Time and Eternity in Mid-Thirteenth-Century Thought (Oxford Theology and Religion Monographs) [1 ed.] 0199285756, 9780199285754

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OXF O R D T H E O LO G I C A L M O N O G R A P H S Editorial Committee

m. mcc. adams m. j. edwards p. m. joyce d. n. j. macculloch o. m. t. o’donovan c. c. rowland

OXFORD THEOLOGICAL MONOGRAPHS THEODORE THE STOUDITE The Ordering of Holiness Roman Cholij (2002) HIPPOLYTUS BETWEEN EAST AND WEST The Commentaries and the Provenance of the Corpus J. A. Cerrato (2002) FAITH, REASON, AND REVELATION IN THE THOUGHT OF THEODORE BEZA Jeffrey Mallinson (2003) RICHARD HOOKER AND REFORMED THEOLOGY A Study of Reason, Will, and Grace Nigel Voak (2003) THE COUNTESS OF HUNTINGDON’S CONNEXION Alan Harding (2003) THE APPROPRIATION OF DIVINE LIFE IN CYRIL OF ALEXANDRIA Daniel A. Keating (2004) THE MACARIAN LEGACY The Place of Macarius-Symeon in the Eastern Christian Tradition Marcus Plested (2004) PSALMODY AND PRAYER IN THE WRITINGS OF EVAGRIUS PONTICUS Luke Dysinger, OSB (2004) ORIGEN ON THE SONG OF SONGS AS THE SPIRIT OF SCRIPTURE The Bridegroom’s Perfect Marriage-Song J. Christopher King (2004) AN INTERPRETATION OF HANS URS VON BALTHASAR Eschatology as Communion Nicholas J. Healy (2005) DURANDUS OF ST POURC¸AIN A Dominican Theologian in the Shadow of Aquinas Isabel Iribarren (2005) THE TROUBLES OF TEMPLELESS JUDAH Jill Middlemas (2005)

Time and Eternity in Mid-ThirteenthCentury Thought Ro r y Fox

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3 Great Clarendon Street, Oxford ox2 6dp Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York ß Rory Fox 2006 The moral rights of the author have been asserted Database right Oxford University Press (maker) First published 2006 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by SPI Publisher Services, Pondicherry, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn ISBN 0–19–928575–6

978–0–19–928575–4

1 3 5 7 9 10 8 6 4 2

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 Benet’s 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 1995–7, 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 contributions 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

1. 2. 3. 4. 5. 6. 7. 8. 9. 10.

Introduction The Language of Time Temporal Simultaneity Priority, Posteriority, and Causality Relations and Reductions The Reality of Time On Measurement and Numbering Time and Atemporality Sempiternity, Angelic Time, and the Aevum Eternity God and Time

Bibliography Subject Index Index of Ancient and Medieval Text References Index of Ancient Medieval and Pre Modern Authors

1 10 50 95 130 165 193 225 244 282 309 330 359 366 382

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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 another 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 God’s relationship to time. The motivation for this study arose from a dissatisfaction with standard accounts of Aquinas’ views on the question of God’s 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 language 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 examining the framework in which thirteenth-century thinkers were discussing the question of knowledge of future contin-

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Introduction

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 God’s 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 God’s 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 everlasting 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 judgements about what views can accurately be ascribed to Aquinas and his contemporaries. It will be helpful before embarking on this study to set out some of my methodological assumptions. One of the key assumptions which I make is that thirteenth-century thinkers

Introduction

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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 individuals 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 philosophers, 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 durational 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 Augustine 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 which involved durational issues. For further information see propositions [57], [87], [100], [156], [200] in H. Denifle and E. Chatelain, Chartularium Universitatis Parisiensis, i. 544–55 and on the condemnation itself, J. F. Wippel, ‘The Condemnations of 1270 and 1277 at Paris’, 169–201. R. Hissette, Enqueˆte sur les 219 articles condamne´s a` Paris le 7 mars 1277, 147–57.

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Introduction

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 treatment 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 treatment 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 investigation, examining figures sequentially, and comparing and contrasting developments inworks of different dates, I have instead 2 There is an extensive literature analysing the ancient and patristic background to thirteenth-century thought on time. On Aristotle, M. White, The Continuous and the Discrete, 3–115. R. Sorabji, Time, Creation and the Continuum, 46–51, 84–97. J. Annas, ‘Aristotle, Number and Time’. H. Barreau, ‘Le traite´ aristote´licien du temps’. M. de Tollenaere, ‘Aristotle’s Definition of Time’. For a bibliography of works on Aristotle’s concept of time, E. Hussey, Aristotle’s Physics, Books III and IV, 201–7, and for an analysis of the different translations of Aristotle’s Physics in use during the twelfth and thirteenth centuries, B. G. Dod, ‘Aristoteles Latinus’. For studies of patristic accounts of time, B. Otis, ‘Gregory of Nyssa and the Cappadocian Conception of Time’. J. F. Callahan, Four Views of Time in Ancient Philosophy, 88– 187. For a discussion of aspects of medieval views on time, A. Mansion, ‘La the´orie aristote´licienne du temps chez les pe´ripate´ticiens me´die´vaux: Averroe`s, Albert le Grand, Thomas d’Aquin’, 279–88. J. M. Quinn, ‘The Concept of Time in Albert the Great’. V. C. Bigi, ‘La dottrina della temporalita` e del tempo in San Bonaventura’, 437–88. J. M. Quinn, The Doctrine of Time in St. Thomas: Some Aspects and Applications, 15–55. J. M. Quinn, ‘The Concept of Time in Giles of Rome’, 310–52. V. C. Bigi, ‘Il concetto di tempo in S. Bonaventura e in Giovanni Scoto’. R. C. Dales, Medieval Discussions of the Eternity of the World, passim. R. C. Dales, ‘Time and Eternity in the Thirteenth Century’. A Maier, Metaphysische Hintergru¨nde der Spa¨tscholastischen Naturphilosophie, 45–137. 3 Elements of Scotus’ account of time are explained in R. Cross, The Physics of Duns Scotus, 214–56, which supplants earlier treatments of the question, all

