we can account for sensations through the only

properties we know matter to possess.

Before turning to Spinoza’s criticism of the metaphysics of Descartes’ mechanism

in Chapter 2 I want to look briefly at Descartes’ explanatory system in action. In the

latter parts of the Principles Descartes takes on the task of explaining a wide variety of

natural phenomena: the tides, the circular orbits of the planets, and magnetism, among

many others. In fact Descartes claims at the very end that “no phenomena of nature have

51 Principles I.69: MM, 31: AT VIIIA, 34. 52 Principles IV.198: MM, 282: AT VIIIA, 322-323.

22

been omitted by me in this treatise.”53 In what follows I will briefly look at a couple of

these phenomena. A nice illustration of this method is his account of the fragility of

glass. The explanation for glass’ fragility, according to Descartes, is that “the surfaces

along which its particles touch one another are few and very narrow. And many other

softer bodies are more difficult to break, because their parts are interwoven in such a way

that they cannot be separated unless many of their tiny branches are broken and torn

away.”54 Thus the explanation for glass’ fragility (and the concomitant durability of

other bodies) lies in the shape of its insensible component parts.

Consider another example: saltwater, according to Descartes, is composed of two

types of particle: long flexible eel-like particles and long rigid eel-like particles.

Separating these two types of parts yields fresh water (the flexible particles) and salt (the

rigid particles). From this Descartes explains both the distinctive taste of salt (as opposed

to fresh water) and its capacity to preserve meat: “it is not surprising that the particles of

salt have a sharp and penetrating taste…for because they cannot be bent by the fine

material that surrounds them, they must always enter rigidly into the pores of the tongue,

and thereby penetrate far enough into it to sting.”55 Fresh water, on the other hand, since

its parts are flexible, “flows softly over the surface of the tongue.”56 Likewise salt

preserves meat because its rigid particles get into the pores of the meat and essentially

plug them up. The salt keeps other particles from getting into the meat’s pores and

“disarranging the meat particles.”57

53 Principles IV.199: MM, 282: AT VIIIA, 323. 54 Principles IV.128: MM, 240: AT VIIIA, 272. 55 O 275-276. Referred to in Principles IV.48: MM 205: AT VIIIA, 232. 56 Ibid. 57 Ibid.

23

Descartes is not so bold as to think that the explanations he offers for natural

phenomena correspond directly to reality. He is quite willing to say that just as two

clocks might tell time in the same fashion but be constructed using wholly different

mechanisms, so too, there are other explanations for, say, the distinctive taste of salt.

Nevertheless, Descartes thinks that his explanations are right, at least in kind: natural

phenomena really are as they are in virtue of the sizes, shapes, and motions of

imperceptible particles of matter. Ultimately, Descartes claims to have met his goal if he

has offered sufficient explanations of natural phenomena: “I have achieved enough if

those things which I have written are only such that they correspond accurately to all the

phenomena of nature, {whether these effects are produced by the causes I have explained

or by others}.”58 Given this general understanding of Descartes’ mechanism I turn in

section 3 to demonstrate Spinoza’s own commitment to mechanism. I conclude by laying

out the plan for the rest of my dissertation.

Section 3: Spinoza’s Mechanism and the Plan of the Dissertation

Spinoza’s commitment to the mechanical philosophy is apparent from his

correspondence with Robert Boyle. This correspondence took place through an

intermediary named Henry Oldenburg. Oldenburg and Spinoza had met in 1661 and

soon thereafter began a fairly regular correspondence. As mentioned earlier, it was

Oldenburg who sent Spinoza a copy of Robert Boyle’s Certain Physiological Essays in

hopes of eliciting Spinoza’s judgment on this work. I want to draw two conclusions

about Spinoza from his comments on Boyle’s work.

58 Principles IV.204: MM, 286: AT VIIIA, 327.

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First, we can clearly see that Spinoza is committed to the mechanical hypothesis.

Perhaps Spinoza’s chief criticism of Boyle’s work concerns Boyle’s discussion of niter.

In general terms Spinoza’s objection is that Boyle’s experiments do not show that the

nature of niter is as Boyle says it is. Boyle’s response was not to deny Spinoza’s

conclusion, but to deny that uncovering the nature of niter was his goal in the first place.

Using Oldenburg as an intermediary Boyle claimed that the

…purpose was not so much to show that this is a truly Philosophic and perfect Analysis of Niter, as to explain that the common doctrine of Substantial Forms and Qualities, received in the Schools, rests on a weak foundation, and that what they call the specific differences of things can be referred to the size, motion, rest, and position of the parts (Ep. 11: C 197, S 784, G IV 48).

Spinoza’s response to Boyle’s dodge was disbelief. He wrote in response “I did not

think, indeed I could not have persuaded myself, that this Most Learned Gentleman had

no other object in his Treatise on Niter than to show the weak foundations of that childish

and frivolous doctrine of Substantial Forms and Qualities”. Spinoza takes the falsity of

the doctrine of Substantial Forms and Qualities to be manifest. That such a well regarded

figure (amongst the innovators) as Boyle would seek to prove this claim, Spinoza regards

as absurd. In a later letter, Oldenburg tried to smooth over the issue, ultimately claiming

that at the very least Spinoza and Boyle could agree that “the various textures of bodies

produce their various differences” (Ep. 16: C 217, S 801, G IV 74), that is, that the

differences between bodies is ultimately the result of variation of the motions of their

parts.

A second conclusion we can draw about Spinoza by looking at his comments on

Boyle’s Certain Physiological Essays is that Spinoza takes Descartes’ account of the

world to be roughly right. Throughout the correspondence Spinoza argues from a

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Cartesian position. Spinoza i) defends Descartes against Boyle’s claim that “Modern

Writers” have misunderstood the shape of the particles of niter59, ii) claims that Descartes

has better shown the mechanical hypothesis to be true60, iii) claims that Boyle’s account

of Solidity offers nothing Descartes’ account hadn’t already affirmed61, iv) presupposes

the truth of Descartes’ account of fire62, and v) assumes Descartes account and rejection

of vacua63. This confirms not only that Spinoza was well acquainted with Descartes

physics, but that he took it to be mostly true. Thus Nancy Maull concludes that “Spinoza

was ostensibly a supporter of Cartesian ‘normal science’.”64

At roughly the same time as his correspondence with Boyle, Spinoza was

completing his presentation and commentary on Descartes’ Principles. Descartes’

Principles of Philosophy began as a series of lessons delivered to a student, but Spinoza

tells us that a number of his friends asked for a copy of these lessons. Ultimately Spinoza

allowed these lessons to be published, however only on the condition that a preface be

added explaining that he “did not acknowledge all the opinions contained in this treatise”

(Ep. 13: C 207, S , G IV 63). Spinoza’s friend, Lodewijk Meyer, wrote the introduction

to the work saying on behalf of Spinoza

we must not fail to note that what is found in some places…must be taken…as said only on behalf of Descartes. For it must not be thought that our Author offers this as his own opinion…The foundations of the sciences brought to light by Descartes, and the things he built on them, do not suffice to disentangle and solve all the very difficult problems that occur in Metaphysics. Different

59 Ep. 6: C 178, S 771, G IV 24. 60 Ibid., 178-179, S 771, G IV 25. 61 Ibid., C 186, S 775, G IV 34. 62 Ep. 11: C 198, S 785, G IV 49. 63 Ep. 13: C 209, S 794, G IV 65. 64 Nancy Maull, “Spinoza in the Century of Science,” in Spinoza and the Sciences eds. Marjorie Grene and Debra Nails (Boston: D. Reidel Publishing Company, 1986), 3-13.

26

foundations are required, if we wish our intellect to rise to that pinnacle of knowledge (C 230, S 120, G I 132-133).

In my dissertation I focus on Spinoza’s reasons for thinking that the foundations of the

sciences as offered by Descartes need to be replaced. I focus specifically on matter and

show that by Spinoza’s lights, Descartes’ account of matter suffers from several

considerable problems and so cannot serve as one of the foundations of the new science.

I will argue that much of what is distinctive about Spinoza’s metaphysics is the result of

his attempt to offer a philosophically adequate account of matter (or corporeal substance).

Given this thesis, I proceed as follows. In chapter 2 I justify my claim that many

of the distinctive features of Spinoza’s metaphysics are, at least partially, the result of his

effort to replace Descartes’ account of matter with what he took to be a philosophically

adequate one. I show that Spinoza took Descartes’ metaphysics of body to be deeply

problematic, by isolating two arguments for the conclusion that Descartes’ account of

matter is inconsistent with a number of foundational metaphysical principles. First I

examine Spinoza’s so-called vacuum argument. According to this argument Descartes’

account of body is inconsistent with the impossibility of a vacuum. The second argument

I examine concludes that Descartes’ account of body is inconsistent with the simplicity

and independence of substance. Spinoza’s resolution to both of these inconsistencies is

to deny that corporeal substances have parts that are themselves substances. While such

a move successfully reconciles the inconsistency, it has far-reaching consequences.

Descartes had maintained that all bodies are corporeal substances. If Spinoza is right

that, in fact, no bodies are corporeal substances, what is it to be a body? Further, if

27

bodies are not corporeal substances, how are the two related? I take up the first question

in chapter 3 and the second in chapter 4.

Recall the mechanist’s slogan that all phenomena are to be reduced to matter and

motion. Spinoza takes this seriously, interpreting ‘matter’ as corporeal substance. Given

that no body is a corporeal substance (and that bodies exist) it follows that bodies are

among the phenomena to be reduced to corporeal substance and motion. Thus, in order

to determine what a body is for Spinoza we need to understand how Spinoza thinks about

motion. In chapter 3 I take on this task through an examination of one of corporeal

substance’s immediate infinite modes, what Spinoza refers to as “motion and rest”. In

this chapter I examine and evaluate the most developed interpretation of this mode. I

then develop an alternative interpretation according to which the subjects of motion, are

not bodies, but rather regions of corporeal substance. With this account on the table I

show that what it is to be a body is to be a region of corporeal substance in motion

relative to its immediately contiguous environment.

Perhaps the chief obstacle to understanding Spinoza’s substance monism is

accounting for the relation between bodies and the one corporeal substance. Given my

account of bodies and of the immediate infinite mode of extension, I argue in chapter 4

that Spinoza avoids the problems with Descartes’ account of matter by adopting the

scholastic-Aristotelian conception of the relation between a part and whole according to

which a whole’s parts come to be only upon its division. Consider a simple divisible

whole. The potential parts of this whole are those parts into which it may be divided, but

is not. In dividing the whole, one actualizes previously only potential parts. Thus, in the

same way that a pie must be cut before there are slices, so too extension, for Spinoza,

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must be “cut” before there are bodies. It is Spinoza’s immediate infinite mode of

extension, i.e. motion-and-rest, which divides extension and creates bodies.

In the final chapter I turn to Spinoza’s resolution of the tension between

mechanical and theological explanation. The explanations that the mechanical

philosophy seeks to offer take the form of showing that any particular observable

phenomenon is the effect of a series of causal relations obtaining between particles of

matter. However, on its face, this view conflicts with the traditional theological

commitment that God is the sole cause and author of all things, a view to which Spinoza

adheres. In chapter five, I argue that Spinoza is a concurrentist, and as a result resolves

this problem by maintaining that instances of secondary causation are instances in which

God and finite modes concur in causing an effect. In making this case I outline Spinoza’s

unique account of force and show how, according to Spinoza, it grounds the laws of

nature.

29

CHAPTER 2: SPINOZA AND THE REJECTION OF DESCARTES’ ACCOUNT OF

MATTER

Introduction

In this chapter I begin to make good on my claim in the introduction to chapter 1

that much of what is distinctive about Spinoza’s metaphysics arose, at least partially, as

the result of Spinoza’s efforts to replace Descartes suspect account of matter. I will do so

by showing that Spinoza’s claim that there is only one corporeal substance falls out of his

criticisms of Descartes’ account of matter. I proceed by showing that Spinoza thinks

there are at least two significant problems with Descartes’ account. First, Descartes’

account of matter entails the possibility of a vacuum. Second, if Descartes’ is right, then

corporeal substance is dependent on its parts. Spinoza thinks that these problems justify

the rejection of Descartes’ account of matter. However, if we replace Descartes’ account

of matter with one that does not suffer from the aforementioned problems, as Spinoza

does, it follows that if corporeal substance exists, then there is only one unlimited

corporeal substance. In order to make this case I consider a simple question that will

structure the chapter: why aren’t bodies, substances according to Spinoza? Answering

this question will expose the reasons for Spinoza’s rejection of Descartes’ account of

matter and lead to Spinoza’s replacement.

30

On its face, in order to determine why bodies are not substances we need look no

further than the very beginning of the Ethics. Spinoza asserts in the fifth proposition of

book 1: “In nature there cannot be two or more substances of the same nature or

attribute” (C 411, S 218, G II 48). According to this proposition, bodies aren’t

substances because there are many bodies, and all bodies share the attribute of extension.

This is only a superficial answer, however. The real answer to the question lies in

determining why there can only be one substance per attribute, and indeed there is a good

deal of secondary literature examining the argument Spinoza offers on behalf of E1P5.65

However, Spinoza had reasons besides those offered on behalf of E1P5 for maintaining

that bodies aren’t substances. In the so-called “Physical Digression” immediately

following E2P13s, Spinoza writes “…that bodies are not distinguished by reason of

substance is evident both from E1P5 and from E1P8. But it is more clearly evident from

those things which are said in E1P15s” (C 459, S 252, G II 97).

In this chapter I follow up on the latter reference and turn to E1P15s to determine

why bodies aren’t substances. I proceed as follows: in section 1, I lay out Spinoza’s

project in E1P15s and locate two relevant arguments. In section 2 I turn to the first of

these arguments which I call the ‘Vacuum Argument’. Spinoza argues that if corporeal

substance has really distinct parts, then a vacuum is possible. Since vacua are

impossible, it follows that it is not the case that corporeal substance has really distinct

parts. I show that Spinoza’s target in this argument is Descartes’ account of matter, and

65 Perhaps the most recent addition is J. Crane and R. Sandler, “Identity and Distinction in Spinoza’s Ethics,” Pacific Philosophical Quarterly, 86 (2005): 188-200. See also Jonathan Bennett, A Study of Spinoza’s Ethics [Study] (Indianapolis: Hackett Publishing, 1984), 66-70; and Don Garrett, “Ethics IP5: Shared Attributes and the Basis of Spinoza’s Monism” in J.A. Cover and Mark Kulstad eds., Central Themes in Early Modern Philosophy [Central Themes], (Indianapolis: Hackett, 1990).

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that the argument highlights an inconsistency in Descartes’ metaphysics of body. I close

section 2 by considering the prospects for a Cartesian rejoinder. Ultimately, I argue that

Descartes can, in a way consistent with his other metaphysical commitments, deny the

conclusion of the vacuum argument. In section 3 I take on the second argument E1P15s

offers. According to this argument, which I call the ‘Divisibility Argument’, no

substance is a composite. Here too I argue that Spinoza’s target is Descartes’ account of

matter, and that his Divisibility Argument exposes an inconsistency in Descartes’

metaphysics of body. I end section 3 by considering the prospects for a successful

Cartesian rejoinder. I conclude that there is no easy answer for Descartes. In section 4 I

make good on my claim that much of what is distinctive about Spinoza’s metaphysics

arises out of Spinoza’s attempt to replace Descartes’ problematic account of matter by

showing how Spinoza’s one corporeal substance doctrine is the result of offering an

account of matter that doesn’t suffer from the weaknesses of Descartes’. In doing so, I

simultaneously explain why bodies aren’t substances according to Spinoza. I will begin

by examining E1P15s.

Section 1: Spinoza’s Project in E1P15s

In E1P15 Spinoza explicitly denies the transcendence of God, saying “Whatever

is, is in God, and nothing can be or be conceived without God” (C 420, S 224, G II 56).

God is not separate from the world but, in some sense, is the world. More specifically he

claims in the scholium that “extended substance is one of God’s infinite attributes” (C

421, S 225, G II 57). God, according to Spinoza, is a corporeal or extended substance (as

well as a thinking substance). This was certainly a controversial claim, and Spinoza was

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well aware of his violation of orthodoxy. The tradition had reasons for affirming the

incorporeality of God, and in the scholium to E1P15 Spinoza set out to respond to these

concerns. Spinoza considers a number of the traditional reasons for thinking that God is

incorporeal, all of which ultimately reduce to the following argument:

1) All corporeal substances are composite. 2) God is not composite. 3) So, God is not a corporeal substance.

Spinoza responds to this argument by denying premise 1): “These are the arguments

which I find authors using, to try to show that corporeal substance is unworthy of the

divine nature, and cannot pertain to it. But…these arguments are founded only on their

supposition that corporeal substance is composed of parts…” (C 422, S 225, G II 58). In

E1P15s Spinoza points to two arguments against premise 1). First he explains that he has

already shown the absurdity of a substance having parts in E1P12-E1P13c, and second he

argues that if vacua are impossible, then no corporeal substance is a composite. Before

turning to the arguments themselves it is important to note that these two arguments

against 1) are intended to serve two purposes. First, they are intended to pull the rug out

from underneath his opponents’ arguments that God is not a corporeal substance.

Second, given that Spinoza points to E1P15s as a locus for understanding why bodies

aren’t substances, there is good reason to believe that Spinoza intends these arguments

against 1) to be sufficient for making it “clearly evident” why bodies can’t be substances.

Keeping this in mind, I’ll begin by looking at Spinoza’s Vacuum Argument.

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Section 2: The Vacuum Argument

I maintain that Spinoza, in the Vacuum Argument, is pointing to an inconsistency

in Descartes’ metaphysics of body, the only resolution of which entails the denial both

that all corporeal substances are composite and that bodies are substances. Here is the

argument:

…if corporeal substance could be so divided that its parts were distinct in reality, why, then, could one part not be annihilated, the rest remaining connected with one another as before? And why must they all be so fitted together that there is no vacuum? Truly, of things which are really distinct from one another, one can be, and remain in its condition without the other. Since, therefore, there is no vacuum in Nature (a subject I discuss elsewhere), but all its parts must so concur that there is no vacuum, it follows also that they cannot be really distinguished, i.e., that corporeal substance, insofar as it is a substance, cannot be divided (C 423, S 226, G II 59).

There are actually two arguments packed into this little passage. Each argument has

roughly the same structure: if corporeal substance has really distinct parts, then a vacuum

is possible; the impossibility of a vacuum allows us to conclude that corporeal substance

doesn’t have really distinct parts. The difference between the two arguments lies in how

they connect the really distinct parts of corporeal substance with the possibility of a

vacuum: one connects the possibility of a vacuum with the annihilation of corporeal

substance’s parts and the other with the composition of corporeal substance’s parts. I’ll

call the former the ‘Annihilation Vacuum Argument’ (hereafter AVA) and the latter the

‘Composition Vacuum Argument’ (hereafter CVA).

Before we can get to the arguments we need to answer some preliminary

questions. Both arguments are grounded in the impossibility of vacua and so I want to

begin by asking: what does Spinoza mean by ‘vacuum’, and why he is so sure that they

are impossible? Furthermore, Spinoza nowhere mentions Descartes in these arguments,

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or for that matter in E1P15s. That being the case, why think that the vacuum argument

offers us an example of Spinoza’s reasons for breaking with Descartes? I’ll begin by

considering Spinoza’s account of vacua.

In Ep.13 Spinoza writes to Henry Oldenburg:

But I do not know why he [Robert Boyle] calls the impossibility of a vacuum a Hypothesis, since it follows very clearly from the fact that nothing has no properties. And I am surprised that the Distinguished Gentleman doubts this, since he seems to maintain that there are no real accidents. I ask whether there would not be a real accident if there were Quantity without Substance? (C 209, S 794, G IV 65)

This shows that Spinoza followed Descartes both in his understanding of vacua and in his

reasons for denying them. According to the Cartesian definition of a vacuum as

“extension without corporeal substance”66, the existence of a vacuum would entail the

existence of an accident—extension—in the absence of substance. However, there are no

real accidents according to Descartes: “no properties or qualities belong to nothingness;

and that accordingly, wherever we perceive some properties or qualities, there we must

necessarily find a thing or substance to which they belong.”67 As the passage above

shows, Spinoza agrees with Descartes’ conception of a vacuum insofar as he takes the

possibility of a vacuum to consist in the existence of Quantity or extension without

substance.68 Further, it is clear that Spinoza follows Descartes in his reasons for denying

the possibility of vacua given his claim that the impossibility of a vacua follows from the

fact that “nothing has no properties”.69

66 DPP 2d5: (C 263, S 147, G I 181). 67 Principles I.11: MM, 6: AT VIIIA, 8. 68 Spinoza uses ‘quantity’ as a synonym for ‘matter’, ‘corporeal substance’, and ‘extension’. See E1P15s. 69 There has been some debate about how best to interpret Spinoza’s parenthetical remark directly following his claim that there is no vacuum in nature: “which is discussed elsewhere”. Everyone agrees that Spinoza is referring to his presentation of Descartes’ argument against the vacuum in Descartes’

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Why think that the vacuum arguments are aimed at Descartes’ account of matter?

After all, Spinoza says nothing about Descartes in the proof. The vacuum argument is

offered with Spinoza’s opponents in mind; recall that the task at hand in E1P15s is

defending the thesis that God is a corporal substance in the face of those who would

claim the opposite on the grounds that all corporeal substances are composite. As such,

the challenge is to determine exactly who Spinoza had in mind when formulating the

argument. To begin with, there are good circumstantial reasons for thinking that

Spinoza’s argument is structured with Descartes in mind. Descartes’ Principles was

especially well known to Spinoza. Spinoza’s first published work was a reformulation

of, and commentary on, the piece. In addition, Descartes’ system was the philosophical

paradigm of Spinoza’s place and time. Thus, it makes sense that in considering

objections to his thesis that God is extended, Spinoza would consider them as formulated

in Cartesian terms. Second, and more importantly, Descartes explicitly maintains that

corporeal substance has really distinct parts, which is exactly the claim the vacuum

argument is offered to refute.70 Further the vacuum argument refutes this thesis using

Descartes’ own account of the vacuum. All of these facts taken together suggest that

Spinoza, in the vacuum argument, is pointing to what he takes to be an inconsistency in

Principles of Philosophy. However, Jonathan Bennett takes this as the interpretive key to the argument as a whole, ultimately claiming that this argument when properly interpreted confirms his “field metaphysic” account of the mode-substance relation. See Bennett, Study, 97-103. On the opposing side is Tad Schmaltz who argues that this parenthetical remark is intended only to justify the claim that a vacuum is not possible and tells us nothing further. See Tad M. Schmaltz, “Spinoza on the Vacuum” [“Vacuum”] Archiv fur Geschichte der Philosophie 81, (1999): specifically 182-186. As will become clear, I agree with Bennett that the parenthetical remark is the key to properly interpreting the argument, although I do not take it that my interpretation offers any support to the field-metaphysic interpretation of the mode-substance relation. 70 Descartes says, “corporeal substance exists…and…each and every part of it…is really distinct from the other parts of the same substance”: Principles I.60: MM, 27: AT VIIIA, 28-29.

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the Cartesian account of matter.71 With these preliminaries out of the way I now turn to a

consideration of Spinoza’s arguments. I’ll start with the AVA.

Annihilation Vacuum Argument

As we’ve seen Spinoza claims in E1P15s that “…if corporeal substance could be

so divided that its parts were distinct in reality, why, then, could one part not be

annihilated, the rest remaining connected with one another as before…Truly, of things

which are really distinct from one another, one can be, and remain in its condition

without the other.” Spinoza seems to be reasoning as follows: take a round cookie-

shaped substance and suppose that its middle is suddenly annihilated, that is, pops out of

existence. The residual parts of the object remain “connected with one another as before”

thus rendering our cookie-shaped substance, now donut-shaped. But if we are left with a

hole in our cookie, we are left with a place which can be characterized in terms of length,

71 Two worries. First, Wolfson argues that Spinoza cannot be referring to Descartes in E1P15s because i) at least one of the arguments Spinoza offers on behalf of his opponent’s claim that nothing infinite can have parts (and as such be corporeal) ultimately refers back to Averröes and ii) “Descartes was far from considering corporeal substance to consist of parts really distinct from one another.” See Harry Austryn Wolfson, “Spinoza on the Infinity of Corporeal Substance” Chronicon Spinozanum iv, (1924-26), 84. The quotation in footnote 7 shows that Wolfson is plain wrong on the second point. On the first point, I do not disagree, but I question its relevance. In E1P15s Spinoza is collecting and diagnosing arguments that extension can’t be one of God’s attributes. The problem with each of these arguments is that they maintain that everything extended has parts, a mistake that Descartes’ view shares. A second worry is that Spinoza borrows Descartes’ technical term ‘real distinction’ and redefines it in E1P10. For Spinoza, a ‘real distinction’ between x and y entails a conceptual but not necessarily a numerical distinction between x and y. This is the relation that obtains between God’s attributes. Thus it is important to determine whether Spinoza is using the term in Descartes’ sense or in his own. In this scholium Spinoza is trying to argue that his opponents’ arguments are based on a false premise: namely that corporeal substance is made up of bodies. But if Spinoza were using his own peculiar sense of ‘really distinct’, then his saying that corporeal substance is made up of bodies is to say that corporeal substance is made up of, and divisible into, conceptually, but not necessarily numerically, distinct bodies. This is an odd account of corporeal substance and so it is open to Spinoza’s opponents to accept the vacuum argument and its conclusions, but nevertheless maintain that since the vacuum argument rules out such an unusual conception of corporeal substance, they are under no pressure to deny that corporeal substance has parts in Descartes’ sense. Thus, I think it makes much more sense that Spinoza is using ‘really distinct’ in Descartes’ sense of the term.

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breadth, and width in the absence of substance, that is, we are left with a vacuum.72 I

offer the following reconstruction of the AVA:

4) If corporeal substance has really distinct parts, then it is possible for one part, call it ‘x’, to be annihilated, and that upon the annihilation of x, all the parts contiguous to x preserve their relative spatial relations.

5) If it is possible for x to be annihilated, and that upon the annihilation of x, all the parts contiguous to x preserve their relative spatial relations, then a vacuum is possible.

6) A vacuum is not possible. 7) So, it is not the case that corporeal substance has really distinct parts.

In what follows I want to briefly justify each of the premises on Spinoza’s behalf, and

doing so consists in explaining how Descartes is committed to each premise. In order to

do so I will need to begin with Descartes’ real distinction.

Descartes holds that a real distinction “properly exists only between two or more

substances.”73 Thus if corporeal substance has really distinct parts, then corporeal

substance has substances as parts. 74 That the parts of corporeal substance are

themselves corporeal substances, gives some insight into why Spinoza thinks Descartes is

committed to 4). One of the defining features of finite substance common to the

scholastics and to Descartes is that no substance is dependent for its existence on

72 Cf. Bennett, Study, 102-103. 73 Principles I.60: MM, 27: AT VIIIA, 28. 74 I am putting aside a prominent interpretation of Descartes according to which there is only one corporeal substance. Recent adherents of this view include Jorge Secada, Cartesian Metaphysics: The Late Scholastic Origins of Modern Philosophy (Cambridge: Cambridge University Press, 2000); Alice Sowaal, “Cartesian Bodies,” Canadian Journal of Philosophy 34, no. 2 (2004): 217-240; Thomas Lennon, “The Eleatic Descartes,” Journal of the History of Philosophy 45, no.1 (2007), 29-45. For a succinct statement of the account and the traditional reasons for accepting it, see Georges Dicker, Descartes: An Analytical and Historical Introduction (Oxford: Oxford University Press, 1993), 212-217. I won’t comment on this interpretation other than to say first, I am suspicious that this really was Descartes’ view. For an argument that this is right see Justin Skirry, Descartes and the Metaphysics of Human Nature, (London and New York: Continuum, 2005), Chapter 3). Second, I am sure that Spinoza thought that according to Descartes’ there are many corporeal substances. For an argument that this is right see John Carriero, “Monism in Spinoza” [Monism] in Olli Koistinen and John Biro eds., Spinoza: Metaphysical Themes [Metaphysical Themes], (Oxford: Oxford University Press, 2002), especially 47-54.

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anything else besides God.75 In his definition of substance in the Principles Descartes

characterizes an independent being as “a thing which exists in such a way as to depend on

no other thing for its existence.”76 Elsewhere Descartes explains this independence in

terms of a capacity to exist apart. He notes in the 2nd Replies that “two substances are

said to be really distinct when each of them can exist apart from the other.”77 This

explains Spinoza’s comment that “Truly, of things which are really distinct from one

another, one can be…without the other.”78 Spinoza interprets the capacity of the

hypothesized really distinct parts of corporeal substance to exist apart from one another

in terms of annihilation: x and y can exist without the other only if upon the annihilation

of x, y remains, and vice versa. Thus in premise 4) Spinoza is merely noting that, for

Descartes, if the parts of corporeal substance are really distinct, then it follows that each

one must be independently annihilable.

However, premise 4) claims not only that everything contiguous to an annihilated

part remains, but also that everything retains its previous spatial position, i.e. nothing is

“sucked in” to take the annihilated body’s place. On its face this is problematic since this

is flat out inconsistent with Descartes’ stated view; he explicitly denies the possibility of

a vacuum upon the annihilation of a body.79 In the Principles Descartes considers this

situation, taking for his example a vessel filled with water:

75 Principles I.51: MM, 22-23: AT VIIIA, 24. 76 Ibid. 77 CSM II, 114: AT VII, 162. Note that this principle only applies to contingent substances. 78 See also Spinoza’s account of Descartes’ real distinction in MT II.5 (C 323-324, S 194-195, G I 257-260). 79 Cf. Bennett, Study, 99. Jonathan Bennett worries that Spinoza is claiming that the contiguous bodies do not rush in to fill the void because they are bound by “metaphysical rubber bands”. See also Charlie Huenemann, “Predicative Interpretations of Spinoza’s Divine Extension,” [“Predicative Interpretations”] History of Philosophy Quarterly 14 (1997), 63-64.

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if anyone asks what would occur if God removed the whole body contained in any vessel and did not permit anything else to take the place of the body which had been removed, the answer will have to be that the sides of the vessel would thereby become contiguous to each other. For, when there is nothing between two bodies they must necessarily touch each other…80

Thus according to Descartes, upon the annihilation of the water, the contiguous bodies’

spatial relations change. Thus we are left with a puzzle. According to Spinoza,

Descartes’ claim that the parts of corporeal substance are really distinct entails that on the

annihilation of one, the contiguous parts remain as before, whereas Descartes explicitly

says there is a change in the spatial relations of the contiguous parts. The resolution to

this puzzle is that Spinoza thinks there is something wrong with Descartes’ story—

namely that he isn’t justified in telling it.81 As we’ll see, the problem is that the change

of the sides from distant to contiguous is inconsistent with the principle of sufficient

reason.

We have to look again to Spinoza’s Descartes’ “Principles of Philosophy” to

determine why he thinks Descartes’ scenario is problematic. Let’s suppose that

Descartes is right and upon the annihilation of the contents of a vessel, the sides collapse

and become contiguous. The chief problem with the sides of the vessel collapsing, for

Spinoza, is that it would make a privation the cause of the sides becoming contiguous.

Spinoza writes “since the cause of an effect must always be positive (by 1A8), it should

never be said that a body moves in order that there not be a vacuum. A body moves only

80 Principles II.18: MM, 48: AT VIIIA, 50. 81 Descartes’ account is a contentious one; both More and Gassendi agree with Spinoza that something isn’t right. More holds that divine space remains whereas Gassendi argues that the presence of an accident need not entail the presence of a substance. See Denis Des Chene, Physiologia: Natural Philosophy in Late Aristotelian and Cartesian Thought,[Physiologia] (Ithaca, New York: Cornell University Press, 1996), 384.

