0199285756 - Rory Fox - Time and Eternity in Mid-Thirteenth-Century Thought - Oxford University...

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THE TROUBLES OF TEMPLELESS JUDAH

Jill Middlemas (2005)

Time and Eternityin Mid-Thirteenth-Century Thought

Rory Fox

1

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Preface

This book began life as a D.Phil. thesis (1999) and I would

like to take the opportunity to acknowledge some of the

debts incurred in bringing that thesis to completion. I owe

particular thanks to Professor Richard Swinburne for his

patient and thoughtful supervision of the thesis. Without

his assistance, I would never have been able to embark upon,

or complete, a research project of this kind.

I would also like to thank Fr. Henry Wansbrough, the

Master of St Benets Hall, for extending the hospitality of the

Hall to me throughout the time of my studies. I am specially

grateful to the Warden and Fellows of Keble College for

electing me to the Liddon Junior Research Fellowship

19957, and to Merton College for providing means for

me to return to Oxford in the Summer of 2000 to begin

the process of revising the thesis. I am indebted to the

British Academy for financial support and to the Oxford

University Theology Faculty for awarding me the Denyer

and Johnson scholarship. Amongst those who provided

helpful feedback, I would like to acknowledge the contribu-

tions of Richard Cross, Dominic Perler, John Marenbon and

Cecilia Trifogli. Finally, I thank my wife Helen for her help

with the final draft and support throughout.

RF

January 2005

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Contents

Introduction 1

1. The Language of Time 10

2. Temporal Simultaneity 50

3. Priority, Posteriority, and Causality 95

4. Relations and Reductions 130

5. The Reality of Time 165

6. On Measurement and Numbering 193

7. Time and Atemporality 225

8. Sempiternity, Angelic Time, and the Aevum 244

9. Eternity 282

10. God and Time 309

Bibliography 330

Subject Index 359

Index of Ancient and Medieval Text References 366

Index of Ancient Medieval and Pre Modern Authors 382

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Introduction

The purpose of this study is to examine thirteenth-century

views about time, particularly the views of Thomas Aquinas

and his contemporaries in the middle of the century. As

medieval thinkers typically considered time to be just an-

other duration alongside the durations of aeviternity (the

aevum) and eternity, the scope of the study extends to cover

all three durations, culminating in an examination of Gods

relationship to time.

The motivation for this study arose from a dissatisfac-

tion with standard accounts of Aquinas views on the ques-

tion of Gods knowledge of future contingents. Rather than

sensitively exegeting what thirteenth-century thinkers were

actually trying to say, some contemporary treatments

seemed to me to be at risk of eisegeting contemporary

ideas and philosophical frameworks into the medieval lan-

guage and thought which they claimed to be critiquing. In

order to avoid this problem it seemed to me that I needed to

give significantly more space than was customary, to exam-

ining the framework in which thirteenth-century thinkers

were discussing the question of knowledge of future contin-

gents. I therefore decided to embark upon a study which

I envisaged extending to three volumes. Part 1 would be my

doctoral thesis and would focus on thirteenth-century views

of time, concluding with a preliminary interpretation of

thirteenth-century accounts of Gods relation to time. Part

2 would examine thirteenth-century accounts of knowledge,

causation, and agency; and Part 3 would draw together the

elements of the study from Parts 1 and 2, to offer what I

believed would be a more sensitive account of Aquinas

views about Gods knowledge of future contingents.

This volume represents Part 1 of that study, outlining

what I believe to be the elements of a medieval approach to a

philosophy of time. It culminates with what will be the

somewhat contentious claim that Aquinas God, and the

God of his contemporaries, should not be thought of as

timeless. This is not to say that we should think of such a

God as existing in time. It seems to me that medieval

thinkers are struggling to say something entirely different,

something which it is anachronistic to think can be captured

with the modern distinction between timeless and everlast-

ing existence. Instead, I suggest in the concluding chapter

that the most accurate representation of their views is as

claiming that God is outside but existing along with time.

Whether that represents an ultimately coherent conception

or not I leave an open question at the moment, as my

purpose in this particular study is simply to arrive at judge-

ments about what views can accurately be ascribed to Aqui-

nas and his contemporaries.

It will be helpful before embarking on this study to set

out some of my methodological assumptions. One of the key

assumptionswhich Imake is that thirteenth-century thinkers

2 Introduction

shared a world view about time. It is a world view that can

often be detected between the lines of what they actually say,

but which is not always stated clearly by particular individ-

uals in particular discussions. Although it can be potentially

misleading to look for a common world view amongst the

writings of a disparate group of thirteenth-century philo-

sophers, especially when elements of the account have to be

reconstructed, one of the things that I believe that this study

does demonstrate is that there were significant common

threads in medieval thought. An appreciation of which

helps us to better understand the nuance and import of

both what figures such as Aquinas were writing and what

was at issue when isolated propositions concerning dur-

ational issues were identified and condemned.1

This study is focused upon thirteenth-century writers

whom I shall also occasionally refer to as medieval figures. I

make no pretence to offer a comprehensive survey of all

thirteenth-century writers. Instead I have focused on the

three undisputedly central figures of Thomas Aquinas, Albert

the Great, and Bonaventure, introducing other figures to

illustrate how widely a view was held or to indicate nuanced

differences.Where the views of earlier writers such as Augus-

tine or Boethius, or later writers such as Ockham or Cajetan,

help to illustrate an issue, I have also occasionally made

1 Amongst the propositions condemned in 1277 were at least five whichinvolved durational issues. For further information see propositions [57],[87], [100], [156], [200] in H. Denifle and E. Chatelain, Chartularium Uni-versitatis Parisiensis, i. 54455 and on the condemnation itself, J. F. Wippel,The Condemnations of 1270 and 1277 at Paris, 169201. R. Hissette,Enquete sur les 219 articles condamnes a` Paris le 7 mars 1277, 14757.

Introduction 3

reference to them, but in doing so I make no attempt to set

out anything like a background to thirteenth-century views.2

Noticeably absent from this study is an extended treat-

ment of such major (later) thirteenth-century figures as

Henry of Ghent, and Scotus. I have occasionally introduced

their contributions to the debate, but it seemed to me that

many aspects of their thought warranted an extended treat-

ment which it was simply not possible to include within the

scope of the present study. Consequently it seemed better to

leave consideration of their thought for a separate study.3

Rather than taking a historical structure for this investiga-

tion, examining figures sequentially, and comparing and con-

trastingdevelopments inworksofdifferentdates, Ihave instead

2 There is an extensive literature analysing the ancient and patristic back-ground to thirteenth-century thought on time. On Aristotle, M. White, TheContinuous and the Discrete, 3115. R. Sorabji, Time, Creation and theContinuum, 4651, 8497. J. Annas, Aristotle, Number and Time.H. Barreau, Le traite aristotelicien du temps. M. de Tollenaere, AristotlesDefinition of Time. For a bibliography of works on Aristotles concept oftime, E. Hussey, Aristotles Physics, Books III and IV, 2017, and for an analysisof the different translations of Aristotles Physics in use during the twelfth andthirteenth centuries, B. G. Dod, Aristoteles Latinus. For studies of patristicaccounts of time, B. Otis, Gregory of Nyssa and the Cappadocian Concep-tion of Time. J. F. Callahan, Four Views of Time in Ancient Philosophy, 88187. For a discussion of aspects of medieval views on time, A. Mansion, Latheorie aristotelicienne du temps chez les peripateticiens medievaux: Aver-roe`s, Albert le Grand, Thomas dAquin, 27988. J. M. Quinn, The Conceptof Time in Albert the Great. V. C. Bigi, La dottrina della temporalita` e deltempo in San Bonaventura, 43788. J. M. Quinn, The Doctrine of Time in St.Thomas: Some Aspects and Applications, 1555. J. M. Quinn, The Concept ofTime in Giles of Rome, 31052. V. C. Bigi, Il concetto di tempo inS. Bonaventura e in Giovanni Scoto. R. C. Dales, Medieval Discussions ofthe Eternity of the World, passim. R. C. Dales, Time and Eternity in theThirteenth Century. A Maier, Metaphysische Hintergrunde der Spatscholas-tischen Naturphilosophie, 45137.

3 Elements of Scotus account of time are explained in R. Cross, The Physicsof Duns Scotus, 21456, which supplants earlier treatments of the question, all

4 Introduction

organized this book thematically. Chapter 1 opens the discus-

sion by examining some of the key language and terminology

which thirteenth-century thinkers used. Chapters 25 then

proceed to examine the topological properties of time: those

properties that determine its shape and structure. Chapter 6

investigates the metrical properties of time: those properties

thatpertain to timewhen it is consideredas ameasure.Chapter

7 rounds off the examination of time by looking at the criteria,

factors, and language which thirteenth-century thinkers typ-

ically took as entailing that a particular would be in time.