Introduction

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organized this book thematically. Chapter 1 opens the discussion by examining some of the key language and terminology which thirteenth-century thinkers used. Chapters 2–5 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 that pertain to time when it is considered as a measure. Chapter 7 rounds off the examination of time by looking at the criteria, factors, and language which thirteenth-century thinkers typically took as entailing that a particular would be in time. Chapter 8 opens the exploration of what I will term atemporality by examining how thirteenth-century thinkers discussed existence outside of time, particularly as it was applied to aeviternity and aeviternal beings. Chapter 9 moves on to examine 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 language. Chapter 10 concludes the study by examining the specific question of how thirteenth-century thinkers viewed God’s relationship to time.

of which are recorded in Cross’s bibliography. Amongst other figures writing after Aquinas’ death, I have also included occasional references to the figures who contributed to the Correctorium literature. Although this literature was produced some 15–20 years after Aquinas’ death it features conflicts and disagreements about Aquinas’ writings that often involve durational aspects. The original Correctorium was written by William de la Mare but many of the replies to his work were written anonymously so I have followed Roensch’s identification of sources, attributing the Correctorium Correctorii Quare to Richard Knapwell, The Correctorium Correctorii Sciendum to Robert Orford, and the Correctorium Correctorii Quaestione to William Macclesfield. For further details see F. J. Roensch, Early Thomistic School, 28–57 and P. Glorieux, ‘La Faculte´ de The´ologie de Paris et ses Principaux Docteurs au XIIIe Sie`cle’.

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Introduction

The neatness of attempting to divide this book in this way is undermined in places by the fact that thirteenthcentury thinkers seem to have generally been confused about the differences between topological and metrical properties. This meant that they were not averse to appealing 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 discussion, 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 references. 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

Introduction

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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

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Introduction

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 medieval 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 attached to them. Textual evidence indicates that the de Tempore, 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 PseudoAquinas. 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-

Introduction

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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 complicate 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 contemporary scholars. As a general policy for dealing with extracts from texts such as Alexander’s 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 examined 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 midthirteenth-century figures featured in this study see J. Marenbon, Later Medieval Philosophy (1150–1350), 194–231, and N. Kretzmann et al. (eds.), The Cambridge History of Later Medieval Philosophy, 855–92. On the historical significance of mid-thirteenth-century thought a recent overview is provided by P. Porro (ed.), The Medieval Concept of Time: The Scholastic Debate and Its Reception in Early Modern Philosophy.

1 The 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 Aristotle’s 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 Aristotle’s 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 Aristotle’s 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 Aristotle’s Physics, see A. Mansion (ed.), Aristoteles Latinus 7.1, i–xxvii and B. Dod, ‘Aristoteles Latinus’. On the broader question of sources and intellectual inXuences, G. LeV, Paris and

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As with almost every area of philosophy, Aristotle’s contribution 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 motion’2

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. Aristotle’s deWnition of time was a useful contribution to debates about the nature of time, but for the most Oxford Universities in the Thirteenth and Fourteenth Centuries, 127–37; J. Marenbon, Later Medieval Philosophy, 53–64; M. Haren, Medieval Thought: The Western Intellectual Tradition from Antiquity to the Thirteenth Century, 37–82; and P. Dronke, A History of Twelfth-Century Western Philosophy, 54–148. 2 ‘hoc enim est tempus: numerus motus secundum prius et posterius’ Phys. (Vetus) 4. 11 (AL 7.1.2, 175).

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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 Categories was so widely studied that no educated thirteenthcentury thinker could be unaware of its existence and content. 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). Attempting 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 Aristotle’s Physics and the briefness of the discussion gave rise to more questions than it settled. According to the Categories, accidents must inhere, or exist, in substances and so if time was 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 fundamentally of all questions arose about the relationship between the account set out in the Categories and the account in the Physics. Were they to be seen as discussions of time which had equal authority or did one represent further development of the other?. As if the Categories and Physics had not provided enough questions and challenges for medieval thinkers, they were

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also confronted by the peculiarly medieval Christian requirements 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 writings of the ancient Christian fathers. As many of the Christian 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 theological reXection. This inevitably gave rise to its own problems 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 Although Aristotle 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 constitutive parts was an important focus for thirteenth-century

3 For more details about Bede’s account see his de Temp. (ed. Weber Jones, 295–303). Although possessing considerable authority Bede’s account represented only one of many diVerent approaches to this matter. St Isidore of Seville’s account of time proposed just eight fundamental temporal quantitative elements, Etym. 5. 29 (1, 15–21).

