Spinoza's Account of Composition - John R. T. Grey

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BOSTON UNIVERSITYGRADUATE SCHOOL OF ARTS AND SCIENCES

Dissertation

SPINOZA'S ACCOUNT OF COMPOSITION

by

JOHN R. T. GREYB.A., University of Minnesota, 2006

Submitted in partial fulfillment of therequirements for the degree of

Doctor of Philosophy2012


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Copyright byJOHN R. T. GREY2012


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Approved by

First ReaderK

Aaron Garrett, Ph.D.Associate Professor o f PhilosophyBoston University

Second ReaderDavid Licbesinan. Ph.D.Assistant Professor o f PliilosopliyBoston University

Third ReaderMichael Delia Rocea, Ph.D.Professor of PhilosophyYale University


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DEDICATION

to Sarah Grey,sine qua non

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AcknowledgmentsWhile composing this dissertation, I received a great deal of guidance from my

committee, without which the work would be much impoverished. Aaron Garrettintroduced me to Spinoza during my first year of graduate school. His passionatediscussions of the Early Moderns initiated my interest inthe history of philosophy, andI greatly appreciated his continued support and feedback while writing this workinspite of his claim to be a "lapsed Spinozist." Dave Liebesman provided extensivesuggestions for each chapter, leading in most cases to serious revision and (I think) aphilosophically stronger view overall. Michael Delia Rocca likewise gave me numeroussuggestions for each chapter, along with far more of his time than I had any rightto ask. Perhaps it goes without saying that his challenging but invigorating work onSpinoza is the central reason that I chose to research this topic; I'll say it anyway.

A number of friends and colleagues gave me feedback on various sections. Thanksto Alex Silverman, Amelie Rorty, and the proseminar gang, who offered very helpfulcriticism on what are now Chapters 2 and 3.

I want to thank my wife, Sarah Grey, to whom this dissertation is dedicated. Shehas been patient, kind, and supportive throughout the entire process of writing andrevising the work.

Finally, I want to thank my family, especially Kathryn, Sam, and Hugh Tietze.My father, Thomas Tietze, passed away while I was writing the first draft of thisdissertation, and without my family's encouragement it is probable that I never wouldhave completed it.

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SPINOZA'S ACCOUNT OF COMPOSITION(Order No. )JOHN R. T. GREY

Boston University, Graduate School of Arts and Sciences, 2012Major Advisor: Aaron Garrett, Associate Professor of Philosophy

ABSTRACT

The aim of the dissertation is to develop and defend a new interpretation ofSpinoza's metaphysics of individuals, focusing on his account of the conditions underwhich several things compose one.

Spinoza's discussion of composition in the Ethics focuses on complex bodies, soChapter 1 provides an interpretation of Spinoza's physics in order to lay the groundwork for interpreting his metaphysics. Although it may appear that Spinoza's physicsis of the same stripe as the mechanical physical theories endorsed by Hobbes andDescartes, his claims about the power of finite bodies suggest that his physical theoryis dynamic rather than mechanistic. Using that discussion of the physics of complexindividuals as background, Chapter 2 presents an argument that Spinoza reducescomposition to a certain causal relation among an individual's parts (their "pattern"[ratio] of causal relations), and that particular individuals are tokens of this causalrelation. This conception of the part-whole relation explains Spinoza's account ofpersistence while preserving the intuition that wholes depend upon their parts. Toclarify the central thesis of Spinoza's account, Chapter 3 fleshes out the notion ofa pattern of causal relations. The pattern of causal relations among an individual'sparts is what generates and explains that individual's causal powers.

Having established the central claims of Spinoza's account of composition, Chap


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ter 4 contains a series of arguments intended to motivate that account. Thereare several plausible metaphysical principles that most rival contemporary accountsof compositionuniversalism, nihilism, organicism, and several othersfail to satisfy. Spinoza's account does satisfy those principles; other things being equal, then,Spinoza's account is preferable to these contemporary alternatives. Finally, Chapter5 considers a possible reply to the strongest principled argument against Spinoza'sview, the argument from vagueness. Although the notion of a "pattern" of causalrelations seems vague, Spinoza can appeal to the causal powers generated by suchpatterns in order to provide a principled cutoff between patterns and non-patterns.Spinoza's metaphysics of composition, then, is as good as, or better than, the viewschampioned by contemporary metaphysicians. Although Spinoza's view has beenlargely ignored, it remains viable even today.

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Contents

Contents viiiIntroduction 11 Spinoza's Physics of Individuals 9

1.1 The purported mechanical influence 111.1.1 Hobbes' physics 131.1.2 Descartes' physics 181.1.3 The Alternative 27

2 Spinoza's Account of Composition 292.1 Spinoza on Composition 322.2 Consequences ; Further Questions 44

3 Patterns and Powers 563.1 A Powers-Based Account of Patterns of Causal Relations 57

3.1.1 The Case for Necessity 583.1.2 The Case for Sufficiency 65

3.2 The Composition of the Mind 723.3 Conatus and the Power of a Composite 76

4 Defending the Account 874.1 What Composition Could Not Be 884.2 What Composition Is 1074.3 In Defense of Spinoza's Account of Composition Ill


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5 Spinoza on Vagueness and Degrees of Composition 1285.1 The Argument from Vagueness 1295.2 Composition by Degrees 144

Conclusion 156Bibliography 164

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IntroductionThis dissertation provides a detailed examination and philosophical defense of

Spinoza's metaphysics of compositionof when and why several things compose onewhole. Although the topic appears obscure, it has subtle connections with manyand varied parts of his philosophical system. The reason for this is that Spinoza'sEthics is, at the end of the day, a treatise about how human beings ought to live.For a rationalist like Spinoza, the first question that must be answered before wecan determine how human beings ought to live is, what is a human being? Andone of Spinoza's answers to that question is that a human being is a highly compositeindividual If we want to understand Spinoza's work, then, we will want to understandhis account of composition.

Spinoza's account of composition can be summarized very briefly indeed: severalindividuals compose asingle complex whole if and only if those individuals instantiatea pattern of causal relations. The precise meaning of "a pattern of causal relations"has of course to be filled out, but already some interesting consequences of the account can be observed. It is not necessarily the case that given several individuals,they compose a single complex individual. Nor is it the case that the only complexindividuals are living organisms. Nor is it the case that whether several individualscompose a complex whole is merely a linguistic matter, or a question of how we (arbitrarily) restrict (or relax) our quantifiers.1 Composition, on Spinoza's view, reducesto certain structures of efficient causation.

As I will argue, Spinoza's way of reducing composition to causal relations is highly1At least not on the assumption that causal relations are not figments of language. I mention

these examples because theydistinguish Spinoza's account from its leading competitors.


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original, and it does not deserve to be ignored by contemporary philosophers. Beforemaking my case, however, it will be useful for me to make clear the way in whichaccounts of composition, individuation, and persistence are logically connected (orunconnected, as the case may be). Many commentators have considered Spinoza'saccounts of individuation and persistence, and it may not at first be clear what morecould be added to these discussions. However, though his approaches to these threeproblems are related, they are in fact logically distinct. The merits and flaws ofSpinoza's approach to any one of these problems need not extend to the others.

An account of individuation cannot rely upon an account of composition or ofpersistence. In order to explain the composition or persistence of a given individual,we must already be able to distinguish that individual from all others. By contrast, anaccount of persistence depends upon our having already provided an account of bothindividuation (so we can pick out the individuals whose persistence is to be accountedfor) and of composition (so we know the nature of the complex individuals that areto be accounted for). However, the way in which we account for individuation andcomposition does not determine the way in which we must account for persistence.Neither does the way in which we account for persistence determine the way in whichwe must account for individuation or composition.2

Therefore in developing an account of composition, we are in the following logicalposition. W e must assume that we have some way of individuating one thing fromanother. But what answer we give to the problem of individuation will not impactour account of composition, so long as there is an answer, and that answer tracks ourintuitions, at least roughly. (The point about tracking our intuitions is more important than it might seem. If Spinoza were to say that there is no correct metaphysical

2Admittedly, the intuitions that lead you to endorsea certain account of persistence will almostcertainly lead you toendorse certain accounts of individuation and composition. But no interestinglogical entailment relations hold among the three sorts of account.


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principle of individuation, and hence no correct way of divvying up the world intodistinct individuals, it would be a waste of time to inquire into the metaphysics ofcomplex individuals. Fortunately, Spinoza doesnot say this.) Further, we may whollyignore the problem of persistence, for whether several individuals compose a complexwhole is logically independent of whether that complex whole, if it exists, persiststhrough any particular change.