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on account of the impulse of another body” (C 274, S 157, G I 197).82 The axiom (1A8)

Spinoza refers to for justification is a gloss of Descartes’ causal adequacy principle: there

must be at least as much reality in the cause as in the effect. Spinoza takes Descartes’

causal adequacy principle to be ultimately grounded in the truth that something cannot

come from nothing, i.e. in the principle of sufficient reason. Spinoza writes in Descartes’

Principles of Philosophy: “No actually existing thing and no actually existing perfection

of a thing can have nothing, or a thing not existing, as the cause of its existence” (C 244,

S 131, G I 155).83 The annihilation of a corporeal substance results in a privation—in “a

thing not existing”. Given that something cannot come from nothing, the privation that

follows from the annihilation of a part of corporeal substance is causally impotent. In

sum, the reason that Descartes is unjustified when he holds that the sides of a vessel

would become contiguous given an annihilation of its contents is that such an event

would require the movement84 of the sides from non-contiguous to contiguous to have

been caused by the privation of corporeal substance: a violation of the principle of

sufficient reason. Accordingly, in order to be consistent with his principles, Descartes

82 This principle has a long history going back at least as far as Aristotle’s Physics. There he claims that “it is clear that the void cannot be a cause of locomotion….” (214b 15-16) See Aristotle, The Complete Works of Aristotle, ed. Jonathan Barnes, (Princeton: Princeton University Press, 1995), 364. 83 Descartes does not infer that the causal adequacy principle follows from the principle of sufficient reason in either the Meditations or the Principles (see Mediation 3; CSM II, 28 and Principles I.18: MM, 10: AT VIIIA, 11-12), but he does in the 2nd Replies where he claims that “if we admit that there is something in the effect that was not previously present in the cause, we shall also have to admit that this something was produced by nothing” (CSM II, 97: AT VII, 135). 84 Slowik rightly cautions us that for Descartes, the sides of the vessel do not move to become contiguous upon the annihilation of the contents since this would imply that there was some empty space into which the sides could move. Nevertheless there is an objective change in the world: formerly non-contiguous vessel sides have become contiguous. This change requires a cause, but the cause of this change cannot lie in the annihilation. See Edward Slowik, Cartesian Spacetime: Descartes’ Physics and the Relational Theory of Space and Motion (Dordrecht: Klewer Academic Publishers, 2002), 105 footnote 25.

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must affirm a distance between the sides of a vessel despite the annihilation of the

vessel’s contents, i.e. he must affirm the existence of a vacuum. I now turn to the CVA.

Composition Vacuum Argument

Spinoza sketches a second argument saying “if corporeal substance could be so

divided that its parts were really distinct…why must they all be so fitted together that

there is no vacuum?” The general thrust of the argument is that if corporeal substance

has really distinct parts, then it is possible for these parts to be spatially isolated, that is

for a part to be discontiguous to all other parts. However this entails the possibility of a

vacuum since in such a case a gap or distance without substance is left between the parts.

We can lay out Spinoza’s argument as follows:

8) If corporeal substance has really distinct parts, then it is possible for its parts to be spatially isolated.

9) If it is possible for corporeal substance’s parts to be spatially isolated, then a vacuum is possible.

10) But vacua are impossible. 11) So it is not the case that corporeal substance has really distinct parts.

Again, I’ll justify these premises on Spinoza’s behalf where this consists in explaining

why Descartes’ commitment to the really distinct parts of corporeal substance ultimately

entails the possibility of a vacuum. As we’ll see, the CVA is, in some sense, the inverse

of the AVA.

Why does Spinoza think that Descartes’ commitment to corporeal substance

having really distinct parts entails the possibility of the spatial isolation of those parts?

There are two senses in which the parts might be spatially isolated, and in what follows I

will explain how if Descartes’ account of matter is right, the possibility of spatial

isolation in both senses follows. Consider a cubic corporeal substance completely

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surrounded by, and contiguous to, other corporeal substances, call it ‘C’. Suppose the

corporeal substance immediately to the left of C is annihilated. As we saw in the analysis

of the AVA Descartes cannot assert that the corporeal substances immediately contiguous

to the annihilated substance take the place of the annihilated body, since that would entail

denying the principle of sufficient reason. Thus C is right where it was prior to the

annihilation. However, now the left face of C no longer touches or is contiguous to

another corporeal substance. In this case, C is only partially isolated from other corporeal

substances since although its left face is no longer contiguous to any other corporeal

substance, its other faces are. Compare this situation with one in which all the corporeal

substances immediately contiguous to C are annihilated. Upon the annihilation of C’s

immediately contiguous surroundings those corporeal substances immediately contiguous

to the annihilated substance or substances remain in place, as does C. Thus C comes to

be wholly isolated from other corporeal substances since none of its faces are contiguous

to any other corporeal substance. Thus it follows from the supposition that corporeal

substance has really distinct parts, that it is possible for a part of corporeal substance to

be partially or wholly isolated from other corporeal substances.

Similarly, it seems clear that Spinoza is justified in thinking that Descartes is

committed to the truth of premise 9). If it is possible for the parts of corporeal substance

to be spatially isolated (either partially or wholly), then it is possible for any single part

not to touch any other part, that is, it is possible for there to be a gap or distance between

the parts. However, if it is possible for gaps to exist between their parts, then a

distance—extension—in the absence of corporeal substance is possible. Thus, again we

see that if corporeal substance has really distinct parts, then a vacuum is possible.

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Although Descartes is committed to thinking that the possibility of corporeal

substances’ parts being spatially isolated entails the existence of a gap or vacuum, there is

a deeper connection between the possibility of a spatially isolated corporeal substance

and the possibility of a vacuum. The real problem with the existence of a spatially

isolated corporeal substance is that it entails the existence of a corporeal substance which

is limited by nothing. In order to see this consider a case in which every substance

besides x is annihilated. In this case x is wholly spatially isolated and since there are no

other corporeal substances and so we are not forced to posit a gap between x and some

other corporeal substance. Nevertheless Descartes is committed to thinking that such a

situation entails the existence of a vacuum. Consider the biggest corporeal substance, the

material universe. Descartes writes in the Principles,

…we understand that this world, or the universe of material substance, has no limits to its extension. For wherever we may imagine those limits to be, we are always able, not merely to imagine other indefinitely extended spaces beyond them; but also to clearly perceive that these are as we conceive them to be, and consequently, that they contain an indefinitely extended material substance.85

Descartes’ point is that try as we might we cannot conceive of a limit or boundary to

extension beyond which there is no extension, that is, a boundary separating the extended

from the unextended. To conceive of a limit to the material universe is to conceive of

extension beyond it. Our conceptions correspond to reality, so there really is extension

beyond the any hypothesized limit of the material universe. But if there is extension

beyond the hypothesized limit, then there is substance beyond this limit because there can

85 Principles II.21: MM, 49: AT VIIIA 52. Similarly, in a letter to Arnauld, Descartes claims “I cannot conceive of…a space which is wholly empty, or of an extended piece of nothing, or of a limited universe; because no limit to the world can be imagined without its being understood that there is extension beyond it; and no barrel can be conceived to be so empty as to have inside it no extension, and therefore no body; for wherever extension is, there, of necessity, is body also” (CSM III, 359: AT V 224).

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be no extension in the absence of substance, that is, there can be no vacuum. Thus, it

follows from the fact that a vacuum is impossible, that there can be no limit to corporeal

substance beyond which there is extension but no substance. This conclusion applies

equally to all corporeal substances, not just the biggest one, and indeed Descartes’

material universe is a plenum—there are no gaps or holes separating corporeal

substances.

From this we can see the deeper problem with the possibility of spatially isolated

(either wholly of partially) corporeal substances. The existence of a spatially isolated

corporeal substance entails the existence of a limit to corporeal substance. Given that we

cannot conceive of a limit to corporeal substance beyond which there is no extension, the

existence of a spatially isolated corporeal substance entails the existence of an extension

beyond the limits of the corporeal substance. But this extension exists in the absence of

corporeal substance since the substance at hand is spatially isolated and so does not touch

any other corporeal substance. Thus the existence of a spatially isolated corporeal

substance entails that it is limited by an extended nothing, that is, a vacuum.

I have examined both of Spinoza’s vacuum arguments against Descartes and

before moving on I want to briefly summarize the results. What the vacuum arguments

ultimately show us is that Spinoza thinks Descartes is faced with an inconsistent set of

metaphysical principles. Descartes maintains that i) corporeal substance is divisible into

really distinct parts, ii) something cannot come from nothing (that is, that the principle of

sufficient reason is true), and iii) vacua are impossible. The vacuum arguments show that

a commitment to i) and ii) entails the denial of iii). Given Descartes’ commitment to the

impossibility of a vacuum it follows that he must reject either i) or ii). Certainly this is

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no easy decision: Descartes takes both i) and ii) to be conceived clearly and distinctly and

consequently to be certain.86 Nevertheless, denying i) seems preferable given that ii)

plays a bigger part in Descartes’ overall project; after all, Descartes needs ii) to prove

God’s existence and ultimately to ground the truth of his clear and distinct ideas. This

leaves us only one option: reject i); and this is exactly what the vacuum argument

demands. Thus by Spinoza’s lights, the consistent Cartesian should deny that corporeal

substance has really distinct parts. Recall, however, that the vacuum arguments are

ultimately intended to defend Spinoza’s claim that God is extended. I will now turn to

this issue.

The Consistent Cartesian and Corporeal Substance

Recall that in E1P15s Spinoza claims that all his opponents’ arguments against

God’s extension reduce to the following pattern of reasoning: since all corporeal

substances are composites, and God isn’t a composite, God is not a corporeal substance.

Spinoza’s response is to deny his opponents’ premise that all corporeal substances are

composites, and the conclusion of the vacuum arguments purport to have established this.

Unfortunately the vacuum arguments’ shared conclusion fails to explicitly establish this

thesis. Accordingly, in this part of the chapter I show how the vacuum arguments’

conclusion entails the denial that all corporeal substances are composites.

As we’ve seen, the vacuum argument exposes an inconsistency in Descartes’

metaphysics between i) his account of corporeal substance as having really distinct parts,

ii) the principle of sufficient reason, and iii) the impossibility of a vacuum. The

86 That we know that corporeal substances’ parts are really distinct see Principles I.60: MM, 27: AT VIIIA, 28. That the principle of sufficient reason is known clearly and distinctly see: Principles I.18: MM, 10: AT VIIIA, 11-12 and CSM II, 97: AT VII, 135.

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conclusion of the vacuum argument is a recommendation intended to render Descartes’

metaphysics consistent. Suppose a Cartesian agrees both with Spinoza’s diagnosis of the

inconsistency and his suggested remedy. I will call such a Cartesian ‘the consistent

Cartesian’. According to Spinoza, the consistent Cartesian is committed to claiming that

corporeal substance is non-composite. In what follows I will reconstruct Spinoza’s

argument from the conclusion of the vacuum arguments to the claim that corporeal

substance is non-composite.

The consistent Cartesian is committed to the shared conclusion of the vacuum

arguments which, as I have presented it, is as follows:

12) It is not the case that corporeal substance has really distinct parts.

This is ambiguous between two claims: a) corporeal substance doesn’t have parts and a

fortiori those parts aren’t really distinct and b) corporeal substance has parts, but not

really distinct parts. The consistent Cartesian maintains that corporeal substance exists

and that it is extended: according to Descartes, “extension in length, breadth, and depth

constitutes the nature of corporeal substance.”87 Descartes holds that everything that is

extended has parts. He writes, “it is impossible to have the idea of an extended thing

without also having the idea of half of it, or a third of it….”88 Descartes’ point is that no

matter how small a bit of extension you’ve got, it has a top half and a bottom half, and

these in turn have top halves and bottom halves. Since the Cartesian holds that corporeal

substances exist and are extended, she can scarcely deny that corporeal substance has

87 Principles I.53: MM, 23: AT VIIIA, 25. 88 CSM III, 202: AT III, 477.

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parts. Rather the consistent Cartesian is forced to deny that these parts are really distinct.

Accordingly I will represent the disambiguated 12) as:

13) Corporeal substance has parts, but not really distinct parts.

It follows from this that corporeal substance’s parts are dependent for their existence on

the whole, for if their existence were independent of the whole, then they would be really

distinct parts. Thus:

14) If corporeal substance has parts, then they are dependent for their existence on the whole.

According to Descartes “all composition is evidence of dependence.”89 Thus, the

consistent Cartesian is committed to maintaining that composite entities are dependent on

their parts. However, for the consistent Cartesian corporeal substance is not dependent

on its parts, rather its parts are dependent on corporeal substance as a whole. So it is

clear that:

15) If corporeal substance’s parts are dependent on the whole for their existence, then corporeal substance is non-composite.

From 13)-15) it follows that

16) Corporeal substance is non-composite

Consequently, the consistent Cartesian is committed to claiming that corporeal substance

is non-composite. And further, if this right, then the consistent Cartesian does not have

grounds for denying Spinoza’s claim that God is a corporeal substance.

Before I turn to evaluate Spinoza’s vacuum arguments I want to pause and briefly

summarize. Spinoza uses two different arguments to point out an inconsistency in

Descartes’ metaphysics. Descartes cannot consistently maintain both that corporeal

89 CSM I, 128: AT VI, 35.

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substance has really distinct parts and that a vacuum is impossible. Spinoza’s resolution

of this inconsistency is to give up the real distinction among corporeal substance’s parts,

which as it turns out, pulls the rug out from underneath his opponents’ arguments that

God is not a corporeal substance.

Evaluating the Vacuum Arguments

Spinoza introduces the vacuum argument as applicable to “all those who know

that clear reason is infallible…” (C 423, S 226, G II 59). Is Spinoza right—must the

consistent Cartesian deny that corporeal substance has really distinct parts and

consequently give up their objections to God’s corporeality? In general there are two

ways Descartes can respond: he can either deny the shared conclusion of the vacuum

arguments, or he can consent to Spinoza’s conclusion that corporeal substance doesn’t

have really distinct parts, but deny that this entails giving up the objection that God’s

being composite follows from being a corporeal substance. I think the best prospects for

a rejoinder lie with the former strategy and so in what follows, I will focus on replying on

Descartes’ behalf to the vacuum arguments. Responding to the vacuum arguments

involves denying both the AVA and the CVA. The argumentative core of both of these

arguments lies in Spinoza’s claim that if corporeal substance has really distinct parts, then

it is possible for one to be annihilated and the contiguous bodies retain their relative

spatial relations.90 Thus, this is the assertion that Descartes will have to deny. I think

Descartes has the resources to reject the vacuum arguments, but before I present this

defense I want to briefly consider a plausible but ultimately unsuccessful strategy.

90 See premise 4) of the AVA and the justification for 8) of the CVA.

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Perhaps the most obvious response available to Descartes is to maintain that God,

upon annihilation, must immediately replace the annihilated body with another one. This

is a tempting response to offer on Descartes’ behalf, and in fact, Descartes is explicitly

committed to the occurrence of such an event at every Mass.91 However, Descartes

cannot reject the vacuum arguments on this basis. The problem with this response is that

it doesn’t actually resolve the contradiction. Spinoza’s argument is not about what

Descartes’ God can or must do—it concerns his metaphysics of body. That corporeal

substance has really distinct parts entails the annihilability and mutual independence of

these parts; it is these features of corporeal substance that render vacua possible.

Consequently, Spinoza’s claim is that Descartes’ metaphysics of body is incoherent.

Claiming that God immediately replaces annihilated bodies doesn’t resolve the problem;

rather it tells us that God will reach out and plug the hole in His metaphysics if necessary,

thus guaranteeing that although creation is by nature inconsistent, such a contradiction as

the actual existence of a vacuum will never occur. Beyond the fact that such a response

doesn’t resolve the problem there is a further difficulty: if the vacuum argument forces

Descartes to take refuge in the divine will to save his metaphysics of body, then Spinoza

has shown that Descartes metaphysics is untenable and requires modification, not that we

ought to genuinely defer to a miracle. Putting aside Spinoza’s own view of miracles,92

the new scientists of the 17th century were concerned to explain bodies and their

91 See Descartes’ account of the Eucharist at CSM II, 172-178: AT VII 247-256. 92 Spinoza explains that “…there is the ordinary power of God, and his extraordinary power…the extraordinary is exercised with he does something beyond the order of nature, e.g., all miracles…Concerning this last there could, not without reason, be considerable doubt. for it seems a greater miracle if God always governs the world with one and the same fixed and immutable order, than if, on account of human folly, he abrogates the laws which…he himself has most excellently decreed in nature, from sheer freedom….” (C 333, S 203, G I 267).

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interactions mechanistically and a metaphysics of body that requires miracles is

antithetical to this methodology.

A much more promising response is to note that according to Descartes’

cosmology, all bodies are in vortices and in virtue of this there is a constant pressure

pushing on them.93 If this is right, then when the water inside the vessel is annihilated,

the sides become contiguous not as the result of the privation, but as the result of the

bodies surrounding the vessel pushing them inwards. Thus, we need not think Descartes

is committed to an inconsistency; for according to this way of resolving the vacuum

arguments, the bodies immediately contiguous to the vessel, as opposed to the privation,

cause the sides to become contiguous. This is a nice resolution, but it has a curious

consequence. Consider the possibility of a solid body the parts of which possess a force

of rest stronger than the force of motion impressed by the vortex. Suppose instead of a

vessel we envision a solid (maybe steel or diamond) sphere containing a drop of water in

the center.94 If the sphere is hard enough, that is, if its parts possess a high enough force

of rest relative to one another, then upon the annihilation of the water, the sides of the

sphere will remain discontiguous. Thus, if such a body is possible, then a vacuum is

possible. It is worth noting that, at least in Le Monde, Descartes considers such a

possibility prima facie plausible: “It follows, on my view, that if a vacuum can exist

anywhere, it must be in hard bodies rather than in fluid ones. For obviously it is easier

for the parts of hard bodies to press and arrange themselves against one another than for

the parts of fluid bodies to do so, since the latter are moving about while the former are

93 Thanks to Brandon Look for suggesting this response. 94 The sphere must be solid in order to guarantee that subtle matter cannot “fill” the void.

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motionless”.95 The mature Descartes need not take this too seriously, and can run the

argument above, contrapositively. Since vacua are metaphysically impossible, it follows

that it is impossible for there to be a solid body so hard that it can’t be squeezed in by its

surroundings upon an annihilation of one of its parts. Nevertheless, this is an odd

consequence and given its prima facie implausibility, it is a consequence one might

prefer not to endorse if given the choice. Regardless, this response resolves the apparent

inconsistency raised by the vacuum arguments without having to significantly revise

Descartes’ metaphysics of body. I will now turn to the other argument Spinoza points us

to in E1P15s: E1P12.

Section 3: EIP12 and the Divisibility Argument

Recall that, as Spinoza sees it, all the arguments against his view that extension is

an attribute of God ultimately reduce to the following: since 1) all corporeal substances

are composite and 2) God is not composite, it follows that 3) God is not a corporeal

substance. As we’ve seen, Spinoza’s response to this argument is to deny 1) and in

E1P15s he points to two justifications of this denial. Having discussed the second of

these arguments in Section 2 (concerning vacua), I turn in this section to a consideration

of the first. On behalf of his claim that corporeal substance is non-composite, Spinoza

refers us to two earlier propositions of the Ethics, saying

These are the arguments which I find authors using, to try to show that corporeal substance is unworthy of the divine nature, and cannot pertain to it. But anyone who is properly attentive will find that I have already replied to them, since these arguments are founded only on the supposition that corporeal substance is

95 CSM I, 85-86: AT XI, 17-18.

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composed of parts which I have already (P12 and P13C) shown to be absurd. (C 422, S 225, G II 58)

E1P12, to which Spinoza points us, reads “No attribute of substance can be truly

conceived from which it follows that the substance can be divided” (C 419, S 223, G II

55). I take it that this proposition expresses the following conditional: ‘if substance is

truly conceived, then it is conceived as indivisible’. From this it follows a fortiori that

corporeal substance is indivisible, and this is exactly the conclusion that Spinoza draws in

the other proposition to which he refers, E1P13c.96 In what follows I will focus my

discussion on Spinoza’s argument for E1P12.

The overall structure of the argument that Spinoza presents at E1P12 for the

indivisibility of substance is fairly simple. Spinoza begins by supposing that substance is

divisible. On this supposition it follows, he claims, that the parts of substance are either

of the same nature as substance or not. But, he continues, substance is neither divisible

into parts of the same nature as substance nor into parts of a different nature. Thus he is

able to conclude after having rejected both disjuncts that the original supposition (that

substance is divisible) is false. While the structure may be simple enough, the

argument’s contents are not. Sticking close to the text, Spinoza’s argument is as follows:

20) If substance is divisible, then the parts either retain the nature of substance or they don’t.

21) If they retain the nature of substance, “then (by P8) each part will have to be infinite, and (by P7) its own cause, and (by P5) each part will have to consist of a different attribute. And so many substances will be able to be formed from one, which is absurd (by P6). Furthermore, the parts (by P2) would have nothing in common with their whole, and the whole (by d4 and P10) could both be and be conceived without its parts, which is absurd, as no one will be able to doubt.” (C 419, S 223, G 55)

96 E1P13c reads: “From these [propositions] it follows that no substance, and consequently no corporeal substance, insofar as it is a substance, is divisible” (C 420, S 224, G II 55).

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22) If they do not retain the nature of substance, then “since the whole substance would be divided into equal parts, it would lose the nature of substance, and would cease to be, which (by P7) is absurd.” (C 419, S 223, G 55)

23) So substance is indivisible. Even a cursory look at this argument reveals that Spinoza’s argument that substance is

indivisible depends heavily on the deductive apparatus already established in the Ethics.

Specifically, it depends on propositions 5-8, but insofar as propositions 6, 7, and 8

themselves depend on 5 we can trace Spinoza’s reasoning back to E1P5. This makes a

lot of sense since E1P5 tells us that there is only one substance per attribute: if substance

is divisible into parts of the same nature—that is, substances—then on the assumption

that parts must be of the same attribute as the whole, it follows that it is possible for there

to be more than one substance of the same attribute. Given this, is there anything

significant to say about the argument for E1P12 outside of a discussion of E1P5 and its

derivatives? I think so, and that a close look at the argument reveals a distinct argument

for the inconsistency of Descartes’ account of matter, the only resolution of which is to

deny that corporeal substance is composite.

Premise 21) consists of a cluster of arguments for the conclusion that substance is

not divisible into parts of the same nature as the whole. In what follows I want to focus

on just one of these arguments, the last one. Spinoza argues that if substance is divisible

into parts of the same nature as substance, then “the whole (by d4 and P10) could both be

and be conceived without its parts, which is absurd, as no one will be able to doubt.”

More formally:

a) Suppose that substance is divisible into parts of the same nature as substance, then the whole could both be and be conceived without its parts.

b) It is absurd to think a whole could both exist and be conceived without its parts.

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c) So, it is not the case that substance is divisible into parts of the same nature as substance, i.e., into parts that are themselves substances.

Premise a) of what I will henceforth call the ‘Divisibility Argument’ makes explicit

substance’s independence: substances exist and are conceived of independently from

everything else. Thus if a substance is divisible into parts which are themselves

substances, then each of the parts exist and is conceived of independently of the whole

(and of every other part). Perhaps the chief obstacle to following this argument, lies in

understanding b). As it stands, b) is vague and Spinoza provides no help insofar as he

does not justify the claim. How, then, should we interpret this claim? Jonathan Bennett

interprets this claim as saying that it is absurd to think that a composite whole could both

be and be conceived without its parts.97 Composite wholes are dependent for their

existence and conception on their parts, each of which exist and are conceived of

independently from the whole (and from all other parts). As Spinoza says elsewhere:

“…it is clear through itself that component parts are prior in nature at least to the thing

composed and the other parts” (C 324, S 196, G I 258). If this is right, and I think it is,

then it shows that Spinoza, in supposing that substance is divisible into parts,

simultaneously supposes that substance is composite. Thus, in more general terms,

Spinoza is using the Divisibility Argument to show that being a substance is inconsistent

with being a composite. Spinoza, then, is offering an argument for which Leibniz is

much more well-known.98 Thus Bennett concludes “it is clearer in Leibniz than in

Spinoza, but probably Spinoza was the pioneer and Leibniz the follower”.99

97 Bennett, Study, 82. 98 See e.g Leibniz’s April 30 1687 letter to Arnauld in G.W. Leibniz, Philosophical Essays, eds., Roger Ariew and Daniel Garber, (Indianapolis: Hackett Publishing, 1989), 85. 99 Bennett, Study, 82.

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This is an attractive account of the argument; however there are a couple of prima

facie difficulties that need to be resolved. First, is there any independent reason to think

that Spinoza is thinking of the properties of ‘being composed’ and ‘being divisible’

interchangeably? There are two reasons. First, in E1P15s Spinoza characterizes the

argument at E1P12 as showing that corporeal substance is not composed of parts,

whereas E1P12p’s stated conclusion is that substance is not divisible into parts. Second,

again in E1P15s, Spinoza characterizes his opponents as maintaining that “corporeal

substance is composed of parts” and then proceeds to use the vacuum argument to refute

this, concluding that “corporeal substance, insofar as it is a substance, cannot be divided”.

Thus there is positive reason to think that Bennett’s proposal is right and that Spinoza is

thinking of divisibility and compositionality interchangeably.

A second worry comes from a consideration of the other consequences of

supposing that substance is divisible into parts of the same nature as the whole. If we

look back at premise 21) of the argument for E1P12 we find Spinoza says, if substance is

divisible into parts of the same nature as substance, then “…many substances will be able

to be formed from one, which is absurd (by P6)”. It is Spinoza’s use of the term ‘formed’

that is problematic, for it suggests that the parts into which substance are divisible come

to be (are “formed”) as the result of the division.100 If this correct, then it isn’t right,

contrary to the interpretation under consideration, to say that corporeal substance is a

composite, since corporeal substance cannot be composed of non-existent parts. In this

case, corporeal substance is divisible but non-composite. I think that this tension can be 100 See J.A.Cover, “Spinoza’s Extended Substance: Cartesian and Leibnizian Reflections” [“Spinoza’s

Extended Substance”], in Rocco J. Gennaro and Charles Huenemann eds., New Essays on the Rationalists, (Oxford: Oxford University Press, 1999), 122. Cover notes this objection, but nevertheless does not endorse a “whole-prior-to-part reading” of E1P12p.

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resolved by looking at the word ‘formed’. Both prominent contemporary translators of

Spinoza, Samuel Shirley and Edwin Curley, use the term ‘formed’ to translate the Latin

‘constitui’. While ‘formed’ is a fine translation of this verb it is not clear that there is any

reason to prefer this translation over a number of other available interpretive options that

do not suggest that substance is divisible but non-composite. For example, on its face

both ‘determined’ and ‘resolved’ are acceptable translations neither of which indicates

that Spinoza is thinking of substance as divisible but non-composite. Ultimately, my

point is not to recommend one translation over another; rather it is to note that there need

not be any tension within the interpretation at hand as long as we are not wedded to the

translation of ‘constitui’ as ‘formed’.

Having clarified Spinoza’s claim that a whole can’t both exist and be conceived

without its parts, in terms of the dependence a composite has on its parts, we can turn to

the broader topic at hand. I maintain that in offering the Divisibility Argument, Spinoza

is highlighting an inconsistency in Descartes’ metaphysics. As will become clear,

although Descartes is committed to the denial of the conclusion, he is also committed to

the truth of the premises, and as such, to an inconsistency. Premise a) of the Divisibility

Argument asserts that on the supposition that substance is divisible into parts of the same

nature as substance, then the whole could both be and be conceived without its parts.

Descartes is committed to both the supposition and the conditional. As we’ve seen

Descartes maintains that corporeal substance is divisible into really distinct parts, where

this is just to say that corporeal substance has substances as parts. Consequently each of

a corporeal substance’s parts exists and is conceived independently of whole and every

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other part.101 Likewise, the whole, as a substance, exists and is conceived independently

of all other substances, and so is independent of its parts.

Premise b) of the Divisibility Argument asserts that it is absurd to think a whole

could both exist and be conceived without its parts. As we’ve seen, this premise

contends that composite wholes depend on their parts for their existence and conception.

Descartes is likewise committed to this premise. As we’ve already seen, Descartes

explicitly claims in the Discourse on Method: “all composition is evidence of

dependence.”102 But even without textual evidence, there is good reason to believe that

Descartes would have agreed to b). Spinoza doesn’t think that he is making a

controversial claim in saying that composites depend for their existence on their parts

(after all, his only justification is that it would be absurd to think otherwise), and I think it

is worth showing why this is so obvious. Consider a paradigm composite whole: a brick

wall. A brick wall is built up out of bricks; it comes into being in virtue of previously

existing bricks coming to stand in some relation. While a brick wall may be capable of

surviving the substitution of some or even all of its bricks, or a net loss or gain in bricks,

no brick wall can exist independently of any parts: no bricks, no brick wall. It follows,

then, that Descartes is committed to the premises of the Divisibility Argument and so to

its conclusion.

The Divisibility Argument highlights an inconsistency in Descartes’ metaphysics.

Descartes maintains that i) corporeal substance is divisible into parts which are

101 Principles I.60: MM, 26-27: AT VIIIA, 28-29. See also Dan Kaufman, “Divine Simplicity and the Eternal Truths in Descartes” British Journal for the History of Philosophy 11 (2003): 553-579 and “Descartes on Composites, Incomplete Substances, and Kinds of Unity” Archiv für Geschichte der Philosophie (forthcoming), for interesting discussions of composition in Descartes. 102 CSM I, 138: AT VI, 35.

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themselves substances, ii) substances exist and are conceived independently of all other

substances, and iii) composites depend on their parts for their existence and conception.

The Divisibility Argument shows that i) and ii) entail the denial of iii), and as such that

Descartes is committed to an inconsistent set of metaphysical principles. Rather than

give up the obviously true principle that composites depend on their parts or that

substances exist and are conceived independently of all other substances, Spinoza again

pushes the Cartesian to resolve the inconsistency by giving up i).

Evaluating Spinoza’s Divisibility Argument

The Divisibility Argument offers a strong critique of Descartes’ metaphysics, to

which there is no easy reply. In order to illustrate this, I will begin by laying out the

general strategies Descartes might pursue in offering a rejoinder. I take it that there are

really only two strategies for developing a response on Descartes’ behalf: i) deny that the

Divisibility Argument highlights an inconsistency in his metaphysics by denying the

original supposition that corporeal substance is divisible into parts of the same nature as

substance, or ii) deny that the Divisibility Argument highlights an inconsistency in his

metaphysics by rejecting its conclusion and therefore denying at least one of its premises.

Suppose, on behalf of Descartes, we adopt the first strategy. Recall that Spinoza

is taking the property of ‘being divisible’ as interchangeable with ‘being composite’.

One promising line of response lies in denying the original supposition that corporeal

substance is divisible into, and composed by, corporeal substances, by differentiating

divisibility from compositionality. Thus, Descartes might claim that although he is

committed to the claim that corporeal substance is divisible into corporeal substances, he

does not maintain that corporeal substance is simultaneously composed by these parts. If

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Descartes were to adopt this strategy, then he would be claiming that corporeal

substances are compositionally simple, but nevertheless divisible into corporeal

substances. Corporeal substance, then, is like a cheesecake: prior to its division it is one

thing which is nevertheless divisible into many slices. This is a plausible reply and it is

not unheard of to think that some wholes exist in this way; in fact, virtually all the

scholastics believed in such wholes.103 In brief, according to this view, a material body,

e.g., is ontologically simple prior to division—it is not composed of parts. Only upon

division do its parts come to be.104 One justification for this position is that there is

exactly one substance per substantial form. Consider a human being: a human being is

ontologically simple in that it has one form. The parts of a human being, say the hands,

do not exist independent of the body and compose it. Rather hands exist in virtue of the

instantiation of form of a human being. Thus, if Descartes were to claim a similar account

of corporeal substance, he could deny the supposition present in the first premise of the

Divisibility Argument.