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thinkers who wanted to reconcile patristic authorities with Aristotelian philosophy.4 Focusing upon the quantitativeness and divisibility of time, thirteenth-century thinkers found Aristotle’s distinction 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-quantitativeness, 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 divisible 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, 25–35) 5 Aristotle, ‘consequenter quidem enim est quorum nullum est medium proximum, punctorum autem semper medium est linea et ipsorum nunc tempus est’ Phys. (Vetus) 6.1. 231b7–10 (AL 7.1.2, 217) and ‘InWnitis quidem igitur secundum quantitatem non contingit sese tangere in Wnito tempore, eius autem que sunt secundum divisionem contingit; et namque ipsum tempus 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, 39–43). Albert, Meta. 5. 3. 2 (16.1, 260, 40), de Prin. Mot. Proc. (12, 50, 1–2), who also points out that this deWnition is taken ultimately from Euclid. Sum. Theol. 5. 1. 1. 1 (34.1, 124, 35–6).

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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 indivisibility: 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 alternative 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 the unacceptable use of ‘in atomo tempore’ Phys. 8. 3. 6 (4.2, 634, 37), and Aquinas 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 Moses Maimonides were more open to the idea that atoms could possess the property of extension. For further information and references to texts, R. Sorabji, ‘Atoms and Time Atoms’, and with more detail about Aquinas’ position, E. J. MacKinnon, ‘Thomism and Atomism’. For more comprehensive discussions of medieval atomism, B. Pabst, Atomtheorien des Lateinisher Mittelalters and A. Maier, ‘Kontinuum, Minima Und Aktuell Unendliches’. For a contemporary philosophical account of what temporal atomism would amount to see, G. J. Whitrow, The Natural Philosophy of Time, 200–5.

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The distinction between physical and logical indivisibility is essential for appreciating the claims made by contemporary 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 Leucippus, 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 arguments during the thirteenth century was developed particularly 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. 605–42; C. D. Broad, ScientiWc Thought, 348–58, and J. D. Mabbot, ‘The Specious Present’. The notion has also been called the ‘psychological present’ (G. J. Whitrow, The Natural Philosophy of Time, 74–7) and even the ‘precious present’ (A. C. Moulyn, ‘The Functions of Point and Line in Time Measuring Operations,’ 150–1). On the notion of the ‘specious present’ and its application to models of eternity see, in particular, A. F. Whitehead, The Concept of Nature, 66–8 and J. F. Harris, ‘An Empirical Understanding of Eternality’, 174–81. 8 Albert, de Gen. et Cor. 1. 1. 11 (5.2, 120, 5–8); de Caelo 1. 2. 1 (5.1, 32, 87–92); Phys. 6. 1. 3 (4.2, 451–3); Aquinas, de Gen. et Cor. 1. 3 [20], [23]; In Phys. 6. 2 [758]–[765]. Grosseteste, In Phys. 6 (116–18).

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in a time T. If S1 is postulated as traversing D in T, then S2 travelling at double the velocity of S1 would traverse D in 1⁄2 T. If we now imagine S1 to speed up so that it is travelling at twice the velocity of S2, then it would traverse D in 1⁄4 T. By continuing this thought experiment and alternating the relationship between the respective velocities of S1 and S2 ad inWnitum, the velocity argument demonstrates that time must be inWnitely divisible and that there can be no indivisible 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 S1 and S2 alternating in velocities in such a way that it is necessary to postulate fractions of T. And so the implication of 9 For Averroes’ argument ‘ex natura velocioris et tardioris’, see his commentary In Phys. 6 [22] on Aristotle’s text, Phys. 6. 2 (232a23–233a12). It has been suggested (D. Bostock, ‘Aristotle on Continuity in Physics VI’) that because velocity is determined as a function of dividing time and motion then Aristotle’s argument begs the question at issue, viz. the inWnite divisibility of time (and motion). Whether or not this is an accurate criticism of Aristotle, it would certainly not seem to apply to medieval thinkers. As we shall see more fully later, Aquinas and his medieval colleagues thought that this argument did not apply to the movements and durations of angels and this limitation of the argument suggests that despite sometimes loose expressions of the argument to the contrary (e.g. Aquinas, In Sent. 4. 44. 2. 3) thinkers such as Aquinas understood the argument to be a conditional one claiming that if either motion or time were inWnitely divisible then necessarily they both were. For an account of the medieval use of Aristotle’s wider arguments against atomism see J. E. Murdoch, ‘Superposition, Congruence and Continuity in the Middle Ages’, 421–4. In reality there were a wide variety of arguments that mid-thirteenth-century thinkers could appeal to. Albert refers to an argument from tenses, Phys. 4. 3. 1 (4.1, 259–61) and Aquinas seems to imply that one can be based on the perceptibility of times, de Sen. et Sen. 18 [270]–[275].