Although Spinoza appears to run.these three problems together, then, we canconsider his solution to any one of them as distinct from his solutions to the others. Iwill at various points consider some of the secondary literature on Spinoza's accountsof individuation and persistence, but by and large this commentary will not be usefulto understanding his account of composition. Far more useful, and more frequentlydiscussed, will be the secondary literature on Spinoza's conceptions of causal power,existence, and essence. Spinoza's views here lead to several important theses thatshape his account of composition.

That having been said, the argument of this dissertation will proceed in the following way. In Chapter 1, I outline the general picture of Spinoza's philosophythat I take as background for the project. Spinoza's physics in particular is of central importance to my project, for it is one of the few places where he expresses hisviews about composition. The key properties and relations governing his notion ofa composite individual are physical; he appeals to undefined conceptions of motion,rest, and the communication of motions. What does Spinoza have in mind whenhe uses these terms? Contrary to much of the scholarly literature on this topic, Iargue that Spinoza does not simply take up Descartes' (or Hobbes') versions of thesenotions. By the time Spinoza was writing the Ethics, he had already expressed inhis correspondence grave doubts about the standard mechanistic theories of physics.Instead, I argue, Spinoza's physics should be seen as a kind of schematic intended


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to solve the problems of material composition and persistence regardless of potentialnew developments in physics.

In Chapter 2, I hone in on the relation that I think is doing the real work inSpinoza's account, the communication of motions "in a certain fixed manner [certaquadam ratione]." After working through several translations of the Latin, I arguethat what Spinoza has in mind here is best understood asa pattern of causal relations.This is the basis for Spinoza's solution to the problem of composition. The parts ofa table bear a particular pattern of causal relations to one another, in virtue ofwhich we say that those parts compose the table. The pattern of causal relationsis supposed to explain how the parts compose a whole. I then appeal to this initialsketch of Spinoza's account of composition to answer two further questions about themetaphysics of composition. First, I consider whether Spinoza takes a whole to beidentical with its parts. I argue that he does not, and that he instead takes a whole tobe identical with the pattern of causal relations among its parts. Second, I considerwhether Spinoza takes a whole to be prior to its parts. I argue, again, that he doesnot, and that he instead upholds a standard conception of parthood on which partsare prior to their whole.

In Chapter 3,1 work out a detailed interpretation of what Spinoza must mean bya pattern ("rafzo") of causal relations. Although it is easy to see how his account ofcomposition could explain why, e.g., the table top and legs compose an individual, itis difficult to see how the account can avoid absurditywhy don't two people shakinghands also stand in a pattern of causal relations? What relevant difference is therebetween these two cases? I propose that Spinoza can draw a sharp line between thesetwo cases by appealing to his view that everything that exists has some causal power.As I argue, several things compose an individual just in case the causal relationsamong those things ground some further causal power. The table top and legs are


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joined in such a way that their interaction grounds causal powers distinct from thecausal powers of the parts taken singly (the power to hold dinner plates off the floor,for instance). Two people shaking hands, by contrast, seem to fail this test: theydon't, in virtue of their interaction, ground any further power. Hence there is noreason to posit the existence of their composite. After fleshing out this view, I applyit to two other aspects of Spinoza's metaphysics, his philosophy of mind and hisconatus doctrine.

In Chapter 4,1consider a variety of rival accounts of composition, both contemporary and historical. Leibniz, for example, develops the claim that several distinctthings compose an individual only if the individual is a living organism. More recently, a number of prominent philosophers have argued that, contrary to intuition,every collection of distinct objects composes an individual. I first show why Spinozamust reject these views by highlighting the ways in which they conflict with certainof his metaphysical principles. Then I outline some reasons for thinking that thosemetaphysical principles are true, and that we too should reject these rival accounts.Finally, I attempt to provide some independent motivation for the account I attributeto Spinozaindependent, that is, of Spinoza's own reasons for adopting it.

Finally, in Chapter 5, I consider the strongest contemporary argument againstSpinoza's account, the argument from vagueness. The argument purports to showthat any moderate account of compositionthat is, any account that (like Spinoza's)claims that certain conditions must be met in order for several individuals to composea complex wholewill imply the possibility of vague existence. The idea is thatif there are any conditions on composition, these conditions must be met in orderthat a given complex whole exists. But for any conditions whatever, there will bea possible scenario in which it is vague whether those conditions are met. So ifthere are any conditions on composition whatever, it is possible for existence to be


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vague. Spinoza would not countenance vague existence, but that doesn't mean hemust capitulate. I show that Spinoza can resist the argument from vagueness byappealing to principled sharp cutoffs: there will never be a possible scenario in whichit is vague whether Spinoza's conditions on composition are met, though there will besome extremely similar scenarios that differ with respect to composition. However,those extremely similar scenarios will also always differ with respect to the causalrelations they involve, a difference that is relevant to composition.

That is the plan of the work. Before proceeding with my argument, however,let me say a few words about methodology. This is a work of history of philosophy,and during the past fifty years or so there have been some shifts in how the projectof history of philosophy is understood. The conflict is this: When considering theworks of a historical figure like Spinoza, do we isolate his axguments and tear intothem using the best of our current analytical tools? Or do we instead try patientlyto reconstruct the historical context of his writings, analyzing his axguments onlyinsofar as they are elements of this larger intellectual constellation? For a time in theeaxly 20th century it was considered acceptable to do research on historical figures inphilosophy in the former way only, by taking the standard English translation of atext and working it over with one's pet philosophical theory in mind.3 More recently,the pendulum has swung the other way, and now it is common for discussions of aphilosopher to include extended analysis of his or her biography, culture, intellectualinfluences, and so on. It is almost impossible to find a book on Spinoza's philosophythat does not begin with a chapter on his biography.

Spinoza's peculiar insights and the structure of his thought seem at once to defyand to demand translation into our contemporary idiom. He has accordingly beenstudied from both sidesas a historical figure reacting to certain intellectual currents

3SeeGarber (2001, 3-6) for anamusing autobiographicaldiscussion of this phenomenon.


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in theology, science, and philosophy, and as a philosopher who presented a timelessmetaphysical picture of the world, a picture that merits our consideration withoutworrying too much about its historical context.4

I cannot say for certain whether both approaches are equally appropriate in thegeneral case. My own temperament as a historian of philosophy lies somewhere inbetween the two extremes. However, in the case of Spinoza, I think both approachesare not only appropriate, but are in fact necessary to understanding his philosophy.It is surely impossible to understand Spinoza's work without understanding that ofDescartes and of Hobbes, without reading Spinoza's letters, or without taking carefulstock of the original Latin text. Yet it is surely also interesting and philosophicallyfruitful to stretch Spinoza's already expansive and fascinating metaphysics to makecontact with our own contemporary philosophical situation.

More historically-minded historians of philosophy may not be convinced; but consider this. The terminology of Spinoza's arguments is hijacked from his historicalpredecessors (Aristotle, the Scholastics, Descartes, Hobbes, and so on) without citation or explicit reference, and he presents his conclusions as timeless metaphysicaltruths standing outside of any particular historical situation. Spinoza understoodhimself as working outsideof, and often at odds with, the perspective of his day. Thehistorical context of Spinoza's work is obscured by design. If we want to understandhis system in the way that Spinoza would have wished, we need to consider it withthe advantage of an outsider's perspective. The places that the system appears contradictory reveal its historically contextual assumptions. The charitable interpreterworks through these apparent contradictions by uncovering the assumptions that resolve them. Ideally, the interpreter then vindicates those assumptions in a way thatmakes them plausible to contemporary readers while preserving the unity of the work

4Wolfson (1983) takes the former tack, Bennett (1984) the latter, to pick two influential examples.


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in question. It seems to me that this is precisely what Spinoza would have desiredreaders of his work to do. So although my approach to Spinoza involves a strangeoverlap of the historical and the contemporary, I maintain that this is the best lensthrough which to understand Spinoza's philosophy.