Unfortunately, however, Descartes can’t respond in this way. Certainly, he could

never adopt the scholastic justification for such a view, but in addition he is explicitly

committed to denying this way of thinking about the parts of corporeal substance.

Descartes doesn’t think that corporeal substances are ontologically simple. Consider any

Cartesian corporeal substance: say a rock. The rock is a composite, its parts are

themselves corporeal substances. According to Descartes, every corporeal substance is

such that “each part of it [which can be] delimited by our mind is really distinct from the

103 See for example Aquinas, Basic Writings of Saint Thomas Aquinas, ed. Anton C. Pegis (Indianapolis: Hackett Publishing, 1997), 704-710 (Summa Theologica I.76 a.3-4). 104 See Thomas Holden, The Architecture of Matter, (Oxford: Oxford University Press, 2004), 18, 91-103.

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other parts of the same substance.” 105 Thus, corporeal substance is not simple prior to

division, but is a whole, the parts of which are themselves substances. In sum, Descartes

can’t adopt the first strategy by arguing that corporeal substance is divisible but not

composite.

What about the second strategy? Can Descartes legitimately deny either premise

of the Divisibility Argument? Recall that the Divisibility Argument claims that if

corporeal substance is divisible into parts which are themselves substances, then the

whole exists and is conceived independently of its parts. However, this is absurd, and

accordingly corporeal substance is not divisible in this way. Descartes is going to have a

hard time denying either of these premises without significantly altering his metaphysical

commitments. The first premise follows from the independence criterion of substance:

what it is to be a finite substance is to exist (and correspondingly to be conceived)

independently of all other finite substances.106 It is even more difficult to see how

Descartes might deny the second premise. The second premise claims that composite

substances are dependent on their parts, and this seems to be a conceptual truth. Thus if

Descartes wants to deny the Divisibility Argument, it seems the only option is to reject

105 See Principles I.60: MM, 26-27: AT VIIIA, 28-29 106 It is worth noting that in the Divisibility Argument Spinoza is not adopting some super-strong sense of independence. Some commentators interpret Spinoza’s substance monism as the consistent application of Descartes claim in Principles I.51 that “By substance we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence”; since bodies and minds are dependent on God for their existence, then they can’t be substances (MM, 22-23: AT VIIIA, 24). For a discussion of this position see Carriero, “Monism”, 42-46. I am skeptical of this interpretation, but for the present purposes I merely note that Spinoza is not relying on this sense of independence in the Divisibility Argument; rather all the argument requires is that corporeal substances are independent from other corporeal substances as Descartes claims in Principles I. 52: “as for corporeal substance and mind…,these can be understood to fall under this common concept: things that need only the concurrence of God in order to exist” (MM, 23: AT VIIIA, 25).

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the independence criterion of substance, and this would be a significant revision of his

metaphysics.

Having briefly considered each approach to denying the Divisibility Argument, it

is clear that there isn’t an easy answer to the challenge this argument presents. Putting

aside the independent evaluation of Spinoza’s arguments, it is clear enough that Spinoza

took them seriously since he directs us to the Vacuum Argument and the Divisibility

Argument for an explanation of his own metaphysics, specifically for an answer to the

question ‘Why aren’t bodies, substances?’ In the next section I turn to Spinoza’s own

account of matter by considering what an account of matter that takes seriously the

lessons of the Vacuum and Divisibility Arguments looks like.

Section 4: Spinoza on Corporeal Substance and Body

In sections 2 and 3 I took a close look at two arguments highlighting an

inconsistency in Descartes’ metaphysics. Further, we’ve seen that Spinoza’s suggested

resolution to these inconsistencies lies in denying that corporeal substance has parts

which are themselves substances, or in Descartes’ idiom, that corporeal substance has

really distinct parts. Keeping this in mind, what does a Spinozistic revision of Descartes’

account of matter look like? As it turns out, if Spinoza wants to maintain that corporeal

substance exists and is extended, he will be forced to maintain that there is only one

corporeal substance unlimited in its extent.

Let’s begin with Descartes’ account of matter or corporeal substance. According

to Descartes, corporeal substance is essentially extended where this means that it is three-

dimensional. Corporeal substance has parts in virtue of being extended in the sense that

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we can discriminate finite sub-volumes within its extension. Thus, Descartes writes that

“it is impossible to have the idea of an extended thing without also having the idea of half

of it, or a third of it….”107 As we’ve seen Descartes takes these parts to be really distinct

and as such to be substances. As the Vacuum Arguments and the Divisibility Argument

show, this is precisely the problem with Descartes’ account of corporeal substance. In

order to avoid the problems raised by the Vacuum Arguments and Divisibility Argument,

corporeal substance cannot be a composite entity having substances as parts.

However, revising Descartes’ account of corporeal substance to accommodate the

problems raised by the Vacuum Arguments and Divisibility Arguments involves more

than merely claiming that corporeal substance is non-composite. It also entails claiming

that there is at most one corporeal substance. Consider the following argument:

24) Suppose that there is more than one corporeal substance. 25) If there is more than one corporeal substance, then every corporeal substance is

wholly contiguous to at least one other corporeal substance. 26) If every corporeal substance is wholly contiguous to at least one other corporeal

substance, then a vacuum is possible. 27) A vacuum is impossible. 28) There is at most one corporeal substance.

Spinoza’s commitment to the Vacuum Arguments and Divisibility Argument entail a

commitment to this line of reasoning and hence ultimately to the conclusion that there is

at most one corporeal substance. Spinoza’s commitment to 27) is clear given the

Vacuum Arguments. Showing that Spinoza is committed to 25) and 26) requires a little

more work. I will start with premise 25).

Let’s suppose that 25) is false and that that there is a corporeal substance that is

not wholly contiguous to at least one other corporeal substance. Let’s call such a

107 CSM III, 202: AT III, 477.

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corporeal substance ‘S’. If S is not wholly contiguous to at least one other corporeal

substance, then S is either partially or wholly spatially isolated. However, if S is either

partially or wholly spatially isolated, then a vacuum exists. Indeed this is precisely the

lesson of the Composition Vacuum Argument. But vacua are impossible, so it follows

that every corporeal substance is wholly contiguous to at least one other corporeal

substance.

In order to confirm that Spinoza is committed to 26) I will again proceed by

reductio. Suppose that every corporeal substance is wholly contiguous to at least one

other corporeal substance, and a vacuum is impossible. As substances, each of our

corporeal substances are independently annihilable. However, as the Annihilation

Vacuum Argument (AVA) shows, the annihilation of a corporeal substance entails the

existence of a vacuum since the surrounding contiguous corporeal substances do not rush

in to fill the void “left” by the annihilation. Thus, in such a case we are left with a

distance without substance, that is, a vacuum. However, this contradicts our original

supposition and so it follows that if every corporeal substance is wholly contiguous to at

least one other corporeal substance, then a vacuum is possible.108

Thus, it follows from Spinoza’s correction of Descartes’ account of matter that if

there is corporeal substance and it is extended, then there is only one corporeal substance,

and this is precisely the account of corporeal substance we find in the Ethics. Further it is

108 One other way to show that a commitment to the existence of corporeal substance and to the Vacuum/Divisibility Argument entails the existence of one corporeal substance is to start with Descartes’ material universe. As extended, the material universe is the biggest corporeal substance. This substance is unlimited in extent (as Principles II.21 shows). Given that the material universe exists and is a corporeal substance it follows that there are no other corporeal substances since any other corporeal substance would be part of the material universe. As we’ve seen, the lesson of the Vacuum Argument and the Divisibility Argument is that corporeal substance is non-composite. Consequently, the parts of the material universe cannot themselves be substances and so it follows that there is only one corporeal substance.

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clear why bodies cannot be corporeal substances. There are many bodies so they cannot

be substances for the same reasons offered above for denying that there can be many

corporeal substances. Given all of this I take it that Spinoza’s one corporeal substance

doctrine is at least partially grounded in his attempt to replace Descartes problematic

account of matter.

Conclusion

My aim in this chapter has been to show that Spinoza’s one corporeal substance

doctrine is the result of Spinoza’s effort to replace Descartes’ account of matter with one

that is philosophically adequate. The problem with Descartes’ account of matter is that

he maintains that corporeal substances have really distinct parts. As we’ve seen, this

entails that the parts of corporeal substance are themselves substances. This has two

unacceptable consequences: that vacua are possible and that corporeal substances are

dependent on their parts. Spinoza rejects Descartes’ account on this basis and replaces it

with one of his own, however as we saw in the last section doing so entails that there is

only one unlimited corporeal substance. In chapters 3 and 4 I complete my argument that

much of what is distinctive about Spinoza’s metaphysics is the result of replacing

Descartes’ account of matter, by considering i) Spinoza’s account of bodies and ii) his

account of the relation between bodies and corporeal substance.

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CHAPTER 3: SPINOZA’S INFINITE MODE OF EXTENSION

Introduction

As we saw in chapter 2, as a consequence of Spinoza’s rejection of Descartes’

account of matter, it follows that bodies are not corporeal substances. Recall the

mechanist’s slogan that all phenomena are to be reduced to matter and motion.

Interpreting ‘matter’ as corporeal substance, Spinoza takes this slogan seriously. Given

that no body is a corporeal substance (and that bodies exist) it follows that bodies are

among the phenomena to be reduced to corporeal substance and motion. Thus, in order

to determine what a body is for Spinoza we need to understand how Spinoza thinks about

motion. In this chapter I take up this challenge by focusing on what has come to be

known as the “immediate infinite mode of extension”.

According to Spinoza “whatever is, is either in itself or in another” (E1a1: C 410,

S 217, G II 46). The world is divided into two categories: substance and mode.

Substance is in itself and modes are in something else, namely substance. The first part

of the Ethics develops the argument that there is only one substance and this substance is

God. Spinoza defines God as an infinite being “consisting of an infinity of attributes, of

which each one expresses an eternal and infinite essence” (E1d6: C 409, S 217, G II 45).

‘Attribute’ is Spinoza’s way of referring to a specific expression of God’s essence and it

is through these specific expressions of God’s essence that modes are understood. Thus,

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modes, on Spinoza’s reckoning, exist in God and are understood through a particular

expression of God’s essence. Spinoza explicitly notes two ways God’s essence is

expressed: as extended and as thinking.109 As such Spinoza defines ‘body’ as follows:

“By ‘body’ I understand a mode that in a certain and determinate way expresses God’s

essence insofar as he is considered as an extended thing” (E2d1: C 447, S 244, G II

84).110 Extension is an attribute; it is one of the many ways that God’s essence is

expressed and every individual body exists in, and is understood through, extension.

In this way, Spinoza accounts for the contents of the material universe: things like

your body and mine, diamonds, and daffodils are modes of extension. But the term

‘mode’ is general; Spinoza asserts the existence of two kinds of modes, finite and infinite.

Spinoza writes, “every mode which exists necessarily and is infinite has necessarily had

to follow either from the absolute nature of some attribute of God, or from some attribute,

modified by a modification which exists necessarily and is infinite” (E1P23: C 430, S

231, G II 66). Infinite modes follow from the absolute nature of one of God’s attributes,

and they do so either directly or indirectly. Although Spinoza does not use these terms, it

has become standard to call those infinite modes that follow directly from the absolute

nature of one of God’s attributes, ‘immediate infinite modes’, and those that follow

indirectly ‘mediate infinite modes’. Mediate infinite modes follow, not from the absolute

nature of one of the attributes, but from another infinite mode. In his correspondence

with Schuller, Spinoza offers as an example of an immediate infinite mode for the

attribute of extension “motion and rest” (motus & quies) and as an example of a mediate 109 Spinoza suggests that although there are many attributes we know only two of them, thought and extension. See for example ST 1.2 and E2P7s. 110 I have added the single quotation marks on each side of the term ‘body’ to make clear that Spinoza is mentioning the term as opposed to using it.

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infinite mode of extension “the face of the whole universe” (facies totius Universi; Ep.

64: S 919, G IV 278).

These examples are not particularly useful for understanding the infinite modes,

and this is unfortunate for more than expository reasons. The infinite modes are crucial

aspects of Spinoza’s metaphysics, in that they causally and explanatorily connect the

everyday world of finite modes to the substance in which they all exist, God. It is in

virtue of motion and rest that Spinoza explains the variety of bodies and properties in the

world: he writes in the Short Treatise “Each and every particular thing that comes to exist

becomes such through motion and rest” (ST Preface to the second part: C 95, S 60, G I

52).111 A great deal of scholarly attention has been paid to Spinoza’s explanation of how

finite modes are caused and explained by God through the infinite modes.112 However, in

this chapter I put this and related questions aside. Rather, I take up a more basic

question. What is the immediate infinite mode of extension—that is, to what does

‘motion and rest’ refer?113 Few commentators have considered this question and among

those that have there has been little agreement.114 But this is unsurprising given the

3 Cf. Principles II.23: MM, 50. 112 See for example, E.M. Curley, Spinoza’s Metaphysics: An Essay in Interpretation [Spinoza’s Metaphysics], (Cambridge, Mass: Harvard University Press, 1969), especially chapter 2; Richard V. Mason, “Spinoza on the Causality of Individuals” in Essays on Early Modern Philosophers: Spinoza. ed. Vere Chappell, (New York: Garland Publishing, Inc., 1992), 255-284; A.J. Watt, “The Causality of God in Spinoza’s Philosophy” [“The Causality of God”] Canadian Journal of Philosophy: 2, (1972), 171-189; and Emilia Giancotti, “On the Problem of Infinite Modes” in God and Nature: Spinoza’s Metaphysics [God and Nature], ed. Yirmiyahu Yovel (Leiden: Brill, 1991). 113 It isn’t clear whether there are other immediate infinite modes besides “motion and rest”; “motion and rest” is the only such mode Spinoza identifies. As such here, and henceforth, I will refer to it as the immediate infinite mode of extension. 114 For example, Stuart Hampshire suggests that it is “energy”. See Stuart Hampshire, Spinoza, (Baltimore, Maryland: Penguin Books, 1951). Curley, on the other hand, gives a very general answer to the question saying that it is the set of general facts that make true the propositions expressing the laws of nature. See Curley, Spinoza’s Metaphysics, pgs; see also Yirmiyahu Yovel, “The Infinite Mode and Natural Laws in Spinoza” [“Infinite Mode”] in Yovel, God and Nature. Bennett takes “motion and rest” to stand for patterns of qualitative change in extension’s regions that can be conceived as local motion, see Bennett,

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paucity of textual resources available. Nevertheless, in this chapter I develop an original

answer to this question. In section 1, I begin by considering the interpretive constraints

any account of motion and rest must meet. I then present the most developed account of

‘motion and rest’ in the literature and show that despite its strengths there are reasons to

doubt that it is really Spinoza’s. In section 2, I develop an alternative interpretation

according to which ‘motion and rest’ refers to the alteration and preservation of the

spatial relations obtaining between extension’s regions. As we will see, my interpretation

of the immediate infinite mode of extension will yield an account of the nature of body. I

conclude the chapter by arguing that my interpretation is to be preferred to most

developed alternative account.

Section1: Reconstructing Spinoza’s Account of Motion-and-Rest

Criteria

Given the few textual resources available, there are at least five basic criteria any

account of motion and rest must meet. First, in his presentation of the infinite modes in

the Ethics Spinoza tells us that infinite modes follow “from the absolute nature of some

attribute of God” (E1P23: C 430, S 231, G II 66). Thus, motion and rest follow from the

absolute nature of extension. Garrett argues, and I think he is right, that x follows from

the absolute nature of an attribute only if x is “manifested pervasively throughout that

Study, 106-110. More recently, Don Garrett has argued that it refers to a quantity of motion or force. See Don Garrett, “Spinoza’s Theory of Metaphysical Individuation” [“Individuation”] in Individuation in Early Modern Philosophy, eds. Kenneth F. Barber and Jorge J.E. Gracia, (Albany: State University of New York Press, 1994), 73-101. Tad Schmaltz (“Spinoza’s Mediate Infinite Mode”, 206) seems to agree in some respect with Garrett, maintaining that Spinoza took “motion-and-rest to be the total sum of the quantities of motion and rest in the physical world.” See Tad M. Schmaltz, “Spinoza’s Mediate Infinite Mode” Journal of the History of Philosophy, vol. 35, no. 2, (1997), 199-235.

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attribute” and x is manifested permanently.115 Thus, any account of motion and rest must

explain how it is both a pervasive and a permanent feature of extension.

Second, according to Spinoza, motion and rest accounts for the existence and

variety of bodies present in the world. As we’ve seen Spinoza claims in the Short

Treatise that “Each and every particular thing that comes to exist becomes such through

motion and rest” (ST Preface to the second part: C 95, S 60, G I 52). So, whatever this

infinite mode turns out to be, it must be clear on some level how the existence of bodies

follows from it. Third, given that the mediate infinite mode of extension, “the face of the

whole universe” follows from the immediate infinite mode of extension (E1P23), an

account of motion and rest must tell us what the mediate mode is, and how it follows

from the immediate. Fourth, whatever the immediate infinite mode of extension is, it is

the sort of thing that can be referred to singularly; Spinoza gives motion and rest as an

example, not examples, of things that immediately follow from God (Ep. 64).116

Elsewhere he says “there is no motion by itself, but only motion and rest together” (ST I,

II footnote: C, 71, S 44, G I 25). Accordingly, motion and rest belong to a package, and

any interpretation ought to account for this.117 Given this feature, henceforth I will reflect

this by modifying the phrase ‘motion and rest’ to ‘motion-and-rest’. Last, we cannot

forget that at the end of the day the immediate infinite mode of extension is still a mode.

That is, however we account for motion-and-rest it must exist in, and be conceived

115 Garrett derives this from a close reading of E1P21p; see Don Garrett, “Spinoza’s Necessitarianism,” in Yovel, God and Nature, 196. Bennett puts it slightly differently saying “they are instantiated everywhere and always”, Bennett, Study, 112. 116 For the one exception to this see ST II.xix: (C 131,S 87, G I 91) where he refers to motion and rest as two modes of extension. However, he qualifies this by saying that “rest is certainly not Nothing”. 117 Garrett notes the same requirement and characterizes it as accounting for motion and rest in such a way that it is a thing “that manifests itself in two different and complementary ways.” Garrett, “Individuation”, 80.

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through, substance as extended. Given these five text-based criteria, let’s turn to an

examination of the most developed account of motion-and-rest in the literature.

Motivations for Garrett’s Account of Motion-and-Rest

In asking the question, ‘To what does ‘motion-and-rest’ refer?’ perhaps the most

obvious response is to take the terms ‘motion’ and ‘rest’ at face value and assume that in

referring to ‘motion-and-rest’ as an immediate infinite mode Spinoza is referring to the

alteration and preservation of spatial relations. Surprisingly, the most developed account

of motion-and-rest, put forth by Don Garrett, does not interpret the infinite mode along

these lines.118 Rather Garrett, following Bennett, argues that there are at least two good

reasons for thinking that whatever Spinoza means by ‘motion-and-rest’ he can’t mean the

alteration and preservation of spatial relations.119 I begin by presenting these reasons. I

then turn to Garrett’s account itself. After having presented this account of motion-and-

rest I argue that despite all its strengths we are justified in looking for an alternative.

The first reason ‘motion-and-rest’ can’t refer to the alteration and preservation of

spatial relations is what I’ll call the ‘Priority of Motion Problem’. In many places

Spinoza appears to use ‘motion’ and ‘rest’ in an ordinary way. For example in book two

of the Ethics Spinoza lays out a rough set of impact rules. The set includes the following:

“when a body in motion strikes against another which is at rest and cannot give way, then

it is reflected, so that it continues to move…” (E2P13a2: C 460, S 253, G II 99). Spinoza

seems to use ‘motion’ to refer to a change in spatial properties, and ‘rest’ to refer to the

preservation of these properties. In these contexts the relata are bodies: “a body which

118 Garrett, “Individuation.” 119 Bennett, Study, 108.

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moves or is at rest must be determined to motion or rest by another body” (E2L3: C 459,

S 252, G II 98). Thus, ‘motion’ and ‘rest’ as ordinarily construed are modes of body.

Thus we can say,

1) Motion and rest are modes of body and so presuppose its existence.

Recall, however, that Spinoza maintains that motion and rest ultimately explain the

variety of bodies and properties found in the world. As we’ve seen, Spinoza writes “Each

and every particular thing that comes to exist becomes such through motion and rest” (ST

Preface: C 95, S 60, G I 52). This approach manifests itself in the Ethics as well. There,

Spinoza claims that bodies are individuated on the basis of differences in motion and rest.

He says that the simplest bodies are “distinguished from one another only by motion and

rest, speed and slowness” (E2P13a2L1: C 460, S 253, G II 99).120 If the simplest bodies

are individuated by motion and rest, then the existence of motion and rest is logically

prior to the existence of bodies. So it is true to say,

2) The existence of bodies presupposes the existence of motion and rest.

Given that the existence of motion can’t both presuppose, and be presupposed by, the

existence of body, we’re left with a problem: motion individuates bodies or motion is a

mode of bodies—Spinoza can’t have it both ways.121 It is this problem that leads both

Bennett and Garrett to claim that Spinoza uses the terms ‘motion’ and ‘rest’ equivocally.

If this is right then we’ve got one set of ordinary senses of the terms ‘motion’ and ‘rest’

that corresponds to the respective alteration and preservation of spatial relations and

120 Cf. E2P13a2* (Spinoza lists two sets of axioms following E2P13. The ‘*’ indicates I am referring to the second axiom 2). See also E2P13L7s. 121 The existence of motion can’t both presuppose, and be presupposed by, the existence of body since if there is only one sense of ‘motion’ and ‘rest’ and this is what Spinoza has in mind in the immediate infinite mode, it would make the immediate infinite mode dependent on bodies, that is finite modes. But this isn’t the case.

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another, more obscure, set that does not. Bennett and Garrett are both inclined to think

that the obscure senses of the terms ‘motion’ and ‘rest’ correspond to the immediate

infinite mode of extension, motion-and-rest. This makes sense: ‘motion’ and ‘rest’ in

their ordinary senses refer to the respective alteration and preservation of the spatial

relations between bodies;122 whereas the immediate infinite mode of extension is

supposed to account for the existence of bodies, and so exists logically prior to them.

Thus whatever Spinoza means when he claims that motion-and-rest is an immediate

infinite mode of extension, he can’t be referring to the alteration and preservation of the

spatial relations among bodies. Thus Bennett and Garrett resolve the Priority of Motion

Problem by claiming that the normal senses of ‘motion’ and ‘rest’ are at work in 1)

whereas the obscure senses of these terms are at work in 2). The problem that remains is

to render more precise the obscure senses of ‘motion’ and ‘rest’ as they are at work in

‘motion-and-rest’. In sum, the Priority of Motion Problem reaffirms that whatever

Spinoza means by ‘motion-and-rest’ it must exist logically prior to the existence of body.

A second, and related, reason for thinking that ‘motion-and-rest’ means

something other than ‘motion’ and ‘rest’ as normally construed I’ll call the ‘Problem of

Diachronic Diversity’. Bennett argues that an interpretation of motion-and-rest according

to which these terms are construed as an alteration/preservation of spatial relations is

inconsistent with the universe being qualitatively diverse over time. Recall that Spinoza

is committed to the claim that all qualitative variety is the result of motion-and-rest.

Bennett writes: 122 As Bennett notes: “he cannot mean by ‘motion’ and ‘rest’ what we mean by them. Only things in space can move….” See Bennett, Study, 106. Likewise Garrett writes “how can motion and rest give rise to the metaphysical distinction of numerically different bodies if motion and rest themselves cannot exist except as characteristics of different bodies?” See Garrett, “Individuation”, 78.

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According to that thesis [that all qualitative variety results from motion and rest as ordinarily understood], the extended world at any instant is homogeneous, and qualitative variety comes in only along the temporal dimension. But that is impossible: if at each instant there is synchronic sameness, then no stringing of instants along a temporal dimension can produce [diachronic] variety.123

I take it that Bennett argues as follows: let’s suppose that Spinoza is right and motion and

rest ultimately account for the qualitative diversity of the extended universe. If so (and

we understand motion and rest as generally construed), then the universe is homogeneous

at an instant, i.e. there is no synchronic diversity. Here is why: for x to be in motion is

for x to have changed spatial relations from t1 to t2. Thus, for x to be in motion requires

an interval of time; so at an instant, we can’t say that there is any motion. But if there is

no motion, then there is no qualitative diversity present at that instance in the universe,

i.e. it is homogeneous. Bennett’s argument continues: if the universe is homogeneous at

an instant, then there can’t be diachronic variety. But since there clearly is diachronic

variety, Bennett concludes that “Spinoza cannot mean by ‘motion’ and ‘rest’ what we

123 Bennett, Study, 108. Three notes: first, ‘diachronic’ in brackets replaces Bennett’s ‘synchronic’. The use of ‘synchronic’ here must be a typographical error. Bennett’s point is that Spinoza isn’t entitled to claim that qualitative variety comes along in the temporal dimension. The conclusion reads “then no stringing of instants along a temporal dimension can produce synchronic variety”, but it is diachronic variety that is at issue. Second, the sentence following this quotation reads: “The most we could get is diachronic variety, with the whole extended universe altering from totally blue to totally green, say, or from warm to cold”. This isn’t right. Given Bennett’s argument, the extended world at any instant has no (what we would call secondary) qualities, since these qualities arise out of variations in motion and rest. Thus the universe could never be totally green or cold at an instant. Third, it is worth noting that Leibniz offers an almost identical criticism of the Cartesian account of motion. In ‘On Nature Itself’ he argues against the “celebrated Sturm” that if Sturm is right, “then at the present moment (and furthermore, at any moment whatsoever) a body A in motion would differ not at all from a resting body B, and the view…would entail that there is no clear criterion in bodies for distinguishing them, since in a plenum, there is no criterion for distinguishing between masses uniform in themselves unless one is provided by motion. From this view it would also follow finally, that absolutely nothing would change in bodies, than that everything would always remain the same. For if no portion of matter whatsoever were to differ from equal and congruent portions of matter…it obviously follows that in the corporeal world there can be no way of distinguishing different momentary states from one another”. This quotation is taken from Philosophical Essays, ed. and trans. by Roger Ariew and Daniel Garber, Indianapolis: Hackett, 1989 (163-164).

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mean by them”.124 In sum, the Problem of Diachronic Diversity gives us another

interpretive criterion that any account of motion-and-rest must meet: whatever ‘motion-

and-rest’ refers to, it must exist synchronically.

Garrett’s Account of Motion-and-rest

With these problems in mind Garrett sets out to reconstruct Spinoza’s account of

the immediate infinite mode of extension. He begins with Spinoza’s presentation and

commentary on Descartes’ Principles inasmuch as this work is “a useful guide to

Spinoza’s own understanding and use of the standard Cartesian terminology from which

his own terminology is often derived”.125 In this work Spinoza follows Descartes by

distinguishing between ‘motion’ understood as the transfer of a part of matter from one

neighborhood to another, and ‘motion’ understood as the force responsible for this

transfer.126 Let’s call motion in the first sense ‘local motion’; and follow both Descartes

and Spinoza by referring to motion in the second sense as ‘quantity of motion’.127 In

each case, a corresponding sense of ‘rest’ is applicable, but for clarity of presentation I

will ignore this for the time being. Garrett’s proposed answer to the question, ‘To what

does ‘motion-and-rest’ refer?’, is that it refers to motion in this second sense: quantity of

motion. Ultimately I think Garrett’s interpretation meets the five interpretive criteria

listed at the beginning of the chapter and is capable of resolving the Priority of Motion

Problem and the Problem of Diachronic Diversity. In what follows I will not discuss how

Garrett’s interpretation meets all five interpretive criteria. Instead I will focus on two

124 Bennett, Study, 108. 125 Garrett, “Individuation”, 79. 126 In fact Descartes uses the term ‘transference’ to draw attention to just this distinction. See Principles II. 25: MM, 51: AT VIIIA, 53-54. 127 That Spinoza followed Descartes in referring to motion in this sense as ‘quantity of motion’ see DPP 2P22p.

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criteria in particular that elucidate the nature of the immediate infinite mode if he’s right.

I then turn to a discussion of how Garrett’s interpretation resolves the two

aforementioned problems.

First, as we’ve seen, according to Spinoza “there is no motion by itself, but only

motion and rest together”. Motion and rest are a package and Garrett argues that his

quantity-of-motion interpretation can account for this fact. He begins by noting that

according to Spinoza (and Descartes), just as there is a quantity of motion, so too there is

a quantity of rest understood as a force of resisting. The quantity of rest varies inversely

to the quantity of motion as does the quantity of motion to the quantity of rest. Garrett

concludes that quantity of motion and quantity of rest are “manifestations of the same

force”.128 Second, whatever motion-and-rest refers to, since it follows from the absolute

nature of the attribute of extension it must be pervasive throughout the attribute. Garrett

claims that his interpretation of motion-and-rest as the quantity of motion explains its

pervasiveness:

…these dual quantities of force need not be distributed to a plurality of individual substances, but rather could be distributed differentially throughout the one extended medium that is Spinoza’s extended substance…at a single time one region of the extended substance might contain greater force as quantity of motion and correspondingly lesser force as quantity of rest than another.129

Apparently, on Garrett’s reconstruction to say that motion-and-rest is a pervasive feature

of extension is to say that every region of extension possesses a particular quantity of

motion (and an inversely proportional quantity of rest).130 All of this gives a better sense

128 Garrett, “Individuation”, 80. 129 Ibid. 130 The faster a body moves the greater its quantity of motion and correspondingly the lesser its quantity of rest. The same goes for slowness: the slower a body moves the greater its quantity of rest and lesser its quantity of motion. This works to a limit. In the case of slowness this limit is rest. At rest a body has no

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of what Garrett means in claiming that the immediate infinite mode of extension is the

quantity of motion: if Garrett is right about Spinoza, then ‘motion-and-rest’ refers to the

property extension has of possessing varying quantities of motion/rest throughout its

infinite expanse.131

How is this interpretation of the infinite mode of extension supposed to meet the

interpretive criteria that fall out of the Priority of Motion Problem and the Problem of

Diachronic Diversity? The Problem of Diachronic Diversity shows that, if Spinoza is to

be consistent, the immediate infinite mode of extension must be the sort of thing that can

account for synchronic diversity in the plenum (and ultimately for diachronic diversity).

Garrett responds that “this differential distribution of the dual manifestations of force

would, or course, introduce synchronic diversity into his one extended substance, for

even at a single time one region of the extended substance might contain greater force as

quantity of motion and correspondingly lesser force as quantity of rest than another”.132 I

think that Garrett is right, but that matters are not quite as simple as he seems to imply.

One might be forgiven for wondering how Garrett’s view can be right given that

according to Spinoza (and Descartes) a body’s (or region’s if Garrett is right) quantity of

motion is equal to the product of its size and speed, and speed is a diachronic property.