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Aristotle’s 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 terms were to medieval Latin speakers, rendering them in English presents some diYculties. As the English language contains the apparently similar terms, ‘discrete’ and ‘continuous’, it is tempting to assume that these English words accurately translate the Latin terms, but such an assumption would be misleading. Whilst the Latin distinction is intended to be logically exhaustive, the distinction expressed 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’. So without further investigation it cannot be assumed that the English words ‘discrete’ and ‘continuous’ are accurately translating the Latin terms ‘discretum’ and ‘continuum’. The word ‘discrete’ is used by contemporary Englishspeaking mathematicians to construe the property of an ordering in which each member has a unique successor. Examples 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, 78–82). In Sent. 1. 9. 1. 2 (Borg. 25, 273). Phys. 6. 1 (4.2, 447, 23); 3. 4 (4.2, 495, 5–13); Theodoric, Tr. de Nat. et Prop. Contin. 1 (3, 252, 21–8) and 2 (3, 255, 102–9). Bonaventure, Hex. 3 [5] (5, 344).

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and/or negative integers in which each numeral has a speciWc predecessor and successor. The property of density is construed in contradistinction as the property of an ordering in which no member has a unique successor and/or predecessor. According to this deWnition, between each and every member 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 a unique ‘next’ number. It is always possible to postulate yet another number between them. Between 1⁄2 and 1 for example 3⁄4 could be placed, but between 1⁄2 and 3⁄4 the number 5 ⁄8 could be placed, and between 1⁄2 and 5⁄8 there is the number 9⁄16, 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 complete 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, 12–24 and more generally E. V. Huntington, The Continuum and Other Types of Serial Order.

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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 Aristotle’s work and so construed as a species of successiveness and contiguity. 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 Wat terminus duorum quae se tangunt, dicitur esse continuum. Et hoc etiam signiWcat nomen . . . quando igitur multae partes continentur in uno, et quasi simul se tenent, tunc est continuum. Sed hoc non potest esse cum sint duo ultima, sed solum cum est unum.’ In Phys. 5. 5 [691]. On the notion of ‘habitus’, Albert informs us that ‘habitum enim est quando ultima sunt simul’, Phys. 5. 2. 3 (4.2, 425, 35). On the more general point at issue, note Aristotle’s deWnition, ‘Linea vero continua est; namque est sumere communem terminum ad quem partes ipsius coniunguntur, hoc est autem punctum, et superWciei linea (superWciei enim partes ad quendam communem terminum coniunguntur).’ Aristotle, Cat. (trans. Boethii) 6.5a1–5 (AL 1.1, 14); Phys. 5. 3. 226b19–227b2 (AL 7.1.2, 200). 13 Phys. 5. 2. 3 (4.2, 425, 44–54). On Aristotle’s usage, E. Hussey, Aristotle, Physics, 113–15.

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through a single point which will then act as a single boundary 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 don’t have parts, they are discrete indivisible 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, 1–7). It is important to stress that the inWnity of the divisibility means that there is merely an inWnity of potential places in which one could cut or divide the particular in question. As Aquinas notes, it does not mean that any particular is capable of an actual division at an inWnity of locations simultaneously, ‘geometra non indiget assumere aliquam lineam esse inWnitam actu, sed indiget accipere aliquam lineam a qua possit subtrahi quantum necesse est, et hoc nominat lineam inWnitam’ Sum. Theol. 1. 7. 3 ad 1; In Sent. 2. 2. 1. 1 ad 6. The contemporary willingness to recognize the possibility of just such an inWnite simultaneous divisibility denotes one of the principal diVerences between medieval and modern notions of inWnity. For further details, A. Moore, The InWnite, 110–30.

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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 concepts denoted by the English term ‘discrete’ and the Latin word ‘discretum’ seem to be co-extensive, there are signiWcant diVerences between the notions implied by the Latin word ‘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 English word ‘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 translating ‘continuum’, to substitute another term might actually cause more confusion. Despite the potential conceptual problems 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 atque discretum; et aliud quidem ex habentibus positionem ad se invicem suis partibus constat, aliud vero ex non habentibus positionem. Est autem discreta quantitas ut numerus et oratio, continua vero ut linea, superWcies, corpus, praeter haec vero tempus et locus’. Cat. (Trans. Boethii), 6. 4b20– 35 (AL 1.1, 13); Albert, ‘continuum est in cuius medio accipere est punctum, ad quem copulantur ambae medietates per hanc enim naturam continuum separatur a discreto’ Phys. 3. 1. 1 (4.1, 146, 43–6); 6. 1. 1 (4.2, 447, 32–7). 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 on Aristotle’s Physics by St. Thomas Aquinas, 16.

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T E M P O R A L T E R M I N O LO G Y Having clariWed some of the fundamental terms and concepts 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 complex as 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 the editorial scholion in S. Bonaventurae Opera Omnia 3.92. For examples of diVering English words used as synonyms of each other see J. Owens, An Elementary Christian Metaphysics, 207, and G. E. L. Owen, ‘Aristotle on Time’, 141. Similar policies can be seen with languages such as French as indicated by J. Nizet, ‘La temporalite´ chez Soren Kierkegaard’, 227. On some occasions translators establish their own idioysncratic equivalents, as for example where occurrences of ‘nunc’ in Aquinas’ text are rendered with the terms ‘present’ and ‘moment’ in J. P. Rowan (trans.), St. Thomas Aquinas: Commentary on the Metaphysics of Aristotle, 5. 13 [940] (1, 362). One of the particularly popular editorial decisions seems to be the use of ‘moment’ to render the Latin ‘instans’, as in, ibid., 5. 13 [941] (1, 362); Liam Walsh (trans.), St. Thomas Aquinas Summa Theologiae 3a: 7–15 (49, 14–5) and A. Vos Jaczn et al. (eds.), John Duns Scotus: Contingency and Freedom, Lectura I, 39 (40).