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Chapter 1

Spinoza's Physics of IndividualsIn this short chapter, I will lay the historical and philosophical groundwork needed

in order to understand Spinoza's metaphysics of composition as it is presented in theEthics.1 What Spinoza says about composition, he says (or says most cleaxly) usingthe language of physics. In the so-called "physical digression" after Ethics IIpl3s,Spinoza presents the following definition of composite individuals:

When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon one another, or if they so move,whether with the same degree or different degrees of speed, that they communicate their motions toeach other in a certain fixed manner, we shall say thatthose bodies are united with one another and that they all compose one bodyor individual, which is distinguished from the others by this union of bodies.(Definition after MIpl3s)

This passage is the core of Spinoza's physics of individuals, and in the series of lemmasthat follow it he uses this definition to develop a sketchy but intriguing account ofpersistence. In chapter 2, I will present a reading of this passage as laying out thenecessary and sufficient conditions for several things to compose one thing. However,

1References toSpinoza's Ethics, Descartes' Principles of Philosophy (PPC), Short Treatise onGod, Man and His Weil-Being KV),and Treatise on the Emendation of the Intellect (TIE) arefrom Spinoza (1988) (thoughreferencesto the Latin are fromSpinoza1925). References toSpinoza'sletters are from Shirley (1995), and references to the Tractatus Theologico-Politicus (TTP) are toShirley (2001). References to Descartes' Principia Philosophiae (PP) are from Descartes (1983)(though Latin references are from Descartes 1904). References to Hobbes' De Corpore (DC) arefrom Hobbes(1655), unless otherwise noted. I useoriginal translations of Hobbes'Latin, with someguidance from the English translation inHobbes (1905) and suggestions from Brian Marrin. BecauseHobbes proofread and modified, but did not himself write, the translation in Hobbes (1905), thereare occasional discrepancies between the two texts; it would require lengthy examination of theoriginal manuscripts to discern which discrepancies are due to the translator and which are dueto Hobbes' changes. I therefore use my own translations of passages from the Latin text, makingreference to Hobbes (1905) where there are noteworthydiscrepancies.


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in order to develop such an interpretation, we first need to get clear on the meaningsof the critical terms in the passage.

The main hurdle to understanding Spinoza's physics is that he uses terms thateither have different meanings for him than they do for us, or that simply have nocorrelate in contemporary physics. Spinoza's conceptions of extension, motion, andrest pose particular difficulties, for although they are crucial to his discussion of material composition, they receive no more than a few sentences worth of explanationin the Ethics. By way of filling in this conspicuous absence, commentators have todate taken one of two approaches: either assume that Spinoza adopted the mechanistic physical theory of his predecessors, Descartes and Hobbes, or that he simplydid not have a fleshed-out physical theory and uses the terms as "placeholders" forthe fundamental physical concepts provided by some future theory.2 The way oneanswers this question has a rather large influence on how one understands Spinoza'saccount of composition. After considering the relevant aspects of the Cartesian andHobbesian theories of physics, I ultimately conclude that Spinoza can adopt neitherthe Cartesian nor the Hobbesian notions of extension, motion, and rest. However,the investigation of Descartes does suggest an important way of understanding thephrase motus communicare that features in Spinoza's definition of individuals: it isa causal notion, such that when one body communicates motion to another body,the first body causes a change in the second. I will use this interpretation in thenext chapter to argue that Spinoza intends to account for composition in terms ofcausation.

2See Garrett (1994) and Bennett (1984, 106-110), respectively.


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1.1 The purported mechanical influence

The interpretive problem for us is that several vital technical terms in Spinoza'sphysics have obscure meaning. Even the most basic terms, 'body' and 'motion', areup in the air. Although we are given a definition of the term 'body'"By body Iunderstand a mode that in a certain and determinate way expresses God's essenceinsofar as he is considered as an extended thing" (J57IIdl)it means little withouta further definition of extension, which Spinoza does not give. Further, motion andrest are simply undefined in the Ethics. Their nature was the subject of much disputeduring the seventeenth century, so it is unclear what conceptions of motion and restSpinoza has in mind. Are they passive affections or dynamicforces? Are they differentquantitative measures of the same quality, or axe they opposing qualities? Thesequestions are not given direct answers in Spinoza's brief digression in the Ethics. Ifwe are to answer them at all, it has commonly been thought that we must extrapolatethe answers from Spinoza's other writingsspecifically his presentation of Descartes'physics in Descartes' Principles of Philosophy (PPC)or from other likely influences,such as Hobbes' On the Body {DC).

This approach is not unreasonable, though I hope in this chapter to show that itis misguided. That said, it is well known that Spinoza read and was influenced byother aspects of both Descartes' and Hobbes' writings.3 There are clues that suggesthe might have been adopting their conceptions of motion and rest, as well. Motionand rest played a central role in the accounts of physical phenomena developed bymany proponents of the mechanical philosophy, such as Descartes and Hobbes. For

3The influence of Descartes is evident from the fact that Spinoza's first published work is arecapitulation of the first two books of Descartes' Principles. The influence of Hobbes is moresubtle, but thereare fairlyclear allusions to Hobbist political philosophy in Ethics IV and Chapter16of the TTP. Since Spinozaalso owned a copy of DC, one might suppose that Hobbes' influenceonSpinoza's thoughtextended toarenas beyond the political.


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these authors, all real variation in bodies was ultimately due to differences in themotions of the constituent parts of those bodies.4 Descartes writes:

...although our minds can imagine divisions [in matter], this imagining alonecannot change matter inany way; rather, all the variation of matter, or all thediversity of its forms, depends on motion. PP 11.23)

Hobbes, who is elsewhere very critical of Cartesian physics, nevertheless adopts avery similar view, according to which "...it is necessary that change can be nothingelse but motion of the parts of that body which is changed" (DC 9.9). Spinoza seemsto agree about the role of motion and rest as the ultimate cause of real variation inmatter. On his view, more complex bodies are composed from these simple ones,and can have more complex properties since they "can be affected in a great manyother ways, and still preserve [their] nature" (EIIplSs L7s). Ultimately, however, theproperties of these complex bodies are to be explained in terms of the motion andrest of the simple bodies that compose them.

On a first reading, then, Spinoza agrees with Descartes and Hobbes that variationin bodies is due to the motions of their parts. Unfortunately, this observation isratherabstract and high-level. It does not tell usanything about whatSpinoza thinks motionand rest actually are, it only tells us that he thinks motion and rest feature at themost basic level of the physical world. Indeed, this raises as many questions as itanswers.

In this section I will consider both of these possible influences onSpinoza's physics.My aim is to show that Spinoza could not plausibly have accepted the conceptionsof extension, motion, or rest that are advocated by these authors. I will start with

4Otheradvocatesof themechanical philosophy took anatomistic approach. On these accounts,most famously that of Gassendi, variation in matter is explained by the interactions among a fewfundamental propertiesof the atoms composing that matter,e.g. size and shape. Spinozadoes notseem to have been influenced by Gassendi, since Gassendi's account treats space as a backgroundvoid or vacuum,an approach Spinoza repeatedly denounces. See especially Tpl5s.


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Hobbes, which I take to be the easy case, and then consider Descartes. The Cartesianand Hobbesian conceptions of these physical concepts either conflict with Spinoza'smetaphysical principles, or they are unsuited to the work he seeks to put them to inhis metaphysics. If I am right, one common reading of Spinoza's physics is wrong, andinstead we ought to adopt the most plausible alternativesomething like JonathanBennett's "placeholder" interpretation of these passages.

1.1.1 Hobbes' physics

Spinoza's library contained a copy of Thomas Hobbes' vast work, Elemento-rum Philosophiae , a system of philosophy divvied into three parts: D e Corpore, DeHomine, and De Cive. Additionally, it is certain that Spinoza read and was stronglyaffected by Hobbes' political writings: the Ethics contains several discussions of the'state of nature', and Spinoza's Tractatus Theologico-Pohticus includes an extendeddiscussion of the natural rights of individuals that is almost strictly Hobbesian.5 Thephysical theory Hobbes presents in De Corpore includes definitions of space, time,motion and restterms that Spinoza's theory leaves almost entirely open. It mighttherefore seem reasonable to look to Hobbes' De Corpore for the inspiration andgrounding for Spinoza's physical theory. This search proves to be in vain. As I willpresently show, Hobbes' and Spinoza's ideas about the relative metaphysical priorities of space, time, bodies, and their motions are almost entirely at odds. However,comparing them reveals some important but unstated restrictions upon Spinoza'sphysics. These restrictions take us part of the way to an understanding of the physicsof individuals.

In spite of its title, the scope of De Corpore (DC) is not restricted to physics. Thefirst six chapters of the text deal rather with logic and methodological concerns. By

5See,e.g., IVp37 and TTP Ch. 16.