How, then, can the quantity of motion synchronically diversify extension? The root of

this objection is that the existence of a quantity of motion requires the existence of speed

quantity of motion; only a quantity of rest. 131 Garrett, in “Individuation” is concerned to account for all Spinoza’s uses of the terms ‘motion’ and ‘rest’. He concludes at the end of the section entitled “Motion and Rest” that “In this way, then, ‘motion and rest’ can refer sometimes to local motion and rest, sometimes to the closely related underlying force(s) of motion and rest that produce local motion and rest, and sometimes—since the former are a function of the latter—to either one indifferently” (82). Garrett is accounting for all the uses of ‘motion’ and ‘rest’; he is not claiming that ‘immediate infinite mode of extension’ is ambiguous. 132 Ibid., 80.

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and so quantity of motion is a property that is only had over time. However, from the

proposition ‘quantity of motion = size x speed’ we can infer nothing about ontological

priority. This equation merely tells us about a relation between three quantities—not

about ontological dependence. Consequently, we cannot infer that the existence of a

quantity of motion requires the existence of speed. In sum, Garrett resolves the Problem

of Diachronic Diversity by claiming that motion-and-rest is distributed differentially, or

“sprinkled”, throughout extension in various quantities so that there is synchronic

diversity (and therefore diachronic diversity).

Explaining how Garrett’s interpretation accommodates the lesson of the Priority

of Motion Problem is a little more complicated. Garrett asks us to consider Spinoza’s

definition of the simplest bodies as those things “distinguished from one another solely

by motion and rest” (E2P13L7s: C 461, S 254, G II 101). Recall that it is this passage

(among others) which suggests that the existence of simple bodies presupposes the

existence of motion. As we’ve seen, this is problematic in light of many other passages

in which Spinoza appears to hold that motion is a property of bodies. If Garrett is right

and by ‘motion-and-rest’ Spinoza means ‘quantity of motion’ we have an apparent

resolution to this problem. According to Garrett’s interpretation, the simplest bodies just

are regions of extension homogeneous with respect to their quantity of motion (and rest).

A simple body is a region of extension x, no subregion of which has a different quantity

of motion/rest from x. This resolves the Priority of Motion Problem because, if Garrett’s

right, Spinoza uses the term ‘motion’ equivocally. Recall that Spinoza is committed to

both 1) and 2):

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1) Motion and rest are modes of body and so presuppose its existence.

2) The existence of bodies presupposes the existence of motion and rest.

The fact that motion presupposes the existence of body does not conflict with the claim

that the simplest bodies presuppose the existence of motion, because in the former case

Spinoza is referring to the quantity of motion whereas in the latter he is referring to local

motion.

Before turning to an evaluation of Garrett’s reconstruction I want to discuss two

consequences of his view. First, Garrett claims that motion-and-rest is pervasive insofar

as different quantities of motion (and rest) are synchronically distributed throughout

extension’s regions. This needs to be a little more precise. On Garrett’s view, simple

bodies are extended; what makes a simple body x, simple, is that x is a body no subregion

of which has a distinct quantity of motion from the whole. Consider a simple 1m3 cubic

body. Let’s represent this body’s quantity of motion as, say, 12 units. Now consider a

1cm3 subregion of this cubic body. Does this part have a quantity of motion? It is

tempting to think that this subregion has a smaller quantity of motion and that by

somehow combining the quantities of all the parts, we get a total quantity of motion of 12

units. However, this is not right. If our 1cm3 had a quantity of motion, then it would

itself be a body and our 1m3 cubic body wouldn’t be simple. Thus, our 1cm3 part does

not have a quantity of motion and what goes for this cubic cm goes for every cubic cm of

our cube. Thus it isn’t the case that every region of extension has a quantity of motion.

Motion-and-rest is not pervasive in the sense that every region of extension has some

quantity of motion or rest; rather, the best Garrett can do is to say that every region of

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extension either has a quantity of motion or is part of a region that has a quantity of

motion.

Second, if Garrett is right, then Spinoza’s account of local motion diverges

significantly from Descartes’. When Spinoza talks about bodies having local motion he

doesn’t mean that extension’s regions are actually moving from one vicinity or

neighborhood into another. Rather he means that these regions are taking on different

quantities of motion. Garrett explains: “the spatiotemporal path of bodies would be a

function of momentary qualitative variety together with the continuous temporal

“passage” of certain aspects of this momentary qualitative variety through contiguous

regions of an extended medium”.133 This goes to show that all Spinoza’s talk about the

motion of bodies is really shorthand for a complicated story about the translation of

various quantities of motion from one region of extension to another according to the

laws of nature.

Evaluating Garrett’s Account

Garrett’s reconstruction of Spinoza’s immediate infinite mode of extension is

impressive, but nevertheless, I am unconvinced that this is Spinoza’s view for two

reasons. First, I find it implausible to think that Spinoza’s account of local motion

diverges so significantly from Descartes’. If Garrett is right, then Spinoza acknowledges

no such thing as local motion in the normal Cartesian sense of the term. In the Principles

Descartes makes the effort of distinguishing between motion “as commonly interpreted”

and motion “properly speaking”.134 It is local motion in this latter sense that corresponds

133 Ibid. 134 See Principles II.24 and 25 respectively.

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to the “truth of the matter” and it is defined as the transference of a part of matter from

one vicinity into another. It is this true and proper sense of ‘local motion’ that lies at the

root of Descartes’ mechanistic account of the world. The problem is that if Garrett is

right, then at bottom this “proper” sense of local motion is absent from Spinoza’s account

of the world. The account of local motion that follows from his interpretation of ‘motion-

and-rest’ as referring to the differential distribution of force (quantity of motion) is

certainly different from Descartes’ proper sense of motion; for according to Garrett’s

Spinoza, the subjects of motion—the parts of matter—never change in their spatial

relations. Rather different quantities of motion float across unmoving regions of

extension merely giving the illusion that there is change among the spatial relations of the

underlying regions. At bottom all there is, is the ordered progression of various

quantities of motion across regions of extension over time. This certainly doesn’t show

that Garrett’s account isn’t Spinoza’s, but if it makes sense to think that Spinoza’s

understanding of the concepts of motion and rest are rooted in his Descartes’ Principles

of Philosophy, and both Garrett and I think it does, then it seems implausible that Spinoza

would hold such a radically different account of local motion without ever directly

indicating as much.135

A second worry with Garrett’s account of the immediate infinite mode of

extension is that it is in conflict with a passage from the Metaphysical Thoughts appended

to Descartes’ Principles of Philosophy. Garrett’s account depends on Spinoza having

distinguished local motion from quantity of motion. It is Spinoza’s having made this

distinction that allows him to account for motion-and-rest in Cartesian terms yet avoid

135 Cf. Huenemann, “Predicative Interpretation”, 57-58.

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the apparent pitfalls of interpreting it as a change in spatial relations. The problem is that

Spinoza seems to deny that quantity of motion and local motion are distinct in this way.

In section 1.6 of the Metaphysical Thoughts Spinoza briefly considers the reasons “why

some have maintained that there is a metaphysical good”. His diagnosis of the problem is

that people tend to falsely think that the distinction between a thing and its striving to

preserve in its own being, is a modal or real distinction, when the two are only rationally

distinct and “are not in any way really distinct”. To illustrate his point he offers the

following argument:

How the thing and the striving it has to persevere in its state are distinguished. To make this clear, let us take an example of a very simple thing. Motion has a force of persevering in its state; this force is really nothing other than the motion itself—that is, the nature of motion is such. For if I say that in this body, A, there is nothing but a certain quantity of motion, it follows clearly from this that, so long as I attend to A, I must always say that it is moving. (MT 1.6: C 314, S 188,G I 248)

Spinoza’s thesis in this passage is that the force a body possesses to persevere in its state

is only rationally distinct from that body’s local motion, since it is in the nature of motion

to persevere. The reason this is relevant to our discussion of the immediate infinite mode

is that Spinoza takes the force a body possesses to persevere in its state to be identical to

its quantity of motion.136 As such, Spinoza is arguing in this passage that quantity of

motion is only rationally distinct from local motion. If quantity of motion and local

motion are only rationally distinct, then Spinoza cannot have held that ‘motion-and-rest’

refers to quantity of motion without simultaneously holding that it refers to local motion.

However, this is exactly what Garrett’s interpretation maintains—for Garrett’s Spinoza,

136 Recall that both Spinoza and Descartes refer to the force a body possesses to persevere in its own state is the body’s quantity of motion. That Spinoza follows Descartes in this regard see DPP 2P22p.

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‘motion-and-rest’ refers to the quantity of motion and not local motion. Recall that it is

precisely this feature of Garrett’s interpretation that resolves the Priority of Motion

Problem: when Spinoza suggests that bodies presuppose the existence of motion he

means ‘quantity of motion’, whereas when he suggests that motion presupposes the

existence of bodies, he means ‘local motion’.137

These two worries open the door to the possibility of a more attractive alternative

interpretation. Such a view would meet all the textual and philosophical criteria Garrett’s

does, in addition to attributing a more Cartesian account of local motion to Spinoza and

resolving the conflict with MT 1.6. In section 2 of this chapter, I aim to develop just such

an account.

Before turning to my own account, however, I want to take a close look at the

Problem of Diachronic Diversity. Contra Bennett and Garrett, I don’t think this is a

problem with which we need to concern ourselves in reconstructing Spinoza’s account of

motion-and-rest. Recall that the Problem of Diachronic Diversity arises out of Descartes’

and Spinoza’s insistence that all qualitative diversity arises out of motion. Given that

there is no motion at an instant, and so no synchronic diversity, there cannot be

diachronic diversity either. This argument is analogous to one of Zeno’s paradoxes—the

so-called paradox of the arrow. Zeno argues against the existence of motion as follows:

137 The inconsistency between Spinoza’s apparent claim that local motion and quantity of motion are only rationally distinct and Garrett’s reading can be illustrated in a second way. On Garrett’s account of motion-and-rest, simple bodies are “those regions of the one extended substance that are, at that time, entirely homogeneous with respect to the distribution of quantity of motion….” Garrett, “Individuation”, 80-81. Let’s name one such simple body ‘A’. Spinoza tells us in the passage above “if I say that in this body A there is nothing else than a certain quantity of motion, from this it clearly follows that, as long as I am attending to the body A, I must always say that the body is moving”. Garrett’s account is committed to the denial of this conditional. If Garrett is right, then A exists at a time with a particular quantity of motion. But if A exists at a time, it can’t be in local motion; local motion occurs only over time. Thus on Garrett’s view it doesn’t follow from A’s having a particular quantity of motion that A is moving.

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consider an arrow in flight; at an instant the arrow is not in motion because motion can

only occur over an interval of time. But if, at an instant, an arrow is not in motion, then

the flying arrow is never in motion. Both the Problem of Diachronic Diversity and

Zeno’s arguments rely on a premise such as: intervals of time are made up of, or

composed by, moments of time. This premise is manifested in the Problem of Diachronic

Diversity in the assumption that there is diachronic diversity only if there is synchronic

diversity.

Despite this premise’s prima facie plausibility, Spinoza, following Aristotle,

denies it; thus Spinoza can disarm the Problem of Diachronic Diversity in the same way

that Aristotle disarms Zeno’s paradox of the arrow. Aristotle explains “Zeno’s reasoning,

however, is fallacious, when he says that…if that which is in locomotion is always in a

now, the flying arrow is therefore motionless. This is false; for time is not composed of

indivisible nows any more than any other magnitude is composed of indivisibles”.138

Spinoza is committed to the same view. In his presentation of Descartes’ Principles,

Spinoza stops to consider at length several paradoxes he attributes to Zeno. In particular

he considers an argument that motion cannot exist, and in his response, parrots Aristotle.

Spinoza claims that one of the two chief problems with the argument is that it

“supposes…that time is composed of moments just as others have conceived that quantity

is composed of indivisible points.”(DPP 2P6s: C 271, S 154, G I 193) Elsewhere

Spinoza reiterates this point saying, “For composing Duration of moments is the same as

composing Number merely by adding Noughts” (Ep. 12: C 204, S 789, G IV 58).139

138 Aristotle, Collected Works, vol. 1, 404 (239b 5-9). 139 Ultimately in DPP 2P6s Spinoza argues that time, as a measure of motion, is continuous. Every interval of time is divisible into smaller intervals ad infinitum: there are no temporal atoms.

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Thus intervals of time aren’t composed by moments and so the fact that there is no

synchronic diversity is irrelevant to whether there is diachronic diversity. The upshot of

this discussion is that the Problem of Diachronic Diversity yields no definitive basis for

preferring any particular interpretation of ‘motion-and-rest’ in Spinoza’s texts. Thus of

the two problems, the Priority of Motion Problem is the only one that pushes us to think

that motion-and-rest as the immediate infinite mode of extension means anything other

than the alteration and preservation of spatial relations.

Section 2: Spinoza’s Account of Motion-and-Rest

So far I’ve shown that we’ve got reasons to doubt that Garrett’s account of the

immediate infinite mode of extension is Spinoza’s. In this section, I develop an alterative

account that not only has all the strengths of Garrett’s account in that it meets the basic

interpretive criteria already laid out and resolves the challenge offered by the Priority of

Motion Problem, but also goes beyond Garrett’s in its consistency with MT 1.6 and its

attribution of a more Cartesian account of local motion to Spinoza. Ultimately, I argue

that ‘motion-and-rest’ should be interpreted at face value: as referring to the alteration

and preservation of spatial relations. However, I claim that the relata are regions of

extension, not bodies. In order to make this case, I’ll begin with an argument found in

the Short Treatise.

Motion and Extension in the Short Treatise

The Short Treatise is one of Spinoza’s early unfinished works (the other being the

Treatise on the Emendation of the Intellect) and in it we find many of the metaphysical,

epistemological and ethical theses that he ultimately presented in the Ethics. Included

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among these theses is one of Spinoza’s most controversial claims: that extension is an

attribute of God. Spinoza was well aware that this claim would be contentious and on at

least two occasions considers objections to this thesis (E1P15s and ST 1.2). As we’ve

seen, in E1P15s Spinoza takes all the arguments against extension being an attribute of

God (or as it was glossed in chapter 2, God’s being a corporeal substance) to reduce to

the claims that all corporeal substances are composite and God isn’t a composite. In the

Ethics Spinoza’s response to his critics is to deny that all corporeal substances are

composite. In the Short Treatise Spinoza argues similarly, albeit using slightly different

terms. He writes: “From all that we have said so far it is clear that we maintain that

extension is an attribute of God. Nevertheless, this does not seem possible at all in a

perfect being. For since extension is divisible, the perfect being would consist of parts”

(ST 1.2: C 70, S 43-44, G I 24). Spinoza’s claim is that God is extended (corporeal) and

that his opponents argue that from God’s extension we can infer God’s divisibility. As

we saw in Chapter 2 Spinoza thinks of the properties of ‘being divisible’ and ‘being

composite’ interchangeably, and so it is clear that Spinoza’s presentation of his

opponents’ argument against God’s corporeality in the Short Treatise mirrors his

presentation of his opponents’ argument in E1P15s.

In his defense of God’s corporeality in the Short Treatise, Spinoza is more

forthcoming about his opponents’ reasons for thinking that God doesn’t have parts (i.e.

that God is non-composite). Perhaps the chief reason for denying that God has parts is

that it is prima facie inconsistent with God’s incorruptibility: to have parts is to be

divisible into them. Given his commitment to God’s extension and incorruptibility,

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Spinoza’s challenge is to show that despite being extended, God isn’t corruptible.140 In

the Ethics Spinoza takes on this challenge by arguing that no corporeal substance is

composite. As we will see, in the Short Treatise Spinoza argues analogously that being

extended doesn’t entail having parts (where by ‘parts’ Spinoza means ‘composite

parts’).141 If God doesn’t have parts, i.e. isn’t a composite, then God isn’t corruptible.

Keeping this in mind, I want to take a close look at an argument which is of

particular interest. In a footnote in the Short Treatise Spinoza stops to consider an

objection to his claim that God is extended, knowing full well that God’s incorruptibility

is at stake. He writes:

…if this [extension] were divided, its nature and being would be destroyed at once, since it consists only in infinite extension, or what is the same, being a whole. But, you will say, is there no part in extension prior to all its modes? None, I reply. But, you say, if there is motion in matter, it must be in a part of matter, not in the whole, since the whole is infinite. For in what direction would it be moved, since there is nothing outside it? Then in a part. I reply: there is no motion by itself, but only motion and rest together; and this is, and must be, in the whole; for there is no part in extension. If you still say that there are parts in extension, then I ask: when you divide the whole extension, can you also, according to the nature of all parts, cut off from the others the part you cut off with your intellect? Assuming that you can, I ask what there is between the part cut off and the rest? You must say: either a vacuum, or another body, or something of extension itself. There is no fourth alternative. Not the first, for there is no vacuum, something positive, but not a body. Not the second, for then there would be modes where there can be none, since extension as extension is without and prior to all modes. The third then. And so there is no part, but only extension as a whole. (ST 1.2: C 71, S 44, G I 25)

140 See E1P19. 141 See E1P15s. As we saw in Chapter 2, it is not that Spinoza denies that God or corporeal substance has parts, it is that he denies that those parts exist independent of corporeal substance. Ultimately Spinoza thinks that denying that corporeal substance has really distinct parts is sufficient for denying that corporeal substance is corruptible. Shortly, we will see that Spinoza does the same thing (in slightly different terms) in the Short Treatise.

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A detailed consideration of this passage yields, I will argue, an account of motion-and-

rest that meets all of the aforementioned criteria.142 Here is the argument Spinoza

envisions against his position, which I will refer to as the ‘Argument from Motion’:

assuming there is motion in matter (extension),

1) Either motion is in a part of matter or in the whole. 2) But, it cannot be in the whole because it is infinite. 3) So motion is in a part.

This argument’s structure is simple enough, but what it means and why anyone would

think it is sound are not. First, it isn’t clear what it is for motion to be in the part or in the

whole. Second, premise 2) is doing the heavy lifting, but it isn’t clear why the fact that

matter is infinite entails that motion can’t be in the whole. We can make sense of this

argument if we consider from whose perspective Spinoza foresees it coming. There are

two reasons to think that Spinoza envisioned this argument coming from a Cartesian

interlocutor. First, Spinoza’s thought developed in a Cartesian environment and so

Spinoza would have been prepared to defend his view from objections coming out of this

perspective. Second, no more than a year or two after having written the Short Treatise

Spinoza offered only a slightly different version of this same argument on Descartes’

behalf in Descartes’ Principles of Philosophy.143

142 Given the second and third sentences of this passage this might seem an odd thesis to maintain. Those sentences tell us that the argument concerns extension prior to all its modes; likewise at the end of the passage Spinoza tells us that “extension as extension is without and prior to all modes”. Consequently, extension’s having motion (“there is motion in matter”) is prior to the existence of modes, and so this passage has nothing to tell us about the immediate infinite mode of extension. But Spinoza doesn’t mean to rule out all modes, only all finite modes. Suppose this is wrong: then Spinoza, in this passage, is committed to the existence of motion prior to the existence of modes. Then what is this motion? It certainly isn’t substance, but if it isn’t a mode, there is nothing left for it to be (recall: everything that is, either is in itself or in something else; that is it is either a mode or substance). As such, by “prior to all modes” he must be referring to all finite modes. 143 In his exposition of Descartes’ Principles Spinoza represents Descartes’ reason for maintaining that God is incorporeal by saying “Body is the immediate subject of local motion. So if God were corporeal, he

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Given that this is right, we can make sense of 1) and 2) by assuming that the

Argument from Motion presupposes Descartes’ definition of motion. As we’ve seen,

Descartes defines motion properly speaking as “the transference of one part of matter or

of one body, from the vicinity of those bodies immediately contiguous to it and

considered as at rest, into the vicinity of [some] others”.144 Motion, on this account, is a

mode of bodies; which is to say, among other things, that it requires a subject.145 Thus, to

say that matter is in motion is to say either that matter, considered as a totality, is in

motion (motion in the whole) or that some part of matter, so-considered, is in motion

(motion in a part). Further we can see why 2) is true; if motion is in the whole, then it

will have changed its position relative to its surroundings. But extension cannot have

changed its position relative to its surroundings because, as infinite, there is nothing

outside or beyond it to constitute its surroundings (“wither shall it be moved, when there

is nothing outside of it”).146 Thus extension as a whole cannot be in motion relative to

anything else. So, motion must be in a part. It is this inference that allows the further

conclusion that extension has parts: if motion is in a part, extension must have parts

logically prior to the existence of motion to serve as the subjects for that motion; and thus

the objector could conclude, extension (and therefore God) is corruptible.

would be divided into parts” (C 260, S 145, G I 176).The date of the Short Treatise’s completion is controversial. However, it seems to have been in 1660 or 1661 with revisions into 1662. Descartes’ Principles of Philosophy was published in 1663 and most likely completed in 1662. See C 46-53, 221-224; S 31-32, 108-109. 144 Principles II.25: MM, 51. Spinoza repeats this definition in DPP 2d8. 145 Principles II.27. 146 Specifically, it is in virtue of the fact that extension has no boundaries can it be said not to have a neighborhood. In DPP Spinoza follows Descartes in arguing “we cannot imagine the boundaries of extension, that is, of matter, without conceiving other spaces immediately following or beyond them, and so on indefinitely” (DPP 2P6p). Cf. E.M. Curley, Behind the Geometrical Method: A Reading of Spinoza’s Ethics [Behind the Geometrical Method], (Princeton: Princeton University Press, 1988), 35-36.

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After having presented this argument against his own position, Spinoza’s

rejoinder is twofold. First he denies the conclusion of the Argument from Motion: it is

not the case that motion is in a part because there are no parts in extension. Second, he

infers from this fact, and contrary to the critic, that motion is in the whole (“it must be, in

the whole; for there is no part in extension”). Responding to the critic’s argument in this

way leaves two tasks. First, Spinoza denies the conclusion of the critic’s argument and

since the argument is valid, Spinoza is committed to denying at least one of the Argument

from Motion’s premises. Thus, Spinoza owes us an explanation of why the critic’s

argument isn’t sound. Second, in his reply Spinoza flatly asserts that extension doesn’t

have parts. This, as Spinoza well knows, is a controversial claim and so he owes us an

argument that this is true. In what follows I examine how Spinoza makes good on these

debts in the passage at hand. As it turns out, we’ll need to understand Spinoza’s

argument that extension doesn’t have parts in order to determine why the critic’s

argument is unsound, and so I will start there.

The Argument that Extension Doesn’t Have Parts

In order to understand Spinoza’s argument we need to be clear about Spinoza’s

aim in offering the argument. Spinoza is arguing that extension does not have parts, but

this seems to be flat out contradictory. Everything that is extended has parts insofar as it

has a top half and a bottom half, for example. Indeed, it was commonly accepted during

the 17th century that to be extended is to have parts. I assume that Spinoza agreed with

the vast majority of his contemporaries in this regard.147 In this sense, then, it is true to

say that according to Spinoza, extension has parts. So what does Spinoza mean in the

147 Cf. Bennett, Study, 83; see also section 4 of chapter 2.

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argument at hand when he concludes that extension doesn’t have parts? Clearly there is

an equivocation here. Let’s call the kind of parts possessed by any extended thing, just in

virtue of its being extended, quantitative parts (q-parts for short). Thus Spinoza doesn’t

mean to deny that extension has q-parts. In order to get some sense of what Spinoza is

getting at, recall that Spinoza’s challenge is to show that God’s being extended doesn’t

entail God’s being corruptible. It is the possession of parts of a kind that entail the

possibility of corruption that Spinoza wants to deny; I will call parts of this kind

corruption parts (c-parts for short). Thus, at the end of the day Spinoza maintains that

God has q-parts while simultaneously offering an argument intended to deny that God

has c-parts. What does it mean to possess parts that entail the possibility of corruption,

that is, what exactly is a c-part? The answer to this question will have to wait until we’ve

looked at the argument itself.

Spinoza’s argument, which I will refer to as ‘Spinoza’s Rejoinder’, begins by

asking us to suppose that the critic is right and that we can “cut off” a part of extension

from the rest. We can represent the line of argument following from this supposition as

follows:

4) If we suppose that extension has c-parts, then it is possible for a part of extension, call it ‘P’, to be cut off or separated from the complement, call it ‘C’.

5) It is not possible for P to be cut off or separated from C. 6) So, it is not the case that extension has c-parts.

The critic is arguing that God can’t be extended because everything extended is

corruptible and God isn’t corruptible. Thus, the critic maintains that the possibility of P’s

being separated from C is sufficient for showing that extension is corruptible. Spinoza

challenges the critic: “I ask what there is between the part cut off and the rest?” There

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are only three possible answers according to Spinoza: i) a vacuum, ii) a body, or iii)

another part of extension (“something of extension itself”). Spinoza, like Descartes,

denies the possibility of a vacuum so i) is out.148 The next two possibilities are

confusing. What is the difference between a body and a part of extension? Descartes, for

example, takes them to be identical.149 Spinoza takes the difference between the two to

be that the parts of extension are somehow ontologically prior to bodies. Here is why:

Spinoza rejects the possibility of a body separating P from C saying “Not the second, for

then there would be modes where there can be none, since extension as extension is

without and prior to all modes”. Bodies, for Spinoza, are modes of extension, and given

that the argument is taking place at the level of “extension prior to all its modes”, we

cannot claim that a body separates the parts of extension. In contrast, Spinoza happily

agrees that it must be another part of extension that separates P and C. Thus, the parts of

extension exist in the right logical space to separate P and C and as such must be

ontologically prior to the existence of bodies. What are the parts of extension and what

are bodies? An answer to the latter question will have to wait, but as for the former it

seems clear that Spinoza is referring to a finite sub-region of extension, or what I’ve

called a q-part; after all extension itself is infinitely extended and as such it follows that

there are finite parts or regions of this infinite expanse.

Returning to Spinoza’s Rejoinder, Spinoza accepts that P and C are separated by

“something of extension itself” and at this point Spinoza takes the reductio to be

complete, concluding “And so there is no part, but only extension as a whole”. This is

148 See Ep.13 and E1P15s. 149 For example, Descartes says “When we speak of a body in general, we mean a determinate part of matter, a part of the quantity of which the universe is composed.” CSM III, 243: AT IV, 166.

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very revealing. Spinoza holds that if the only thing that can separate two parts of

extension is itself another part of extension, then extension is not corruptible. In other

words, Spinoza maintains that extension is corruptible only if it is possible for

extension’s parts to be separated by something that isn’t itself one of extension’s parts.

From this account of corruption it follows that a c-part of extension would be a part that

can exist without contact with any other bodies. Since it isn’t possible for something

other than extension itself to separate or stand between the parts of extension, extension

doesn’t have c-parts.150

What’s Wrong with the Critic’s Argument?

Recall the critic’s Argument from Motion: assuming that extension has motion,

then 1) either it is in the whole or in a part, but 2) it isn’t in the whole since the whole is

infinite, and so 3) extension has motion in a part. Spinoza rejects this argument on the

grounds that extension doesn’t have parts, and having looked at the argument we know

that he means to deny that extension has c-parts. Spinoza concludes on this basis that

motion “is, and must be, in the whole”. So the critic’s argument is valid, but unsound.

Which of the critic’s premises are false? Spinoza implicitly accepts the premise that

motion is either in the part or in the whole insofar as he concludes from the fact that

150 All of this allows us to make sense of Spinoza’s introduction to the argument. Spinoza sets up the reductio saying “If you still say that there are parts in extension, then I ask: when you divide the whole extension, can you also, according to the nature of all parts, cut off from the others the part you cut off with your intellect?” Spinoza seems to think that the chief reason to hold that extension has parts is that we can “cut off” part of extension with our intellect. Indeed, this is exactly what Spinoza’s Cartesian interlocutor would maintain. According to Descartes, we can be certain of corporeal substance that “each part of it {which can be} delimited by our mind is really distinct from the other parts of the same substance” because we can clearly and distinctly understand one part without the others (Principles I.60: MM, 27). Descartes’ reasoning here is that the parts of corporeal substance are really distinct given that i) everything we clearly and distinctly conceive is true and ii) we clearly and distinctly conceive that the parts of corporeal substance are really distinct. Ultimately this is relevant because a really distinct part is one that exists independently of all other parts. Thus, it is a c-part.

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motion isn’t in the part that it is in the whole. This leaves only 2): motion is not in the

whole since the whole is infinite. Why does Spinoza think this premise is false? More

importantly how does Spinoza maintain that motion is in the whole without

simultaneously committing himself to the view that extension as a whole moves relative

to its surroundings (and concomitantly that extension is finite)? The only clue we’re

given is the following clarification: “I reply: there is no motion by itself, but only motion

and rest together”. We can explain how this clarification shows 2) to be false if we

attribute something like Descartes’ account of motion to Spinoza.

This assumption warrants some comment. While what there is of Spinoza’s

physics differs in some respects from Descartes’, all of it takes place within the Cartesian

tradition. The differences that can be discerned between Descartes’ and Spinoza’s

physics are not programmatic: Spinoza’s account differs in the details; for example he

disagrees with the sixth rule of motion as formulated by Descartes and further presents an

alternative proof that all motion is rectilinear. 151 Certainly these are significant

differences, but they suggest that Spinoza accepted the general Cartesian program, and

central to this program is Descartes’ definition of motion. This suggests that it is likely

that if Spinoza’s account of motion is not identical to Descartes’, it is probably very

similar.

Premise 2) of the Argument from Motion maintains that motion can’t be in the

whole since it is infinite. Motion can’t be in the whole because this requires motion

relative to its surroundings. Given the supposition that Spinoza’s account of motion is

151 See Alan Gabbey, “Spinoza’s Natural Science and Methodology” in The Cambridge Companion to Spinoza, Don Garrett, ed., (Cambridge: Cambridge University Press, 1996), 155-170.

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similar to Descartes’, it is impossible for anything to be in motion and rest at the same

time. A part of matter is only in motion relative to another part of matter simultaneously

regarded as at rest. Given the infinity of extension, extension and its surroundings cannot

constitute these two subjects: all we have to constitute that which is in motion and that

which is at rest is extension itself. Thus we are faced with the following problem: the

existence of motion and rest requires two subjects of motion, but it looks like all we’ve

got is one—extension. However, as we’ve seen, extension has parts, q-parts. We can

resolve the problem by attributing motion and rest to different q-parts of extension, that

is, to different sub-volumes or regions of extension. As such, Spinoza’s clarification is

intended to show that there is at least one other sense in which motion (and rest) can be in

the whole; in the sense of internal motion. For example, as I sit still (am at rest relative to

my vicinity) my digestive, respiratory, and circulatory systems (amongst others) are in

motion throughout my body. Likewise in the case of extension: while extension cannot

be said to be in motion relative to its vicinity, its regions or q-parts are in motion relative

to one another.152

The Immediate Infinite Mode of Extension: Motion-and-rest

In this passage, then, Spinoza argues that in spite of the fact that matter has

motion, it cannot have parts. Matter has motion in the whole, not in the sense that its

152 In the original argument the critic moved from the fact that extension has motion in the part, to the conclusion that extension has parts to serve as the subjects for that motion. Why doesn’t the same reasoning follow here? If I am right, then Spinoza thinks that extension’s q-parts are the subjects of motion in that they move. Why can’t the critic jump in and claim that extension has parts after all? One response is to agree to with the critic. The whole point of the critic’s argument was to show that extension is corruptible and insofar as Spinoza has shown that extension doesn’t have c-parts, it is no longer all that relevant whether extension’s parts move or not. But this is not how Spinoza responds. Rather he affirms that despite the fact that extension’s parts move, they are not the subjects of motion. Spinoza’s point, I take it, is that the q-parts of extension are not themselves ultimate subjects. They are dependent for their existence on the whole of extension and as such it is the whole of extension that ultimately is the subject of motion or rest.