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I N S TA N S The thirteenth-century use of the Latin word ‘instans’, particularly when used as a technical temporal term, seems to owe much to the Latin translations of Aristotle’s, Averroes’, and Avicenna’s (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 temporal 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 contemporaries 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 praeteriti’, 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. de Anima 3. 11 [756]. On the ‘point-like’ qualities of the instant, note, Grosseteste, ‘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 temporal use of ‘instans’ must be distinguished from a non-temporal use such as ‘instans naturis’ where it picks out distinct locations in a causal sequence. This distinction seems to have developed towards the end of the thirteenth century as Scotus shows, ‘Deinde subdistinguit instantia naturae in eodem instanti temporis’. In Sent. 4. 14. 2 (9, 56). For further background to the discussion, T. Rudavsky, ‘Creation and Time in Maimonides and Gersonides’, 135–8.

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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 particular 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, 36–40). Lib. de Praed. 3. 4 (Borg. 1, 200). Kilwardby, de Temp. 15 [83] (30, 30–4); In Sent. 2. 3 (2, 15, 111–16), 4 (2, 17, 19–22). Theodoric, Tr. de Nat. de Prop. Contin. 2 (3, 253, 12–15). 20 Boethius, In Cat. Aristotelis 2 (PL 64, 205B–C); 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. de Malo 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, 49–51); 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, 180–200).

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Nevertheless there is a looser use of the word, which sometimes 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

Albert’s 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 per instans medium quod est terminus talis copulationis . . . Praeteritum autem dicimus quod terminatur ad praesens per instans quod est praeteriti Wnis et principium praesentis: et praesens etiam copulatur ad futurum per instans quod est Wnis praesentis et principium futuri’, Lib. de Praed. 3. 4 (Borg. 1, 200). For other similar usages, Kilwardby, de Temp. 1 [2] (7, 7–9); John Quidort, 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 quo dicit Priscianus, quod praesens est cuius pars praeteriit, et pars in instanti est, et pars in futuro: et haec copulantur praeterito et futuro. Est etiam praesens nunc indivisibile et hoc non copulantur sed copulat: et hoc quidem est aliquid 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).

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The use of the English word ‘present’ is ultimately identical 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 indivisible 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 Aristotle’s works consistently indicated that this was Aristotle’s own preferred term for picking out the logically indivisible temporal boundaries which we have seen can also be referred to as instants. Encouraged by Aristotelian commentators, thirteenth-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. 218a5–9 (AL 7.1.2, 170); ‘Et adhuc manifestum sit quod nulla pars ipsum nunc temporis est’, ibid., 4. 11. 220a19 (AL 7.1.2, 178); ibid., 4. 13. 222a10 (AL 7.1.2, 184). Besides its role in referring to temporal elements such as parts and boundaries, the word ‘now’ also had a distinct content when used in talk of a ‘Xowing now’ (nunc Xuens) or ‘changing now’ (nunc Xuxibile), as Bonaventure 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 view Boethius 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 motus semper alius, et tempus; simul autem omne tempus idem est: ipsum enim

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Although not as clearly expressed we can see Peter of Tarentaise assuming this very usage. When discussing concepts 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 one—and 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 erat ipsi nunc) in quantum autem quod cum est, est ipsum nunc, idem est.’ Phys. (Vetus) 4. 11. 219b9–14 (AL 7.1.2, 176). The word ‘nunc’ is also used of eternity and aeviternity where the non-moving nature of those durations is depicted by talking of a ‘standing now’, Albert, Sum. Theol. 5. 22. 1 (34.1, 115–17). Avicenna, ‘Si autem fuerit indivisibile tempus; erit id quod appellatur instans quia non est tempus . . .’ SuV. 2. 10. Boethius, Posteriorum Analyticorum 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, 18–19); Aquinas, In Phys. 4. 21 [615–17]. Bonaventure, ‘principium autem temporis est instans vel nunc’ In Sent. 2. 1. 1. 1. 2 ad 4. (2, 23) also In Sent. 4. 17. 2. 2. 2 fund. 2 (4, 444). For further details, J. M. Quinn, ‘The Doctrine of Time in St. Thomas: Some Aspects and Applications’, 268–9. 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 est simplex in quantitate, . . . Primo modo non potest esse inWnitum actu, . . . secundo modo potest, ut punctus, et nunc’. In Sent. 2. 2. 2. 1 ad 6.

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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 secundum alterum. Nullam enim divisibile est sua divisio qua dividitur, ipsa autem divisio temporis est nunc. Nihil enim est aliud divisio continui quam terminus communis duabus partibus hoc autem intelligimus per nunc quod est terminus communis praeteriti et futuri. Sic ergo manifestum est quod id quod est divisibile, non potest esse nunc secundum seipsum’. In Phys. 6. 5 [792] and [788].

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sense, except when it is used to translate Aristotelian passages, and in those contexts it is clearly used in the nonextensional 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.