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the time Hobbes gets down to the business of physics, he has already given a theory ofproperties, a theory of names and definitions, and anaccount of philosophical method.These foundational discussions serve to shape his presentation of physical concepts:rather than providing any sort of mathematical treatment of motion, he states a seriesof interrelated definitions of various physical phenomena and properties. Six of thesedefinitions are relevant to the present discussion: space, time, body, place, motion,and rest.6

Space is the first physical concept that Hobbes defines, though he is somewhatcagey about it. Rather than simply presenting a metaphysical definition of space, hestarts by giving a phenomenal definition, as follows:

Space is the phantasm o f an existing thing, to the extent that it is existing, thatis, with no other accident of the thing being considered except itsappearanceas external to the one imagining it. (DC 7.2)

This conception of space, which Hobbes sometimes refers to as imaginary space[Spatium Imaginarium], treats it as the extension of some imagined body, and henceas relative to our imagination. The idea is that in order to conceptualize space, wemust imagine a body filling it, a 'phantasm' whose imagined size and shape delineatethe space. This is not Hobbes' last word on the topic, however. He later contrastsimaginary space with real space:

The extension of a body is the same as its magnitude, or that which some callreal space. (DC 8.4)

The difference is subtle, but crucial. Imaginary space, he explains, is "an Accidentof the mind" whereas real space is an accident of "a body existing outside the mind"

6Someof theotherdefinitions should beof interest inSpinozascholarship more generally: Hobbes'definition of the infinite bears striking similarity toSpinoza's definition of the 'infinite in its ownkind' (Idl), and his definition of inertia (DC 8.19) isalso close toSpinoza's (IIIpl3s, Lemma 3).


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( D C 8.4). The former definition is epistemological or phenomenologicalat best itaffords us a theory of spatial perceptionbut the latter definition is metaphysical,since it tells us what space is, full stop. On either definition, space is not understoodas substantival, but as derivative of actually existing or imagined bodies. Withoutany actual or conceivable bodies, there would be no space. (To use some slightlyanachronistic terminology, Hobbes is saying that any world that contains neitherbodies nor minds is the empty worldthere is no possible world consisting solely ofa spatial manifold.)

Related to the concept of space is that of place, which Hobbes defines as follows:...the Space (by which name I always understand the imaginary) that coincidesw i t h t h e m a g n i t u d e of s o m e b o d y , i s s a i d to be t h e P l a c e o f t h a t b o d y . (DC8.5)

Though place and bodily magnitude might seem identical since the one always co incides with the other, Hobbes is quick to differentiate them. A body's magnitudeis a property of that body, and is moved along it, whereas a body's place changeswhenever the body moves.

When he moves to considering time, Hobbes at first seems to want to treat itanalogously to space:

...a moving body leaves aPhantasm of its motion in the mind, doubtless theidea of the body in continuous succession of traversing, now in this space, nowin another. And suchan idea or Phantasm...I call Time. (DC 7.3)7

As with imaginary space, Hobbes here addresses our perception of time withoutgiving a metaphysical account of it. The implicit claim is that time can only beconceptualized in terms of motion, but this does not tell us anything about the

7 ...corpusmotum motus sui Phantasma in animorelinquit, nimirum ideam corporis, nunc perhoc, nunc per aliud spatium continua successione transeuntis. Est autem talis idea sive Phantasma. . .appel io, Tempus.


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metaphysical priority of time with respect to motion. That is, our mode of epistemicaccess to time is through motion, but this does not rule out the possibility of timewithout motion; we simply wouldn't be able to perceive it.

One might reasonably expect Hobbes to present a definition of 'real time' tocomplement the definition of 'real space'. Yet Hobbes states without reservation thatthere is no such thing as 'real time'. He explains,

For since all would confess a year to be time, and yet no one would thinkthat a year is an accident or affection, or mode, of the body, so they mustconfess that time is found not in the actual things but in the thought of themind; although people speak of the times of their elders, can it be that aftertheir elders have ceased to exist, their times are anywhere other than in therecollection of memories? (DC ibid)

Time, in contrast tospace, is a purely imaginary phenomenon based on our perceptionof motion. The distinction between time and space, on Hobbes' view, seems similarto the distinction Locke makes, much later, between primary and secondary qualities.Our idea of a space (an imaginary space) corresponds to and resembles the spatialmagnitude of a body (a real space). However, though our idea of time is somehowbased on or generated by the motion of a body, there is nothing in the body thatcorresponds to or resembles time.

He then gives his final definition of time, leaning heavily on his view that time isessentially a figment of our imagination:

Therefore the full definition of time is this: Time is the Phantasm, o f motioninsofar as the motion is imagined as prior and posterior, or in succession. (DCibid)

In spite of subtle differences in his treatment of space and time, Hobbes presentsreductive accountsof bothhe reduces spaceto theextension of bodies and he reducestime to their motion. Although we sometimes describe space and time in substantival


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terms, Hobbes clearly takes that to be nothing more than loose talk. Space and timeare not substances in which bodies and their motions axe embedded or contained.Rather, bodies and their motions constitute the ontological basis for space and time.A world without motion, for Hobbes, is a world without time.

The order of metaphysical dependence in Hobbes' metaphysicsflowing from bodies and motions to spaceand timegives his definitions of bodies and motions specialimportance. Yet his definition of body turns out to be circular.

...the definition of body is this: Body is that which, not depending upon ourthought, coincides or is coextended with some pari of Space. (DC 8.1)

The problem with this definition is that space has already been defined in terms ofbody. To define body in terms of space is circular, and seems to render vacuousHobbes' whole system. Is it a vicious circularity? It certainly seems to be, as it isan instance of the smallest possible Cartesian circle: two definitions, each of whichinvokes the other. Any attempt to clarify the terms in either definition will need torefer to the other, and the reference to the other definition will in turn make referenceto the first. The fact that these terms are interdefinable renders it impossible to useone to informatively account for the other.

If the definition of body is circular, then the definitions of motion and rest aretoo:

Motion is the cont inual abandonment of one place & acquisition of another.(DC 8.10)

That which is in the same place for some amount of time is said to rest... (DC8.11)

Both motion and place are explained in terms of the concept of place, which in turnis explained in terms of the concept of body. Since there are no primitives in which to


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ground this series of definitions, Hobbes' physical theory falls again into circularity.Spinoza would have to reject this collection of definitions as failing to capture theessence of their objects.8

Furthermore, even if Hobbes produced some account of the apparent circularity,Spinoza would still have a substantive disagreement with Hobbes about the properplace of particular finite bodies relative to the whole of extension. Spinoza mustreject the Hobbesian conception of extension as the sum total of "real space," forthis conception entails that the whole of extension depends upon its parts. Spinoza'sdefinition of a substance implies that extension is not simply the sum of the bodies itcontains, contra Hobbes. On Spinoza's theoryof attributes, extension (as an attributeof the one infinite substance) is infinite inits own kind, and is not dependent upon anyother attribute (.EIplO, plls S c pl2). There is and can be only one substanceDeus,sive Naturaand all bodies are merely modes of the attributes of this substance.However the relationship between substance and mode is construed, it is clear thatSpinoza doesnot take bodies to be metaphysically prior to the attribute of extension.9

All of this suggests that Hobbes' influence on Spinoza's physics does not extendbeyond the sharing of various technical terms. If we want the meanings of those termsfor Spinoza, we must look elsewhere.1.1.2 Descartes' physics

A few central physical conceptsextension, motion, rest, and the communicationof motionappear in both Descartes' Principia and Spinoza's Ethics. At issue iswhether both authors shared the same conceptions of these terms. Presently, I willargue that Spinoza rejects the standard Cartesian understandingof extension, motion,and rest, but accepts Descartes' causal conception of the communication of motions.

8I discuss Spinoza's views about definitions and essences in Chapter 3.3.9See especially 2?Ip25c, Ildl.


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There is nodoubt that Spinozaalong with most every intellectual working in thelatter half of the seventeenth centurywas deeply influenced by the new Cartesiantheory of physics. There is also no doubt that even the young Spinoza was deeplycritical of aspects of Descartes' theory. In a letter to Henry Oldenburg from 1665,when Spinoza would have been near completion of a first draft of the Ethics,10 hewrites,

...I think that regarding the sixth rule of Motion in Descartes, both [Huygens]and Descartes are quite inerror... (Ep. 30a)

Descartes' sixth rule of motion says that in any collision of two bodies of equal sizewhere one is in motion (body B) and one is at rest (body C), "necessarily, C wouldbe to some extent driven forward by B and would to some extent drive B back in theopposite direction" (Descartes, 1983, rule 51). W e post-Newtonians know betterBand C will simply exchange their velocity vectors, so B will end up at restbut at thetime the laws governing the collision of rigid bodies were still hotly debated. (In theletter just quoted, Spinoza's reference to Christian Huygens is because Huygens hadbeen proclaiming that he would soon release a treatise disproving and correcting theCartesian laws of collision. Change was in the air.) In spite of these minor disagreements, the young Spinoza seems to have been willing to accept most of Descartes'physical theory. His criticisms of Descartes in his early work, Metaphysical Thoughts,had mostly to do with what he felt were philosophical or theological errors such ashe found in the Cartesian account of the will.11 Could Spinoza's discussion of thephysics of individuals after IIpl3s be relying upon Cartesian physics? I will arguethat it cannot, on pain of contradicting Spinoza's metaphysical views.