Chapter 8 opens the exploration of what I will term atempor-

ality by examining how thirteenth-century thinkers discussed

existence outside of time, particularly as it was applied to

aeviternity andaeviternal beings.Chapter 9moves on to exam-

ine the last of the atemporal durations, eternity; investigating

both the content of the medieval concept of eternity, and also

how we might best render those ideas in contemporary lan-

guage. Chapter 10 concludes the study by examining the spe-

cificquestionof how thirteenth-century thinkers viewedGods

relationship to time.

of which are recorded in Crosss bibliography. Amongst other figures writingafter Aquinas death, I have also included occasional references to the figureswho contributed to the Correctorium literature. Although this literature wasproduced some 1520 years after Aquinas death it features conflicts anddisagreements about Aquinas writings that often involve durational aspects.The original Correctorium was written by William de la Mare but many of thereplies to his work were written anonymously so I have followed Roenschsidentification of sources, attributing the Correctorium Correctorii Quare toRichard Knapwell, The Correctorium Correctorii Sciendum to Robert Orford,and the Correctorium Correctorii Quaestione to William Macclesfield. Forfurther details see F. J. Roensch, Early Thomistic School, 2857 and P. Glorieux,La Faculte de Theologie de Paris et ses Principaux Docteurs au XIIIe Sie`cle.

Introduction 5

The neatness of attempting to divide this book in this

way is undermined in places by the fact that thirteenth-

century thinkers seem to have generally been confused

about the differences between topological and metrical

properties. This meant that they were not averse to appeal-

ing to metrical issues in order to settle what were actually

topological questions and vice versa. Where this occurs

I have tried to distinguish the various elements of the dis-

cussion, but it means that sometimes specifically topological

and metrical considerations have had to be introduced

where otherwise they would not have been.

As this study contains such a large exegetical dimension,

involving judgements based on the interpretation of specific

Latin words and texts, I have tried to include as much of the

medieval source material as possible. Where it appears in the

main body of text it is always translated, but I have generally

left its appearance in footnotes untranslated. To translate it

all would add so significantly to the length of this book as to

make it impracticable. For the sake of non-Latin readers I

have tried to ensure that the point made by Latin texts is

clearly brought out in the main body of the text, so that

there is nothing lost in being unable to read the actual Latin

words themselves.

When it comes to references to sources I have adopted the

convention of referring to sources with their medieval ref-

erences. Unfortunately there was no standard way of setting

out medieval books and even individual authors were not

always consistent between their works. This means that a

reference in the footnotes such as 1.1.1 could mean book

(liber) 1, question (quaestio) 1, article (articulus) 1, or volume

(tomus) 1, book (liber) 1, tractate (tractatus) 1; or it could

6 Introduction

even be referring to some other classification system. The

key to interpreting references to medieval texts is to take the

name of the text in question and to apply the numerical

references to the particular breakdown of text divisions

found within that specific text.

Where there exists a principle modern critical edition of a

text I have endeavoured to provide a volume, page, and line

reference for citations. References always occur in that order.

Occasionally volumes are further divided into sub-volumes

and so occasionally a volume reference will appear in the

form 4.2 where it means volume 4, sub-volume 2. Where

references in parenthesis consist of less than three numbers

the interpretation of the numbers should be determined by

whether the work exists in different volumes and whether it

includes line numbers. A text that does not include line

numbers and exists in a single volume will have merely a

single numerical reference indicating the page number.

Although I have tried to use modern critical editions, this

has not always been possible. In the case of Albert the Great I

have used wherever possible the relatively new Aschendorf

(Cologne) critical edition, but as the series is still incomplete

I have had to supplement it by resorting to the older and less

reliable Vives edition, edited by A. Borgnet.

A similar situation arises with Aquinas. Some of his works

now exist in the critical Leonine edition, but not all. Some of

the earlier volumes of that series were rushed out so quickly

that they are not proper critical editions as we would now

use that term, so some care is needed in basing an argument

on a specific occurrence of terms in those texts. Even where

there are critical Leonine versions of Aquinas texts, often

the texts have been reprinted by other publishers and now

Introduction 7

circulate in editions which are relatively more accessible

than the actual Leonine texts themselves. For these reasons,

and as a way of trying to reduce the complexity of references

in long footnotes, unless there is a very specific reason for

giving a page and line reference to the Leonine edition, such

as a text with a substantial amount of prose that would have

to be read in order to identify what the reference is appealing

to, I have generally cited Aquinas texts with just the medi-

eval text reference.

I have occasionally quoted Aristotle. As thirteenth-century

thinkers almost all read Aristotle in Latin translations, and as

their discussions often meander along courses dictated by

the idiosyncrasies of their translations of Aristotle, it seemed

to make more sense to quote Aristotle from his medieval

translations rather than from the Greek texts which we are

familiar with today. This means that I have taken all quotes

for Aristotle from the Aristoteles Latinus series.

One of the most difficult and complex areas of medieval

studies is establishing the authenticity of texts and authors.

Often texts circulated with multiple names and titles at-

tached to them. Textual evidence indicates that the de Tem-

pore, attributed to Aquinas, is not an authentic work of his,

and as this is now generally accepted by scholars I have

referred to it throughout as being written by Pseudo-

Aquinas. Some texts were written by multiple authors and

this gives rise to particular difficulties in how to refer to

them. We know, for example, that parts of Alexander of

Hales Summa Theologiae were finished after his death and

parts that he himself wrote were revised and altered by

others. The authority and influence of the Summa Theolo-

8 Introduction

giae attributed to Alexander is such that it is important to

include consideration of the text in this study, but in doing

so I acknowledge that the relationship of the historical

Alexander to individual sentences of his text is much more

complex than I explicitly allow for. It would unduly com-

plicate and lengthen already long footnotes if I were to try to

flag up issues of authorship such as this, especially as there is

often disagreement about these matters amongst contem-

porary scholars. As a general policy for dealing with extracts

from texts such as Alexanders Summa, unless there is clear

and generally accepted evidence to the contrary I have

simply cited named authors such as Alexander as the author.

As my methodology is analytic and exegetical, I have

largely avoided wider questions to do with the nature and

transmission of texts, historical relationships between

authors, and the relationship of thirteenth-century thought

to other periods. These are all important issues in the study

of medieval thought, but they transcend the scope of this

particular work. Many of the historical and textual issues

have been addressed by other authors and the issues exam-

ined by this book are so relatively self-contained and tightly

circumscribed that there is no need to explore historical and

textual questions in order to understand and appreciate

what it was that figures in the mid-thirteenth century were

saying about God and time.4

4 For an introduction to historical and textual information about the mid-thirteenth-century figures featured in this study see J. Marenbon, LaterMedieval Philosophy (11501350), 194231, and N. Kretzmann et al. (eds.),The Cambridge History of Later Medieval Philosophy, 85592. On the histor-ical significance of mid-thirteenth-century thought a recent overview isprovided by P. Porro (ed.), The Medieval Concept of Time: The ScholasticDebate and Its Reception in Early Modern Philosophy.

Introduction 9

1The Language of Time

Thirteenth-century thought about time was inXuenced by a

wide variety of sources: Christian, Jewish, Arabic, and pagan.

From the many Wgures within these traditions two sources

stand out above all others: St Augustine as representative of

the Christian tradition and Aristotle as representative of the

pagan non-Christian tradition. As a measure of Aristotles

importance to thirteenth-century thinkers it need only be

noted that he was universally referred to as the philosopher

(philosophus).

One of the most signiWcant of Aristotles works for the

philosophy of time was the Physics. Although it was the

middle of the thirteenth century before reliable translations

circulated freely, this work had been translated and was

inXuencing medieval thinkers from as early as the middle of

the twelfth century. This means that Aristotles inXuence can

be detected in thoughts and formulations about time from

the very beginning of the thirteenth century.1

1 On the medieval Latin translations of Aristotles Physics, see A. Mansion(ed.), Aristoteles Latinus 7.1, ixxvii and B. Dod, Aristoteles Latinus. On thebroader question of sources and intellectual inXuences, G. LeV, Paris and

As with almost every area of philosophy, Aristotles con-

tribution was essential and dramatically signiWcant. In the

case of time, he provided not only a vocabulary and a

framework in which to discuss the notion, but perhaps

most importantly of all he had provided a deWnition.

Time, he had insisted was simply:

the number of before and after in motion2

Despite its apparent simplicity, this deWnition prompted a

wide-ranging set of questions for medieval thinkers. What,

for example, were they to make of a reference to a before and

after? Was it to be thought of as a kind of thing or as a

relation? And if it is a relation then what are the relata, and

what constitutes the relation? Furthermore, was the reference

to motion an appeal to motion in general or was it referring

to a speciWc motion, perhaps even a speciWc kind of motion?

And what does it mean to say that time is a number? Did

that mean that it was to be thought of as existing in the way

that abstract numbers exist? Moreover, what sorts of things

were to be accepted as being in time and what were the

criteria for deciding an answer to that question? Was time

to be thought of as having a beginning and an end? Is there,

or could there be, more than one time? And so the questions

went on. Aristotles deWnition of time was a useful contri-

bution to debates about the nature of time, but for the most

Oxford Universities in the Thirteenth and Fourteenth Centuries, 12737;J. Marenbon, Later Medieval Philosophy, 5364; M. Haren, Medieval Thought:The Western Intellectual Tradition from Antiquity to the Thirteenth Century,3782; andP.Dronke,AHistory of Twelfth-CenturyWestern Philosophy, 54148.

2 hoc enim est tempus: numerus motus secundum prius et posteriusPhys. (Vetus) 4. 11 (AL 7.1.2, 175).

The Language of Time 11

probing thirteenth-century thinkers it could only be, at best,

a starting-point.