PE R IO D U S The word ‘periodus’ occasionally appears in thirteenthcentury texts as a technical temporal term. Neither Kilwardby nor Pseudo-Aquinas use it in their treatises de Tempore, 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 Aristotle’s 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, 72–8). Bonaventure, In Sent. 4. 11. 1. 1. 5 (4, 250). Albert, de Gen. et Cor. 2. 3. 5 (5.2, 205, 80). The passage of Aristotle which they refer to is, ‘Et in equali tempore et corruptio et generatio que secundum naturam. Ideoque et tempus et vita uniuscuiusque numerum habet, et hoc determinantur. Omnium enim est ordo, et omne tempus et vita mensuratur periodo, sed tamen non eadem omnes, sed hii quidem minori, hii autem maiore’. de Gen. et Cor. (Vetus) 2. 10. 336b9–15 (AL 9.1, 75). Apart from its use as a technical temporal term, ‘periodus’ was also used in a non-temporal, grammatical sense as suggested by Isidore, Etym. 2. 18. Aquinas, Com. in Isaiah Prologue, 2 (Leon. 28, 5, 24–5).

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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 thirteenthcentury 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 rendering 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, translators 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, 40–7); de Natura loci 1. 5 (5.2, 9 l, 31–6); In Sent. 1. 8. A. 12 (Borg. 25, 236). Aquinas, Resp. ad lect. Venet. de 36 art. 10 (Leon. 42, 341, 176–9); Quaest. Disp. de Malo 5. 5 ad 6. In some contexts the word ‘periodus’ seems to be treated as a synonym with terms such as ‘seculum’. Aquinas, for example, writes. ‘saecul(um), quod est periodus 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].

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parts,29 there was an equally evident tradition whereby the term was used to refer to non-extended indivisible boundaries. 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, 2–7); 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 Caelo 1. 2. 2 (5.1, 35, 76–80). Albert also quotes Avicenna as a basis for describing time as an ‘aggregatio momentorum’, Phys. 4. 3. 3 (4.1, 263, 40). See also Kilwardby, de Temp. 6 [27] (14, 7); 11 [49] (21, 9). Note also the description of 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 instanti temporis quod dicitur nunc, vel pro aliquo tempore imperceptibili’, Super 1 ad Corinthios. 15. 8 [1007]. Note also his comment, ‘Necesse est enim quod motus caeli sicut et quilibet motus cessat in momento sive in instanti; quia ultimum instans temporis respondet ultimo instanti motus’ Resp. ad Lect. Venet. de 30 art. ad 8 (Leon. 42, 322, 149–51) and Sent. lib. Eth. 10. 5 (Leon. 47.2, 565, 14–40). Aquinas’ reference to an instant of motion should also be noted as an example of the Xexible way this term was used to pick out boundaries; 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. de Malo 4. 6 ob. 13; Sent. Lib. Eth. 10. 5 [2].

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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 eternity (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 looking 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 occurrence 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 momento aeternitatis, i.e mensurantur aeternitate, et inter rem cuius substantia et actio sunt in momento temporis existens est medium, et est illud cuius substantia est 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 aeternitate et rem, cuius substantia et operatio est in tempore, est res media cuius substantia est in aeternitate et actio est in tempore’, In Sent. 2. 2. 1. 1. 1 fund. 1 (2, 55). Bonaventure includes the word ‘momentum’ only when stating 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 the aevum when quoting from, or commenting upon, Proclus’ texts. Kilwardby, In Sent. 2. 11 (2, 44, 43–7). Aquinas, In Sent. 1. 14. 1. 1 ob. 3. Peter of Tarentaise, In Sent. 1. 14. 1. 1 ob. 7.

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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, dicendum quod 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 in mobili quod movetur’, Sum. de Creat. 2. 5. 1 (Borg. 34, 365) and Phys. 6. 1. 1 (4.2, 447, 11–13); 6. 3. 1 (4.2, 487, 9). It is diYcult to trace the origins of this usage, but it was probably encouraged by the fact that it could be found in Avicenna’s texts (SuV. 2. 10). There was clearly a degree of Xuidity in thirteenth-century terminology as Albert seems at times to indiscriminately lump together the terms ‘point’, ‘now’, and ‘moment’, Scientia libri de lineis Indivis. 1 (4.2, 498, 30–5), sometimes even introducing a further term ‘mutatum’ as an equivalent of ‘momentum’, de Div. Nom. 10 [5] (37.1, 400, 77–8). The Venetian lector referred to in notes 28 and 30 seems to have used the word ‘instans’ indiscriminately to pick out a boundary of time and motion.

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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 perspicuous 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, distinguishes between a mover preceding what it moves by dignity 34 Colloquially the word ‘moment’ is often used to refer to small pieces of time, as in the usage of W. Lane Craig, God, Time and Eternity, 21 n. 57. It has been used with a clearer non-extensional import by N. Pike, God and Timelessness, 8. The colloquial English use seems to have been captured in medieval Latin with the non-technical Latin word ‘iam’, as Albert shows, ‘Ipsum vero, quod dicitur iam, dicit quando in praeterito et futuro, quod relinquitur ex tempore, quod propinquum est praesenti nunc indivisibili, sicut dicimus ‘‘Quando vades?’’ et respondetur: ‘‘Iam’’, quia prope est tempus, in quo futurum est, ut eamus, et ‘‘Quando ivisiti?’’, respondemus: ‘‘Iam ivi’’, quia non est procul ab ipso nunc in praeterito’, Phys. 4. 3. 13 (4.1, 286, 14–22). The brief analysis of the term ‘momentum’ is not intended to capture all translational nuances. It has been translated as ‘impulse’, for example, by R. J. Blackwell (trans.), Commentary on Aristotle’s Physics by St. Thomas Aquinas, 486, but as translations such as these have no particular bearing on the matter of this study I shall eVectively ignore them.