Let me begin by giving a brief picture of some of the interpretive concerns about10See the editor'spreface tothe Ethics in Spinoza (1988, 405).11See the introduction to Spinoza's PPC.


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Descartes' physics on which commentators have focused. As I proceed through theseconcerns, I will set aside those parts of the debate about Descartes' conception ofmotion that are irrelevant to my purposes. Then I will show that, on any standardreading of Descartes, Spinoza must reject the Cartesian conceptions of extension andmotion.12

First, what is Descartes' conception of extension? We are told it is opposed to"weight, hardness, colour, or the like," and consists only in possession of "length,breadth, and depth" (PP II.4). These geometrical properties are the only essentialfeatures that a body has.13 Extension, then, is a geometrical space, with one caveat:that geometrical space is not to be understood as an empty space underlying orhousing matter, the "corporeal substance". It is rather to be understood as thecorporeal substance itself (11.11). To put the point another way, the fundamentalproperties of corporeal substance are geometrical properties.

Second, what is Descartes' conception of motion (and rest)? The Cartesian conception of motion involves two levels. At what I will call the physical level, the motionand rest of a body's parts are supposed to provide the objective ground for all of itsproperties (PP 11.23). This suggests that motion and rest are, for Descartes, objectiverather than (merely) relativethey must be generated by forces.u It isn't clear how

12Motionand rest arenot, on theCartesian theory,the resultof twodistinct kinds of force. Theyareboth theresultof the sameforce, and in the strict sense abody inmotion isdistinguished froma body at rest only in virtueof the spatial relations it bearsto the bodies whichare in immediatecontact with it (PP11.25). Inmy discussionto follow, I will often elide mention of rest because allof Descartes' claims about the property of being in motion apply also to the property of being atrest.13It isonlyessential thata body have some quantity or other of length, breadth, and depth. Theparticular quantities may vary over time though the body remains the same. See Descartes' waxargument in the second of the Meditations (AT VII, 30).

14Muchdebate about Descartes'physicshas focused upon whetheror not it iskinematic (atheoryabout motions) or dynamic (a theory about the forces that cause motions). See, e.g., Gabbey(1971), Blackwell (1966, 222), Slowik (1999, Sec. 5), Gaukroger (2002, Ch. 4). I will bypass mostof this debate; suffice it to say that the consistency of Descartes' system hinges upon its inclusionof adynamic component, for without appeal tounderlying forces Descartes' version of relativityof


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a fundamentally geometrical entity like a Cartesian body could have causal power,but it is clear that Descartes speaks as if they can, so let's say the bodies' motionsare caused by their pushing and pulling on one another. (I'll say more about wherethese pushings and pullings come from in a moment.) Descartes also tells us thatthe only causal power that bodies have is their tendency to persist in the same state,so the power of bodies is in some sense purely reactive (PP 11.43).15 Putting theseclaims together: all the properties of a body are due to its extended parts moving(or staying at rest), these motions are the result of forces causing the bodies to pushand pull one another, and these pushings and pullings are the result of each part'stendency to persist in its current state of motion or rest. This general picture is acentral component of Descartes' conception of motion.

At the metaphysical level, however, Descartes adds a furtherstory about where theforces behind each body's motion come from, and in what those forces inhere. This iswhere interpretations of Descartes diverge. On one interpretationthe occasionalistreading, already mentionedCartesian bodies themselves are intrinsically inert, andthey obtain their causal "power to act on, or resist, other bodies" (PP 11.43) fromGod, who continually preserves the same quantity of motion in the world (11.36).motion istoo strong, even byhis own lights. TheCartesianrules ofcollision distinguishbetween(1) abody inmotion collidingwitha smallerbodyat rest, and(2) a body in motion collidingwitha largerbodyat rest (see PP 11.46-52), yet without away objectively to pick out which body is in motionand which is at rest, these two cases collapse. In itself, this would not be a problemDescarteswouldmerely have used more ink than strictly necessary. Unfortunately,Descartes actuallypredictsdifferent outcomes for the two cases, so that the motions, and hence the resulting positions, of thetwo bodies aftercollision will differ depending uponwhich body was movingand which wasat rest.The Cartesian system therefore predicts contradictory outcomes, in virtue of taking motion to betotally relative to the situation of the observer (PP 11.29). According to a frame of reference inwhich the smaller body is movingand the larger isat rest,one outcome is predicted; according toadifferent frame in which the larger body ismoving and the smaller isat rest, a completely differentoutcome is predicted. Yet both reference frames are equally valid from the point of view of thetheory. Sowe need toappeal to forcesto fix the appropriateframeof reference. I think this suggeststhat weshould take Descartes' claim that bodies have the power (or force) toact on other bodiesas more than just loose talk; without that claim, the system iscontradictory.

15Cf. Descartes'arguments for the three lawsof natureat PP 11.37, 39, and 40.


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Indeed, not only does God continually preserve the quantity of motion in all matter,he "preserves all this matter in the same way, and by the same process, by which heoriginally created it" (ibid). So, since all of the apparent causal power of a Cartesianbody is really nothing over and above the causal power of God, the proponent ofthe occasionalist reading says that Cartesian bodies do not have any causal power orefficacy.16

On another interpretationthe concurrentist readingCartesian bodies havesomegenuine power even though God's concurrence is necessary for that power. The concurrentist reading affirms all of the facts about God's creation and continual preservation that the occasionalist reading affirms, but denies that these facts rule outattributing genuine causal power to bodies. That is, the proponent of the concurrentist reading simply rejects the last step in the occasionalist's reasoning: it is irrelevantthat all of the causal power of a body is continually preserved by, and ultimately dueto, God. Rather, God has the power, and the body has it.17

On either reading, Descartes' conception of motion and rest includes both a physical level, at which motion and rest ground all other extended properties, and ametaphysical level, at which motion and rest are imparted to and sustained in bodiesby God. I want to set aside the question of whether Cartesian bodies axe properly saidto act upon one another, or are only acted upon by God. That question, while interesting, turns out to be irrelevant to our main concern: what aspects of the Cartesianpicture could Spinoza adopt? And, more importantly, what aspects of that picturedid he adopt?

Taking the second question first, there is nice evidence that Spinoza did in fact16See Garber (2001a). (Cf. Garber 2001b).17See Delia Rocca (1999): it [is] more plausible that [Descartes]holds that bodies cause changes

in motion and doso, indeed, not despite the fact that God causes changes in motion, but becauseof that fact (49). Pessin (2003) likewise develops acase for reading Descartes as a certain sort ofconcurrentist.


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reject the Cartesian conception of extension. A decade after Spinoza's mild criticismof Descartes' rules of collision, he condemns the very foundation of Cartesian physicsin a curt but revealing letter to E. W. v. Tschirnhaus:

...from Extension as conceived by Descartes, to wit, an inert mass, it is...quiteimpossible to demonstrate the existence of bodies. For matter at rest, as faras in it lies, will continue to be at rest, and will not be set in motion exceptby a more powerful external cause.18 For this reason I have not hesitated ona previous occasion to affirm that Descartes' principles of natural things are ofno service, not to say quite wrong. (Ep. 81)

This terse characterization of Descartes' view highlights the importance of the activenature of substance in Spinoza's philosophy. Spinoza's criticism of the Cartesian theory is that, since it treats bodies as mere "inert masses," it cannot account for thedynamic interactions between bodies.19 Descartes might reply that since extendedsubstance is inert mass, any apparently dynamical interactions between such substances must be explained by the action of an external thingbut from Spinoza'sperspective, this reply simply amounts to the denial that there are any extendedsubstances at all. For this reason, along with his other metaphysical commitments,Spinoza comes down on the side of a dynamic conception of extension: bodies, asfinite expressions of extended substance, exert forces upon one another. Spinozaappears to think that the Cartesian picture rules this out.

So it seems that Spinoza came to reject the Cartesian conception of extensionbecause he took Descartes tobe committed toan occasionalist conception of motionthat is, Spinoza thought that Descartes' view entails that it is impossible for finite

18Shirley's translationhastheawkward phrase as faras init lies for the Latin quantum in se est,whichfeaturesprominently inSpinoza's conatus doctrineat IIIp6. See Cohen (1964) fortheclassicdiscussion of the role of this ubiquitous phrase in seventeenth century natural philosophy. In mydiscussionof Spinoza's conatus doctrine in Chapter 3, I will advert to the slightly less cumbersometranslation, insofar as it isin itselP.