This was particularly so as Aristotle himself had actually

provided a slightly diVerent approach to the question of time

in yet another of his works, the Categories. Translated into a

popular Latin edition by Boethius in the sixth century, the

Categorieswas sowidely studied that no educated thirteenth-

century thinker could be unaware of its existence and con-

tent. In the Categories, Aristotle had developed a categorical

framework dividing reality into diVerent kinds of existence

such as substances (which have existence in their own right)

and accidents (which can only exist in substances). Attempt-

ing to apply that distinction to time he had concluded that it

could not be a substance, and so that it must be an accident,

and an accident of a type that he labelled quantity. This was a

rather diVerent approach than was to be found in Aristotles

Physics and the briefness of the discussion gave rise to more

questions than it settled. According to the Categories, acci-

dentsmust inhere, or exist, in substances and so if timewas to

be thought of as just an accident then a question immediately

arose as to what was the substance in which it inhered? If it

was to be thought of as a quantity, then it was necessary to

establish what precisely it was a quantity of, and most fun-

damentally of all questions arose about the relationship be-

tween the account set out in theCategories and the account in

the Physics. Were they to be seen as discussions of time which

had equal authority or did one represent further develop-

ment of the other?.

As if the Categories and Physics had not provided enough

questions and challenges for medieval thinkers, they were

12 The Language of Time

also confronted by the peculiarly medieval Christian re-

quirements of authority and tradition. If their conclusions

were to have validity as expressions of Christian theology

then they needed to be integrated with, and demonstrably

consistent with, the traditional authoritative patristic writ-

ings of the ancient Christian fathers. As many of the Chris-

tian fathers were heavily inXuenced by Plato, against whom

Aristotle was often reacting, there was a tendency to Wnd a

bedrock of often disparate and not always reconcilable

philosophical views lying beneath a surface level of theo-

logical reXection. This inevitably gave rise to its own prob-

lems of integration.

Nevertheless in the case of reXection about time, there

was a superWcial overlap between the diVerent approaches.

Patristic authors had tended to focus upon cataloguing and

labelling diVerent quantitative elements of time. St Bede, for

example, had identiWed at least Wfteen quantitative elements,

all of which corresponded to terms used to distinguish

temporal divisions such as day, month, year, and so on.3

AlthoughAristotle had not been interested in enumerating

a full list of terms for temporal divisions, he had focused on

time as a quantitative phenomenon and so it is not altogether

surprising that the divisibility of time into quantitative con-

stitutive parts was an important focus for thirteenth-century

3 For more details about Bedes account see his de Temp. (ed. Weber Jones,295303). Although possessing considerable authority Bedes account repre-sented only one of many diVerent approaches to this matter. St Isidore ofSevilles account of time proposed just eight fundamental temporal quanti-tative elements, Etym. 5. 29 (1, 1521).


thinkers who wanted to reconcile patristic authorities with

Aristotelian philosophy.4

Focusing upon the quantitativeness and divisibility of

time, thirteenth-century thinkers found Aristotles distinc-

tion between the temporal elements of parts and boundaries

to be an important part of their analyses. In order to explain

this distinction, Aristotle himself had suggested the analogy

of a geometrical line consisting of line segments (or parts)

into which it could continuously be divided. Bounding the

line, and indeed bounding each of its parts, are points. These

points are distinguished from the line segments in virtue of

the fact that the line and its parts are quantitative and can

always be divided into further quantitative parts, but the

point is deWned precisely in terms of its non-quantitative-

ness, as that which has no part.5

With parts and boundaries deWned in this way, a clear

logical distinction between them is established. Parts are div-

isible and boundaries are (logically) indivisible. In order to

express this distinction medieval thinkers had the option of

4 Aquinas, In Met. 5. 15 [977]. Albert, Meta. 5. 3. 1 (16.1, 256, 2535)5 Aristotle, consequenter quidem enim est quorum nullum est medium

proximum, punctorum autem semper medium est linea et ipsorum nunctempus est Phys. (Vetus) 6.1. 231b710 (AL 7.1.2, 217) and InWnitis quidemigitur secundum quantitatem non contingit sese tangere in Wnito tempore,eius autem que sunt secundum divisionem contingit; et namque ipsumtempus sic inWnitum est . . . (ibid. 224). Aquinas, deWnimus punctum,cuius pars non est Sum. Theol. 1. 11. 2 ad 4; In Phys. 6. 1 [755], 6. 2 [765].Bonaventure, In Sent. 3. 29. 1. 2 ad 5 (1, 643) and In Sent. 1. 8. 2. 1. 2 arg. 2(1, 167) and with an attempt to explain the nature of a point, 1. 17. 2. 1. 2 arg.2 (1, 312). Theodoric of Freiberg, Tr. de Nat. et Prop. Contin. 1 (3, 252,3943). Albert,Meta. 5. 3. 2 (16.1, 260, 40), de Prin. Mot. Proc. (12, 50, 12),who also points out that this deWnition is taken ultimately from Euclid. Sum.Theol. 5. 1. 1. 1 (34.1, 124, 356).


using the Latin word indivisibile but in doing so they were

not always alert to the fact that ancient philosophers had

bequeathed to them two diVerent conceptual notions of in-

divisibility: logical indivisibility and physical indivisibility.

Logical indivisibility is particularly evident in the notions

of the point and boundary which are deWned as having no

parts into which they can be divided. Because they are

deWned as having no parts then it makes no logical sense

to talk of a point or boundary as having a part. The alter-

native concept of indivisibility is physical indivisibility and

this is encountered in those particulars often referred to as

atoms. Although they were considered to be indivisible, they

were clearly not thought of as logically indivisible. Instead

their indivisibility was thought to arise because there were

no natural processes or powers which could divide them.

Temporal atoms, or chronons as contemporary philosophers

might refer to them, were thus thought of as extended

indivisible elements because they were supposed to be such

small amounts of time that there were no actual processes

for dividing them.6

6 Medieval use of the word atom varied signiWcantly between authors.Albert, for example, contrasts an acceptable usage of in atomo nunc with theunacceptable use of in atomo tempore Phys. 8. 3. 6 (4.2, 634, 37), andAquinas echoes this approach by insisting that atoms can have no extension,In Phys. 6. 3 [769]; In de Caelo 1. 12 [122]. Authors such as Bede and MosesMaimonides were more open to the idea that atoms could possess theproperty of extension. For further information and references to texts,R. Sorabji, Atoms and Time Atoms, and with more detail about Aquinasposition, E. J. MacKinnon, Thomism and Atomism. For more comprehen-sive discussions of medieval atomism, B. Pabst, Atomtheorien des LateinisherMittelalters and A. Maier, Kontinuum, Minima Und Aktuell Unendliches.For a contemporary philosophical account of what temporal atomism wouldamount to see, G. J. Whitrow, The Natural Philosophy of Time, 2005.


The distinction between physical and logical indivisibility

is essential for appreciating the claims made by contempor-

ary advocates of what has come to be known as the specious

present. Although advocates explain the notion in diVerent

ways, ultimately it is a concept of a physically indivisible

boundary of time lying between the past and the future,

such that it constitutes an ever-changing, extended present

time.7

Most mid-thirteenth-century thinkers would have found

this hypothesis uncongenial, if not unintelligible, for to them

the notion of an extended present would have seemed to be

simply an example of the atomism of Democritus or Leucip-

pus, which had been refuted long previously by Aristotle, and

more recently by Averroes.8

Aristotle provided a variety of explicit arguments against

atomism, and further ones were identiWed in his texts by

commentators. One of the most popularly quoted argu-

ments during the thirteenth century was developed particu-

larly forcibly by Averroes, who also labelled it as the velocity

argument. The argument proceeds by taking two token

particulars S1 and S2, and a distance D which they traverse

7 Classic descriptions of the specious present can be found in W. James,Principles of Psychology, i. 60542; C. D. Broad, ScientiWc Thought, 34858,and J. D. Mabbot, The Specious Present. The notion has also been called thepsychological present (G. J. Whitrow, The Natural Philosophy of Time, 747)and even the precious present (A. C. Moulyn, The Functions of Point andLine in Time Measuring Operations, 1501). On the notion of the speciouspresent and its application to models of eternity see, in particular, A. F.Whitehead, The Concept of Nature, 668 and J. F. Harris, An EmpiricalUnderstanding of Eternality, 17481.

8 Albert, de Gen. et Cor. 1. 1. 11 (5.2, 120, 58); de Caelo 1. 2. 1 (5.1, 32,8792); Phys. 6. 1. 3 (4.2, 4513); Aquinas, de Gen. et Cor. 1. 3 [20], [23]; InPhys. 6. 2 [758][765]. Grosseteste, In Phys. 6 (11618).


in a time T. If S1 is postulated as traversing D in T, then S2travelling at double the velocity of S1 would traverse D in

12T. If we now imagine S1 to speed up so that it is travelling at

twice the velocity of S2, then it would traverse D in14 T. By

continuing this thought experiment and alternating the

relationship between the respective velocities of S1 and S2ad inWnitum, the velocity argument demonstrates that time

must be inWnitely divisible and that there can be no indivis-

ible extended parts of time.9

The implications of this argument for what we would now

refer to as the specious present, are severe. The concept of a

specious present assumes that there can be a time T that is

indivisible but the velocity argument shows that for any

specious present T, it is always possible to think of an S1and S2 alternating in velocities in such a way that it is neces-

sary to postulate fractions of T. And so the implication of

9 ForAverroes argument ex natura velocioris et tardioris, see his commen-tary In Phys. 6 [22] on Aristotles text, Phys. 6. 2 (232a23233a12). It has beensuggested (D. Bostock, Aristotle on Continuity in Physics VI) that becausevelocity is determined as a function of dividing time and motion then Aris-totles argument begs the question at issue, viz. the inWnite divisibility of time(andmotion).Whetheror not this is an accurate criticismofAristotle, it wouldcertainlynot seemtoapply tomedieval thinkers.Aswe shall seemore fully later,Aquinas and hismedieval colleagues thought that this argument did not applyto the movements and durations of angels and this limitation of the argumentsuggests that despite sometimes loose expressions of the argument to thecontrary (e.g. Aquinas, InSent. 4. 44. 2. 3) thinkers such asAquinas understoodthe argument tobe a conditionalone claiming that if eithermotionor timewereinWnitely divisible then necessarily they both were. For an account of themedieval use ofAristotleswider arguments against atomism see J. E.Murdoch,Superposition, Congruence and Continuity in the Middle Ages, 4214. Inreality there were a wide variety of arguments that mid-thirteenth-centurythinkers could appeal to. Albert refers to an argument from tenses, Phys. 4. 3.1 (4.1, 25961) and Aquinas seems to imply that one can be based on theperceptibility of times, de Sen. et Sen. 18 [270][275].