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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 existence (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’ is provided by John Locke in his ‘On Succession and Duration’ (2, 14). For the reference to Aquinas see In Sent. 2. 2. 1. 1; also 1. 19. 2. 1; and for the reference to Albert see Phys. 4. 4. 2 (4.1, 296, 23–6); Sum. Theol. 5. 23. 1. 1. 1 (34.1, 122, 18– 22). Sum. de Creat. 2. 2. 3 ad 1 (Borg. 34, 348). This extensional use of ‘duratio’ occurs widely in mid-thirteenth-century texts. Note Bonaventure’s ‘posterius tempore sive duratione’, In Sent. 1. 9. 1. 3 ad 2 (1, 184) and 4. 43. 1. 4 (4, 888). Also Alexander of Hales, Sum. Theol. 1. 1. 1. 2. 4. 2. 4 (1, 95). William of Auxerre, Sum. Aurea. 2. 8. 2. 1. 1 (2.1, 176, 23–5). The extensional implications of ‘duratio’ occurs often as an objection to non-extensional notions of an eternal duration. Note Albert, ‘omnis duratio protensa est, nullum protensum est totum 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, 231–2) as does Aquinas, In Sent. 1. 8. 2. 1 ad 6.

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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 distinctions which they made between successive and non-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 est in actu; tamdiu enim res durare dicitur quamdiu in actu est, et non dum est in potentia’, In Sent. 1. 19. 2. 1 sol. Albert, ‘Per hoc enim quod incipit esse et initium habet esse, ab ipso eodem initiatur duratio esse, secundum quod 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 deo idem est omnino esse et durare’, Quaest. Disp. de Myst. Trin. 5. 2 ob. 6; ‘nunc aeternitatis nominat illam durationem quantum ad simplicem simultatem, aeternitas vero quantum ad interminabilitatem divinae simplicitatis et simultatis secundum rem nihil quidem addit’, ibid. 5. 1 ad 13 (5, 92); also Peter of Tarentaise, ‘Si mundus fuit ab aeterno, aut duratio eius fuit omnino simplex et invariabilis, et ita fuit ipsa aeternitas divina’, In Sent. 2. 1. 2. 3 con. 9; and 1. 8. 3. 1. And similarly Philip the Chancellor, Sum de Bono, 1. 1. 4 (1, 53, 47–8), 1. 2. 2 (1, 59, 70–4). Note also Henry of Ghent’s ‘. . . cum duratio duplex est: aeternitas et tempus, potest dici aliquid principium duratione quae est aeternitas, vel duratione quae est tempus’, Lect. Ord. 1 (36, 42, 43–5). 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. 17 ad 20. Sum. Theol. 1. 10. 1 ob. 2. The signiWcance of Alexander of Hales’ views on duratio should not be underestimated as they have clearly inXuenced Aquinas’ views and language. Compare, for example, Aquinas’

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It is not altogether clear that contemporary commentators appreciate that there were two distinct notions of duratio. 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 Alexander’s ‘duratio autem respicit esse’, Sum. Theol. 1. 1. 2. 4. 3 (1, 87). According to Theodoric of Freiberg, the question of whether a particular can possess a duratio reduces to the question of whether its esse can have the property of pastness, presentness, or futureness. de Mensuris 3 (3, 226, 22–6). 38 E. Stump and N. Kretzmann have defended as an accurate reading of Aquinas, a non-successive but apparently extensional use of the word ‘duration’ (duratio) in ‘Eternity’, 434–5, and ‘Atemporal Duration’, 217. The philosophical cogency of their position has been challenged by P. Fitzgerald, ‘Stump and Kretzmann on Time and Eternity’, 260–9; K. Rogers, ‘Eternity Has No Duration’, 1–16; B. Leftow, ‘Eternity and Simultaneity’, 148–79; and ‘The Roots of Eternity’, 189–212. H. J. Nelson, ‘Time(s), Eternity and Duration’, 11–17. D. B. Burrell, ‘God’s Eternity’, 389–406; D. Lewis, ‘Eternity Again: A Reply to Stump and Kretzmann’, 73–9. 39 As soon as the distinction is made between the two notions of duratio it becomes clear that one cannot claim that a duration is necessarily extended (P. Fitzgerald, ‘Stump and Kretzmann on Time and Eternity’, 262–3), or argue against an instantaneous notion of eternity on the grounds that it is referred to as a duratio (Stump and Kretzmann, ‘Eternity’, 435). Nor must the use 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 be assumed that ‘duration means an interval of time’ and that ‘an atemporal duration is . . . a contradiction in terms’ (A. Padgett: God, Eternity and the Nature of Time, 67). Nor is it the case that ‘Duration is a category which is prima facie not even applicable to a timeless being in any literal sense’

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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 successive 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 notion of ‘duratio’.