19Though see Donagan (1988,99-100) foran interesting opposingreading of therelevant passagesin Ep. 82 & 83: [Spinoza's]objection to Descartes was that, having correctly identifiedone of Nature's infinite attributes, Descartes spoiledhis achievement bythinking of extension as anabstractlyconceivable property, and not asexpressing an eternal and infinite essence... (ibid).


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bodies to cause one another to move. As I suggested above, this is not to say thatDescartes was in fact an occasionalist of this sort, nor that he recognized his view asentailing occasionalism. If the concurrentist reading of Descartes is a live possibility,then the Cartesian system need not be occasionalist. My claim here is that Spinozathought the Cartesianconception of extension led to occasionalism, and for this reasonrejected it.

What about our other question: should Spinoza have rejected this conceptionof extension? I think the answer, given Spinoza's other metaphysical views, is yes.Spinoza rejects as mystical nonsense the premise that an immaterial being (the Cartesian God) could causally interact with the material world, which premise is fundamental to Descartes' conceptionof extension on any available interpretationwhethermotion is due to God's direct action, or only due to his concurrent action, motion isdue to God's action. At the metaphysical level, then, Descartes' conception of extension is simply incompatible with Spinoza's. The possibility of either occasionalismor concurrentism is ruled out by Spinoza's view that the attributes of God (thoughtand extension) cannot interact: bodies act on bodies and ideas act on ideas, butideas do not act on bodies or vice versa (J57IIIp2). Unless God is an extended thing,there is no conceivable way for it to act upon the material world (EIpl5s). Spinozatherefore rejects the Cartesian picture of an external creator-god sustaining the worldfrom moment to moment.20 But this part of the picture underlies both Descartes'conception of extension and his conception of motion, insofar as these conceptionsrequire either God's direct action or His concurrence.

20There isa way in which Spinoza's picture might look like the Cartesian one. Spinoza's reasonforthinking that bodieshave causal power isthat Whateverexists expresses thenature, oressenceof God inacertain and determinate way...[so]some effect must follow [from theirnature] ('Ip36d).So, like Descartes, it seems that the causal power of a body is ultimately due to God. However,although the power or force that Spinoza assigns to bodies is ultimately a manifestation of God'scausal power, that power is not (as Descartes would have it) due toa creator-God acting upon aworld external toHim.


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So Spinoza must, and does, reject the Cartesian conception of extension as fundamentally inert, and the Cartesian conception of motion as due to the actions ofan external, immaterial God. Nonetheless, there is one technical notion from theCartesian physics that I think Spinoza did adopt: the communication of motion.

The communication of motionsThere is textualevidence that Descartes' usage of the phrase "xcommunicates motionto y is intended to imply that x exerts a force upon y. The phrase does not appearoften in the Principia, and when it does, it appears as a synonym for the phrase "xtransfers motion to yn. For instance, at PP 11.51, the sixth rulegoverning the collisionof bodies in Descartes' physics, he writes, "Thus if [a body] B were to approach[a body] C with four degrees of speed, it would communicate one degree to C..."(my emphasis; cf. a similar example at PP 11.49). Elsewhere in the collision rules,describing the same phenomenon, Descartes does not use the idiom of communicationof motions. Instead he states that one body transfers [transfert, or the subjunctivetransferret] its motion to another. It therefore seems that Descartes intended the twophrases to be synonymous: x "communicates" motion to y whenever x "transfers"motion to y, and vice versa.

Earlier, at PP 11.25, Descartes uses the term 'transference' in his definition ofmotion. After stipulating that motion is "the transference of one part of matter...fromthe vicinity of those bodies immediately contiguous to it and considered as at rest,into the vicinity of others," he explains,

I also say that it is a transference [translationem], not the force or actionwhich transfers [non vim vel actionem quae transfert], in order to showthat this motion is always in the moving body and not in the thing which


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moves it...

The distinction Descartes is trying to emphasize is between the verb "transfers" andthe noun "transference".21 The subject of the verb "transfers", for Descartes, issupposed to be the cause of the ensuing action.

If we combine Descartes' intended meaning for the verb "transfers" with the factthat he takes "transfers motion" to be synonymous with "communicates motion," weobtain a causal interpretation of the communication of motions. One body communicates motion to another only if the first exerts some force upon the second, causingit to move. The result of all this is a simple observation that will be useful to us inanalyzing Spinoza's physics: whatever else might be said about the communicationof motions, it is a fundamentally carnal relation.

That Spinoza adopts this dynamic and causal understanding of communicatedmotions is suggested by his definition of individuals (quoted above). Recall that hesets aside several sorts of relations between bodies as irrelevant to their composition:it is supposed to be irrelevant "whether [bodies are] of the same or of different size,"or whether they move "with the same degree or different degrees of speed" (E'UplSs,Def). Why? I claim that Spinoza's reason for discounting these relations (i.e., beingof a different size than... and moving at a different speed than...) is that they arenot causal relations. That is, they are not born by two bodies in virtue of any causalpower that one exerts on the other; they merely mark a comparative difference in thebodies' properties. Spinoza seems tobe assuming that composition must involve somegenuine interaction among the composing bodies. Given the proposed interpretationof Descartes' notion of the communication of motions, it is plain to see why Spinoza

21It might bemoreproper to translate translationem hereas translation inits geometricalsense.Miller and Miller (in Descartes1983) use transference tohighlight the distinction Descartes wantsto draw between the action (the transference) and its cause (that which transfers). Since thisdistinction ismy focus here, I take up Miller and Miller's translation.


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claims that relation is relevant to composition. Since Spinoza (along with Descartesand Hobbes) thinks that any property of any extended thing is ultimately reducibleto motion and rest, the communication of motions turns out to be the fundamentalcausal relation thatextended things bear toone another. All extended causal relationsare reducible to the communication of motions among bodies, so the composition ofany extended thing is reducible to the communication of motions among bodies.

Why should composition ultimately reduce to a causal relation of some sort? Ithink the answer here liesin Spinoza's understanding of causation as involving conceptual dependence. For one thing to causeanother implies that there is some conceptualconnection between the two, such that the effect can be understood through the cause('Ia4). So the reason that the communication of motions is essential to the composition of an individual from a group of bodies is that their communication of motionsis what makes those bodies mutually dependent upon one another. It is the reasonthey must be conceived as a unified wholeit explains how, as Spinoza puts it ina famous letter, their natures are "adapted" to one another.22 Merely comparativerelations do not mark such dependence, only causal relations do; and communicationof motions is the relevant causal relation when we are considering bodies.

1.1.3 The Alternative

So, Spinoza seems to have adopted neither Descartes' nor Hobbes' conceptionsof motion and rest. He does not lay out any alternative definitions, either in theEthics or elsewhere. Yet motion and rest are the fundamental properties of extendedthings, those properties from which all other properties of extended things are derived. What, then, are we to say about Spinoza's conceptions of motion and rest?Bennettwho leapfrogs to this conclusion without considering Spinoza's philosoph

22See Ep. 32. I discuss this letter at length in Chapter 5.


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ical predecessorshas suggested that 'motion and rest' is simply shorthand for thefundamental qualities of some yet-to-be-established physical theory, whatever theymay turn out to be (Bennett, 1984, 106-10). While Bennett's suggestion is perhapstoo generous,Spinoza's explicit dismissal of the Cartesian notion of extension (quotedabove) lends some credence to the idea that Spinoza recognized the difficulties in extant definitions of basic physical concepts, but (for whatever reason) was not veryconcerned with making precise his own alternative conceptions of these things.

The situation is this: Spinoza must reject the Cartesian and the Hobbesian conceptions of extension and their accompanying conceptions of motion and rest; yetmotion and rest are presented in the Ethics as the most primitive modes of extendedthings, from which all variation in extension is ultimately derived. This suggests thatBennett's somewhat haphazard reading is in fact close to the mark. Motion andrest are best understood as names for whatever happen to be the most fundamentalopposing qualities of extended things, those qualities ultimately responsible for variation in extended things. "Communication of motions" is then simply a name forwhatever the fundamental physical causal relation turns out to be. I am not entirelycomfortable with this reading, as it involves rather zealous application of the principle of charity: it gives just a bit too much to Spinoza to be completely plausibleas an interpretation. Nonetheless, for whatever reason, Spinoza chose not to wadevery deeply into the murky lake of seventeenth century physical theory. The focusof his discussion of physics is on composition and persistence, and these are properlymetaphysical topics that transcend any particular physical theory.