Aristotles argument is that the very concept of a specious

present must be incoherent.

In order to refer to the logically indivisible boundaries and

divisible parts thirteenth-century thinkers found it useful to

use the Latin terms discretum and continuum, using the

word discretum to pick out the indivisible points and

boundaries whilst the term continuum was used to refer

to the divisible parts and line segments.10

Useful though these termswere tomedieval Latin speakers,

rendering them in English presents some diYculties. As the

English language contains the apparently similar terms, dis-

crete and continuous, it is tempting to assume that these

Englishwordsaccurately translate theLatin terms,but suchan

assumptionwouldbemisleading.Whilst theLatindistinction

is intended to be logically exhaustive, the distinction ex-

pressed by these two English terms is not. In Latin, orderings

can be distinguished as a discretum or a continuum, but in

English the distinction is between discrete, continuous, and

dense. Sowithout further investigation it cannot be assumed

that the English words discrete and continuous are accur-

ately translating the Latin terms discretum and continuum.

The word discrete is used by contemporary English-

speaking mathematicians to construe the property of an or-

dering in which each member has a unique successor. Ex-

amples of such an ordering might include the set of positive

10 Aquinas, In Phys. 6. 5 [789]; In Meta. 3. 13 [507]; 5. 19 [1044][1045];In de Caelo 1. 12 [122]; Albert,Meta. 5. 3. 2 (16.1, 259, 7882). In Sent. 1. 9. 1. 2(Borg. 25, 273). Phys. 6. 1 (4.2, 447, 23); 3. 4 (4.2, 495, 513); Theodoric, Tr.de Nat. et Prop. Contin. 1 (3, 252, 218) and 2 (3, 255, 1029). Bonaventure,Hex. 3 [5] (5, 344).


and/or negative integers in which each numeral has a speciWc

predecessor and successor. The property of density is con-

strued in contradistinction as the property of an ordering in

which nomember has a unique successor and/or predecessor.

According to this deWnition, between each and everymember

of the dense ordering there is always another member, ad

inWnitum. Perhaps the clearest example of a dense ordering

would be the set of positive and/or negative rational numbers

(fractions). For any rational number that is taken, there is

never aunique next number. It is alwayspossible topostulate

yet another number between them. Between 12 and 1 for

example 34 could be placed, but between12 and

34 the number58 could be placed, and between

12 and58 there is the

number 916, and so on. For any fraction there is no unique

predecessor or successor because for any given number it is

always possible to identify another between them.

Density might seem suYcient as a description of a com-

plete set of numbers, but a dense ordering has what we

might think of as gaps. It does not contain root 2, nor

other numbers which cannot be represented as a rational

number. So the set of Real Numbers, containing integers,

rational numbers, and values such as root 2, cannot be

adequately described as merely dense. In order to reXect

the fact that it contains numbers such as root 2 another term

must be used to describe the ordering, and the term used for

this purpose is continuous. A continuous ordering is one

which is more than dense, it has no gaps.11

11 For more details on the notions of continuity and density, R. Dedekind,Essays on the Theory of Number, 1224 and more generally E. V. Huntington,The Continuum and Other Types of Serial Order.


In order to appreciate the content of the medieval Latin

terms, it is useful to begin with the term continuum against

which the term discretum can be explicated. The medieval

notion of a continuum is based closely on Aristotles work

and so construed as a species of successiveness and contigu-

ity. In Aquinas words:

Continuity is a species of contiguity. For when two things which

touch have one and the same terminus, they are said to be

continuous, and this is what the word (continuous) means . . .

When, therefore, many parts are contained in one, and are held as

if together, then there is a continuum. This cannot occur when

there are two extremities, but only when there is one.12

Commentators on Aristotle have never found it easy to

explain his notions of touching and being held together.

Perhaps this is why Albert seems to prefer giving examples

of the idea rather than trying to deWne it carefully.13

We can get a rough idea of what medieval thinkers meant

by thinking of a line bisected at a point. The cut goes

12 continuum est aliqua species habiti. Cum enim unus et idem Watterminus duorum quae se tangunt, dicitur esse continuum. Et hoc etiamsigniWcat nomen . . . quando igitur multae partes continentur in uno, et quasisimul se tenent, tunc est continuum. Sed hoc non potest esse cum sint duoultima, sed solum cum est unum. In Phys. 5. 5 [691]. On the notion ofhabitus, Albert informs us that habitum enim est quando ultima suntsimul, Phys. 5. 2. 3 (4.2, 425, 35). On the more general point at issue, noteAristotles deWnition, Linea vero continua est; namque est sumere commu-nem terminum ad quem partes ipsius coniunguntur, hoc est autem punc-tum, et superWciei linea (superWciei enim partes ad quendam communemterminum coniunguntur). Aristotle, Cat. (trans. Boethii) 6.5a15 (AL 1.1,14); Phys. 5. 3. 226b19227b2 (AL 7.1.2, 200).

13 Phys. 5. 2. 3 (4.2, 425, 4454). On Aristotles usage, E. Hussey, Aristotle,Physics, 11315.


through a single point which will then act as a single bound-

ary to both the left and right segments of the line. By

extension, and thinking back from this, we can then think

of these two segments as joined together, as perhaps even

touching and held together at the cut, and it is this that makes

the two segments a continuum, in the medieval sense. As

anything that admits of this sort of cut could be considered

as a continuum then, by extension, the term came to be

synonymous with the predication of inWnite divisibility.14

The concept of a discretum is deWned against the notion

of a continuum, and as such simply implies the lack of a

common boundary at which particulars can be said to join

or to be able to join. Aristotle gives the example of a number

series, 1, 2, 3, which consists of distinct elements which can

be added but, unlike chairs and tables, they cannot be cut

such that their parts can then be joined at a common

boundary. Numbers dont have parts, they are discrete indi-

visible entities constituting by addition aggregates rather

14 Aristotle, Dico autem continuum divisibile in semper divisibilia . . .Phys. 6. 2. 232b25 (AL 7.1.2, 222); Albert, Phys. 3. 1. 1 (4.1, 146, 38); Aquinas,In Phys. 3. 1 [277]; 3. 12 [393][395]; 6. 1 [757]. Grosseteste, In Phys. 6 (117).Theodoric, Tr. de Nat. et Prop. Contin. 1 (3, 251, 17). It is important to stressthat the inWnity of the divisibility means that there is merely an inWnity ofpotential places inwhich one could cut or divide the particular in question. AsAquinas notes, it does not mean that any particular is capable of an actualdivision at an inWnity of locations simultaneously, geometra non indigetassumere aliquam lineam esse inWnitam actu, sed indiget accipere aliquamlineam a qua possit subtrahi quantum necesse est, et hoc nominat lineaminWnitam Sum. Theol. 1. 7. 3 ad 1; In Sent. 2. 2. 1. 1 ad 6. The contemporarywillingness to recognize the possibility of just such an inWnite simultaneousdivisibility denotes one of the principal diVerences between medieval andmodern notions of inWnity. For further details, A.Moore,The InWnite, 11030.


than extended continua. And so it was entities such as

numbers that were typically referred to as a discretum.15

It should be clear by now that the Latin terms continuum

and discretum do not mean exactly the same as the English

terms continuous and discrete.Whilst the conceptsdenoted

by the English term discrete and the Latin word discretum

seem to be co-extensive, there are signiWcant diVerences be-

tween the notions implied by the Latinword continuum and

the English word continuous. We have seen that the Latin

word continuum is deWned in terms of the notion of inWnite

divisibility, but it is the Englishword dense, not continuous,

which is similarly so deWned. So, although continuous is

often used as the translation for continuum, it is not entirely

adequate. Nevertheless, as it is such a popular way of translat-

ing continuum, to substitute another term might actually

causemore confusion.Despite thepotential conceptual prob-

lems surrounding using continuous for continuum I shall

continue to do so in this book, but in doing so I stress the

signiWcance of the considerations above as determining the

content of the translation.16

15 Aristotle, Quantitatis aliud est continuum, aliud disgregatum atquediscretum; et aliud quidem ex habentibus positionem ad se invicem suispartibus constat, aliud vero ex non habentibus positionem. Est autem dis-creta quantitas ut numerus et oratio, continua vero ut linea, superWcies,corpus, praeter haec vero tempus et locus. Cat. (Trans. Boethii), 6. 4b2035 (AL 1.1, 13); Albert, continuum est in cuius medio accipere est punctum,ad quem copulantur ambae medietates per hanc enim naturam continuumseparatur a discreto Phys. 3. 1. 1 (4.1, 146, 436); 6. 1. 1 (4.2, 447, 327).Aquinas, Quaest. disp. de Pot. 9. 7 sed con. 7.