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surroundings change, but rather in the sense that its regions or q-parts are in motion

relative to one another.153 It is this sense of motion in the whole which I take to

correspond to the immediate infinite mode of extension. Thus, according to my

interpretation Spinoza’s term ‘motion-and-rest’ refers to the relative motion of

extension’s regions (or q-parts). But this is only a very general answer to the question “to

what does motion-and-rest refer”. A full answer to this question requires explaining how

my interpretation of motion-and-rest meets the aforementioned interpretive criteria,

including how it resolves the Priority of Motion Problem. Thus, in what follows I will

show how we can account for each of the interpretive criteria given this conception of

motion-and-rest.

I argued that there are reasons to doubt that Garrett’s interpretation is Spinoza’s.

First, it seems to me implausible to think that Descartes’ sense of local motion is

completely absent in Spinoza. My interpretation accommodates this desideratum in that

the regions of extension genuinely change their spatial relations relative to one another.

Second, I showed that Garrett’s reading is inconsistent with a passage from the

Metaphysical Thoughts where Spinoza argues that quantity of motion is only rationally

distinct from local motion. My interpretation is consistent with this passage in that it

requires nothing beyond a rational distinction between these two senses of motion. Thus,

insofar as my reading meets these desiderata and Garrett’s doesn’t, my reading is to be

preferred. However, at this point I need to make good on my claim that my interpretation

can do everything that Garrett’s can. I turn now to these criteria.

153 For ease of expression and since I do not need to distinguish different sense of part in this context, I will drop ‘q-part’ in favor of ‘region’.

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As we’ve seen, the immediate infinite modes follow from the absolute nature of

extension, where this means that the immediate infinite modes are both permanent and

pervasive. If I am right that motion in the whole corresponds to motion-and-rest, what

does it mean to say that motion in the whole is permanent and pervasive? To say that

motion in the whole is a permanent feature of extension is to say that over every interval

of time there is at least one region in motion relative to another simultaneously

considered at rest. Accounting for motion-and-rest’s pervasiveness is slightly more

complicated: while it might seem to commit Spinoza to saying that that for every region

x, x can be regarded as in motion relative to its immediately contiguous regions, I think it

need not. Such a view would entail that no region is without internal motion; that is,

every region of extension is such that all its sub-regions are in motion relative to their

individually contiguous sub-regions. While we might account for motion-and-rest’s

pervasiveness in this fashion, it seems sufficient to attribute a much more limited account

of motion-and-rest’s pervasiveness to Spinoza: for every region x, there is at least one

contiguous or non-contiguous region y, such that x can be regarded as in motion relative

to y. In other words, there is no region of extension that can’t be considered as in motion

relative to at least one other region, be that region contiguous or non-contiguous.154 This

allows Spinoza to account for the motion of a sub-region that is not in motion relative to

its immediate surroundings, but is in motion nevertheless as a part of, or sub-region of, a

greater region of extension that is moving relative to its contiguous surroundings. In

154 Note that given the Cartesian definition of motion, no region of extension can simultaneously be regarded as in motion relative to, and as at rest relative to, the same region. But a region can simultaneously be regarded as in motion relative to some region, and also at rest relative to some other region or regions. As an example of this consider the following three bodies: the sun, the earth, and the moon. The moon is in motion relative to both the earth and the sun, the sun is at rest relative to both the earth and the moon, but the earth is in motion relative to the sun and at rest relative to the moon.

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short, accounting for pervasiveness in this way allows for the existence of regions of

extension, no sub-region of which is in motion, a point that will become important

shortly.

Interpreting ‘motion-and-rest’ as referring to the relative motions of extension’s

regions explains both why Spinoza refers to the infinite mode in the singular and why

motion doesn’t exist without rest. Since an object is in motion only relative to something

else simultaneously regarded as at rest, there is no motion without rest and so, to refer to

one is to indirectly refer to the other. Further we can account for motion-and-rest’s status

as a mode. A mode exists in and is conceived through something else: in this case the

motion of extension’s regions exists in extension and is further conceived through

extension, i.e. one cannot conceive of motion without conceiving of extension, according

to Spinoza (DPP 2a6: C 265, S149, G I 184). As a consequence, we can account for

motion-and-rest’s permanence, pervasiveness, singularity in Spinoza’s language, and its

status as a mode. This leaves only two more interpretive criteria for which to account. I

am left the task of explaining how motion-and-rest so conceived accounts for the

existence of bodies, and the closely related task of deducing the mediate infinite mode

from motion-and-rest.

As we’ve seen, motion-and-rest immediately follows from extension and it is in

virtue of this that Spinoza accounts for all the variations in matter. According to Spinoza

there are two kinds of body for which motion accounts: simple and complex. As we saw

in section 1, simple bodies “are distinguished from one another only by motion and rest,

speed and slowness” (E2P13a2*: C 460, S 253, G II 99); whereas complex bodies are

ultimately composed of simple bodies and are distinguished from one another according

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to the preservation of a “proportion of motion and rest” which obtains among the body’s

constituent parts (ST 1.2: C 95, S 60, G I 52).155 I follow Garrett in holding that these

conditions for distinguishing bodies are criteria of metaphysical individuation. 156 A

simple body, then, is distinguished from other simple bodies by its degree of motion or

rest; whereas complex bodies are distinguished from other complex bodies by a particular

relation amongst their parts. Complex bodies are ultimately reducible to the motion of

their simplest constituents. But these simple bodies are what they are only in virtue of

possessing a particular degree of motion and rest. I’ve argued that Spinoza denies the

Argument from Motion by affirming that regions of extension, not bodies, are the

subjects of motion. This suggests that in some sense, a body for Spinoza just is a region

of extension in motion. But what makes it simple? Complex bodies have other bodies as

parts, simple bodies do not. Since bodies are individuated by motion, if a body (x) were

to have internal motion, that internal motion would itself constitute a further body (y) and

so render x complex. Thus a simple body is a region of extension of which no sub-region

is in motion relative to any other of its sub-regions. Given all of this, I offer the following

definitions of both simple and complex bodies on Spinoza’s behalf:

x is a simple body iff i) x is a region of extension, ii) x’s immediately contiguous environment is changing, and iii) there are no sub-regions of x in motion relative to one another. x is a complex body iff i) x is a region of extension and ii) every sub-region of x is in motion relative to at least one other contiguous or non-contiguous sub-region of x. A simple body consists in a region of extension in motion relative to its vicinity but

without internal motion. Simple bodies according to this definition are not indivisible:

155 See also E2P13d: C 460, S 253, G II 100. 156 Garrett, “Individuation”, 74-78.

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any simple body may be divided if one of its sub-regions is put into motion relative to its

immediately contiguous environment. A complex body, on the other hand, consists in the

persistence of a pattern or system of motions among various regions of extension.

Interestingly, simple and complex bodies are different in the following respect: complex

bodies can endure even when they are not in motion relative to their immediately

contiguous environment, whereas simple bodies cannot. A complex body is defined by

the maintenance of the motions of its parts whereas simple bodies are defined solely by

changes in their contiguous environment. As such, for a simple body to come to rest with

respect to its immediately contiguous environment is for a simple body to go out of

existence.157

With this analysis of simple and complex bodies under our belt, we are in a

position to explain what Spinoza means when he offers as an example of a mediate

infinite mode of extension, the “face of the whole universe”, and to show how this

follows from the immediate infinite mode of extension. Spinoza points to the scholium

of Lemma 7 of book 2 of the Ethics for a clarification of what he means by ‘the face of

the whole universe’ (Ep. 64). In this scholium Spinoza outlines a hierarchy of bodies.

He notes that simple bodies compose (what we might call) first-order composite bodies.

These first-order composite bodies compose more complicated composite bodies:

second-order bodies. The discussion ends with Spinoza asserting “If we thus continue to

infinity, we shall readily conceive the whole of Nature as one individual whose parts—

that is, all the constituent bodies—vary in infinite ways without any change in the whole” 157 To say that a simple body is at rest with respect to its immediate surroundings is different from saying that it is regarded as at rest with respect to its immediate surroundings. A simple body exists in the latter case whereas it doesn’t in the former. With regard to the difference between simple and complex bodies Cf. Schmaltz, “Spinoza’s Mediate Infinite Mode”, 208.

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(E2P13L7s). This suggests that by ‘the face of the whole universe’ Spinoza is referring

to all the bodies that exist, that is, the universe of bodies.158 The face of the whole

universe is mediate because it only indirectly follows from the absolute nature of

extension, through the immediate infinite mode. As we’ve seen the existence of bodies is

a function of the relative motions of extension’s regions. Thus, from the fact that

extension’s regions are in motion relative to one another, it automatically follows that

there is a universe of bodies. Why? If there is only one region of extension in motion

relative to the rest, then two (and only two) simple bodies exist. Suppose extension is

such that exactly one region is in motion relative to all others. Call this region ‘R’ and

the complement ‘C’. Given the definition of a simple body as a region of extension, no

sub-region of which is in motion relative to any other, and whose immediately contiguous

environment is changing, it follows that R is a body. But it also follows that C is a body

since C’s immediately contiguous environment (which is wholly constituted by R) is

changing. In this case, the relative motion of one region divides extension into two

bodies. Thus, extension exists prior to the universe of bodies and it is the motion of

extension’s regions that bring the universe into existence. It follows from the

permanence of motion-and-rest that there has been and always will be, a universe of

bodies. Thus we can see how the face of the whole universe follows from motion-and-

rest.

158 Cf. Ibid., 209 and Charlie Huenemann, “Spinoza and Prime Matter” Journal of the History of Philosophy 42 vol. 1, (2004), 31. It is unclear whether Spinoza thought of the material universe itself as a body. In the passage cited above he calls it an individual and makes clear earlier (see Lemma 4) that he takes the term ‘individual’ to be co-extensive with ‘complex body’ (he writes “corporis, sive, individui…”). I will argue later that there are systematic reasons for thinking that the mediate infinite mode is not a body. See Garrett, “Individuation”, 88-89.

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Given that all of the basic textual criteria have been accounted for, there are five

issues still dangling. First, I’ve argued that for Spinoza, the proper objects of motion are

regions of extension. What then of the motions of bodies; i.e. if regions of extension are

the subjects of motion what does Spinoza mean when he says something like “a body

which moves or is at rest must be determined to motion or rest by another body…”

(E2P13L3: C 459, S 252, G II 98)? There are two different answers to this question

corresponding to the two kinds of body. To say that a simple body is in motion is to say

that a region of extension, no subregion of which is in motion relative to any other, is

changing in its immediately contiguous environment. Whereas to say that a complex

body is in motion is to say that a region of extension, every sub-region of which is in

motion relative to at least one other sub-region, is changing in its immediately contiguous

environment.

With this clarification in mind we can turn to the second issue that’s been left

dangling: how does my account resolve the PMP? Recall that this is one of the problems

that led Bennett and Garrett to think that whatever Spinoza means by ‘motion-and-rest’

he can’t have understood this to refer to the alteration/preservation of spatial relations.

The problem comes down to an apparent inconsistency between two claims to which

Spinoza seems committed: 1) motion and rest are modes of body and so presuppose its

existence, and 2) the existence of bodies presupposes the existence of motion and rest.

I’ve argued that regions, not bodies, are the subjects of motion. Thus, I deny 1): motion

and rest are not modes of bodies and as such do not presuppose their existence.

Third, claiming that corporeal substance’s regions or q-parts are the subjects of

motion makes sense of Spinoza’s rejection of the critic’s Argument from Motion and

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resolves the Priority of Motion Problem by denying that motion and rest presuppose the

existence of body. However, there is a sense according to which this answer merely

pushes the question back a level. While motion-and-rest does not presuppose the

existence of bodies, it does presuppose the existence of distinct regions. How do we

account for the plurality of regions? I take the answer to be that extension’s regions are

necessarily distinct. Extension exists necessarily and insofar as motion-and-rest is the

immediate infinite mode of extension, its existence is necessary as well. If I am right and

motion-and-rest presupposes the existence of distinct regions, then it automatically

follows that the regions of extension are necessarily distinct. Thus, it is part of the nature

of extension or corporeal substance to have a plurality of regions. What accounts for the

plurality is the nature of extension itself.

Fourth, my account of ‘motion-and-rest’ entails that extension’s regions move.

But by ‘extension’ Spinoza meant nothing more than we would mean by ‘space’ and we

certainly don’t think of space as having regions that move. Space (extension) is the

backdrop for the motion of bodies and is that which allows us to say where any particular

thing is. While such an objection is intuitive, it presupposes the truth of a Newtonian

account of motion and space. Spinoza had no such absolutist presuppositions; rather it is

likely that his presuppositions about space and motion were rooted in Descartes’

Principles. There Descartes maintains that space is nothing over and above body: “the

extension in length, breadth, and depth which constitutes the space occupied by a body, is

exactly the same as that which constitutes the body”.159 Space is nothing in addition to

bodies and as such it is not the stage on which bodies move. If space “does not in fact

159 Principles II.10: MM, 43: AT VIIIA, 45.

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differ from material substance”160, that is body, and bodies move, then on Descartes’

account, space itself moves. But if space is movable, then it cannot give us the absolute

location of any particular body. Descartes explains “if we think that no truly motionless

points of this kind are found in the universe… then, from that we shall conclude that

nothing has an enduring [fixed and determinate] place…”.161 Thus space for Descartes is

neither the backdrop of motion nor the means by which we determine an object’s

absolute location.162 Thus, while the objection at hand is intuitive we need to keep in

mind that a) it is not as if there aren’t alternative ways of thinking about space and

motion and b) this interpretation of Spinoza seems to make sense given Spinoza’s

context.

Nevertheless, Spinoza’s account is not identical to Descartes’ and this merits

some comment. I have argued that for Spinoza the subjects of motion are the regions of

extension, not bodies. This allows us to characterize perhaps the most significant

difference between Descartes’ metaphysics of body and Spinoza’s: for Descartes

extension is nothing different from body. Spinoza, on the other hand maintains that the

existence of body presupposes the existence of extension (and motion). One way to

illustrate this difference is to consider the following thought experiment. Suppose (per

160 Principles II.11: MM, 44: AT VIIIA, 46. 161 Principles II.13: MM, 45: AT VIIIA, 47. 162 It is on exactly these grounds that Newton criticizes Descartes. In De Gravitatione he writes “the parts of space are motionless. If they moved, it would have to be said either that the motion of each part is a translation from the vicinity of other contiguous parts, as Descartes defined the motion of bodies, and it has been sufficiently demonstrated that this is absurd…the parts of space are individuated by their positions, so that if any two could change there positions, they would change their individuality at the same time and each would be converted numerically into the other” Issac Newton, Philosophical Writings ed. Andrew Janiak, (Cambridge: Cambridge University Press, 2004), 25. On the immovability of space see also John Locke, An Essay Concerning Human Understanding, ed. Peter H. Nidditch, (Oxford: Oxford University Press, 1979), 173 (2.13.14).

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impossible) that all motion in the universe ceases: in each case what remains? In The

World Descartes considers an analogous occasion; he writes

…let us rather conceive it [matter] as a real, perfectly solid body which uniformly fills the entire length, breadth and depth of this huge space in the midst of which we have brought our mind to rest…Let us suppose, moreover, that God really divides it into many such parts…let us regard the differences he creates within this matter as consisting wholly in the diversity of the motions he gives to its parts.163

For Descartes all diversity is to be accounted for in terms of motion and so what remains

in the absence of motion is one undifferentiated body; a static plenum. As we’ve seen,

for Spinoza the existence of body presupposes the existence of both extension and

motion-and-rest. As such, what remains in the absence of motion (and rest) is pure

extension: space.

Fifth, and last, I have argued that a body is a region (or group of regions) in

motion relative to its immediately contiguous environment. What, then, is the relation

between bodies and regions? Suppose, though impossible, that there was a time, call it t1

at which the immediate infinite mode of extension did not manifest. Thus at t1 all we

have is corporeal substance and its regions. Suppose at t2 the immediate infinite mode

begins manifesting and so all of a sudden many of corporeal substance’s regions are in

relative motion. Thus bodies have come to be. What has happened to corporeal

substance’s regions? I think the answer has to be that corporeal substance’s regions are

co-located with bodies. It doesn’t seem that we can claim that corporeal substance’s

regions go out of existence upon the introduction of motion since motion presupposes the

163 CSM I, 91; AT XI, 33-34. (My italics).

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existence of regions.164 Nor can we deny that bodies exist; after all they are finite modes

of extension and as such are explicitly given ontological status according to Spinoza.

Thus at t2 I take it that corporeal substance’s regions are co-located with bodies

Conclusion

I have argued that Spinoza’s ‘immediate infinite mode of extension’ refers to the

relative motion of extension’s regions, and that the universe of bodies arises out of these

relative motions. In the first part of this chapter I laid out the basic interpretive criteria

any interpretation of the immediate infinite mode of extension must meet. I then argued

that we’ve got good reasons for thinking that Don Garrett’s account of this mode is not

Spinoza’s and in so doing justified the search for an alterative. In the second part I

developed just such an account. I showed how my conception of motion-and-rest falls out

of the proper analysis of Spinoza’s discussion of motion in the whole in the Short

Treatise. I then turned to the interpretive criteria specified in Part 1, arguing that my

account fulfills each criteria, including resolving the PMP. Although the interpretation I

attribute to Spinoza has the counter-intuitive consequence that that the regions of

extension, or space, move relative to one another, I’ve suggested that this is no obstacle

to attributing this view to Spinoza, and in fact is just what we’d expect given Spinoza’s

Cartesian roots. My interpretation of Spinoza’s immediate infinite mode of extension

yields an account of bodies according to which a body, for Spinoza, is a region (or

regions) of extension in motion relative to its immediately contiguous environment. Thus

164 In addition, given my account of the pervasiveness of motion-and-rest, I am committed to the continued existence of corporeal substance’s regions.

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I have shown how Spinoza reduces body to the twin mechanist principles of matter and

motion.

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CHAPTER 4: THE MODE-SUBSTANCE RELATION

Introduction

I argued in chapter 2 that Spinoza took Descartes’ account of matter to be deeply

problematic. As we saw, Spinoza replaces Descartes’ account of matter with a

philosophically adequate account, one consequence of which is that bodies are not

corporeal substances. In the last chapter we saw how Spinoza uses the twin mechanist

principles to account for body. There I argued that a body, for Spinoza, is a region of

corporeal substance in motion relative to its immediately contiguous environment. With

an account of bodies under our belt, I turn in this chapter to determining the precise

relation between bodies and corporeal substance.

The traditional approach to determining Spinoza’s views about the relation

between bodies and corporeal substance is to begin with his claim in E2d1 that “by a

‘body’ I understand a mode that in a certain and determinate way expresses God’s

essence insofar as he is considered as an extended thing” (C 447, S 244, G II 84). If

bodies are modes of substance, and Spinoza understood ‘mode’ in the conventional

philosophical sense of his day, then bodies are what we might think of as properties of

corporeal substance. The task, given this approach to the question is to explain how it is

a body can be something like a property. However, there is another way to approach this

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question. There are a number of occasions in which Spinoza refers to bodies as the parts

of corporeal substance. For example consider the following passages:

…we depend on what is most perfect in such a way that we are a part of the whole, i.e. of him, and so to speak contribute our share to the accomplishment of as many well-ordered and perfect works as are dependent on him. (ST II. xviii: C128, S 85, G I 87) However, I conceive that in respect to substance each individual part has a more intimate union with its whole…since it is of the nature of substance to be infinite, it follows that each part pertains to the nature of corporeal substance, and can neither be nor be conceived without it. So you see in what way and why I hold that the human body is part of Nature. (Ep. 32: S 849, G IV 173)

In both of these passages, Spinoza refers to human beings (human bodies in the second)

as parts of God or corporeal substance. Another example comes out of the Ethics. In

E1P15s Spinoza explains that

…matter is everywhere the same, and that parts (partes) are distinguished in it only insofar as we conceive matter to be affected in different ways, so that its parts are distinguished only modally, but not really. For example, we conceive that water is divided and its parts separate from one another—insofar as it is water, but not insofar as it is corporeal substance. (C 424, S 226-227, G II 59-60)

In this passage Spinoza is explaining what a true conception of matter, or corporeal

substance, looks like. If we come to understand matter using our intellect instead of our

imagination, it will become clear to us that matter has parts only modally. As an example

of such a part, he refers us to water. Thus, water is a part, albeit a modally distinct part

(whatever that is), of corporeal substance. A similar point comes out of the Short

Treatise.

Furthermore, concerning the parts in Nature, we say (as we said before) that division never occurs in the substance, but always and only in the modes of the substance. So if I want to divide water, I divide only the mode of the substance, not the substance itself; the substance is always the same, [though] now [it is the substance] of water, now [the substance] of something else. (C 72, S 45, G I 26)

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In a footnote immediately prior to this passage Spinoza clarifies that by ‘Nature’ he

means ‘substantial extension’.165 Thus his statement concerns the parts of substantial

extension (corporeal substance), and again as an example of such a part he refers to a

body, specifically water. Thus, a number of texts from throughout Spinoza’s corpus

claim that bodies are, in some sense, parts of corporeal substance.166

However, even putting aside these texts, there is good reason to think that bodies

are parts of corporeal substance. If a body is anything, it is something with a finite

length, breadth, and depth. Corporeal substance is the entirety of extension: it is the

unlimited expanse of length, breadth, and depth.167 Given this, how could a body not be

at least a spatial part of corporeal substance? On its face, it seems that the only way to

deny that a particular body is a spatial part of corporeal substance is to claim that it is

somehow separated from corporeal substance so that it isn’t encompassed within it.

However, this is impossible since the only way a body could fail to be encompassed

within corporeal substance is for corporeal substance to be limited. But this is false by

definition (E1P8). In other words, there is nowhere a body could be, that isn’t

encompassed by corporeal substance. So at least in some minimal sense, every body is a

part of corporeal substance.

In this chapter I argue that these prima facie reasons are right, and that bodies are

parts of corporeal substance. I argue that the relation between bodies and corporeal

substance is a kind of part-to-whole relation. In section 1, I locate and introduce this

165 Spinoza writes in the footnote: “In Nature, i.e. in substantial extension” (C 71 footnote g, S 44 footnote 12, G I 25) 166 In addition to the texts I discuss, other good examples include Ep.4 (C 172, S 767,G IV 14) and ST II. XX (C 136 footnote c2, S 91 footnote 21, G I 97 lines 29-31) 167 Cover, “Spinoza’s Extended Substance”, 108.

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species of the part-to-whole relation and show that it was a commonplace in scholastic-

Aristotelian metaphysics. In section 2, I argue that this species of the part-to-whole

relation obtains between bodies and corporeal substance for Spinoza. In section 3 I turn

to perhaps the most potent challenge to my interpretation. If Spinoza holds that bodies

are parts of corporeal substance, why does he routinely refer to them as ‘modes’?

Ultimately, I argue that i) Spinoza’s use of the term ‘mode’ diverges from Descartes’ use,

ii) Spinoza reserved the term ‘part’ to refer to a part-to-whole relation inconsistent with

the relation between bodies and corporeal substance, and iii) that Spinoza’s account of

bodies and their dependence and inseparability from substance render them similar to the

traditional account of the mode/substance relation.

Section 1: The Relation of p-part to Whole and the Potential Parts Doctrine

I think that the relation between bodies and corporeal substance for Spinoza is a

species of the part-to-whole relation. The species of the part-to-whole relation I attribute

to Spinoza was commonly accepted among the scholastics, and like many scholastic

views, is ultimately rooted in Aristotle. Thus, as an introduction to this relation a fine

place to start is with Aquinas’ Commentary on the Metaphysics of Aristotle. Consider the

following passage:

He [Aristotle] says that a thing is actual when it exists but not in the way in which it exists when it is potential. For we say that the image of Mercury is in the wood potentially and not actually before the wood is carved; but once it has been carved the image of Mercury is then said to be in the wood actually. And in the same way we say that any part of a continuous whole is in that whole, because any part (for example, the middle one) is present potentially inasmuch as it is possible for it to

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be separated from the whole by dividing the whole; but after the whole has been divided, that part will now be present actually.168

Consider the relation between a figure of Mercury and the block of wood from which it

was carved. In carving the wood, does the sculptor release the figure as Michelangelo

thought? Not according to Aristotle. In order for the sculptor to release or expose the

figure, it must already be actually present in the block, but it is not. Prior to the division

of the wood, the figure is only potentially present in the block. Thus the sculptor creates,

as opposed to reveals, the figure. It is the relation between the block of wood and the

completed sculpture in which I am primarily interested. In more abstract terms this is the

relation between a whole whose parts are present only potentially and those parts after

they have come to be. I want to make explicit several features of this relation, which for

reasons that will become clear, I will refer to as the ‘p-part to whole’ relation.

First, according to Aquinas and Aristotle, wholes that have their parts potentially

are non-composite. In order to see why, consider a continuous solid body. This body is

extended in three dimensions, but it does not have actually existing parts. How can this

be given that the body is extended? The body obviously has parts since it has a top half

and a bottom half. Parts in this sense are what I called in chapter 3, quantitative parts or

q-parts for short. However, according to Aquinas and Aristotle in wholes of this kind, q-

parts do not have any ontological status. That is, the top half and the bottom half are not

themselves independent beings. If they were actual independent beings, then the whole

wouldn’t have its parts potentially, but actually. Thus, there is only one single

continuous body. The two halves come to be as independent beings only upon division

168 St. Thomas Aquinas, Commentary on the Metaphysics of Aristotle. 2 volumes, trans. John P. Rowan (Chicago: Henry Regnery Company, 1961), vol. 2, section 1825, pg 675.

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of the body. Thus Aquinas summarizes, “one half of the cube, which is another figure, is

not present actually; but it becomes actual in this way when a cube has already been

divided into two halves.”169 Prior to the division of a continuous body, there is exactly

one entity or being; after the division, there are either two or three (two if the single

continuous body’s persistence conditions are inconsistent with its being split into a top

half and bottom half, three otherwise). The second feature I want to make explicit is that

in wholes of this kind, division is generative. The division of a simple whole creates new

beings. In the case just discussed, where there was previously only one being, after

division there are two (or three). Third, wholes of this kind are ontologically prior to the

parts into which they are divisible. The parts of such wholes only come to be through the

division of the already existing whole, that is, they are posterior to the whole. It is for

this reason I refer to the relation in question as ‘posterior part to whole’ or ‘p-part to

whole’ for short.170 In contrast with continuous wholes, Aquinas notes that parts are

“actually present in a whole which is not continuous, as stones are actually present in a

heap.”171 Thus wholes whose parts are present actually are aggregates as opposed to the

simplicity of wholes whose parts are present potentially.

Wholes and parts of this kind are common in the scholastic-Aristotelian world.

As we’ve seen Aquinas reads Aristotle as maintaining that all continua are wholes in

169 Ibid. vol. 1, section 509, pg 204. 170 One worry: in many cases of division the whole is corrupted, that is, it does not persist through its division. The p-part to whole relation obtains between a whole and the part which has come to be upon the whole’s division. If the whole has gone out of existence how can there be a relation between the part and the whole. We might have the same question about the ‘great-grandson-of’ relation. If my great grandfather is dead and gone, do I really stand in the great-grandson relation to him? My guess is that how you answer this question will depend on your view of time. For the purposes of this paper, however, I need not offer an answer to the question since the only instance of this relation I am interested in is a case in which the whole persists through its division. 171 Ibid. vol. 1, section 1102, pg 411.

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which the parts are present only potentially. Furthermore Aquinas, for example, takes the

paradigm instances of material substances to be wholes of this kind. In order to show this

I’ll again start with his commentary on Aristotle’s Metaphysics.

…he [Aristotle] shows here that the parts of which substances are composed are not actually existing substances but potential ones. He says that, since it was stated above that there are some things which are thought by all to be substances, namely, sensible substances and their parts, it is evident that most substances of this kind are potential and not actual, as is clear of the parts of animals and all other parts…And it is evident that parts exist potentially, because none of them are separate, but all parts as parts are rather united in the whole. For everything which is actual must be distinct from other things, because one thing is distinguished from another by its own actuality and form, as was stated above. But when those things which are assumed to be parts have been separated from each other when the whole is dissolved, they are then actual beings, not as parts but as matter existing under the privation of the form of the whole.172

Summarizing Aristotle, Aquinas begins with a sociological point: most people think of

things, like animals and their parts, as substances. However, most people are wrong.

While things like plants and animals are substances, their parts are not. The parts of

animals are not independent beings, but only potentially existing substances. Aquinas

explains that the parts of animals are only potential because they are not separate, where

by ‘separate’ Aquinas means “having its own actuality and form”. Thus, for example, a

bear’s paw is not an actual part because it is informed by the same form as the rest of the

bear. When, through an unfortunate series of events, the bear’s paw is severed from its

body, the paw becomes an “actual being” since it no longer is informed by the bear’s

form—or as Aquinas would put it, the paw becomes “matter existing under the privation

of the form of the whole”. It is clear that Aquinas does not merely summarize this view,

he adopts it. Thus in his arguments concerning the soul in the Summa, he claims

172 Ibid. vol. 2, section 1631-3, pg 605.

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…the substantial form perfects not only the whole, but each part of the whole…the soul is a substantial form, and therefore it must be the form and act, not only of the whole, but also of each parts. Therefore, on the withdrawal of the soul, just as we do not speak of an animal or a man unless equivocally (as we speak of a painted animal or a stone animal), so it is with the hand, the eye, the flesh and bones, as the Philosopher says.173

Thus, paradigm instances of material substances (humans, animals, and plants) are not

composed of actually existing substances. Rather, these material substances are

ontologically simple. To be sure, such material substances are form/matter composites,

but they are ontologically simple in the sense that each form/matter composite has no

independently existing beings as parts. Not every scholastic-Aristotelian agreed to this

account of the relation between material substances, continua, and their respective

parts.174 Nevertheless, the view persisted into the 17th century where it came into conflict

with the new mechanical account of the world.

According to the mechanist worldview that arose in the 17th century, the

explanation for natural phenomena lies in the motions of tiny particles. If, for example,

we want to know why wood is capable of being consumed by fire we should look to the

arrangement of wood’s parts. Thus the early mechanists can explain that wood is

consumed by fire because its parts are widely enough spaced to allow a fire’s particles to

get between and separate them. Material bodies, for the mechanists, are not simple but

rather are complexes of independently existing insensible particles all of which move in

173 St. Thomas Aquinas, Basic Writings of Saint Thomas Aquinas. ed. Anton C. Pegis, (Indianapolis: Hackett Publishing, 1945), 716. This quotation is from Summa Theologica. I. 76.8. 174 Duns Scotus, for example, questioned the ontological simplicity of paradigm material substances: see Duns Scotus, Questions on the Metaphysics of Aristotle trans. Etzkorn and Wolter, (St. Bonaventure, New York: Franciscan Institute Publications, 1998); Book VII Question 20. Ockham seems to reject this account of continua. For a discussion see John E. Murdoch, “William of Ockham and the Logic of Infinity and Continuity” in Infinity and Continuity in Ancient and Medieval Thought. ed. Norman Kretzmann, (Ithaca, New York: Cornell University Press, 1982).

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varying ways. Thus, the new mechanists denied the scholastic-Aristotelian account of

material substances and continua. For example consider the 17th century atomist Walter

Charleton’s 1654 Physiologia. The context of the following passage is Charleton’s

consideration of the composition of physical continua. In this section Charleton is

looking to rule out the possibility that continua are simple and consequently to adopt his

favored conclusion that physical continua are composed of atoms. A continuum, he says

is

…not of a simple entity before Division, indistinct; as not a few of our Modern Metaphysicians have dreamt, among whom Albertinus was a Grand Master. Who, that he might palliate the Difficulty of the Distinction of Parts, that threatned an easie subversion of his phantastick position; would needs have that all Distinction doth depend ab Extrinseco, i.e. ariseth only from mental Designation, or actual Division. But, O the Vanity of affected subtilty! All that He, or his whole faction hath erected upon this foundation of Sand, may be blown down from one blast of this single Argument. Those things which can exist being actually separate; are really distinct: but Parts can exist being actually separate; therefore are they really distinct, even before division. For Division doth not give them their peculiar Entity and Individuation, which is essential to them and the root of Distinction.175

Continua, claims Charleton, are not simple entities whose parts come to be upon the

division of the whole. Putting aside the fact that Charleton’s argument begs the question,

he reasons that since the parts of a continuum may exist independent of the whole (once it

is divided), the parts are not potentially present in the whole, they are actually present.