Now, having explained how Spinoza's physics can (and cannot) be interpreted, weare ready to connect this interpretation with his definition of composite individuals.


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Spinoza's Account of CompositionPhysics need not guide philosophy, but in this case it does; Spinoza's physics

of individuals suggests a certain metaphysics of composition. In this chapter, I willdevelop the main outlines of Spinoza's account of composition as it is presented in theEthics. My approach takes two steps. In the first step, I will outline and interpretSpinoza's discussion of material composition, based on the dynamic interpretationof his physics proposed in the previous chapter. Then I will articulate the general(attribute-neutral) account of composition which I take to be motivating that accountof material composition.

Suppose there axe several things, call them the xs. Under what conditions is therea single individual, call it y, such that the xs compose yl The problem, in otherwords, is to figure out what conditions (if any) must obtain in order for several thingsto compose a single thing. Call this the special composition question; a variety ofresponses to it are available. (Nihilism: no xs compose any y. Universalism: all xscompose some y. Contact: the xs compose a y whenever the xs are topologicallyconnected. Organicism: the xs compose a y whenever the xs constitute a life. Andso on.1)

1 Universalism has beenmost famously advocated by Lewis (1986, 212-3) and Sider (2003, 120-32); I consider Sider's argument (the Argument from Vagueness) in chapter 5. More recently, anumber of philosophers (including, surprisingly, Sider 2009) have articulated defenses of Nihilism.Contact isnot generally taken tobe aviableanswerto the special composition question. (Somethinglike Contact isimplicitly endorsed inthe mereotopologyof Casati& Varzi (1999), but their interestisin the structure needed for the representationof compositeobjects rather than the metaphysicalquestion about their existence.) And van Inwagen (1995) gives the classic articulationand defenseof Organicism, though more recently Merricks (2001) has argued for a view in between Organicism


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In traditional Aristotelian and Scholastic metaphysics, composition is accountedfor in terms of substance, that is, as the unity of matter with a substantial form. Forinstance, Leibniz, who advocates a roughly Scholastic view of composition, accountsfor the difference between the unity of the parts of a sheep and the (merely apparent)unity of the parts of a block of marble by claiming that former constitute a substanceand the latter do not. If several parts do not constitute a substance, then they are notgenuinely unifiedthey present the appearance of composing an individual, but thatappearance is in some sense illusory, like the appearance of a rainbow.2 Spinoza'sviews on composition are of particular interest because, unlike the Scholastics (andLeibniz), he does not want to account for composition in terms of the concept ofsubstance. Spinoza is a substance monist, and sees all particular things as modesinhering in the one infinite substance. He cannot appeal to substance to accountfor composition, for neither the parts of a sheep nor the parts of a block of marbleconstitute a substance.

Spinoza cannot appeal to substance to account for composition, so he appeals tocausal power instead. I claim that Spinoza's account of composition is:

COMPOSITION: Some things compose an individual if and only if they instantiate apattern [ratio] of causal relations.

A number of commentators on Spinoza's physics of individuals have adopted a viewclose to this, but their interest has been to draw out the lessons of Spinoza's physicsfor his account of individuation or his account of persistence. My aim here is furtherto develop the consequences of this claim as an answer to the special compositionand Nihilism on which some xs compose an individual just in case they constitute a person (andspecificallya conscious person). This dissertation will engage with many of these views at variouspoints throughout, but I consider them indetail in Chapter 4.

2See Leibniz's letter to Arnauld, Leibniz (1989, Nov. 28-Dec. 8 (1686)).


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question, in order to leaxn more about what things Spinoza's ontology includes.3More must be said about what it means for several things to "instantiate a pattern

of causal relations." But even this initial sketch of Spinoza's account allows us toanswer severalinteresting questionsabout Spinoza's understandingof the metaphysicsof part and whole.

The special composition question is about the relations that must be exemplifiedby several things in order for them to compose one thing. There is another, closely related question with a similarly grand tradition in metaphysics: supposing that the xscompose y, what exactly is the relation between the xs and yl Contemporary metaphysicians call this the general composition question.4 One prominent answer to thisquestion in recent decades has been, "The parts and the whole stand in the relationof identity, the whole is nothing more than its parts (or: nothing more than its parts,arranged in a certain way)." Given certain of Spinoza's other metaphysical views,however, I will argue that he rejects this version of composition as identity. Instead,he takes a whole to be identical with the arrangement of its partsmore precisely, acomposite individual is identical with the pattern of causal relations instantiated byits parts.

3Bennett (1984, 232), Garrett (1994, 82-97), Garber (1994, 54-55), Delia Rocca (1996a, Ch. 2),Barbone (2002) and Lin (2005, 248-252) each agree that weshould take ratio to mean somethinglike pattern, and recognize that any composite individual has such a pattern. (These authorssometimes usedifferent terms, but the spirit of their interpretation is thesame. Forexample,Garbersometimes uses rational organization and stable configuration to refer to what I am callingpatterns. Delia Rocca uses the more open translation relation , but I think this is meant simplyto stand opposed to traditional interpretations on which ratio is taken to denote a mathematicalratio. Viljanen (2007, 409-410) likewise develops a view on which the metaphysical descriptionof an individual involves a fixed arrangement of interaction between power quanta [which is] therelation of motion and rest between the bodies composing the individual. As I understand them,each of these views is compatible with COMPOSITION. Any differences we have will come in howbest tounderstand how best to understand these patterns (or configurations , or arrangements ).

4The twoquestions aremostly independent, butnot strictly logically independent. Ifoneanswersthe special composition question bysaying, Necessarily,no xscomposeany y,regardless of the relationsamong the xs, then thatanswer will clearlyentail a certain answer to the general compositionquestion. However, inevery other case I am awareof, one's answer to the formerquestion does notdetermine one's answer to the latter.


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Finally, a third question that has been particularly relevant in contemporary discussions of monism is: supposing that the xs compose y, must the :cs be prior to y?Since Spinoza is a monist, it might be thought that he would say that the whole isprior to its parts. I will argue to the contrary that, given his account of composition,Spinoza ought to take parts to be prior to the whole they compose. I will close thechapter by highlighting some passages which suggest that this is indeed his view.

2.1 Spinoza on Composition

I will first argue that Spinoza endorses COMPOSITION as an answer to the specialcomposition question. I'll proceed by first arguing that Spinoza endorses a version ofCOMPOSITION restricted to material things (bodies), and then arguing that his metaphysical principles force him to accept COMPOSITION without restriction to bodies.

Spinoza's account of material composition is given as part of an extremely condensed discussion of physics in Ethics II, often called the "Physical Digression."5There, he gives the definition quoted in the previous chapter:

When a number of bodies, whether of the same or of different size, are so constrained by other bodies that they lie upon one another, or if they so move,whether with the same degree or different degrees of speed, that they communicate their motions to each other in a certain particular pattern [certa quadamratione\, we shall say that those bodies are united with one another and thatthey all compose one body or individual, which is distinguished from the othersby this union of bodies. ("Definition" after 2IIpl3s)6

As I said, most commentators have focused upon the role this passage plays in settingupSpinoza's accountsof individuation and persistence. Let's instead read this passage

5I will assume inwhat follows that the conditions given in thequoteddefinition are intended tobesinglynecessary and jointlysufficient for composition. Thetext isambiguous regarding necessitySpinozaonly explicitly claims that they are sufficientbut it seems reasonable tosuppose that inorder for Spinoza's definitionof composite individuals tobe a definition, it must be a necessary aswell as sufficient condition on composition.

6I have slightly modified the translation from Spinoza (1988).


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through the lens of the special composition question. Suppose thereaxe several things,the xs. When do the xs compose an individual, y?

Spinoza's claim in the quoted passage only gives us a partial answer. When doseveral extended thingscompose an extended individual? When those things "lie uponone another" or "communicate their motions to each other in a certain particularpattern." At first glance, it looks like Spinoza is giving a disjunctive account ofmaterial composition. However, I think the former condition should be read as aspecial case of the latter. If the x's lie upon one another, thenSpinoza surely assumedthat they would communicate their motions to one another.7 So the composition ofbodies is ultimately characterized by reciprocal communication of motions amongthose bodies "in a certain particular pattern [certa quadam ratione].

Certa quadam ratione...''''I have argued that the central condition Spinoza places on composition is ex

pressed in this sentence from the quote above, if [some bodies] so move...that theycommunicate their motions to each other in a certain particular pattern...they all together compose one body or individual..." (emph. added). Given that we have cometo an understanding about what Spinoza means by the communication of motions, wenow need to pinpoint the role that this relation of communicated motion is supposedto play in the account.