16 For examples of traditional translation compare Aquinas, In Phys. 1. 3[22] with the translation in R. Blackwell et al. (eds.), Commentary onAristotles Physics by St. Thomas Aquinas, 16.


TEMPORAL TERMINOLOGY

Having clariWed some of the fundamental terms and con-

cepts for referring to parts and boundaries, we can now

focus on how those notions were applied to time, and in

particular to the distinct temporal terminology that was

utilized in doing so.

Altogether, thirteenth-century thinkers seem to have

deployed ten basic terms to refer to temporal elements:

instans, praesens, nunc, periodus, momentum, duratio, mora,

diurnitas, protensio, and quando. Of these terms the Wrst six

can seem deceptively straightforward because they seem to

have prima facie English equivalents, so it is on those and

their apparent equivalents that we shall initially focus.17

17 The meaning of these Latin and English words is particularly complexas diVerent authors have taken diVerent terms to be synonyms of each other.For examples of the Latin words used as synonyms of each other see theeditorial scholion in S. Bonaventurae Opera Omnia 3.92. For examples ofdiVering English words used as synonyms of each other see J. Owens, AnElementary Christian Metaphysics, 207, and G. E. L. Owen, Aristotle onTime, 141. Similar policies can be seen with languages such as French asindicated by J. Nizet, La temporalite chez Soren Kierkegaard, 227. On someoccasions translators establish their own idioysncratic equivalents, as forexample where occurrences of nunc in Aquinas text are rendered with theterms present and moment in J. P. Rowan (trans.), St. Thomas Aquinas:Commentary on the Metaphysics of Aristotle, 5. 13 [940] (1, 362). One of theparticularly popular editorial decisions seems to be the use of moment torender the Latin instans, as in, ibid., 5. 13 [941] (1, 362); Liam Walsh(trans.), St. Thomas Aquinas Summa Theologiae 3a: 715 (49, 145) andA. Vos Jaczn et al. (eds.), John Duns Scotus: Contingency and Freedom, LecturaI, 39 (40).


INSTANS

The thirteenth-century use of the Latin word instans, par-

ticularly when used as a technical temporal term, seems to

owe much to the Latin translations of Aristotles, Averroes,

and Avicennas (Arabic) works, where it is often used as an

synonym of nunc. Used in this way the word became a

technical way of referring to the indivisible, discrete tem-

poral boundaries which needed to be contrasted with the

continuous temporal parts. As Aquinas put it:

the deWnition of an instant is . . . that which is the beginning of the

future and the end of the past.18

Examples can be cited from a wide variety of contemporar-

ies including Bonaventure, Albert, Kilwardby, Theodoric,

and Henry of Ghent, leaving little doubt that deWning an

instant in terms of a boundary reXected a widely accepted

understanding of the word instans. In so far as the English

18 Aquinas, deWnitio instantis est . . . quod est initium futuri et Wnis prae-teriti, In Sent. 4. 48. 2. 2. ob. 9. Quaest. Disp. de Pot. 3. 17 ad 15; 8. 2 ad 10.Quaest. Quodlib. 7. 4. 2 and 9. 4. 3; Quaest. Disp. de Ver. 28. 2 ad 10; In Lib. deAnima 3. 11 [756]. On the point-like qualities of the instant, note, Grosse-teste, instans est sicut punctus, In Phys. 4 (103). Averroes, In Phys. 4 [105],[106], and with an explicit denial that an instans is a pars temporis [107].Avicenna, instan(s) quod est extremitas temporis, SuV. 2. 10. The temporaluse of instans must be distinguished from a non-temporal use such asinstans naturis where it picks out distinct locations in a causal sequence.This distinction seems to have developed towards the end of the thirteenthcentury as Scotus shows, Deinde subdistinguit instantia naturae in eodeminstanti temporis. In Sent. 4. 14. 2 (9, 56). For further background to thediscussion, T. Rudavsky, Creation and Time in Maimonides and Gersonides,1358.


word instant is used to convey the idea of a logically

indivisible temporal boundary then it can be taken as an

accurate translation of the term instans.19

PRAESENS

The word praesens seems to have had both a technical

meaning and a looser more generalized popular usage. Its

technical temporal meaning was established by ancient

commentators who used the word for picking out a particu-

lar indivisible temporal boundary, the boundary between

the past and future. Used in this sense, the praesens is

actually an instans, although it remains a very particular

instance of an instans.20

This technical temporal usage of the word praesens is

widely reXected in the writings of thirteenth century Wgures,

who often use the same analogy of a logically indivisible

geometrical point in order to illustrate what they mean by

talk of a praesens.21

19 Bonaventure, In Sent. 2. 1. 1. 1. 2 ad 4 (2, 23); 3. 18. 1. 1 (3, 381). Albert,Phys. 5. 3. 3 (4.2, 432, 3640). Lib. de Praed. 3. 4 (Borg. 1, 200). Kilwardby, deTemp. 15 [83] (30, 304); In Sent. 2. 3 (2, 15, 11116), 4 (2, 17, 1922).Theodoric, Tr. de Nat. de Prop. Contin. 2 (3, 253, 1215).

20 Boethius, In Cat. Aristotelis 2 (PL 64, 205BC); In Porphyrum (PL 64,307B).

21 Aquinas, In Sent. 1. 37. 4. 3 and 3. 3. 5. 2 ad 4 and 4. 11. 1. 3 ad 2; Sum.Con. Gen. 2. 33;Quaest. Disp. de Ver. 29. 8 ob. 6.Quaest. Disp. deMalo 16. 2 ob.7; Quaest. Quodlib. 7. 4. 2 and 9. 4. 4; de Interpretatione 1. 5 [12]. Grosseteste,In Phys. 4 (99). Albert, Super Diony. de Div. Nom. 4 [46] (37.1, 151, 4951);Lib. de Praed. 3. 9 (Borg. 1, 209); Bonaventure, In Sent. 2. 1. 1. 1. 2 ad 3 (2, 23);4. 11. 1. 1. 5 (4, 250); Theodoric, de Nat. et Prop. Cont. 6 (3, 272, 180200).


Nevertheless there is a looser use of the word, which some-

times creeps into the works of thirteenth-century thinkers,

where it seems that the word was being used to pick out a

continuous part of time. Albert, for example, wrote:

The present time is joined to the past and future through an instant

which is the terminus of such a join. That which we call the past is

that which is distinguished from the present by an instant, which is

the end limit of the past and the beginning point of the present. The

present is also joined to the future through an instant, which is the

end limit of the present and the beginning point of the future.22

Alberts reference to a present time (praesens tempus)

reXects the fact that there was indeed a loose popular notion

of an extended continuous praesens, one that could be traced

back to Priscian. But, as he himself points out, this was very

much a non-technical usage. As far as Albert is concerned,

even when people refer to a present time what they must be

referring to is a small segment of time which will necessarily

include a segment of the past bounded by the instant which

alone marks the actual present.23

22 praesens enim tempus copulatur et ad praeteritum et ad futurum perinstans medium quod est terminus talis copulationis . . . Praeteritum autemdicimus quod terminatur ad praesens per instans quod est praeteriti Wnis etprincipium praesentis: et praesens etiam copulatur ad futurum per instansquod est Wnis praesentis et principium futuri, Lib. de Praed. 3. 4 (Borg. 1,200). For other similar usages, Kilwardby, de Temp. 1 [2] (7, 79); JohnQuidort, Cor. Cor. Circa (89, 10); Albert, In Sent. 1. 8. A. 12 (Borg. 25, 235).

23 Albert, Dicendum quod praesens accipitur ut divisibile tempus, de quodicit Priscianus, quod praesens est cuius pars praeteriit, et pars in instanti est,et pars in futuro: et haec copulantur praeterito et futuro. Est etiam praesensnunc indivisibile et hoc non copulantur sed copulat: et hoc quidem estaliquid temporis, sed non est aliqua pars temporis, Lib. de Praed. 3. 9 ad 2(Borg. 1, 210). In Sent. 1. 8. A. 8 ad 12 (Borg. 25, 232).


The use of the English word present is ultimately iden-

tical to that of the Latin word praesens. As with the Latin

notion the English word is sometimes used in a popular way

to refer to a present time. But, apart from those advocates of

a specious present, the technical use of the word present is

almost invariably reserved for describing the logically indi-

visible bounding instant between the past and the future.