Another of the new mechanists, Descartes, doesn’t even bother to mention the scholastic

account of material bodies. He claims that if we are careful in the examination of our

idea of corporeal substance we will discover that we clearly and distinctly understand that

175 Walter Charleton, Physiologia Epicuro-Gassendo-Charltoniana. Intro. Robert Hugh Kargon, reprinted from the London ed. 1654, (New York: Johnson Reprint Corporation, 1966), 108.

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“each part of it…is really distinct from the other parts of the same substance”.176 Given

that the objects of real distinctions are themselves substances, it follows that corporeal

substance’s parts are themselves substances and hence actually present in the whole.

Recently Thomas Holden has persuasively argued that much of the 17th century

debate concerning the nature of matter ultimately boils down to the conflict between

precisely these two ways of thinking about material wholes and the presence of their

parts.177 Holden refers to the view of Charleton, Descartes, and the rest of the mechanists

according to which the parts into which any extended entity may be divided are actually

present, as the ‘Actual Parts Doctrine’. He refers to the scholastic-Aristotelian view

according to which some or all extended entities are simple prior to division, as the

‘Potential Parts Doctrine’.

Where does Spinoza fit into this picture? Following Holden’s denominations, is

Spinoza an Actual Parts theorist or a Potential Parts theorist? Given that Spinoza is

committed to mechanism and the concomitant rejection of scholastic-Aristotelianism, it

follows that we have got good prima facie reason to think that Spinoza is an Actual Parts

theorist. However, we need to be careful. I have characterized the two doctrines as

concerning the relation between material wholes and their parts. Spinoza maintains that

there are two kinds of material whole. As we’ve seen, Spinoza, unlike Descartes,

maintains that no body is a corporeal substance. Given his commitment to the existence

of both bodies and corporeal substance, we need to be careful to specify the relevant

material whole. In this chapter I will be concerned with corporeal substance.178 So is

176 Principles I. 60; MM, 27; AT VIIIA, 28-29. 177 Holden, Architecture of Matter.178 Ultimately I think that Spinoza adopts both the Actual Parts Doctrine and the Potential Parts Doctrine

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Spinoza an actual or potential parts theorist about corporeal substance? As it turns out,

despite the prima facie evidence, it is clear that he isn’t an actual parts theorist about

corporeal substance. As we’ve seen Spinoza rejects Descartes’ claim that the parts of

corporeal substance are really distinct on the grounds that such a view entails both the

possibility of vacua and the dependence of corporeal substance on its parts.

Unfortunately, however, this is no disjunctive syllogism: we are not allowed to infer from

the fact that Spinoza isn’t an actual parts theorist, that he is a potential parts theorist.179

Nevertheless, I think he is, and in the next section I will argue that this is so.

Section 2: The Relation between Bodies and Corporeal Substance

I think that Spinoza is a potential parts theorist about corporeal substance, which

is just to say that corporeal substance is simple, but nevertheless divisible into parts

which come to be only as the result of division. Further, I think that for Spinoza, bodies

are these parts. Thus, it follows that the relation between bodies and corporeal substance

is one of p-part to whole. In order to make this case I take it to be sufficient to show that

for Spinoza i) corporeal substance is simple prior to division, ii) corporeal substance is

divisible, and iii) dividing corporeal substance generates bodies.

Corporeal substance is simple

As we saw, Aquinas’ material substances are simple in that they do not have

independently existing beings as parts. In order to show that Spinoza’s corporeal

with respect to bodies. For Spinoza there are two kinds of body: simple and complex. Complex bodies have actually existing simple bodies as parts, and as such possess actual parts. Simple bodies, on the other hand, are extended and ultimately divisible, but simple (see Chapter 3). Thus, I take it that Spinoza is an Actual Parts theorist with respect to composite bodies and a Potential Parts Theorist with respect to simple bodies. 179 He might think, for instance, that corporeal substance isn’t divisible.

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substance is simple in this way we need to consider corporeal substance as it is in itself.

As we’ve seen in previous chapters the logical order of Spinoza’s extended universe

begins with corporeal substance and is followed by the immediate infinite modes, the

mediate infinite modes, and ultimately, the finite modes. So to get at corporeal substance

as it is in itself we will need to consider it in the logical moment prior to the existence of

the infinite modes, etc. It is clear that corporeal substance, the unlimited three-

dimensional expanse, is simple. This is the lesson of Spinoza’s criticism of Descartes

account of matter discussed in chapter 2. Spinoza doesn’t think that corporeal substance

can have independently existing parts because i) it entails the possibility of a vacuum and

ii) it makes corporeal substance dependent on its parts. As we’ve seen, both of these

consequences are unacceptable for Spinoza. Thus, part of Spinoza’s correction of

Descartes account of matter is holding that whatever corporeal substance is, it is simple

and non-composite.

Corporeal substance is divisible

On its face, arguing that Spinoza’s corporeal substance is divisible looks to be an

impossible task: Spinoza explicitly says “no corporeal substance, insofar as it is a

substance, is divisible” (E1P13c: C 420, S 224, G II 55). My response is that Spinoza

recognizes two senses of divisibility, only one of which he denies of corporeal substance

in E1P13c. In order to make this case, I will begin by offering an account of what it is for

a material entity to be divisible. It seems clear that being divisible presupposes the

possession of parts in some sense of the term ‘part’; that is, something has the property of

divisibility only if it already has parts. Is this sufficient? That is, can we say: x is

divisible iff x has parts (in some sense of the term ‘part’)? It seems not, since the x’s

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parts might be necessarily contiguous. Divisibility carries with it the presumption that

the parts may be separated in some sense. Thus, I put forth the following modified

account of divisibility: x is divisible iff a) x has parts and b) those parts are separable.

Spinoza’s two senses of divisibility arise from the fact that he recognizes two

different ways for an object’s parts to be separable. I argued in chapter 3 that corporeal

substance’s regions, or q-parts, are movable. Thus in the logical moment prior to the

existence of the infinite modes, all contiguous parts are only contingently contiguous.

Thus, these parts are separable. Spinoza is very careful to distinguish the sense in which

corporeal substances’ q-parts are separable from the sense in which they aren’t. Recall

the defense of God’s corporeality Spinoza offers in the Short Treatise (chapter 3). There

Spinoza defends his view of corporeal substance from those who would claim that

corporeal substance has parts and as such is corruptible. As we’ve seen, Spinoza’s

response is to confront the critic with a trilemma: if corporeal substance is divisible into

parts in a way that is consistent with corruption, then “I ask what there is between the part

cut off and the rest? You must say: either a vacuum, or another body, or something of

extension itself”. Spinoza argues that it can be neither a vacuum nor a body, and so it

follows that another region or q-part is all that lies between the part cut off and the rest.

But Spinoza holds that if the only thing that separates two parts of corporeal substance, is

itself another part of corporeal substance, then it is not corruptible.

The point I want to take from this is that the parts at hand are separated, but not in

a way that renders corporeal substance corruptible. Thus we can distinguish two senses

of ‘separability’: the sense in which corporeal substance’s parts are separable from one

another which I will call ‘substance separability’ or ‘s-separability’ for short, and the

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sense of ‘separable’ that would render corporeal substance corruptible, which I will call

‘corruption-separability’ or ‘c-separability’. Abstracting from corporeal substance these

two senses can be represented as follows. Consider a whole, x, and any two of its

contiguous parts, y and z.

s-separability: y and z are s-separable parts of x iff the only thing that can lie between y and z is another part of x. c-separability: y and z are c-separable parts of x iff it is possible for something other than another part of x to lie between y and z.

Because the q-parts of corporeal substance are moveable, they are separable from one

another, but only by another q-part of corporeal substance. Thus corporeal substance’s

parts are s-separable from one another. Virtually every other extended entity’s parts are

c-separable from one another.180 Thus, for example, two parts of a birthday cake are c-

separable because the cake can be cut with a knife (or a spoon, or a finger, or a shovel,

etc.). Given the account of divisibility offered above we can distinguish two senses of

divisibility corresponding to these two senses of separability.

s-divisibility: x is s-divisible iff for any two of x’s contiguous parts, they are s-separable. c-divisibility: x is c-divisible iff for any two of x’s contiguous parts, they are c-separable.

180 An exception to this claim would be an extended entity whose contiguous parts are necessarily contiguous. I have claimed that corporeal substance has parts that are s-separable from each other. What about the parts themselves? Consider a particular q-part of corporeal substance, ‘P’. As extended, P has q-parts. Are P’s q-parts s-separable or c-separable? If P’s parts are s-separable, then it is impossible for P’s parts to be separated by anything other than another one of P’s q-parts. But this isn’t the case: there are many other q-parts of corporeal substance, and it is possible for some other q-part to separate P’s parts. Thus, P’s parts are c-separable. The fact that corporeal substance’s parts have, considered themselves as wholes, c-separable parts, does not entail that corporeal substance has (despite my claim otherwise) c-separable parts. A necessary condition for having c-separable parts is being finite: there must be something outside of a particular whole that could get into the cracks (so to speak) of the whole. While corporeal substance’s q-parts are limited in some respects, corporeal substance is not.

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Given that corporeal substance has only s-separable parts it is clear that Spinoza is

committed to the s-divisibility of corporeal substance. However, Spinoza denies that

corporeal substance is c-divisible, since by his lights this would entail the possession of

c-separable parts and the concomitant possibility of corruption.

In maintaining that corporeal substance is s-divisible Spinoza isn’t introducing a

radical new conception of divisibility. In fact, it seems to be just the way that Descartes

thinks about the division of the plenum in the hypothetical cosmogony he presents in Le

Monde. Descartes imagines that God begins by creating matter: a simple homogeneous

mass. Descartes continues,

Let us add that this matter may be divided into as many parts having as many shapes as we can imagine, and that each of its parts is capable of taking on as many motions as we can conceive. Let us suppose, moreover, that God really divides it into many such parts…It is not that God separates these parts from one another so that there is some void between them: rather, let us regard the differences he creates within this matter as consisting wholly in the diversity of the motions he gives to its parts.181

In this hypothetical case of creation we find the plenum divided by its motions. The

division of the plenum is not the result of separating the plenum’s parts by something else

(like a void), but rather is the result of differing motions among the parts. Here is another

example: stir a glass of water. The stirring forms a vortex in the glass. The water in the

glass is divided in the same sense that Descartes’ plenum is divided by motion in that the

vortex motion entails spatial changes between particular sub-volumes of water. In some

181 CSM I, 91: AT XI, 34. Nothing in my argument depends on Spinoza’s having read Le Monde prior to the construction of his own account, although my guess is that he would have despite the fact that Le Monde remained unpublished until 1664, several years after Spinoza developed his account. The reason such a guess is reasonable is that copies of Le Monde were circulating among students at Dutch universities by the early 1640’s, and given Spinoza’s proximity to the University of Leiden and well known reputation as a Cartesian, there is reason to believe that Spinoza might have gotten his hands on the work. See Theo Verbeek, “Regius’s Fundamenta Physices” Journal of the History of Ideas vol. 55, no. 4, (1994), 543 footnote 51.

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respects it seems counter-intuitive to call this a case of division. Rather we might prefer

to call it a case of mixing or spinning. Nevertheless, the vortex motion involves

previously contiguous sub-volumes of water being separated by other sub-volumes, and

so this is a case of division. These cases differ from the divisibility of Spinoza’s

corporeal substance because in each of these cases the subject may be divided by

something other than another part of itself. Thus in the case of the water, we can separate

volumes using a spoon, etc. Likewise, if Spinoza is right about Descartes, then the

plenum’s parts can be separated by something other than another part of the plenum,

namely a vacuum. Interestingly, however, if we add some modal force to Descartes’

cosmogony and say that Descartes’ plenum cannot be divided by anything other than its

internal motions, then we have an entity not too different from Spinoza’s corporeal

substance.

Although Spinoza is committed to the s-divisibility of corporeal substance,

throughout his works he uniformly uses the term ‘divisibility’ to denote c-divisibility.

Spinoza’s interest in division is always in terms of corruption. For example, Spinoza

notes in the Short Treatise, “Division, then, or being acted on, always happens in the

mode, as when we say that a man perishes, or is destroyed, that is only understood of the

man insofar as he is a composite being…”(ST I. II: C 72, S , G I 26). Likewise he writes

in the Ethics, “we conceive that water is divided and its parts separated from one

another—insofar as it is water, but not insofar as it is corporeal substance…water, insofar

as it is water, is generated and corrupted, but insofar as it is substance, it is neither

generated nor corrupted”. For water to be divided “insofar as it is water” is for it to be

corrupted. Thus in E1P13c when Spinoza claims that “no corporeal substance, insofar as

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it is a substance, is divisible” he is denying that corporeal substance is c-divisible, that is,

corruptible.

Dividing corporeal substance generates bodies

Bodies, for Spinoza, come to be only through the division of corporeal substance.

The best way to see why this is true is to contrast Spinoza’s corporeal substance with

Descartes’ plenum. Descartes suggests that we think of the material universe prior to

God’s introduction of motion as a homogeneous “perfectly solid body”.182 Such a

description implies that prior to God’s introduction of motion there is only one substance

and that it takes God’s initiating motion to cut that one substance up into many.183 If this

is right, then Descartes looks a lot like a potential parts theorist. But this isn’t right.

Descartes uses ‘body’ equivocally. In many cases Descartes uses ‘body’ or ‘bodies’ to

refer to the objects of physics.184 Bodies in this sense are extended substances physically

individuated by their respective motions. According to this sense all bodies are corporeal

substances, but not all corporeal substances are bodies since not all corporeal substances

are physically individuated. I’ll refer to bodies in this sense as ‘PI-bodies’ (physically

individuated bodies). In other places Descartes uses ‘body’ to refer to the really distinct

parts of matter. Descartes writes of any corporeal substance that “each part of it [which

can be] delimited by our mind is really distinct from the other parts of the same

substance”. 185 According to Descartes, matter is indefinitely divisible and so there are

an indefinite number of really distinct parts to any PI-body; that is, there are an indefinite

182 Ibid. 183 Cf. Emily R. Grosholz, Cartesian Method and the Problem of Reduction, (Oxford: Oxford University Press, 1991), especially the discussion of whether the plenum, prior to the introduction of motion, has any structure 63-71. 184 See Garber, Metaphysical Physics, 175-176. 185 See Principles I.60: MM, 27: AT VIIIA 28-29.

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number of corporeal substances. This is to use ‘body’ synonymously with ‘corporeal

substance’ such that all and only corporeal substances are bodies. I’ll call bodies in this

sense RD-bodies (really distinct bodies). The set of all PI-bodies is a subset of all RD-

bodies, thus all PI-bodies are RD bodies but not all RD-bodies are PI-bodies. Given

these distinctions it is correct to say that prior to the introduction of motion into the

material universe no PI-bodies exist, but incorrect to say that in virtue of this there are no

bodies.186 Since the spatial parts of the material universe are really distinct and matter is

indefinitely divisible187, when God creates the material universe He simultaneously

creates an indefinite number of RD bodies, that is, an indefinite number of corporeal

substances. Given this when God introduces motion into matter he does not

simultaneously create bodies; rather He gives accidents (individual motions) to a subset

of all corporeal substances. In short, Descartes isn’t a potential parts theorist because

bodies exist prior to division, that is, prior to the introduction of motion into matter.

Does Spinoza agree with Descartes in maintaining the existence of bodies prior to

the introduction of motion? No. Spinoza does not use ‘body’ equivocally. According to

Spinoza all bodies are physically individuated. Spinoza says of the simplest bodies: they

“are distinguished from one another only by motion and rest, speed and slowness”

(E2P13a2: C 460, S 253, G II 99). Given that this is an account of the metaphysical

individuation of the simplest bodies it is clear that the existence of motion is a necessary

prerequisite for the existence of bodies and as such Spinoza can’t think that bodies exist

prior to the introduction of motion as Descartes does. Further, I argued in Chapter 3 that 186 In the passage quoted above from Le Monde Descartes suggests that the material universe is the only PI-body. But this can’t be right since there is nothing outside of the material universe from which it could be individuated. 187 Principles II.20: MM, 48-49: AT VIIIA 20.

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the following account of a finite body falls out of a proper analysis of the immediate

infinite mode of extension:

x is a simple body iff i) x is a region of extension, ii) x’s immediate surroundings are changing, and iii) there are no sub-regions of x in motion relative to one another.

Corporeal substance and its regions exist prior to the introduction of motion and only

once motion is introduced, do bodies come to be. In fact, the introduction of motion is

sufficient for the creation of bodies. Thus bodies come to be, for Spinoza, only through

the introduction of motion into corporeal substance; that is, bodies only come to be as the

result of division.

However, this argument seems open to the following objection: “Sure motion is

essential to bodies for Spinoza; but it is only essential in the same way that motion is

essential to PI-bodies for Descartes. The fact that motion is essential to PI-bodies didn’t

lead us to claim that bodies cannot exist prior to the introduction of motion for Descartes,

and consequently the fact that motion is essential to the existence of bodies shouldn’t lead

us to conclude that bodies cannot exist prior to motion for Spinoza”. If this is right, then

the only difference between regions and bodies is that bodies have motion and this is

merely accidental to them. A region, prior to motion is identical to that region after it

gains motion, it just that we call it a ‘body’.

Perhaps the best way to respond to this challenge is to ask the following question:

if a body, for Spinoza, merely refers to a region with accidental motion, then what is a

mode? When Spinoza says that “except for substances and modes there is nothing”

(E1P15p: C 420, S 224, G II 56-57) to what does ‘mode’ refer? By ‘mode of extension’

Spinoza certainly means ‘body’; the question is, does he also mean to refer to the regions

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of corporeal substance? Suppose by ‘mode’ (of extension) Spinoza means both ‘bodies’

and ‘regions’; then in the logical moment prior to the introduction of motion, substance

and all of its (finite) modes exist. But this cannot be right, for at least three reasons.

First, regardless of what ‘mode’ means, at bottom the term refers in some sense to the

way a thing is. Spinoza tells us that “by mode I mean the affections of substance” (E1d5:

C 409, S 217, G II 45). In the logical moment prior to the introduction of motion all that

exists is the infinite three-dimensional expanse, but there is no way that this three-

dimensional expanse is. Second, if modes exist prior to the introduction of motion, and

motion and rest is the infinite mode of extension, then the finite modes of extension exist

logically prior to the infinite modes of extension. But Spinoza holds that finite modes

exist in virtue of the infinite modes.188 Third, Spinoza writes “every individual thing, i.e.

anything whatever which is finite and has a determinate existence, cannot exist or be

determined to act unless it be determined to exist and to act by another cause which is

also finite and has a determinate existence” (E1P28: C 432, S 233, G II 69). Spinoza

makes clear in the proof that by “individual thing” he means ‘mode’, and so according to

this passage every finite mode is caused by something finite. The problem is that regions

of extension exist only in virtue of corporeal substance existing and corporeal substance

is necessarily infinite: they are not caused by something finite.189 It is clear then that by

‘mode’ Spinoza means ‘body’ and not ‘region’. Thus the introduction of motion into

corporeal substance corresponds to the introduction of another category of entity; and as

such division creates bodies. Before leaving this section I want to make explicit that

188 ST II.5: “The next are all those modes which we have said are the cause of the singular modes” (C 105, S 68, G I 62). 189 E1P8

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there are many divisions of corporeal substance. Motion and rest divide corporeal

substance and generate bodies. However, the pattern of motion and rest in corporeal

substance is ever-changing and thus it follows that corporeal substance’s divisions are

ever-changing as well.190

I have argued that i) corporeal substance is simple, ii) corporeal substance is

divisible, and iii) dividing corporeal substance generates bodies. Thus it follows that

Spinoza is a potential parts theorist about corporeal substance. If this is right, then the

relation between bodies and corporeal substance is one of posterior part (or p-part) to

whole. I follow Bennett in thinking that Spinoza’s metaphysics was formulated

primarily with the attribute of extension in mind and once that account had been

developed he applied it across the metaphysical board.191 Given this, I take it that the

mode-substance relationship is one of p-part to whole where (at least in some limited

sense) what it is to be a p-part is relativized to the attribute of the mode in question. 192 I

next turn to a consideration of what I take to be the chief obstacle to accepting the

conclusion of my argument: if Spinoza thought of bodies as parts of corporeal substance,

why does he call them ‘modes’?

190 Spinoza seems to follow Descartes’ in claiming that all possible configurations of matter will obtain. For Descartes see Principles III.47. Spinoza’s version of this principle is found in E1P17 where he suggests that God creates everything that can be created. 191 Bennett, Study, 94. 192 It is worth noting at the end of my argument that Spinoza is a potential parts theorist about corporeal substance, that Wolfson sees Crescas arguing for something similar. See Harry Austryn Wolfson, Crescas’ Critique of Aristotle: Problems of Aristotle’s Physics in Jewish and Arabic Philosophy, (Cambridge, Mass: Harvard University Press, 1929). This may be of some importance given that Spinoza certainly was aware of Crescas’ work (Ep. 12). Crescas is perhaps most well known for denying Aristotle’s claim that there can be no infinite magnitude, and it is in just this context that Wolfson sees the potential parts account. He writes “by the same token, the infinite, simple, homogeneous, incorporeal extension can be divisible despite its being simple; and though divisible into parts each of which is infinite, it will not be composed of those parts. It is simple in the same sense as a mathematical line is simple…for those infinite parts never actually co-exist with the infinite whole, just as the linear parts never actually co-exist with the linear whole” (63).

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Section 3: Curley’s Challenge

In his book, Spinoza’s Metaphysics, Edwin Curley argues for a particular

interpretation of the substance/mode relation. He starts by outlining two alternative

interpretations only one of which I will discuss. Perhaps the most common interpretation

of the substance/mode relation is to claim that the relation that obtains between finite

modes and substance is the same as the relation that obtains between a property and its

bearer. Curley distinguishes two elements of this latter relation as understood in the 17th

century (and especially by Descartes). First, finite substances are independent beings;

their existence is independent of every other substance and property besides God.

Properties, on the other hand, are dependent for their existence on substances. Second,

substances have or bear properties, whereas properties are had by, or inhere in,

substances. The relations of dependency and inherence coincide in the 17th century

treatment of the substance/mode relation. Thus, if Spinoza thinks of the substance/mode

relation in the same way as virtually all of his contemporaries, then it follows that modes

are dependent on, and inhere in, corporeal substance. However, Spinoza cannot have

thought that this is right. Curley writes:

Spinoza’s modes are, prima facie, of the wrong logical type to be related to substance in the same way Descartes’ modes are related to substance, for they are particular things…not qualities. And it is difficult to know what it would mean to say that particular things inhere in substance. When qualities are said to inhere in substance, this may be viewed as a way of saying that they are predicated of it. What it would mean to say that one thing is predicated of another is a mystery that needs solving.193

193 Curley, Spinoza’s Metaphysics, 18.

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Curley concludes that Spinoza’s use of the term ‘mode’ diverges from Descartes’ and

then goes on to offer his own account of the substance/mode relation according to which

modes do not inhere in substance.

Before we accept Curley’s conclusion we need to get clear on the problem: why

are Spinoza’s modes of the wrong logical type to inhere in substance? Curley seems to

be pointing to two problems. First, Spinoza’s modes are of the wrong logical type

because they are particulars. Curley seems to be assuming that accidents or properties

cannot be particulars or individuals. I want to put this objection aside and focus on

Curley’s second objection.194 Curley’s second reason for thinking that Spinoza’ modes

are of the wrong logical type is that they are things, that is, they are property bearers.

This is where the deep problem lies. How is it that three-dimensional property bearers

are properties? That is, how is it that things like daffodils and diamonds are properties of

corporeal substance?

This objection throws down the interpretive gauntlet: if you want to maintain that

Spinoza thinks that modes are properties of corporeal substance in the same way that, say

Descartes does, then you have to explain how three-dimensional bodies inhere in

corporeal substance. There are three strategies for dealing with this challenge. The first

approach is to deny Curley’s set-up and argue that (at least in the 17th century) the

substance/mode relation did not carry with it the assumption that modes inhere in

substances. The second approach is to take up the challenge and explain how bodies

inhere in corporeal substance. The third approach is to acquiesce, accept the force of

194 For a critical discussion of this objection see John Carriero, “On the Relationship between Mode and Substance in Spinoza’s Metaphysics” Journal of the History of Philosophy. vol 33, no. 2: (1995), 245-273.

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Curley’s argument, and conclude as Bennett puts it, Spinoza’s use of the term “silently

deprives ‘mode’…the meaning it had in Descartes’ idiolect and in the Latin language

generally”.195 The task, if one adopts this last approach to Curley’s challenge, is to

explain why Spinoza uses the term ‘mode’ to refer to finite bodies, if he doesn’t think

that finite bodies inhere in corporeal substance.

I am inclined to think that Curley is right that the mode/substance relation is one

of inherence and so I reject the first strategy. In this chapter I have argued that the

relation of mode to substance is one of p-part to whole. Thus, adopting the second

approach would entail showing how the p-part to whole relation is at least a species of the

inherence relation. It is not clear how such an argument would go and so I will forgo this

means of answering Curley’s challenge.196 This leaves only the third approach. Pursuing

this strategy means explaining i) why Spinoza doesn’t consistently use the term ‘part’ for

bodies and ii) why he decides to call p-parts ‘modes’ instead.

Spinoza doesn’t consistently use the term ‘part’ for bodies because he reserves his

strict philosophical uses of the term to refer to parts which actually exist in their wholes.

Recall that I argued in chapter 2 that Spinoza’s use of the term ‘part’ in E1P12-13 is of a

part which exists prior to the whole. Thus his use refers to parts that actually exist in the

whole. He does the same in both the Short Treatise and the Metaphysical Thoughts

195 Bennett, Study, 93. 196 I am drawn to this way of answering Curley’s challenge, and I think there are some prospects for developing an account that shows how p-parts are adjectival on corporeal substance’s regions. Recall that a simple body is a region of extension in motion relative to its immediately contiguous environment no sub-region of which is in motion relative to any other sub-region. In making the case that p-parts are adjectival I would want to claim that simple and complex bodies are merely ways regions are arranged. However, in the absence of such a case, I will capitulate to Curley’s challenge.

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appended to Descartes’ “Principles of Philosophy”. 197 In the latter he writes:

“component parts are prior in nature at least to the thing composed” (DPP II. 5: C 324, S

196, G II 258).198 Likewise this is the case in the physical digression immediately

following E2P13.199 Thus, Spinoza uses ‘part’ to refer to actual parts without noting that

he is using the term in a specialized sense. Second, this seems to have been normal.

Descartes, for example, uses ‘part’ to refer only to actual parts.200 Further, this seems not

to have been limited to the new mechanists. In his textbook Institutiones Logicae Franco

Burgersdijck, a Dutch neo-scholastic with whose work Spinoza was undoubtedly

familiar, takes care in Section 15 of Part 1 to lay out what we mean by ‘part’ and

‘whole’.201 The very first axioms tell us that “A Whole is that which consists in the

Union of many things, or Parts” and “Those things which, united compose or constitute

the whole, are called Parts”. It appears that Burgersdijck takes parts to be actual parts

and this is confirmed in axiom 4: “The Parts are by Nature before the Whole…”.202

Given all of this, there is good reason to think that Spinoza saves the term ‘part’ for parts

which actually exist in their wholes. Thus, in the few cases in which Spinoza calls bodies

‘parts’ he is letting his guard down and allowing the underlying sense of bodies as p-parts

to slip through.

197 Spinoza writes in the Short Treatise: “A thing composed of different parts must be such that each singular part can be conceived and understood without the others. For example, in a clock that is composed of many different wheels, cord, etc., I say that each wheel, cord, etc., can be conceived and understood separately, without needing [the understanding of] the whole as a whole. Similarly with water, which consists of straight, oblong particles. Each part of it can be conceived and understood, and can exist, without the whole” (ST I. 2: C 71, S 44, G I 25). 198 See also Ep.35 199 There Spinoza discusses the nature of composite bodies, the parts of which exist prior to the whole and compose it. 200 e.g. Principles I.60. 201 See Alan Gabbey, “Spinoza’s Natural Science and Methodology” in Cambridge Companion, 144. 202 Franco Burgersdijck, Monitio logica, or, An abstract and translation of Burgersdicius his logick, trans. by a gentleman (London: Printed for Ric. Cumberland ..., 1697): 43-48.

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Why did Spinoza use the term ‘mode’ as opposed to some other term to refer to

bodies? I do not think that Spinoza misunderstood or was ignorant of Descartes’ use of

the term ‘mode’. Rather, it seems that Spinoza’s view of bodies as p-parts shares at least

two significant features with modes understood in Descartes’ sense. First, both p-parts

and modes are dependent on substance for their existence. If you annihilate a substance,

then all its properties are simultaneously annihilated. Although it is impossible,

nevertheless were corporeal substance to be suddenly annihilated, so too would all of

corporeal substance’s p-parts. Second, both p-parts and modes are inseparable from their

whole or bearer respectively. This is significant because one of the chief differences

traditionally drawn between properties and parts is in terms of separation. For example

in the Categories, Aristotle characterizes properties (those things that exist in a subject)

saying: “by ‘in a subject’ I mean what is in something, not as a part, and cannot exist

separately from what it is in”.203 Aristotle’s suggestion is that the parts of a (material)

substance are separable from the whole in a way that properties aren’t.204 This distinction

is echoed in Norman Swartz’s contemporary introduction to properties. He writes:

Physical parts of material objects are themselves (smaller) physical parts and may in their turn be physically separated from the larger thing of which they are parts. One might for example remove chips of chalk from a larger piece of chalk. The chips are (or were) parts of the original chunk. But the property of whiteness is not part of that chunk. The whiteness cannot be removed so that we could then say: “Here on the left is the whiteness which used to be in the chalk, and here on the right is what remains of the chalk…”205

203 Categories 1a22-25 204 Aristotle is referring to the fact that properties cannot exist without substance. My guess is that he would have taken this to entail that a property cannot exist spatially separated from a substance. But strictly speaking given that it is possible for i) x to depend on y for its existence and ii) x to be spatially discontiguous from y, I take it I can treat ontological dependence and spatial separation as two distinct properties. 205 Norman Swartz, Beyond Experience: Metaphysical Theories and Philosophical Constraints. (Toronto: University of Toronto Press, 1991), 261-262.

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We can spatially separate a piece of chalk from the whole of which it is a part, that is, the

chalk’s parts are c-separable. However, the chalk’s modes or properties are not c-

separable. We cannot spatially separate the chalk’s whiteness from the chalk. Things are

different for Spinoza. No body can exist spatially separated from corporeal substance.

Such a separation could occur only if it were possible for the body to be separated from

corporeal substance by something other than another part of corporeal substance. But

this would mean that there would have to be something other than a body to stand

between the c-separable body, and given the infinity of corporeal substance (and that

there can be no vacua), this is impossible.