In asking whether some xs compose an individual, not just any communicationof their motions seems to be relevant. The sentence just quoted involves a peculiarcondition on the way inwhich motions must be communicated among the xsnamely,

7AlthoughSpinoza had his doubts about aspects of Descartes' physics (as I discussed in Chapter1), he never expressed any doubts about Descartes' plenum theory. Part of that theory involvestheclaim that whenevera body moves, it communicates its motion toall immediatelysurroundingbodies(PP 11.33). SoSpinozawould have assumed that several bodies constrained byother bodies[so] that they lie upon one another would communicate their motions to one another.


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the xs must communicate their motions among one another "in a certain particularpattern". Turning to the Latin here clarifies the scene a bit, but we need to do somemore work to make sense of it. The text reads, "ut motus suos invicem certa quadamratione communicent..." The key phrase is "certa quadam ratione". Curley translatesthis as "in a certain fixed manner", which translation I have implicitly rejected; letme first give an argument for my preferred translation, then evaluate the view mytranslation attributes to Spinoza.

'Ratio' (the nominative of ratione) might just as easily be translated 'pattern','system', 'scheme', or even 'procedure', though this last would be a stretch given thecontext. I will follow a number of recent commentators in taking 'ratao' to mean apattern rather than a mathematical ratio.8 It is, in any case, easy to see why weshould take the Latin 'ratio' to denote something other than a mathematical ratio.Spinoza intends a thing's ratio of communicated motions to explain its persistencethrough changes; but mathematical ratio of the motions (or even the forces) that anindividual's parts communicate to one another is capable of drastic variation evenin quite ordinary circumstances. When I am sitting sedately, the parts of my bodydo bear a certain mathematical ratio of communicated motions (primarily dictatedby my heart rate and breathing); but if I stand up and go for a jog, that ratio willcertainly not be preserved. It is hard to see why Spinoza would have made such amistake, especially when the text easily supports an alternative reading. While thenotion of a pattern is a bit unclear as yet, it is enough for now to get at the basicidea underlying Spinoza's account of composition.9

We further know that the pattern governing the communication of motions mustbe a "certain particular" one. There isan ambiguity in the Latin that isnot marked by

8Seefn. 3 above. Each of the authors cited there concurs that the rationes in question shouldnot be understood literally as mathematical ratios.

9I return to (and flesh out) the notion of a pattern in Ch. 3.


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Curley, namely whether 'certa' ought to be translated as 'certain'Curley's choiceor as 'determined'. Curley's choice is probably motivated by the fact that elsewherein the Ethics, Spinoza uses the adjective determinata' in a way that is pretty clearlyintended to mean that the object is determined (,Ip26&7). Spinoza's language isusually carefully chosen, especially when he is using terms in a technical way. It wouldtherefore be odd for him to switch from 'determinatd' to 'certa' when expressing thesame technical notion. Let's follow Curley in translating 'certa' as 'certain'.

'Quadam' presents a similar ambiguity. Curley's choice here, 'fixed', is adequate,but 'quadam' only has one of the several senses of that English term. Specifically,the Latin 'quadam' translates to 'fixed' only in its sense of denoting particularity orspecificity. Importantly, it does not have the sense of denoting being unchanging orunmoving. So Curley's translation is less than optimal. The ambiguity, though, isthat 'quadam' may also be used simply to soften an otherwise strong description,along the lines of the English phrase, "What one might call..." or "Something like..."If Spinoza is using the sense preferred by Curley, then quadam' does not add muchto the sentence. "Certa quadam ratione" would, on that reading, translate to "ina certain particular pattern," and it is unclear what would be lost if we simplifiedthis to "in a certain pattern." If, by contrast, Spinoza is using the softening sense of'quadam\ the translation comes out as, "in what one might call a certain pattern."I do not ultimately think that this second reading is right, but I do not have anystraightforward reason for thinking so. The softening sense of quadam' just doesn'tfit with Spinoza's usually boldstyle, especially inhis definitions, whereashecommonlyuses redundant descriptions as ways of specifying his meaning.10

10Thebestexample ofSpinoza's redundancy,even incrucialclaims, is his unusual wayof expressing his conatus doctrine. Delia Rocca (1996b) hasobserved that Spinoza's claim that each thing,insofar as it is in itself, strives to persevere in its being (IIIp6) is redundant, in that the standardCartesian sense of theexpression lx does F insofar as it is in itself' and of theexpression 'x strivestodo F'are equivalent. So Spinoza'sclaim appears literally to mean, For each thing x, x's state


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"In a certain particular pattern" therefore seems to be a good translation of thekey phrase, "certa quadam ratione". So what does it mean to say that some bodiescommunicate their motions to one another in a certain particular, presumably complex, pattern? The communication of motions is itself a relation, of course, and weknow that the communication of motions required by Spinoza's definition is intendedto be two-waythe bodies "communicate their motions to each other in a certainparticular pattern". This suggests that the objects instantiating the pattern are notsupposed to be the bodies communicating their motion, but the occurrences of thecommunication of motion relation that those bodies exemplify. If the xs compose anindividual, the causal interactions among the xs are not momentary or accidental,but are (in some sense) the way the xs normally act on one another.11

We will want to know more about what it means for occurrences of communicatedmotion to follow a pattern, but already this interpretation suggests a few things aboutthe internal structure of individuals. First, to say that the communication of motionshappens in accordance with a certain pattern leaves open the question of how densethe network of causal powers binding the bodies must be. On the face of it, thenetwork of interactions connecting composing bodies could be quite sparse. If thisis right, it is not necessary for the bodies to communicate their motions to each ofis such that, unless prevented by external causes, x's state will be such that, unless prevented byexternal causes, x will persevere in its being (198). But this is nonsensical, so the best course istoread it as if Spinozahad usedonly oneof thepair of terms 'insofaras it is in itself' and 'strives '(199).nThis is arough sketchof the view, since I do not think Spinoza's viewson teleology ultimately

allow him toappeal to the paradigmatic normal functioning of an individual in a robust Aristotelian sense. AsI see it, Spinozawould wantsuch roughcharacterizations of normal activity tobe scrubbedoutof themostcareful formulationof the theory and replaced with statements referringonly to the efficient causal relations among the individual's parts. Themetaphysicianshould not besatisfied with explanations from final causes, for all final causes are nothing but human fictions(El Appendix;Geb 11/80). How, and whether, theelimination of teleologicalexplanation should becarried out isa matterof debate among commentators. (Topick twoprominent examples, Bennett(1984, 213-26; cf. 244-246) argues thatSpinoza wholly rejects teleology. Garrett (1999) replies thatSpinoza infact makes room fora certain sort of teleological explanation, namely the explanation ofanaction by appeal to the consciously intended goal of the action.)


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the others: several bodies might indeed communicate their motions to each of theothers, but this is not the only conceivable relation of communicated motions thatthey might bear. In other words, Spinoza should be read as requiring only that eachbody's motions be communicated to some, not necessarily all, of the others. Requiringthat any one of the bodies communicate their motions immediately to all the otherswould be too strong on the face of it, for it would ruleout taking the human body to bea composite individual, yet that is the one composite individual that Spinoza needsfor his later arguments.12 Most things that we recognize as composite individualshave distinct parts that are causally connected only transitively. My brain does notimmediately cause my hand to move, but starts a chain of causal events mediatedthrough other parts of the body. Further, when my brain causes my hand to move,it need not cause any motion in my toes.

Second, and related to the fact that the definitiondoes not require direct communication connectingevery part, it would seem unnecessary for each part to communicateits motions to the same connecting part. The pattern governing the communicationof motions among the various bodies need not be uniform. Whenever one of thebodies moves, its motion will produce a range of effects in the other bodiesbut thesize of this range will vary from motion to motion, from body to body. For any givenpart, some of its motions might be communicated to one part, other motions to another part. Some motions may produce drastic consequences throughout the rest ofthe communicating bodies, while others may have almost negligible effect. The network of causal powers binding the bodies will therefore often be distributed unevenly:some parts will communicate all of their motions to the same part, while others willcommunicate some motions to one part, some to another. The causal structure of anindividual may be quite imbalanced.

12See the propositions immediatelyfollowing the Physical Digression, IIpl4and onward.


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The final axis upon which we might measure the density of the network of causalrelations connecting the given bodies is whether or not each of them communicatesevery motion it undergoes. Again, since the pattern governing the communication ofmotions among the bodies is left almost entirely open, it does not seem necessary foreach of the bodies to communicate their entire range of motions. Most machines areconstruct

Spinoza's Account of Composition - John R. T. Grey

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