NUNC

One of the most widely used of the medieval temporal terms

must undoubtedly be the word nunc. Latin translations of

Aristotles works consistently indicated that this wasAristotles

own preferred term for picking out the logically indivisible

temporal boundaries which we have seen can also be referred

to as instants. Encouraged byAristotelian commentators, thir-

teenth-century thinkers had no hesitation in adopting this

term as a synonym of instans and thus using it to refer to

discrete logically indivisible temporal boundaries.24

24 Aristotle, Ipsum autem nunc non est pars, Phys. (Vetus) 4. 10. 218a59(AL 7.1.2, 170); Et adhuc manifestum sit quod nulla pars ipsum nunctemporis est, ibid., 4. 11. 220a19 (AL 7.1.2, 178); ibid., 4. 13. 222a10 (AL7.1.2, 184). Besides its role in referring to temporal elements such as parts andboundaries, the word now also had a distinct content when used in talk of aXowing now (nunc Xuens) or changing now (nunc Xuxibile), as Bonaven-ture indicates, In Sent. 2. 2. 1. 1. 1 (2, 56). Albert, Sum. de Creat. 2. 5. 3 (Borg.34, 373); Phys. 4. 3. 6 (4.1, 270, 32). Alexander of Hales seems to viewBoethius as one of the main progenitors of the notion, Sum. Theol. 1. 1. 2.4. 1. 1. 1 (1, 84) although Aristotle also recognized the idea, Et sicut motussemper alius, et tempus; simul autem omne tempus idem est: ipsum enim


Although not as clearly expressed we can see Peter of

Tarentaise assuming this very usage. When discussing con-

cepts of inWnity he identiWes the nunc with the geometrical

point:

There is an inWnity, said privatively and this refers to that which

can have a boundary but does not actually have oneand such an

inWnite counts as a quantity. There is another kind of inWnity

which is said negatively, and this refers to that which does not

naturally have a boundary. We can refer to this inWnity as a simple

in quantity. The Wrst kind of inWnity cannot exist in actuality, but

the second kind can; as for example the point and the now.25

As with the word praesens, besides its strict technical sense

there seems to have been a looser more popular usage of the

word now, a usage which accepted that it could be applied

to very small extended continuous periods. Such a usage was

nunc idem est quod forte erat. Esse autem ipsi alterum est (hoc autem eratipsi nunc) in quantum autem quod cum est, est ipsum nunc, idem est. Phys.(Vetus) 4. 11. 219b914 (AL 7.1.2, 176). The word nunc is also used ofeternity and aeviternity where the non-moving nature of those durations isdepicted by talking of a standing now, Albert, Sum. Theol. 5. 22. 1 (34.1,11517). Avicenna, Si autem fuerit indivisibile tempus; erit id quod appel-latur instans quia non est tempus . . . SuV. 2. 10. Boethius, PosteriorumAnalyticorum Aristotelis Interpretatio 2. 12 (PL 64, 754A); Averroes, In Phys.4 [120, 121]; Albert, Lib. de Praed. 3. 9 (Borg. 1, 210). Phys. 8. 3. 6 (4.2, 634,17); Grosseteste, In Phys. 4 (99). Kilwardby, de Temp. 17 [106] (34, 1819);Aquinas, In Phys. 4. 21 [61517]. Bonaventure, principium autem temporisest instans vel nunc In Sent. 2. 1. 1. 1. 2 ad 4. (2, 23) also In Sent. 4. 17. 2. 2. 2fund. 2 (4, 444). For further details, J. M. Quinn, The Doctrine of Time in St.Thomas: Some Aspects and Applications, 2689.

25 Est inWnitum privative dictum quod est aptum natum Wnem habere,nec habet et tale inWnitum est quantum: et est inWnitum tantum negative,quod non est aptum natum Wnem habere, nec habet et tale inWnitum estsimplex in quantitate, . . . Primo modo non potest esse inWnitum actu, . . .secundo modo potest, ut punctus, et nunc. In Sent. 2. 2. 2. 1 ad 6.


clearly contrary to the strict philosophical and technical

usage which Aristotle had bequeathed, and Aquinas was

keen to point this fact out:

If the now is divisible, it will not be a now in the proper sense,

but in an extended sense. For nothing which is divisible is the very

division by which it is divided. And the division of time is the

now. For the division of a continuum is nothing other than the

terminus which is common to the two parts. And this is what we

mean by the now; the common terminus of past and future. Thus

it is clear that that which is divisible cannot be a now in the

proper sense.26

With his distinction between using the word now in its

proper sense and using it in an extended sense, Aquinas is

actually making use of an analytic methodology which we

will see applied again later in Chapter 6, where it is applied

to the very word time itself, in order to generate diVerent

understandings of time. The force of the distinction in this

context is to stress that although the word nunc (now) was

sometimes used to refer to parts of time, when it was used in

its most proper sense then the word was used to refer to the

indivisible temporal boundaries.

The English word now contains a similar degree of

ambiguity, although it cannot be said to have a single

proper sense. In reality the term lacks a technical temporal

26 Si nunc sit divisibile, non erit nunc secundum seipsum, sed secundumalterum. Nullam enim divisibile est sua divisio qua dividitur, ipsa autemdivisio temporis est nunc. Nihil enim est aliud divisio continui quam ter-minus communis duabus partibus hoc autem intelligimus per nunc quod estterminus communis praeteriti et futuri. Sic ergo manifestum est quod idquod est divisibile, non potest esse nunc secundum seipsum. In Phys. 6. 5[792] and [788].


sense, except when it is used to translate Aristotelian pas-

sages, and in those contexts it is clearly used in the non-

extensional sense. Although the word nunc can therefore

be translated as now, the nuance of its uses would be better

brought out by using a more clearly extensional and a more

clearly non-extensional term, as was appropriate in the

diVerent contexts which are being translated.

PERIODUS

The word periodus occasionally appears in thirteenth-

century texts as a technical temporal term. Neither Kil-

wardby nor Pseudo-Aquinas use it in their treatises de Tem-

pore, and where Albert uses it he seems to feel that his

readers will not really understand the term unless he glosses

it with a lengthy etymological explanation of what it means.

In so far as it is possible to trace the origins of the term as a

technical temporal term, it would seem to derive from the

Latin translations of Aristotles works and in particular from

a passage in the De Generatione.27

27 Aquinas, In Sent. 2. 19. 1. 4 and 4. 43. 1. 3b ob. 1; Albert, de Gen. et Cor.2. 3. 5 (5.2, 205, 728). Bonaventure, In Sent. 4. 11. 1. 1. 5 (4, 250). Albert, deGen. et Cor. 2. 3. 5 (5.2, 205, 80). The passage of Aristotle which they refer tois, Et in equali tempore et corruptio et generatio que secundum naturam.Ideoque et tempus et vita uniuscuiusque numerum habet, et hoc determi-nantur. Omnium enim est ordo, et omne tempus et vita mensuratur periodo,sed tamen non eadem omnes, sed hii quidem minori, hii autem maiore. deGen. et Cor. (Vetus) 2. 10. 336b915 (AL 9.1, 75). Apart from its use as atechnical temporal term, periodus was also used in a non-temporal, gram-matical sense as suggested by Isidore, Etym. 2. 18. Aquinas, Com. in IsaiahPrologue, 2 (Leon. 28, 5, 245).


In this passage in the De Generatione Aristotle talks of

change occurring in periodi, which the content indicates

must be interpreted as extended temporal parts, rather than

as boundaries. InXuenced by this usage, where thirteenth-

century writers use the word periodus, it is little surprise

that they tend to do so to refer merely to extended temporal

parts.28

The English word period admits of a similarly Wxed

extensional sense and so it provides a good basic term for

referring to extensional temporal parts. As a way of render-

ing the Latin periodus, the word period would thus seem

to provide a good translation.

MOMENTUM

The word momentum has traditionally been widely used

by Latin speakers to refer to temporal elements. Perhaps as a

result of its very popularity, diversity of usage is particularly

evident with this term. Whilst patristic authorities, trans-

lators of Arabic works and thirteenth-century writers would

all explicitly use the word to refer to extended temporal

28 Albert, de Gen. et Cor. 2. 3. 4 (5.2, 205, 407); de Natura loci 1. 5 (5.2, 9l, 316); In Sent. 1. 8. A. 12 (Borg. 25, 236). Aquinas, Resp. ad lect. Venet. de36 art. 10 (Leon. 42, 341, 1769); Quaest. Disp. de Malo 5. 5 ad 6. In somecontexts the word periodus seems to be treated as a synonym with termssuch as seculum. Aquinas, for example, writes. saecul(um), quod est peri-odus durationis alicuius rei, Sum. Theol. 1. 10. 6 ad 1, 1. 10. 2 ad 2, and 1. 10.6 ad 1. He then goes on to stress that a saeculum is a spatium (space) of time.Super Epist. ad Titum 2. 3 [70].


parts,29 there was an equally evident tradition whereby the

term was used to refer to non-extended indivisible bound-

aries. As Aquinas illustrates, thirteenth-century thinkers

were clearly aware of both uses:

It must be borne in mind that momentum can be taken as

referring to an instant of time, which we call a now, or as referring

to an imperceptible piece of time.30

Besides these two temporal uses, the word momentum was

also used in at least two further contexts: in descriptions of

eternity and in analyses of motion. Its use as a descriptive

term for eternity seems to be related closely to the Liber de

Causis tripartite analysis of time, eternity, and the aevum,

where the word momentum is used explicitly of eternity:

29 Boethius, de Cons. Phil. 2. 6 [15] (33, 47); Bede, de Temporibus 1 (ed.Weber Jones, 295, 27); Aquinas, Super ad 1 Thess. 4. 2 [101]; Super ad 1 Cor.15. 8 [1006]; In. Sent. 4. 46. 1. 3; Sum. Theol. 1-2. 87. 3 ad 1; Albert, de Caelo1. 2. 2 (5.1, 35, 7680). Albert also quotes Avicenna as a basis for describingtime as an aggregatio momentorum, Phys. 4. 3. 3 (4.1, 263, 40). See alsoKilwardby, de Temp. 6 [27] (14, 7); 11 [49] (21, 9). Note also the descriptionof a momentum as a brief mora in Philip the Chancellor, Sum. de Bono, 1.4.9(1, 295, 140).