Conclusion

Perhaps the chief obstacle to understanding Spinoza’s substance monism is

accounting for the relation between bodies and the one corporeal substance. I have

argued that the relation between bodies and corporeal substance is one of p-part to whole

where I understand this to be the relation between a whole and the parts into which it has

been divided and which have come to be upon its division. Spinoza adopts this

scholastic-Aristotelian account of the relation between a whole and its parts to avoid the

problems raised by Descartes’ Actual Parts account of matter. By adopting a Potential

Parts account of corporeal substance, Spinoza is able to have both a metaphysically

coherent account of matter and an account of bodies that allows for mechanist

explanation. Thus, we’ve seen in chapters 2-4 that Spinoza’s acceptance of the one

corporeal substance doctrine, his account of bodies, and his explanation of the relation

between bodies and corporeal substance all are the result, in a significant sense, of his

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attempt to ground the metaphysics of mechanism by offering a philosophically

respectable account of matter.

In the final chapter of this dissertation I turn to one last problem raised by the

mechanist worldview. The explanations the mechanical philosophy seeks to offer take

the form of showing that any particular observable phenomenon is the effect of a series of

causal relations obtaining between particles of matter. However, on its face, this view

conflicts with the traditional theological commitment that God is the sole cause and

author of all things, a view to which Spinoza adheres.

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CHAPTER 5: SPINOZA’S NATURALISTIC CONCURRENTISM

Introduction

‘Divine concurrentism’ refers to a family of views according to which God

cooperates or concurs in the actions of finite beings. Divine concurrentism is one of a

number of philosophical options for those who are committed to God’s omnipresent

causal activity in the world. A commitment to this thesis, while common to traditional

theists, is not exclusive. Despite the fact that Spinoza’s God is vastly different from the

God of Judaism, Christianity, and Islam, Spinoza agrees with tradition that God is the

cause of all things. In this chapter I aim to explain how God is causally connected to the

world of finite modes. I argue that we can account for God’s causal relation to finite

modes in terms of divine concurrence; specifically, I argue that Spinoza adopts a roughly

Thomistic model of concurrence. In section 1, I begin by laying out the so-called

“problem of the deduction of the finite from the infinite”.206 I then lay out the scholastic

background for thinking about God’s causality, and show that Spinoza is committed to

concurrentism. In section 2, I offer a reconstruction of Spinoza’s concurrentism by

explaining how finite modes are causally efficacious, the nature of God’s power, and how

these two causal influences interact. I conclude the paper by showing that this

cooperation dovetails perfectly with a prominent interpretation of Spinoza’s divine

206 Giancotti, “On the Problem of Infinite Modes,” 107.

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causality according to which the existence and action of finite modes can be deduced

using the D-N model of explanation.

Section 1: God and Finite Modes

The Problem of God’s Causal Relation to Finite Modes

The very first axiom of the Ethics tells us “Whatever is, is either in itself or in

another” (E1a1: C 410, S 217, G II 46). Spinoza interprets this claim later in E1P15p as

“except for substances and modes there is nothing” (C 420, S 224, G II 56-57). There are

only two kinds of being, substance and mode. Spinoza defines ‘substance’ as that which

exists in itself (E1d3) and ‘mode’ as that which exists in another (E1d5). So x is a

substance if and only if x exists in itself. According to E1P7, every substance is a thing

whose essence involves existence. Likewise from E1P11p it is clear that if something’s

essence involves existence, then it’s a substance. Here’s why: Spinoza argues that if God

doesn’t exist, then his essence does not involve existence, but this is absurd since God is

a substance, so God necessarily exists. The chief assumption in this argument is that if a

substance doesn’t exist, then its essence does not involve existence. By transposition,

this assumption is that if its essence involves existence, then substance exists. Thus we

can draw two sub-conclusions: i) x’s essence involves existence if and only if x is a

substance and ii) x is a substance if and only if x is in itself. We can thus conclude that

x’s essence involves existence if and only if x is in itself.

Since God is the only thing that exists in itself, God is the only thing whose

essence involves existence. All other things, modes, exist in God and are such that their

essence does not involve existence. From the fact that a thing’s essence does not involve

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existence, Spinoza concludes: “So their essence can be the cause neither of their

existence nor of their duration, but only God to whose nature alone it pertains to exist”

(E1P24c: C 431, S 232, G II 67). Thus, the existence of any mode, finite or infinite,

requires a cause independent from itself, and ultimately this cause is God.207

Furthermore, God is the cause of every mode’s action: Spinoza writes in E1P26 “A thing

which has been determined to produce an effect has necessarily been determined in this

way by God; and one which has not been determined by God cannot determine itself to

produce an effect” (C 431, S 232, G II 68). Thus God is the cause of both the existence

and action of every mode.

How does God cause the existence and action of modes? In order to pursue an

answer to this question we need to note that Spinoza talks about ‘x causing y’

interchangeably with ‘x producing y’, ‘y following from x’, ‘y flowing from x’, and ‘y

being determined by x’.208 Spinoza most commonly uses the locution ‘follows from’

(sequi) and commentators have almost uniformly taken this seriously, claiming that for

Spinoza, the relation between cause and effect is akin in some way to the relation of

logical entailment that obtains between the premises and conclusion of a valid

argument.209 For the purposes of this paper, I’ll take this admittedly incomplete account

207 This also seems to follow from E1P16 where Spinoza claims in the corollary that “God is the efficient cause of all things that can come within the scope of the infinite intellect” (C 425, S 227, G II 60). However, Margaret Wilson has argued that in E1P16 Spinoza is not referring to finite modes. See Margaret D. Wilson, “Infinite Understanding, Scientia Intuitiva, and Ethics I.16” Midwest Studies in Philosophy 8 (1983): 181-191. 208 See E1P28p and E1P6p for ‘producing’; E1P16 and proof, E1P21, and E1P28p, among many others for ‘follows’; E1P17p, E1P28, E3P2 for ‘determining’; E1P17s for ‘flowing’, 209 See e.g., Curley, Spinoza’s Metaphysics,45; Bennett, Study, 30; Michael Della Rocca, Representation and the Mind-Body Problem in Spinoza [Representation], (New York: Oxford University Press, 1996), 12; Harold H. Joachim, A Study of the Ethics of Spinoza, (Oxford: Clarendon Press, 1901), 60. For a critical discussion of this interpretation, see Margaret D. Wilson, “Spinoza’s Causal Axiom (Ethics I, Axiom 4)” in God and Nature; Kenneth Clatterbaugh, The Causation Debate in Modern Philosophy, 1637-1739, [The

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of causality to suffice. Insofar as this is the case, in focusing on how God is causally

related to modes I am asking how modes are analogously deduced from God.

Spinoza is fairly explicit about how God causes the infinite modes. The existence

and nature of the infinite modes follow, ultimately, from God’s essence. God’s essence

expresses itself in the various attributes of thought and extension and each of these

attributes has a particular nature which expresses itself through the infinite modes.

Spinoza writes in E1P23: “Every mode which exists necessarily and is infinite has

necessarily had to follow either from the absolute nature of some attribute of God, or

from some attribute, modified by a modification which exists necessarily and is infinite”

(C 430, S 231, G II 66). Thus infinite modes follow from God either by following from

the absolute nature of one of his attributes (what I have previously called the ‘immediate

infinite modes’) or by following from an infinite mode that itself follows from the

absolute nature of one of the attributes (what I have previously called that ‘mediate

infinite modes’). In short, if x is an infinite mode, then x follows (immediately or

mediately) from the absolute nature of one of God’s attributes. Furthermore, Spinoza

maintains that if x follows from the absolute nature of one of God’s attributes, then x is

an eternal and infinite mode. He says in E1P21, “All the things which follow from the

absolute nature of any of God’s attributes have always had to exist and be infinite, or are,

through the same attribute, eternal and infinite” (C 429, S 230, G II 65).210 In sum,

Causation Debate] (New York: Routledge, 1999), 132-141. An apparent exception to this is Hallett, see H.F. Hallett, Benedict De Spinoza: The Elements of his Philosophy, (London: University of London Athlone Press, 1957), 9-11. 210 Although Spinoza does not use the term ‘mode’ in E1P21 it is clear that this is what he is referring to when he says “all the things…” since as we’ve seen “except for substances and modes there is nothing” (E1P15p).

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Spinoza is committed to the principle that x is an infinite mode if and only if x follows

(immediately or mediately) from the absolute nature of one of God’s attributes.

Consequently, finite modes cannot follow from the absolute nature of one of God’s

attributes.

So how are finite modes related to God? Spinoza appears to take this up in the

proof to E1P28, he writes “Whatever has been determined to exist and to produce an

effect has been so determined by God…But what is finite and has a determinate existence

could not have been produced by the absolute nature of an attribute of God; for whatever

follows from the absolute nature of an attribute of God is eternal and infinite” (C 432, S

233, G II 69). As such, it is in E1P28 and its proof that we would expect to find

Spinoza’s account of how God causes finite modes. Here is his conclusion to the proof:

“It [that which is finite and has a determinate existence] had, therefore, to follow from, or

be determined to exist and produce an effect by God or an attribute of God insofar as it is

modified by a modification which is finite and has a determinate existence” (C 432, S

233, G II 69). Spinoza’s answer to the question, ‘How are finite modes related to God?’

is that finite modes are determined to exist by “God or an attribute of God insofar as it is

modified by a modification which is finite and has a determinate existence”. This is an

awkward way of referring to a finite mode. We know this because in E2P13L3p Spinoza

justifies the claim that “each [body] must be determined necessarily to motion or rest by

another singular thing, viz. by another body…”(C 459, S 252, G II 98) by reference to

E1P28. Unfortunately, it is unclear how this answer accounts for God’s relation to finite

modes. Spinoza concludes that the existence or action of any finite mode must be

determined by another finite mode, but since God is not a finite mode, it seems that he

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hasn’t accounted for God’s relation to the finite modes. This is the problem of the

deduction of the finite from the infinite.

Curley’s Solution to the Problem of the Finite Modes

The problem of the deduction of the finite from the infinite has inspired a number

of solutions. However, Edwin Curley’s resolution to this problem has been especially

prominent.211 Curley’s account of God’s causal activity in the realm of finite modes

follows the deductive-nomological (D-N) model of explanation.212 According to this

model, explanations of phenomena take the form of deductive arguments the premises of

which include at least one law of nature. Thus if we want to explain a particular finite

phenomenon, for example the motion of a billiard ball after having been struck, we need

only develop a sound deductive argument which has as premises the relevant laws of

motion coupled with the specifics of this situation (the velocity with which the first ball

was moving, the angle at which it hit the second ball, etc.). From these premises we can

deduce the velocity of the billiard ball, and as such, explain it. The D-N model of

explanation can account for both singular and (derivative) general truths, but in order to

explain a singular truth, the explanatory deductive argument must contain a singular truth

as a premise. Recall that, for Spinoza, causation is analogous to the relation between the

211 Many commentators have followed Curley’s resolution in one way or another, including Watt, “The Causality of God”, Bennett, Study; Yovel, “Infinite Mode”, and Della Rocca, Representation. For alternative solutions to this problem see Harry Austryn Wolfson, The Philosophy of Spinoza (New York: Meridan Books, Inc., 1958); Joel Friedman “How the Finite Follows from the Infinite in Spinoza’s Metaphysical System” Synthese 69 (1986): 371-407; James G. Lennox, “The Causality of Finite Modes in Spinoza’s Ethics” Canadian Journal of Philosophy 6 (1976), 479-500; Olli Koistenen, “Causation in Spinoza” in Metaphysical Themes.212 The following summarizes Curley, Spinoza’s Metaphysics, 50-74.

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premises and conclusion of a valid deductive argument. Given this conception of

causality, it makes sense to apply the D-N model to Spinoza. Curley summarizes his

application of this model to Spinoza saying “this is the metaphysical equivalent of the

logical or epistemological claim that propositions describing the existence and actions of

particular things can be deduced from the laws of nature, if and only if the laws are taken

together with a statement of antecedent conditions”.213 Ultimately, Curley makes use of

the D-N model to explain God’s causal relation to the existence and action of finite

modes by i) showing that God is causally efficacious through the infinite modes and ii)

identifying the infinite modes with laws of nature. God is causally related to the

existence and action of every finite mode insofar as the laws of nature are required to

explain the existence and action of every finite mode.

Recall that in setting up the problem of the deduction of the finite from the

infinite we saw, first, that finite modes can’t follow from God’s absolute nature because

otherwise they would be infinite and eternal. Second, we saw that, rather than providing

an account of how God causes finite modes, Spinoza in E1P28, merely tells us that finite

modes cause the existence and action of other finite modes. Curley’s interpretation

makes sense of both of these features of the problem. First, if we identify the infinite

modes with the laws of nature, it becomes clear why finite modes can’t follow from

them: the laws of nature are expressed by universally quantified propositions of the form

(x) (Fx → Gx). From a proposition of this form no singular proposition can be validly

deduced, for example we cannot deduce Fa. Given the analogy between deduction and

causation, the existence or action of any finite mode cannot be deduced from the laws of

213 Ibid, 66.

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nature alone. Second, given this fact it is clear why Spinoza tells us that finite modes

cause the existence and action of other finite modes. The existence and action of a

particular finite mode cannot be deduced from the laws of nature alone, in addition we

need the existence and action of another finite mode. Only from these two individually

necessary and jointly sufficient conditions, does the existence (or action) of a finite mode

follow.

In addition to resolving the problem of God’s causal relation to finite modes,

Curley’s solution gives a metaphysical explanation for Spinoza’s repeated claims that all

natural phenomena are to be explained according to the laws of nature. Spinoza writes in

the Theological-Political Treatise that “Nothing, then, can happen in Nature to

contravene her own universal laws, nor yet anything that is not in agreement with these

laws or that does not follow from them” (S 446, G III 83).214 As such, Spinoza argues

that there are no miracles (understood as a violation of the laws of nature). Likewise,

Curley’s solution explains the fact that, for Spinoza, there is a close relation between the

laws of nature and God’s power. Spinoza says in the Preface to book 3 of the Ethics

“nothing happens in nature which can be attributed to any defect in it, for nature is

always the same, and its virtue and power of acting are everywhere one and the same,

i.e., the laws and rules of nature, according to which all things happen, and change from

one form to another, are always and everywhere the same” (C 492, S 278, G II 138). If

Curley’s interpretation is right that God is causally efficacious through the laws of nature,

then we can understand the close association between God’s power and the laws of nature

in Spinoza’s writings.

214 Shirley trans.

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Curley’s interpretation and resolution of the problem of the deduction of the finite

from the infinite have, for the most part, been accepted by scholars; and I agree that

Curley is right: the deduction of the finite from the infinite roughly follows the D-N

model of explanation. Thus, for Spinoza, the existence and action of any finite mode

follows from the combination of the antecedent conditions (previously existing finite

modes) and the laws of nature (God). However, I want to ask a deeper question: why

does the causation of finite modes take this form? In other words, why does Spinoza’s

account of God’s causal activity take the form of the D-N model of explanation? In what

follows, I argue that the God’s causal activity takes the form it does for Spinoza, because

it is his particular form of divine concurrence.

Scholastic Views of God’s Causality

The problem of accounting for God’s causal activity in the world is not peculiar to

Spinoza, and in fact this particular problem has a long history. In this section I want to

outline the philosophical landscape regarding God’s causality established by the

scholastics.215 Spinoza would certainly have been aware of this tradition given the

vociferous debates in Dutch universities in the 1640’s and 1650’s between adherents of

the new Cartesian philosophy and adherents to the traditional scholastic philosophy on

just this issue.216

215 Alfred Freddoso is the authority on scholastic concurrentism. See Alfred Freddoso, “Medieval Aristotelianism and the Case against Secondary Causation in Nature,” in Divine and Human Action: Essays in the Metaphysics of Theism ed. Thomas V. Morris, (Ithaca, NY: Cornell University Press, 1988); “God's General Concurrence with Secondary Causes: Why Conservation is Not Enough,” [“God’s General Concurrence”] Philosophical Perspectives 5 (1991), 553-585; “God's General Concurrence with Secondary Causes: Pitfalls and Prospects,” [“Pitfalls”] American Catholic Philosophical Quarterly 67 (1994), 131-156; Francisco Suarez, On Creation, Conservation, and Concurrence, trans. and intro. by A.J. Freddoso, (South Bend, Indiana: St. Augustine’s Press, 2002). See also Louis A. Mancha Jr., “Concurrence: A Philosophical Explanation”, (Ph.D. diss., Purdue University, 2003). 216 A number of these debates concerned the issue of whether a Cartesian metaphysic could support

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Turning to the scholastic Aristotelians, we find three general interpretations of

God’s omnipresent causal activity. According to the weakest of these views, mere

conservationism, God is causally active in the world inasmuch as He is a conserving

cause. That is, God is causally active in the world only insofar as He supports or allows

everything that is, to exist. According to mere conservationism, God’s causal activity

does not extend into ordinary inter-substantial causation. For example, a fire is genuinely

causally efficacious in transforming wood into ash; God’s action is necessary only as the

guarantor of the continued existence of the fire and wood (and subsequent ash) and not

for the causal activity of the fire itself. Among the scholastics this was by far the least

popular position. In fact, Freddoso notes that in late medieval and early modern texts

only one proponent of this view is ever mentioned (Durandus).217

A stronger interpretation of God’s causal activity is concurrentism. According to

concurrentism, God’s causal activity extends beyond conservation into the realm of inter-

substantial causation. God cooperates or concurs in the action of finite substances. For

example, the transformation of wood into ash is the effect of a joint action by God and

the fire. This account of God’s causal activity was by far the most popular view among

late medieval and early modern philosophers; among its more prominent proponents were

Aquinas, Molina, Suarez, Boyle, Leibniz, and perhaps Descartes.218 The strongest

concurrentism. See Johan Arie Van Ruler, The Crisis of Causality: Voetius and Descartes on God, Nature, and Change, [The Crisis of Causality] (Leiden: Brill, 1995), Chapter 9. 217 See Freddoso, “God’s General Concurrence, 555; Van Ruler, The Crisis of Causality, 268, footnote 21. 218 This is a controversial topic in Descartes scholarship, but at least two recent commentators have argued that Descartes is a concurrentist. See Kenneth Clatterbaugh, “Cartesian Causality, Explanation, and Divine Concurrence” in History of Philosophy Quarterly, 12, no. 2 (1995): 195-207, and The Causation Debate.See also Andrew Pessin, “Descartes’s Nomic Concurrentism: Finite Causation and Divine Concurrence” Journal of the History of Philosophy, 41, no. 1 (2003): 25-49. For a recent article on Leibniz’s concurrentism see Sukjae Lee, “Leibniz on Divine Concurrence” The Philosophical Review 113 (2004): 203-248. On Boyle’s concurrentism see Timothy Shanahan, “God and Nature in the Thought of Robert

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interpretation of God’s causal activity is occasionalism. According to occasionalism,

God’s causal activity excludes the causal efficacy of finite substances. Thus, the fire is

not causally efficacious; rather, the conjunction of fire and its proximity to combustible

wood is merely the occasion for God’s transformation of the wood into ash. Although

Malebranche is perhaps the most well known occasionalist, this view was maintained by

a number of medieval Muslim thinkers including al-Ghazālī.219 In what follows, I will

argue that Spinoza is committed to a concurrentist interpretation of God’s causal activity.

Causal Efficacy: God and Finite Modes

In this section, I argue that Spinoza is committed to concurrentism by showing

that Spinoza maintains i) God’s conservation of finite modes, ii) the causal efficacy of

finite modes, and iii) God’s activity in finite inter-modal causation. I will begin with

conservation. On its face it seems that Spinoza agrees with the tradition that God is the

conserving cause of all things, after all, he claims that every mode is dependent on God

insofar as it exists in, and is conceived through, God. However, we can show that

Spinoza thinks of this relation as conservation. In order to make this case I will begin by

discussing Descartes’ account of conservation.

In a reply to Gassendi, Descartes (following Aquinas) explains God’s

conservation as follows:

When you deny that in order to be kept in existence we need the continual action of the original cause, you are disputing something which all metaphysicians affirm as a manifest truth—although the uneducated often fail to think of it because they pay attention only to the causes of coming into being and not the causes of being itself. Thus an architect is the cause of a house and a father of his child only in the sense of being the causes of their coming into being; and hence,

Boyle” Journal of the History of Philosophy, 26 (1988): 547-569. 219 See Majid Fakhry, Islamic Occasionalism and its Critique by Averroës and Aquinas, (London: George Allen and Unwin Ltd, 1958).

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once the work is completed it can remain in existence quite apart from the ‘cause’ in this sense. But the sun is the cause of the light which it emits, and God is the cause of created things, not just in the sense that they are causes of the coming into being of these things, but also in the sense that they are the causes of their being; and hence they must always continue to act on the effect in the same way in order to keep it in existence.220

In this passage Descartes distinguishes two senses of ‘cause’: the cause of becoming and

the cause of being. The two senses differ according to the nature of the dependence

relations between cause and effect. The cause of becoming brings its effect into

existence, but is not required for its continued existence. Thus, the house depends on its

architect, but once the house is constructed its existence is independent of the architect.

Likewise, a child depends on its parents for its coming to be, but the death of both parents

doesn’t simultaneously result in the death of the child. The cause of being, on the other

hand, is required for an effect’s continued existence. That is, if x is the cause of being of

y, then x’s continual action is a necessary condition for the continued existence of y.

Thus, the sun is the cause of being of light in that in the absence of the sun’s activity,

there is no light. It is this sense of ‘cause’ that Descartes identifies with God’s

conservation. Thus God’s action is a necessary condition for the continued existence of

finite beings.

Given this background, we can see clearly that Spinoza’s God is the conserving

cause of every mode. In the Ethics, Spinoza uses precisely the same language as we find

in Descartes to explain God’s relation to modes. In the corollary to E1P24 he echoes

Descartes’ remarks, saying: “it follows that God is not only the cause of things’

beginning to exist, but also of their persevering in existing, or (to use a Scholastic term)

220 CSM II, 254-255: AT VII, 368-371. Cf. Aquinas ST.I.104 a. 1

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God is the cause of the being of things (causam essendi rerum)” (C 431, S 232, G II 67).

God is the “cause of being” of things and as such God is the conserving cause of all

modes.

Second, Spinoza is no occasionalist: he maintains that finite modes are causally

efficacious. For example, as we’ve seen, Spinoza tells us in EIP28 that “Every singular

thing, or any thing which is finite and has a determine existence, can neither exist nor be

determined to produce an effect unless it is determined to exist and produce an effect by

another cause, which is also finite and has a determine existence…” (C 432, S 233, G II

69). Thus according to E1P28 individual things, i.e. finite modes, are caused by other

finite modes to exist and act as they do. This is no isolated claim; throughout the Ethics

Spinoza claims that finite modes are causally efficacious. In fact, Spinoza’s ethical

doctrine presupposes that finite modes are causally efficacious. Spinoza defines virtue as

follows: “…virtue, insofar as it is related to man, is the very essence, or nature, of man,

insofar as he has the power of bringing about certain things, which can be understood

through the laws of his nature alone” (E4d8: C 547, S 323, G II 210). Thus, finite modes

are causally efficacious.

Last, God is causally active in finite inter-modal causation. Not only does

E1P24c show us that Spinoza holds that God conserves all modes (“God is the cause of

being of things”), it shows that God is causally efficacious above and beyond this act of

conservation. He writes that God is the cause “of the coming into existence of things”.

Spinoza repeats this at E2P10s2, explicitly claiming that God is the cause of modes

coming into being. He writes:

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Everyone, of course, must concede that nothing can either be or be conceived without God. For all confess that God is the only cause of all things, both of their essence and of their existence, i.e., God is not only the cause of the coming to be of things (secundum fieri), as they say, but also of their being. (C 454-455, S 249, G II 93)

Thus, God not only conserves finite modes, but is actively involved in their generation.221

Given that Spinoza holds that i) God conserves all that is, ii) finite modes are

causally efficacious, and iii) God is causally active in finite inter-modal causation, there

are good systematic reasons for thinking that Spinoza is committed to concurrentism.

The challenge for the concurrentist is to explain how God cooperates with secondary

causes to produce an effect. Spinoza never offers an explicit account of this cooperation

and so, in what follows, I will reconstruct Spinoza’s account of God’s concurrence.

There are two specific challenges that need to be met in order to explain how God

concurs. The concurrentist holds that God and finite things are both causally efficacious.

As such, the first difficulty in reconstructing Spinoza’s concurrentism is explaining how

finite modes are causally efficacious. The second difficulty lies in making clear how God

is causally efficacious. Spinoza’s God is unlike Descartes’ in that He is not a person.

Spinoza’s God does not make decisions; Nature does not have a will. Thus, it isn’t clear

in what God’s power consists, and how Nature can cooperate with finite modes. Only

once these two questions have been answered can we turn to a reconstruction of

Spinoza’s account of concurrence.

221 See also E1P29p where Spinoza claims “God is the cause of these [finite] modes not only in so far as they simply exist, but also insofar as they are considered to be determined to produce an effect” (C 433, S 234, G II 70).

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Section 2: Spinoza’s Concurrentism

The Causal Efficacy of Bodies

In the effort to explain how God cooperates with finite modes, the first task is to

account for the causal efficacy of bodies. It is clear that Spinoza took finite modes of

extension—bodies—to be causally efficacious, however on its face, it is not clear that

Spinoza can consistently do so. Ultimately, the problem is whether Spinoza, and early

modern mechanists in general, can account for the presence of force in their ontology.

The problem is very clear in Descartes and so I will take Descartes as a representative

mechanist and show how this problem arises in his metaphysics of body, before turning

to Spinoza’s solution.

According to the scholastic-Aristotelians, the explanation for a body’s

characteristic properties and behaviors is grounded in the body’s substantial form. In

virtue of its substantial form a body is a member of a natural kind and as such has the

powers appropriate to that kind: a cow’s capacity to produce milk is grounded in that

cow’s being a cow.222 Descartes, among many others, rejected the scholastic explanation

of natural phenomena in favor of mechanistic explanations according to which the

properties and behaviors of bodies are explained in terms of the various motions, sizes,

shapes, and arrangements of their parts. Thus, in Le Monde Descartes claims:

If you find it strange that in explaining these elements I do not use the qualities called ‘heat’, ‘cold’, ‘moisture’ and ‘dryness’—as the philosophers do—I shall say to you that these qualities themselves seem to me to need explanation. Indeed, unless I am mistaken, not only these four qualities but all the others as well, including even the forms of inanimate bodies, can be explained without the

222 Descartes writes that forms “were introduced by philosophers for no other reason but to explain the proper actions of natural things” CSM III, 208: AT III, 506.

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need to suppose anything in their matter other than the motion, size, shape, and arrangement of its parts.223

We can see Descartes’ mechanism in action in the Meteorology. There, for example, he

explains water’s fluidity as follows: “the small particles of which water is composed are

long, smooth, and slippery, like little eels, which are such that however they join and

interlace, they are never thereby so knotted or hooked together that they cannot easily be

separated”.224 Descartes rapidly applied this method of explanation, ultimately claiming

to have explained everything from the nature and behavior of salts, clouds, and rainbows,

to the phenomena of magnetism and light. Implicit in this explanation of natural

phenomena is the assumption that minute particles of matter are causally related.

Consider the following passage:

…you may posit ‘fire’ and ‘heat’ in the wood, and make it burn as much as you please: but if you do not suppose in addition that some of its parts move about and detach themselves from their neighbours, I cannot imagine it undergoing any alteration or change. On the other hand, if you take away the ‘fire’, take away the ‘heat’, and keep the wood from ‘burning’; then, provided only that you grant me there is some power which puts its finer parts into violent motion and separates them from the coarser parts, I consider that this power alone will be able to bring about all the same changes that we observe in the wood when it burns.225

Descartes is arguing that we do not need substantial or accidental forms to explain the

fire’s burning the wood. Rather we can explain this phenomenon mechanistically: the

wood is transformed because its finer parts are separated from its coarser parts by fire’s

parts. Fire’s parts have the power to separate wood’s parts. As such the causal efficacy

of the fire boils down to the efficacy of fire’s parts to act. According to Descartes, the

223 See also Principles IV.198 224 Meterorology, First Discourse: O, 264. 225 CSM I, 83: AT XI, 7-8 (my italics).

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power of a body to act lies in its force.226 But what is force? Descartes’ ontology

contains only substances and modes, and force certainly isn’t a substance. The problem

is that it doesn’t seem that Descartes allows for force in his basic ontology of bodies: the

only modes Descartes allows are the general modes of substance (duration, number, etc.)

and geometric modes (such as shape, size, and motion).227 Thus Garber rhetorically asks

“what place could such forces have in Descartes’ spare and geometrical ontology”.228

Thus an interpretive challenge in claiming that bodies are causally efficacious for

Descartes, and for mechanists more generally, lies in accounting for the presence of

force. Indeed, the lack of such an account is among the reasons that have led a number of

interpreters to claim that Descartes is an occasionalist of some stripe.229

Certainly Spinoza’s system differs in significant ways from Descartes’. For

example, instead of extension and thought constituting the attributes of two different

226 Descartes’ definition of motion includes the following qualification: “I also say that it is a transference, not the force or action which transfers…” (Principles II.25: MM, 51: AT VIIIA, 54). Here Descartes is distinguishing between motion and its cause, that is, the force or action which transfers. For a discussion see Garber, Metaphysical Physics, 161; See also Michael Della Rocca, “If a Body Meet a Body”: Descartes on Body-Body Causation” in New Essays, 58. 227 Descartes was not alone in this respect. Gabbey writes of the traditional mechanists “Force did not appear in the list of components from which they constructed their world, yet it entered continually, as a functional component, into their discourse about that world, coupled with the ineradicable belief that an event must have a cause to which it can be quantitatively related in terms of equality or proportionality. In their considerations of the natural world per se, that is the natural world viewed independently of its divine ground and origin, the mechanists did not make the ontology of force one of their major concerns”. See Alan Gabbey, “Force and Inertia in Seventeenth-Century Dynamics” Studies in the History and Philosophy of Science, vol. 2, no. 1 (1971): 6. 228 Garber, Metaphysical Physics, 293. 229 Recent proponents of this argument include Garber, Metaphysical Physics, 293-294, and Des Chene, Physiologia, 313. I will follow Garber and distinguish different versions of occasionalism. According to body-to-body occasionalism, no body is causally efficacious with respect to another body; according to body-to-mind occasionalism bodies aren’t causally efficacious with respect to any mind; according to mind-to-body occasionalism the mind is not causally efficacious with respect to the body; last mind-to-mind occasionalism is the view that minds are not causally efficacious with respect to other minds. Garber argues that Descartes is what he calls a “quasi-occasionalist” in that he is committed to body-to-body and body-to-mind occasionalism, but not to mind-to-body occasionalism. See Daniel Garber, “Descartes and Occasionalism” in Causation in Early Modern Philosophy: Cartesianism, Occasionalism, and Preestablished Harmony. ed. Steven Nadler, (University Park, Pennsylvania: The Pennsylvania State University Press, 1993).

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kinds of substance, they are the attributes of one singular substance. Nevertheless,

Spinoza accepts the rejection of scholastic modes of explanation in favor of

mechanism.230 Specifically, he agrees that the basic ontology of the material world

consists only in matter and motion.231 Thus, in this respect Spinoza is in the same boat as

Descartes, and given that Spinoza is clearly committed to the causal efficacy of finite

modes, our challenge is determining how Spinoza accounts for the presence of force in

bodies.