30 Sciendum est autem quod momentum potest accipi vel pro instantitemporis quod dicitur nunc, vel pro aliquo tempore imperceptibili, Super 1ad Corinthios. 15. 8 [1007]. Note also his comment, Necesse est enim quodmotus caeli sicut et quilibet motus cessat in momento sive in instanti; quiaultimum instans temporis respondet ultimo instanti motus Resp. ad Lect.Venet. de 30 art. ad 8 (Leon. 42, 322, 14951) and Sent. lib. Eth. 10. 5 (Leon.47.2, 565, 1440). Aquinas reference to an instant of motion should also benoted as an example of the Xexible way this term was used to pick outboundaries; as was his tendency to equate momentum with praesens,Sum. Con. Gen. 3. 85 [2614]; and contrast a momentum with time itself,sed actio corporis non est in momento, sed in tempore, Quaest. Disp. deMalo 4. 6 ob. 13; Sent. Lib. Eth. 10. 5 [2].


Between the thing whose substance and action is in the moment

(momentum) of eternity (i.e. it is measured by eternity) and

between the thing whose substance and action is in the moment

(momentum) of time, there is a middle [kind of existence] of those

[things] whose substance is in the moment (momentum) of eter-

nity (i.e. the aevum) and whose operation is in the moment

(momentum) of time.31

As this distinction played an important part in medieval

thought we shall have occasion to revisit it later when look-

ing at non-temporal durations. Particularly noteworthy at

this point is the occurrence of the word momentum as a

descriptive term for eternity and the aevum. Both of those

concepts are supposed to be non-temporal, so the occur-

rence of an otherwise temporal term such as momentum is

puzzling. Bonaventure seems to have found it so puzzling

that on at least some occasions he deliberately omitted the

term when paraphrasing the liber de Causis.32

In subsequent chapters we shall see that the most plausible

understanding for this usage was that the word momentum

31 Quoted by Aquinas, inter rem cuius substantia et actio est in momentoaeternitatis, i.e mensurantur aeternitate, et inter rem cuius substantia et actiosunt in momento temporis existens est medium, et est illud cuius substantiaest in momento aeternitatis (i.e. aevi) et operatio est in momento temporis,Sup. Lib. de Caus. Prop. 31.

32 Bonaventure, inter rem, cuius substantia et operatio est in aeternitateet rem, cuius substantia et operatio est in tempore, est res media cuiussubstantia est in aeternitate et actio est in tempore, In Sent. 2. 2. 1. 1. 1fund. 1 (2, 55). Bonaventure includes the word momentum only whenstating objections to his position, as at In Sent. 2. 2. 1. 2. 2 ob. 1 (2, 65).Many writers tended to only use the word momentum of eternity and theaevum when quoting from, or commenting upon, Proclus texts. Kilwardby,In Sent. 2. 11 (2, 44, 437). Aquinas, In Sent. 1. 14. 1. 1 ob. 3. Peter ofTarentaise, In Sent. 1. 14. 1. 1 ob. 7.


was being used to refer to an indivisible (non-temporal)

durational element within the aevum and eternity. At this

point in the study it suYces merely to note that there was

such a non-temporal use of the word.

The other (non-temporal) context in which the word

momentum was used arose in descriptions of motion

where the word was used to refer to an indivisible boundary

of the motion segments which constitute a motion. Aquinas

indicates that there was even a sense in which the word

momentum could be thought of as the technical term for

indivisible boundaries in motion that were analogous to the

indivisible boundaries in time picked out by the word

instans.

It is true that each instant is the beginning and end of a time, and

so it should also be said that each moment is the beginning and

end of a motion.33

It is clear that the medieval Latin word momentum had a

rich range of meanings and nuances which varied from

33 Verum est omne instans et est principium et Wnis temporis, dicendumquod verum est quod omne momentum est principium et Wnis motus.Quaest. disp. de Pot. 3. 17 ad 15. In Sent. 1. 37. 4. 3 ob. 2. In Lib. Post. Anal.2. 11 [519]; Sum. Theol. 1. 46. 1 ad 7; In Phys. 8. 2 [990]. Note also Albert,momenta autem duo nihil aliud vocant quam duas renovationes sitas inmobili quod movetur, Sum. de Creat. 2. 5. 1 (Borg. 34, 365) and Phys. 6. 1. 1(4.2, 447, 1113); 6. 3. 1 (4.2, 487, 9). It is diYcult to trace the origins of thisusage, but it was probably encouraged by the fact that it could be found inAvicennas texts (SuV. 2. 10). There was clearly a degree of Xuidity inthirteenth-century terminology as Albert seems at times to indiscriminatelylump together the terms point, now, and moment, Scientia libri de lineisIndivis. 1 (4.2, 498, 305), sometimes even introducing a further term muta-tum as an equivalent of momentum, de Div. Nom. 10 [5] (37.1, 400, 778).The Venetian lector referred to in notes 28 and 30 seems to have used the wordinstans indiscriminately to pick out a boundary of time and motion.


context to context. The English word moment also exhibits

a variety of usages, sometimes being used for indivisible

temporal boundaries and at other times being used to refer

to small parts of time. This means that although translating

the word momentum as moment hardly makes perspicu-

ous the content of the word in particular contexts, the

practice does at least avoid obvious inaccuracy.34

DURATIO

The term duratio also admits of ambiguity as it seems to

have had two basic senses, a temporal extensional sense and a

non-temporal existential (esse) sense.

The temporally extensional sense is apparent in almost all

thirteenth-century writers. Aquinas, for example, distin-

guishes between a mover preceding what it moves by dignity

34 Colloquially the word moment is often used to refer to small pieces oftime, as in the usage of W. Lane Craig, God, Time and Eternity, 21 n. 57. It hasbeen used with a clearer non-extensional import by N. Pike, God andTimelessness, 8. The colloquial English use seems to have been captured inmedieval Latin with the non-technical Latin word iam, as Albert shows,Ipsum vero, quod dicitur iam, dicit quando in praeterito et futuro, quodrelinquitur ex tempore, quod propinquum est praesenti nunc indivisibili,sicut dicimus Quando vades? et respondetur: Iam, quia prope est tem-pus, in quo futurum est, ut eamus, et Quando ivisiti?, respondemus: Iamivi, quia non est procul ab ipso nunc in praeterito, Phys. 4. 3. 13 (4.1, 286,1422). The brief analysis of the term momentum is not intended tocapture all translational nuances. It has been translated as impulse, forexample, by R. J. Blackwell (trans.), Commentary on Aristotles Physics by St.Thomas Aquinas, 486, but as translations such as these have no particularbearing on the matter of this study I shall eVectively ignore them.


and a mover which precedes what it moves by duratio,

where the context makes clear that precedence by duratio

is simply temporal precedence. An even clearer example of

this extensional notion of duratio is provided by Albert

when he uses duratio and tempus interchangeably and

refers to the hypothesis that the world might have existed for

an inWnite time, as the hypothesis that the world has an

inWnite duratio of successive parts.35

The second sense of the word duratio is an existential

sense. It is a non-temporal, non-successive notion. Duratio

in this sense is predicated of any particular which has exist-

ence (esse) and its predication is simply a reference to the

actual being-ness of the thing which is existing. According to

this rather restricted sense of the word, there was almost a

logical relationship of entailment between having actual esse

and possessing a duratio.

The precise nature of the esse which a thing possessed was

thought to determine its type of duratio. In the case of

particulars with an extensional esse they were thought to

35 Perhaps the clearest exposition of an extensional sense of duratio isprovided by John Locke in his On Succession and Duration (2, 14). For thereference toAquinas see InSent. 2. 2. 1. 1; also 1. 19. 2. 1; and for the reference toAlbert see Phys. 4. 4. 2 (4.1, 296, 236); Sum.Theol. 5. 23. 1. 1. 1 (34.1, 122, 1822). Sum. de Creat. 2. 2. 3 ad 1 (Borg. 34, 348). This extensional use of duratiooccurs widely in mid-thirteenth-century texts. Note Bonaventures posteriustempore sive duratione, In Sent. 1. 9. 1. 3 ad 2 (1, 184) and 4. 43. 1. 4 (4, 888).AlsoAlexanderofHales,Sum.Theol. 1. 1. 1. 2. 4. 2. 4 (1, 95).WilliamofAuxerre,Sum. Aurea. 2. 8. 2. 1. 1 (2.1, 176, 235). The extensional implications ofduratio occurs often as an objection to non-extensional notions of an eternalduration. Note Albert, omnis duratio protensa est, nullum protensum esttotum simul, ergo aeternitas quae est duratio non est totum simul, In Sent.1. 8. A. 8 (Borg. 25, 230). He ultimately rejects the argument, ibid., ad 5 (Borg.25, 2312) as does Aquinas, In Sent. 1. 8. 2. 1 ad 6.


have an extensional duratio. As thirteenth-century thinkers

believed that there were non-extensional, non-temporal,

types of esse they felt compelled to aYrm that there were

non-extensional, non-temporal types of duratio ; types

which could not be reduced to an extensional model.36

This distinction between extensional and non-extensional

models of duratio is an important one to medieval thinkers,

and its existence explains the otherwise unintelligible distinc-

tionswhich theymadebetween successive andnon-successive

duratio and between simultaneous and non-simultaneous

duratio. Ultimately it explains why medieval thinkers who

insisted that eternity was non-temporal were also content to

refer to it as a duratio.37

36 Aquinas, duratio autem omnis attenditur secundum quod aliquid estin actu; tamdiu enim res durare dicitur quamdiu in actu est, et non dumest in potentia, In Sent. 1. 19. 2. 1 sol. Albert, Per hoc enim quod incipitesse et initium habet esse, ab ipso eodem initiatur duratio esse, secundumquod duratio forma et dispositio est durantis Sum. Theol. 5. 23. 1. 1. 1 ad 2(34.1, 123, 97); In Sent. 1. 9. A. 1 (Borg. 25, 272). Bonaventure, in deoidem est omnino esse et durare, Quaest. Disp. de Myst. Trin. 5. 2 ob. 6; nuncaeternitatis nominat illam durationem quantum ad simplicem simultatem,aeternitas vero quantum ad interminabilitatem divinae simplicitatis et simul-tatis secundum rem nihil quidem addit, ibid. 5. 1 ad 13 (5, 92); also Peterof Tarentaise, Si mundus fuit ab aeterno, aut duratio eius fuit omninosimplex et invariabilis, et ita fuit ipsa aeternitas divina, In Sent. 2. 1. 2. 3con. 9; and 1. 8. 3. 1. And similarly Philip the Chancellor, Sum de Bono, 1. 1. 4(1, 53, 478), 1. 2. 2 (1, 59, 704). Note also Henry of Ghents . . . cumduratio duplex est: aeternitas et tempus, potest dici aliquid principiumduratione quae est aeternitas, vel duratione quae est tempus, Lect. Ord. 1(36, 42, 435).

37 All things that have an esse necessarily possess a duratio. Bonaventure,et continuatio in esse non est aliud quam duratio, In Sent. 2. 37. 1. 2 fund. 2(2, 804). Aquinas, In Sent. 1. 8. 2. 1. Quaest. Disp. de Pot. 3. 14 ob. 2 and 3. 17ad 20. Sum. Theol. 1. 10. 1 ob. 2. The signiWcance of Alexander of Halesviews on duratio should not be underestimated as they have clearlyinXuenced Aquinas views and language. Compare, for example, Aquinas


It is not altogether clear that contemporary commenta-

tors appreciate that there were two distinct notions of dur-

atio. This means that many of the criticisms levelled against

Aquinas notion of eternity as a duratio assume that Aquinas

was using duratio in the Wrst sense and that he is therefore

committed to the apparently problematic idea of a timeless

but extensional duration.38 Once the diVerent notions of

duratio are appreciated then the notion of a non-extensional

duratio ceases to be a philosophical problem and becomes

instead a simple matter of medieval linguistic convention.39

duratio respicit esse in actu, In Sent. 2. 2. 1. 1, with Alexanders duratioautem respicit esse, Sum. Theol. 1. 1. 2. 4. 3 (1, 87). According to Theodoricof Freiberg, the question of whether a particular can possess a duratio reducesto the question of whether its esse can have the property of pastness, pre-sentness, or futureness. de Mensuris 3 (3, 226, 226).

38 E. Stump and N. Kretzmann have defended as an accurate reading ofAquinas, a non-successive but apparently extensional use of the word dur-ation (duratio) in Eternity, 4345, and Atemporal Duration, 217. Thephilosophical cogency of their position has been challenged by P. Fitzgerald,Stump and Kretzmann on Time and Eternity, 2609; K. Rogers, EternityHas No Duration, 116; B. Leftow, Eternity and Simultaneity, 14879; andThe Roots of Eternity, 189212. H. J. Nelson, Time(s), Eternity and Dur-ation, 1117. D. B. Burrell, Gods Eternity, 389406; D. Lewis, EternityAgain: A Reply to Stump and Kretzmann, 739.

39 As soon as the distinction is made between the two notions of duratio itbecomes clear that one cannot claim that a duration is necessarily extended(P. Fitzgerald, Stump and Kretzmann on Time and Eternity, 2623), orargue against an instantaneous notion of eternity on the grounds that it isreferred to as a duratio (Stump and Kretzmann, Eternity, 435). Nor must theuse of duratio be an attempt to show that eternity is non-evanescent(C. Hughes, On a Complex Theory of a Simple God, 119). Nor can it beassumed that duration means an interval of time and that an atemporalduration is . . . a contradiction in terms (A. Padgett: God, Eternity and theNature of Time, 67). Nor is it the case that Duration is a category which isprima facie not even applicable to a timeless being in any literal sense


When it comes to translating the word duratio we are

immediately faced by the problem that the English word

duration seems to imply necessarily an extensional or suc-

cessive state, and that there seems to be no other term which

encapsulates the non-extensional sense of duratio. As there

is a well established tradition of using duration to translate

the Latin duratio, I shall follow the convention, but with the

caveat that such a usage should not obscure the existence of

what we have seen to be an important non-extensional no-

tion of duratio.

MORA, DIURNITAS, PROTENSIO

None of these three terms appear asmajor temporal technical

terms. Nevertheless, they do sometimes feature within thir-

teenth-century accounts of time and temporality. The word

mora seems relatively straightforward as it is explicitly used

by, amongst others, Albert, Aquinas, and Bonaventure to

refer to an extended temporal part. It seems to have been a

particularly popular term in discussions of the question of

whether there was a temporal lapse (mora) between the

creation of the angels and their decision to sin.40

(W. Lane Craig, God, Time and Eternity, 11). Nor Wnally must it be the casethat predicating duratio of God undermines His timelessness (P. Helm,Eternal God: A Study of God Without Time, 36).

40 Albert, Omnis mora si proprie sumitur habet partes et est tempus velpars temporis, Sum. de Creat. 2. 3. 2 (Borg. 34, 348). Sum. Theol. 5. 22. 2. 1(34.1, 117, 747). Aquinas, Sum. Theol. 1. 63. 6 ob. 4. Bonaventure, In Sent.2. 24. 1 dub. 1.


The terms diurnitas and protensio also seem to have

had a thoroughly extensional import, being used to pick out

and refer to temporal periods of considerable length. Illus-

trating the meaning of all three of these key terms, Albert

doesnt seem to have considered that there was anything to

prevent them from being used synonymously with the word

time.41

THE QUANDO

The Latin word quando is usually translated as when, so

talk of a quando is talk of a temporal location. In English the

word when can be used to denote an instant at which an

action commences, or a period during which it exists, and

we might expect similar Xexibility in the Latin term. Albert,

at least when commenting upon Aristotles Physics, indicates

that he was more familiar with the term when it was used in

an extensional sense referring to the temporal locations of

(extensional) events such as Noahs Xood. Kilwardby, how-

ever, indicated an appreciation of a broader range of uses

which were more similar to our contemporary usage. Dis-

tinguishing between a simple quando and a composite

quando, he was in eVect distinguishing between a non-

41 hoc quod vocat Richardus diuturnitatem, Gilbertus vocat moram,et . . . mora enim dicit durationem extensam a longo praeterito in praesens,quod sine divisione partium esse non potest, Sum.Theol. 5. 23. 1. 1. 1 (34.1,125, 525); also 5. 22. 1 ad 3 (34.1, 117, 615) and In Sent. 1. 8. A. 8 ad 5(Borg. 25, 2312).


extended (simple) temporal location and temporal locations

which had extension.42

Whilst Kilwardby seems to have thought of the quando as

a thoroughly temporal element, Albert indicates that there

were alternative understandings including a pan-durational

notion which meant that the word quando was able to pick

out durational locations rather than merely temporal loca-

tions. We see this sense deployed in discussions involving

multiple durations, as for example, in the discussion of

whether God, an angel, and a motion could all exist in the

same quando. There was considerable diversity of opinion

amongst thirteenth-century thinkers on how to answer this

question; but regardless of their precise responses, the very

fact that the question was formulated in this way shows that

the word quando was accepted as having a durational sense

over and above any merely temporal sense that it had when

used of time. In Chapters 8 and 9 we shall see that the

commonality between the durations was the existence of a

non-extensional element in each duration, an element

42 Albert, Sic ergo exposita est diversitas ipsius quando, quod relinquiturex praeterito et futuro; ex praeterito quidem, sive fuerit remotum a praesentisive propinquum, ex futuro autem non est nisi propinquum, quia id quodremotum est a praesenti nunc, non habet ordinationem in materia. Et hoc estde quando mensurabili, quando autem non mensurabile a nobis est, quodrelinquitur ex tempore imperceptibili, Phys. 4. 3. 13 (4.1, 286, 3340) alsoLib. de Causis 1. 1. 10 (17.2, 72, 413). Albert is probably drawing onAverroes, who seems to have felt that it was particularly important todistinguish the quando from the present. In Phys. 4 [127]. Kilwardbysdistinction was as follows, sic potest dividi quando per simplex et compo-situm: ut dicatur simplex quando derelictum ex presenti nunc indivisibiliter;compositum quando ex tempore continuo, cuius sunt tempus praeteritum etfuturum, de Temp. 16 [99] (33, 2831).


which could be referred to as a quando because in each case

it was a present element.43

A TECHNICAL VOCABULARY

Now that we have examined some of the key terms which

medieval thinkers used in discussions of temporality, we are

in a posit

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