Spinoza’s account of the causal efficacy of finite modes of extension is in some

respects astonishingly simple. We need to begin with Descartes’ reduction of the (real or

apparent) causal powers of a body to its tendency to persist in the same state. Descartes

writes in the Principles:

…we must be careful to note what it is that constitutes the power of any given body to act on, or resist the action of, another body. This power consists simply in the fact that everything tends, so far as it can, to persist in the same state, as laid down in our first law.232

A body’s active and passive causal powers are grounded in its inertial capacity, that is, its

tendency to persist in the same state. Given that Spinoza accepts this, the problem of

accounting for bodies’ causal efficacy reduces to accounting for their tendency to persist

in the same state. Spinoza offers just such an account in the Metaphysical Thoughts

appended to Descartes’ Principles of Philosophy. There Spinoza offers an argument

(familiar from chapter 3) that there is only a rational or conceptual distinction between a

230 See Ep.6 231 Certainly this takes a different form from Descartes’ account. Spinoza takes the basic ontology of the material world to consist in substance, as extended and its immediate infinite mode, motion-and-rest. 232 Principles II.43

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thing and the conatus by which it endeavors to persevere in its state. Here is that

argument:

To make this clear, let us take an example of a very simple thing. Motion has a force of persevering in its state; this force is really nothing other than the motion itself—that is, the nature of motion is such. For if I say that in this body, A, there is nothing but a certain quantity of motion, it follows clearly from this that, so long as I attend to A, I must always say that it is moving. For if I were to say that it was losing, of itself, its force of moving, I should necessarily have to attribute to it something else, besides what we have supposed in the hypothesis, through which it was losing its nature. (MT 1.6: C 314, S 188, G I 248)

In this passage Spinoza claims that the force a body possesses to persist in its own state is

nothing over and above the body’s motion. The second sentence tells us that if a body is

in motion, then it perseveres in that motion. He further claims that if a body, A, has a

certain quantity of motion, then it is moving. Given that Spinoza follows Descartes in

holding that force is identical to quantity of motion,233 Spinoza is adding that just as all

bodies in motion persevere in that motion, there is no force without motion. As such,

Spinoza is claiming that a body has force if and only if it has motion. However, as the

passage makes clear, Spinoza is claiming more than mere co-extension between motion

and force: he claims that the fact that a body in motion perseveres in its motion is part of

the nature of motion. This is synonymous with claiming that perseverance is part of the

essence of motion.234 As such, we can characterize Spinoza’s claim here (although

somewhat anachronistically) by saying that Spinoza denies a genuine distinction between

the kinematical and the dynamic: motion and force are only rationally distinct. The same

233 see DPP 2P22p 234 For Spinoza, to be part of the nature of x is equivalent to being part of the essence of x. For example, Spinoza writes in DPP 2P2 “The nature of Body, or Matter, consists in extension alone” (G 267, S151, G I 187). For Spinoza and Descartes the essence of matter is extension.

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goes for rest: rest is not the privation of motion, but something positive.235 Thus just as a

body in motion possesses a force to persevere in its state, so too does a body at rest. In

sum, Spinoza’s claim is that if a body is in motion or at rest, then it is causally efficacious

(with respect to bodies).236 Given that all bodies are in motion or rest (E2P13a1), it

follows that all bodies are causally efficacious. In sum, there is room in Spinoza’s basic

ontology of the material world for force insofar as the material world contains motion and

rest.237

Before turning to an examination of God’s power, I want to briefly discuss

Spinoza’s account of force in comparison to Descartes’. It seems fairly clear that

Spinoza is offering his own view of the matter in this passage, and not reporting his

account of Descartes’ view, since Descartes takes motion and its causes to be distinct. In

Principles II.25 where Descartes offers his definition of local motion he takes care to add

the following qualification: “I also say that it is a transference, not the force or action

which transfers, in order to show that this motion is always in the moving body and not in

the thing which moves it (because it is not usual to distinguish between these two with

sufficient care).”238 Indeed, Descartes had good reason for distinguishing the two.

According to Descartes, force or quantity of motion is something had by bodies at an

235 In Descartes see Principles II.27; Spinoza repeats this claim at DPP 2P22p 236 There is no trans-attribute causation according to Spinoza (E2P5-6). Thus, no mode of extension can be causally related to a mode of thought and vice versa. 237 Two comments: First, in Ep.59 Tschirnhaus asked Spinoza for “the true definition of motion, together with its explanation” (S 911, G IV 268). Unfortunately, Spinoza offered only a promissory note saying in Letter 60, “As for your other questions, namely, concerning motion, and those which concern method, since my views on these are not yet written out in due order, I reserve them for another occasion” (S 913, G IV 271) . Second, with regard to Spinoza’s claim that motion and force are rationally distinct, it is not clear to me that there is any precedent for this claim with the possible exception of Hobbes. See Thomas Hobbes, Metaphysical Writings, ed. Mary Whiton Calkins, (La Salle, Illinois: Open Court, 1989), 79-80 (De Corpore II.10.6). It is clear that Spinoza read Hobbes, however it isn’t clear if he had read De Corpore prior to having composed DPP.238 Principles II.25: MM, 51: AT VIIIA, 54.

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instant whereas this can’t be true of motion; Descartes writes in the Principles that “no

movment is accomplished in an instant; yet it is obvious that every moving body, at any

given moment in the course of its movement, is inclined to continue that movement in

some direction in a straight line…”239 However, this need not have been a concern for

Spinoza since on his account, time is not composed of instants.240

God’s Power

According to classical western theological tradition, God acts in the world above

and beyond His conservation, and He does so through His will. This is not how

Spinoza’s God acts: Spinoza’s God is not the sort of thing that has a will (E1P17s).

Given this, how does God act? How is God causally efficacious in the world? We would

expect an answer to this question to accompany Spinoza’s denial that God acts through

His will, and here is what Spinoza says:

…from God’s supreme power, or infinite nature, infinitely many things in infinitely many modes, i.e., all things have necessarily flowed, or always follow…So God’s omnipotence has been actual from eternity and will remain in the same actuality to eternity. (E1P17s: C 426, S 228, G II 62).

Spinoza’s answer here is fairly general, but I think a brief effort to clarify Spinoza’s

claim will have interpretive benefits later. Spinoza’s claim is that God is causally

efficacious in so far as the existence of everything flows from his nature and this fact is

sufficient for establishing that God’s omnipotence is eternally actual. Spinoza is clear

that God produces everything that is within his power.241 Given that “an infinity of

239 Principles II.39: MM, 60: AT VIIIA, 64. 240 See chapter 3. For a discussion of whether Descartes was a temporal atomist see Garber, Metaphysical Physics, 266-273 241 In EIP17 Spinoza argues against the view that God has a will, claiming that God’s possession of a will is inconsistent with his omnipotence. According to Spinoza to maintain that God has a will is to maintain that God can “bring it about that those things which we have said follow from his nature…should not come

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things in infinite ways—that is, everything” is within his power, God produces

everything. In other words, there is nothing outside of God’s power to produce, and so at

any given time, everything that can exist, does exist. 242 Thus, however God acts in the

world, his action is continuous insofar as it guarantees that at any time, everything that

can be, will be. E1P17 unfortunately does not give a specific account of God’s causal

activity. In order to determine how God acts, we’ll need to turn to Spinoza’s discussion

of the origins of motion.

In Part II of his Principles, Descartes explains the origins of motion saying “God

is the primary cause of motion”.243 God, on Descartes’ reckoning, is that which

ultimately accounts for the existence of motion in matter and the concomitant phenomena

we find in the world. Matter can never move itself; only an external cause can give

matter motion.244 Spinoza objected to Descartes’ conception of matter or extension

writing in a letter to Tschirnhaus:

Further from Extension as conceived by Descartes, to wit, an inert mass, it is not only difficult, as you say, but quite impossible to demonstrate the existence of bodies. For matter at rest, as far as in it lies, will continue to be at rest, and will not be set in motion except by a more powerful external cause. For this reason I have not hesitated on a previous occasion to affirm that Descartes’ principles of natural things are of no service, not to say quite wrong. (Ep. 81: S 956, G IV 332).

about.” Spinoza argues that if this is right, then God can’t be omnipotent. Thus, Spinoza interprets God’s omnipotence in terms of the production of all that can be produced. See also E1P35 and proof. 242 Here is a worry: suppose I turned left at t1, but I very well might have turned right. God couldn’t have created the world such that at t1 I turned both left and right, thus God can’t have produced everything that is possible at any given time. However, Spinoza’s position is coherent insofar as for any given time there is exactly one possible state of the universe, that is, it isn’t true that at t1 you might have turned either left or right. 243 Principles II.36 244 Descartes writes in response to Henry More’s query: “I agree that ‘if matter is left to itself and receives no impulse from anywhere’ it will remain entirely still. But it receives an impulse from God, who preserves the same amount of motion or transfer in it as he placed in it at the beginning” CSM III, 381: AT V, 404. With respect to the variety of bodies and properties see Principles II.23.

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This is not a criticism of Descartes’ metaphysic itself, since for Descartes, God is the

powerful external cause which accounts for the existence of motion.245 Rather, Spinoza

is criticizing Descartes’ account of extension relative to his own commitment to the

denial of a transcendent God. Spinoza is committed to the following theses:

1) There is nothing external to matter and a fortiori, God isn’t something external to matter.246

2) There is variation of matter.247 3) The variety in nature is ultimately due to variations in the motions of matter.248

The conjunction of these three theses is inconsistent with Descartes’ conception of matter

as static or inert. Here’s why: if Descartes’ conception of matter is correct and it is inert,

then it is incapable of self-motion. But given 2) and 3) matter is in motion. Since matter

can’t have put itself into motion, it must have been put into motion by something external

to itself. But given 1) it can’t have been put into motion by anything external to it, and as

such can’t have motion.249 For this reason, Spinoza rejects Descartes’ account of matter.

245 Strictly speaking, God is the cause of both motion and rest. Rest is not the privation of motion, but is a positive state itself. Given Descartes view that whether a body is in motion or at rest is a matter of one’s frame of reference, in accounting for motion, one simultaneously accounts for rest. Descartes and Spinoza regularly use the term ‘motion’ to refer to both motion and rest, and for ease of presentation I will follow their lead. 246 Spinoza writes “there can be no substance external to God; that is, a thing which is in itself external to God” (E1P18p). Given that the relation ‘being external to’ is symmetric and that extension (matter) is an attribute which expresses the essence of God, it is accurate to say that there is nothing which is in itself external to matter. 247 The following passage confirms not only this particular thesis, but my analysis of it: “The further objection may be made, however, that there must necessarily be a first cause which makes this body move; for when it is at rest, it cannot possibly move itself. And since it is clear that there is motion and rest in Nature, these must, they think, come from an external cause. But it is easy for us to answer this. for we grant that if body were a thing existing through itself, and had no other property than length, breadth, and depth, then if it really were at rest, there would be no cause in it for it to begin to move itself…” (ST 1.2: C 72, S 45, G I 26-27). 248 That Spinoza agrees with Descartes that the variety in nature is ultimately due to motion and rest can be seen from the following passage: “Each and every particular thing that comes to exist becomes such through motion and rest…The differences between [one body and another] arise only from the different proportions of motion and rest, by which this one is so, and not so, is this and not that” (ST 2.1: C 95, S 60, G I 52). As we saw in chapter 4 Spinoza accounts for the existence of bodies using motion whereas Descartes does not. 249 The principle of sufficient reason is being assumed. This is an assumption underlying all of Spinoza’s

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However, this leaves a problem; Spinoza needs to explain the existence of motion, and

concomitantly the existence of the variety of bodies present in the world, without

reference to an external cause. Spinoza offers the following solution to this problem:

“Descartes is wrong in defining matter through Extension; it must necessarily be

explicated through an attribute which expresses eternal and infinite essence” (Ep.83).

Spinoza’s solution to this problem, despite what he seems to say, is not to deny that

matter is extended. Rather it is to claim that matter is both extended and the source of its

own motion. That is, Spinoza denies that matter requires a cause outside of itself to

explain the existence of motion.250 However, in order to see that this is right, we’ll need

to first determine what Spinoza means by “eternal and infinite essence”.

Spinoza seems to take power and essence as somehow equivalent, since E1P34

tells us that “God’s power is his essence itself” (C 439, S 238, G II 76); furthermore we

are told at E3P7p that “the power of each thing…is nothing but the given, or actual,

essence of the thing itself” (C 499, S 283, G II 146). Hence, there is good reason to think

that for an attribute to express eternal and infinite essence is to express eternal and

infinite power. What is it to express eternal and infinite power? Spinoza tells us that

“from the necessity alone of God’s essence it follows that God is the cause of himself and

of all things” (E1P34: C 439, S 238, G II 77). Given that power and essence are

equivalent and that God expresses eternal and infinite power, it follows that to express

eternal and infinite power is to be self-caused and the cause of all things.

work. 250 This account of the origins of motion was certainly nothing new. Consider the following passage from Boyle’s Origin of Forms and Qualities: “That there is local motion in many parts of matter is manifest to sense, but how matter came by this motion was of old, and is till hotly disputed of. For the ancient Corpusclarian philosophers…not acknowledging an Author of the universe, were thereby reduced to make motion congenite to matter and consequently coeval with it.” See Boyle, Works vol. 5, 306.

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On its face, this is problematic. First, Spinoza has told us that the attributes

“express eternal and infinite essence” and we’ve just seen that to express eternal and

infinite essence is to be self-caused and the cause of all things. But the attributes are not

self-caused, rather they are expressions of God’s essence; they are dependent on God.

Second, if the attributes are the cause of all things and every finite mode is included in

the scope of ‘all things’, then Spinoza is committed to the existence of causal relations

between the attribute of extension and finite modes of thought. Likewise, he is

committed to the existence of causal relations between the attribute of thought and finite

modes of extension. But, Spinoza denies both of these possibilities (E2P6). Thus,

despite what Spinoza says, it isn’t clear that he can consistently maintain that the

attributes express eternal and infinite essence.

We can resolve this tension if we take care to notice that Spinoza is working with

two senses of ‘infinite’. Spinoza distinguishes between the absolute infinity of God

(E1d6) and the kind-relative infinity of the attributes (E1P10s). He explains on the first

page of the Ethics that “if something is only infinite in its own kind, we can deny infinite

attributes of it; but if something is absolutely infinite, whatever expresses essence and

involves no negation pertains to its essence” (E1d6exp: C 409, S 217, G II 46). Given

this distinction, Spinoza can consistently maintain that the attributes are infinite and

eternal but dependent on God insofar as the attributes are infinite in kind. Likewise,

Spinoza is not forced to claim that in virtue of the fact that the attributes are infinite, they

are causally related to all modes of every attribute. So, when Spinoza claims that the

attributes express eternal and infinite essence we can read him as maintaining only that

the attributes are “the cause of all things”.

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The issue at hand is determining how Spinoza accounts for the presence of motion

in matter without appealing to a source of motion outside of matter itself. As we’ve seen

Spinoza says that matter (the attribute of extension) expresses eternal and infinite

essence. I have shown that to express eternal and infinite essence is to be self-caused and

the cause of all things. This leaves one question: how does being self-caused and the

cause of all things, explain the origin of motion. In short, what does it mean to be “the

cause of all things”? Recall that God is the cause of all things following from his infinite

power, that is, his omnipotence. As we’ve seen Spinoza interprets omnipotence not

merely as the ability to do everything that can be done, but the manifestation of this

ability. Thus, for an attribute to express eternal and infinite essence is for it to produce

every mode of that attribute that can be produced at any given time. This account of

expressing eternal and infinite essence corresponds nicely with Spinoza’s claim in the

Short Treatise that “we have posited above that Nature is a being of which all attributes

are predicated. This being so, nothing can be lacking to it to produce everything there is

to produce” (ST 1.2: C 72-73, S 45, G I 27). As such, the attribute of extension is the

cause of all extended things and the attribute of thought is the cause of all thinking

things.251 But this still doesn’t answer our original question. We need to know how the

attributes are causally efficacious. Perhaps more to the point, we need to know how

extension is causally efficacious.

Extension is causally efficacious through its immediate infinite mode(s), and

more generally, every attribute is causally efficacious through its immediate infinite

mode(s). First, recall that the existence of the immediate infinite modes follows from “the

251 Given that God consists of all the attributes (E1d6), only God is the cause of all things tout court.

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absolute nature of some attribute of God” (E1P23). Hence, the existence of the

immediate infinite mode of extension follows from the absolute nature of extension.

Second, it is clear that the infinite modes are causally efficacious:

…indeed, these singular, changeable, things depend so intimately, and (so to speak) essentially, on the fixed things that they can neither be nor be conceived without them. So although these fixed and eternal things are singular, nevertheless, because of their presence everywhere, and most extensive power,they will be to us like universals, or genera of the definitions of singular, changeable things, and the proximate causes of all things. (TEI 101: C 41, S 27, G II 37; my italics)

By ‘fixed and eternal things’ Spinoza means the infinite modes, and so, it is through the

immediate infinite mode of extension that matter is the cause of all things.252 Given that

the infinite modes are infinite, eternal, and causally efficacious, they fill the role of God’s

activity, since this action is continuous and guarantees that at any time, everything that

can be, will be. Last, Spinoza, in Ep. 64, refers to the immediate infinite mode of

extension as ‘motion-and-rest’. Extension is causally efficacious—it produces every

mode of extension that can be produced—through the immediate infinite mode of

extension: motion-and-rest. More generally, God’s action in the world consists in

simultaneously accounting for the existence of motion and the concomitant existence of

variety in the material world, through motion-and-rest.

As we’ve seen, in rejecting the existence of a transcendent God, Spinoza is left

with the problem of accounting for the motion present in matter. Spinoza’s claim that

matter must be explained through an attribute that expresses eternal and infinite essence

resolves this problem by replacing the Cartesian account of matter as inert with an

account of matter according to which it is the source of its own motion. Matter, that is,

252 Curley, Spinoza’s Metaphysics, 67-68.

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extension, is capable of producing all possible modes through the immediate infinite

mode of extension (motion-and-rest), the existence of which follows from the absolute

nature of extension itself. At this point I will turn to the question of how these two

agencies cooperate to produce finite effects.

How God Cooperates with Secondary Causes

In considering how Spinoza explains God’s cooperation, I again want to turn to

the scholastics to see how tradition answered this question. I’ll focus on Aquinas and

show that there are good reasons to think that Spinoza’s account of God’s concurrence

with finite modes follows the general model espoused by Aquinas. According to

Aquinas, in order to account for God’s concurrence with a fire’s transformation of wood

into ash, we need to consider the source of the power by which the fire causes this effect.

The power by which a secondary cause acts is not its own: “no lower agents give being

except in so far as they act by divine power”.253 Thus the power that fire has to transform

wood into ash is God’s power. But if this is right, how can we claim that the fire is

genuinely causally efficacious? The answer to this question lies in how secondary agents

manifest God’s power. Aquinas explains that “being is the proper effect of the primary

agent, and all other things produce being because they act through the power of the

primary agent. Now, secondary agents, which are like particularizers and determinants of

the primary agent’s action, produce as their proper effects other perfections which

determine being”.254 We can look at this cooperation between God and creature from

two sides. From the viewpoint of the cause, God contributes the power by which the

253 St. Thomas Aquinas, Summa Contra Gentiles: Providence, Part I, trans. Anton C. Pegis (Garden City, New York: Hanover House, 1956), 218 (SCG III.2.66.1). 254 Ibid., 219 (SCG III.2.66.6).

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creature is able to produce the effect. From the viewpoint of the effect, we can

distinguish two features of the effect: that the effect exists is traced back to God; that the

effect exists as such is traced back to the secondary cause.255 For example, the

explanation for the fact that the fire produces an effect lies in God’s power; that the fire

produces this effect lies in the fire.

Spinoza’s account is strikingly similar; it is clear that the power by which finite

modes exist, persist, and act is not their own. First, Spinoza characterizes finite modes

themselves as determinations of God’s power. At E3P6p Spinoza writes: “singular things

are modes…i.e. things that express, in a certain and determinate way, God’s power, by

which God is and acts” (C 499, S 283, G II 146). Second, the power Spinoza ascribes to

finite modes to persist is not their own. He tells us “The power by which singular things

(and consequently, [any] man) preserve their being is the power itself of God, or Nature,

not insofar as it is infinite, but insofar as it can be explained through the man’s actual

essence” (E4P4p: C 548-549, S 324, G II 213). Last, it is clear that in addition to existing

and persisting through God’s power, finite modes act through his power: at E1P34

Spinoza concludes that “God’s power, by which he and all things are and act, is his

essence itself” (C 439, S 238, G II 77). Thus when a finite mode comes to be, persists,

and acts, it does so through God’s power. Furthermore it is clear that finite modes

determine God’s power. God’s power is infinite and so if finite modes do not determine

or particularize God’s power, then the power of finite modes is itself infinite. But this

isn’t right (E4P3), and so, the power according to which finites modes exist, persist, and

act must be a particular determination of God’s power. Thus, there are thus good reasons

255 Freddoso, “Pitfalls”; also see his introduction to On Creation, Conservation, and Concurrence, xcvi ff.

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for thinking that Spinoza adopts a Thomistic model of concurrence. In what follows I will

reconstruct Spinoza’s account of the cooperation of God with finite modes along these

lines.

In thinking about how God causes finite modes, perhaps it is best to start with a

paradigm instance of body-to-body causation. Consider two simple bodies: A and B.

Body A is in motion towards B and is twice the size of B, whereas B is at rest.

According to Descartes’ rules of impact (specifically Rule 5) if A directly collides with

B, then after the collision B will move at the same speed as A and in the same direction

as A. Let’s focus on B. In colliding with B, A caused B to change from a state of rest

relative to its surroundings to a state of motion. As we’ve seen Spinoza tells us that “A

thing which has been determined to produce an effect has necessarily been determined in

this way by God” (E1P26: C 431, S 232, G II 68). God is not a finite body. So, how is

God causally efficacious in A’s causing B?

We can explain God's causal efficacy by distinguishing between two features of

the effect. Let's start with the obvious source of B's motion: A. A's collision with B

causes B to move; however, the particular motion that led A to collide with B was itself

impressed on A. That is, there was some other body (or set of bodies), Z, that caused A to

have the particular motion that ultimately led to A's collision with B. In fact, every

particular motion is the effect of a distinct finite cause. As Spinoza well knew, this leads

to an infinite regress. Recall Spinoza's claim in E1P28 that "…any thing which is

finite...can neither exist nor be determined to produce an effect unless it is determined to

exist and to produce an effect by another cause...this cause also can neither exist nor be

determined to produce an effect unless it is determined to exist and produce an effect by

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another…and so on, to infinity” (C 432, S 233, G II 69). Further, no finite mode can

cause motion or rest in itself (E1P26-27); that is, no mode is a self-mover.256 While finite

modes are actively and passively causally efficacious, they cannot initiate change in the

way that contemporary libertarians might claim that agent causes can. However, if no

body can initiate motion or rest in itself, then no body can explain the existence of motion

or rest in general. While the explanation for any body's particular motion lies in its most

recent collision, the explanation for the existence of motion itself and rest itself cannot lie

in any body. What accounts for, or explains the existence of motion and rest in

general?257 In short, God. As we've seen, God is causally efficacious in the attribute of

extension through the immediate infinite mode of extension, motion-and-rest. I have

argued that 'motion-and-rest' refers to the property extension has of being always and

everywhere in a state of motion or rest.258 It is the immediate infinite mode of extension

that accounts for the existence of motion and rest and simultaneously it is through this

infinite mode that God is causally efficacious in the realm of finite modes.

At this point we can begin to make sense of the cooperation between God and

finite modes. Let’s start from the perspective of the effect: if we distinguish between B's

motion in general, i.e. the fact that B has motion at all, and B's particular motion, i.e. the

fact that B is moving with this speed in this direction, we can explain God's causal role.

God is the cause of B's motion in general insofar as he is the cause of all motion and rest

in the universe. A is the cause of B's particular motion since it is because A had the size

256 This is the basis of Spinoza's denial of freedom to humans: no man "has absolute power over his actions, and that he is determined only by himself” (E3 Preface: C 491, S 277, G II 137). 257 Spinoza is not Hume in that he doesn’t think that the fact that every member of an infinite causal series has a finite cause thereby explains the series itself. See Ep.12. 258 See Chapter 3.

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and vector it did, that B gained the particular motion it did. Thus just as the scholastic

concurrentists would trace the being of the effect back to God and the being as-such back

to the creature, so too we can see Spinoza’s concurrentism as tracing the existence of

motion back to God and the existence of motion-as-such back to a distinct finite mode.

This cooperation can also be understood from the perspective of the united cause. Recall

that on the Thomist model, creatures cooperate with God insofar as it is through His

power that they are able to act. As we’ve seen, a body’s causal efficacy is grounded in its

inertia which is only rationally distinct from its motion/rest. In accounting for the

existence of motion/rest, God simultaneously accounts for the causal efficacy of all

bodies. Thus, on Spinoza’s account, finite modes are causally efficacious only in virtue

of God.

In grounding the existence of motion, not only does God simultaneously ground

the causal efficacy of bodies, but also the laws of nature. As we’ve seen, in DPP Spinoza

argues that force is only rationally distinct from motion. The rest of this passage contains

an indirect argument for this conclusion. What is interesting is how he sets up the

argument. He writes: “If this reasoning seems somewhat obscure, let us concede that that

striving to move itself is something beyond the laws themselves and nature of motion” (C

314, S 188, G I 248). Not only is the conatus to motion (force) part of the nature of

motion, but so are the laws of motion. Elsewhere Spinoza describes the laws of nature as

“inscribed in” the infinite modes.259 These passages suggest that for Spinoza, the laws of

nature are reducible to the natures of things. Since the variety of properties and objects in 259 TEI 101: C 41, S 27, G II 37. Strictly speaking Spinoza says that the laws of nature are “inscribed in the fixed and eternal things”. There has been some scholarly dispute concerning the referent of ‘fixed and eternal things’, see e.g. Mason (1992). However, it seems clear that Spinoza means the infinite modes. See Curley, Spinoza’s Metaphysics, and Behind the Geometrical Method.

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the world are reducible to matter in motion, the only real laws of nature are the laws of

motion. These laws, then, are reducible to the nature of motion itself: bodies always

move in the ways they do because motion has a nature that dictates certain effects given

certain causes. Thus, God’s contribution to the action of finite modes consists not only in

the power to act, but also in dictating the parameters of action.

Conclusion

I have argued that there are good reasons for thinking that Spinoza is a concurrentist. In

so doing, I have shown how Spinoza is able to maintain that bodies are causally

efficacious and precisely how God is causally related to the realm of finite modes. We

are now in a position to understand why Spinoza’s account of God’s causal activity takes

the form of the D-N model of explanation. As we’ve seen, on my reconstruction of

Spinoza’s concurrentism, God cooperates with the activity of finite modes insofar as he

guarantees the continued existence of motion.260 God accounts for both the existence and

nature of motion, and it follows from the nature of motion and rest that the subjects of

motion move according to particular patterns, that is, they follow particular laws. Thus,

given Spinoza’s account of concurrence, it is accurate to say that at any given time God is

causally efficacious through the laws of nature. This feature of Spinoza’s concurrence

dovetails perfectly with Curley’s interpretation of God’s causal activity according to

Spinoza. Recall that according to this view, the existence and activity of finite modes

follow from the antecedent state of the world (finite modes) and the laws of nature (God).

Thus, this interpretation picks up right where my account of Spinoza’s concurrentism

260 Recall, that the same goes for rest. Rest is not the privation of motion; it is a state in its own right.

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leaves off, and I take it as confirming evidence that my account of Spinoza’s

concurrentism fits so well with Curley’s interpretation of Spinoza’s divine causality.

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1993.

VITA

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VITA

Thaddeus Robinson

Purdue University Department of Philosophy 100 N. University St. West Lafayette, IN 47907-2098 Office Phone: 765-496-3277

Home: 625 S. 10th St. Lafayette, IN 47905 Home Phone: 765-742-0537 Cell: 217-553-6022 Email:robinsts@purdue.edu

Education

2002-2007

Ph.D. Purdue University (August 2007) Dissertation: Spinoza and the Metaphysics of Mechanism Chair: J. A. Cover

2000-2002 1994-1998

M.A. Northern Illinois University (Philosophy) B.A. Luther College (Philosophy and History)

Areas of Specialization

Early Modern Philosophy; Metaphysics

Areas of Teaching Competence

Ethics; Ancient Philosophy; Medieval Philosophy; Logic; Critical Thinking

Papers Presented

“Motion in the Whole: Spinoza’s Infinite Mode of Extension”, Central Division Meeting of the American Philosophical Association; Chicago, April 2007. “Comments on Chris Martin, ‘The Doctrine of Ideas of Ideas’”, Indiana Philosophical Association; Marian College, April 2006. “Comments on Christopher Yates, ‘Absolute and A Priori: Kant, Space, and the Problem of Incongruent Counterparts’”, Midsouth Philosophy Conference; University of Memphis, February 2006.

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“Spinoza’s Infinite Mode of Extension”, Midsouth Philosophy Conference; University of Memphis, February 2006. “Spinoza’s Vacuum Argument and the Inconsistency of Descartes’ Metaphysic of Body”, Central States Philosophical Association; University of Kentucky, October 2005. “Comments on Peter Le Grant, ‘A Defense of Spinoza’s Account of Error Against Bennett’s Attacks’”, Midsouth Philosophy Conference; University of Memphis, February 2005. “Spinoza and the Indivisibility of Corporeal Substance”, Midsouth Philosophy Conference; University of Memphis, February 2005.

Honors

Purdue Summer Research Fellowship (Summer 2006) Purdue Summer Research Fellowship (Summer 2005)

Teaching Experience Instructor:

Introduction to Philosophy (Fall 2004, 2 sections; Spring 2005, 2 sections) Introduction to Ethics (Summer 2004; Fall 2005, 2 sections; Sp. 2006, 2 sections) Critical Thinking (Fall 2006, 2 sections) Symbolic Logic (Spring 2007, 2 sections)

Teaching Assistant:Symbolic Logic (Spring 2002) Philosophy of Religion (Fall 2002) Religions of the West (Fall 2003) Introduction to Philosophy (Fall 2000, Spring 2003 ) Introduction to Ethics (Spring 2001, Fall 2001, Spring 2004)

Professional Service

Graduate Student Representative: 2005-2006, 2006-2007 College of Liberal Arts Grade Appeals Committee

Professional Memberships

American Philosophical Association North American Spinoza Society Indiana Philosophical Association

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Languages

Latin (reading) French (reading)

Graduate Coursework Ancient and Medieval Philosophy

Plato Aristotle Aristotle on Substance Medieval Philosophy: Aquinas Medieval Theories of Material

Substance

James Dye, NIU James Dye, NIU Patricia Curd, Purdue Jeffrey Brower, Purdue Jeffrey Brower, Purdue

Modern Philosophy

Rationalists Early Modern Theories of Causation Spinoza 18th Century Enlightenment Hume Hume Kant Kant

J. A. Cover, Purdue J. A. Cover, Purdue Dan Smith, Purdue James Dye, NIU James King, NIU Michael Jacovides, Purdue James Dye, NIU Jacqueline Mariña, Purdue

Philosophy of Language and Logic

Philosophy of Language Philosophy of Language Intermediate Logic Intermediate Logic

Tomis Kapitan, NIU Rod Bertolet, Purdue David Buller, NIU Dolph Ulrich, Purdue

Philosophy of Religion and Ethics

Philosophy of Religion Philosophy of Religion Contemporary Ethical Theory

William Rowe, Purdue Jacqueline Mariña, Purdue Pat Kain, Purdue

Metaphysics and Philosophy of Science

Philosophy of Science Metaphysics

H. I. Brown, NIU Tomis Kapitan, NIU

19th and 20th Century

20th Century Analytic Philosophy Early Analytic Philosophy Nietzsche

Larry Poncinie, NIU Chris Pincock, Purdue Dan Smith, Purdue

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References Jeffrey Brower J. A. Cover Patricia Curd Michael Jacovides Chris Pincock (teaching letter)

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