M O R A , D I U R N I TA S , P R OT E N S I O None of these three terms appear as major temporal technical terms. Nevertheless, they do sometimes feature within thirteenth-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 case that 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 vel pars temporis’, Sum. de Creat. 2. 3. 2 (Borg. 34, 348). Sum. Theol. 5. 22. 2. 1 (34.1, 117, 74–7). Aquinas, Sum. Theol. 1. 63. 6 ob. 4. Bonaventure, In Sent. 2. 24. 1 dub. 1.

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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. Illustrating the meaning of all three of these key terms, Albert doesn’t 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 Aristotle’s 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 Noah’s Xood. Kilwardby, however, indicated an appreciation of a broader range of uses which were more similar to our contemporary usage. Distinguishing between a simple quando and a composite quando, he was in eVect distinguishing between a non41 ‘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, 52–5); also 5. 22. 1 ad 3 (34.1, 117, 61–5) and In Sent. 1. 8. A. 8 ad 5 (Borg. 25, 231–2).

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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 locations. 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 relinquitur ex praeterito et futuro; ex praeterito quidem, sive fuerit remotum a praesenti sive propinquum, ex futuro autem non est nisi propinquum, quia id quod remotum est a praesenti nunc, non habet ordinationem in materia. Et hoc est de quando mensurabili, quando autem non mensurabile a nobis est, quod relinquitur ex tempore imperceptibili’, Phys. 4. 3. 13 (4.1, 286, 33–40) also Lib. de Causis 1. 1. 10 (17.2, 72, 41–3). Albert is probably drawing on Averroes, who seems to have felt that it was particularly important to distinguish the quando from the present. In Phys. 4 [127]. Kilwardby’s distinction was as follows, ‘sic potest dividi quando per simplex et compositum: ut dicatur simplex quando derelictum ex presenti nunc indivisibiliter; compositum quando ex tempore continuo, cuius sunt tempus praeteritum et futurum’, de Temp. 16 [99] (33, 28–31).

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which could be referred to as a quando because in each case it was a present element.43

A T EC H N I C A L VO C A B U L A RY Now that we have examined some of the key terms which medieval thinkers used in discussions of temporality, we are in a position to identify an appropriate terminology to be used in translation and philosophical discussion of temporal parts and temporal boundaries.44 There is no single generally accepted terminological distinction used by English-speakers to refer to temporal parts and boundaries. The distinction has variously been stated as one between instants and periods,45 instants and intervals,46 and instants and durations.47 There was similar diversity of practice in the medieval period, with the distinction some43 Kilwardby, on at least some occasions, seems to have viewed existence in the quando as arising from existence in time, ‘Ex eo enim quod res est in tempore, dicitur esse quando, et nichil aliud est quando nisi in tempore , et istud est aliud accidens a tempore quia causatur ab ipso.’ de Temp. 16 [99] (33, 25–7). Albert, however, oVered a broader account, one which was stated in terms of durations and the particulars within those durations so that it could be used of any duration and any particular within a duration; ‘quando est natura tertia quae relinquitur ex duabus aliis naturis, scilicet natura durationis extrinsecus adiacentis, et natura durantis’, Sum. de Creat. 2. 3. 5 (Borg. 34, 356–7). See also Peter of Tarentaise, In Sent. 1. 8. 3. 1. 44 For a further exploration of less signiWcant thirteenth-century temporal terms, see Averroes on ‘ecce’ and ‘pauloante’, In Phys. 4 [126] and Albert on ‘olim’ and ‘repente’, Phys. 4. 3. 13 (4.1, 286, 27–30). 45 R. Swinburne, The Christian God, 72. 46 J. R. Lucas, A Treatise on Time and Space, 20. W. H. Newton-Smith, The Structure of Time, 6. 47 W. H. Newton-Smith, The Structure of Time, 127.

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times rendered as one between the now (nunc) and time (tempus),48 whilst at other times it was stated as a distinction between an instant (instans) and time (tempus).49 Given the meanings of the key Latin and English terms which we have examined above, the words ‘instans’ and ‘instant’ stand out as perhaps having one of the most unambiguous references to temporal boundaries, whilst the words ‘periodus’ and ‘period’ seem to be the most unambiguous terms for referring to temporal parts. I shall therefore use the terminological distinction between ‘instant’ and ‘period’ in this study in order to refer to the philosophical distinction between temporal boundaries and parts. Although of less immediate signiWcance, the medieval use of ‘momentum’ to refer to an indivisible motion boundary will also provide the basis for a further distinction between motion parts (motion) and motion boundaries (moments) which I shall introduce when commenting on the relation between motion and time.

TEMPORAL REDUCTIONISM One of the particularly clear points to emerge from our study so far is that thirteenth-century thinkers were able to 48 Kilwardby, de Temp. 6 [29] (15, 1–3), 7 [34] (16, 1–12). Aquinas, In Phys. 8. 17 [1122]. 49 Bonaventure, In Sent. 1. 37. 2. 2. 3 fund. 1 (1, 662). Albert, Sum. de Creat. 2. 5. 1 (Borg. 34, 364). Aquinas, Sum. Theol. 1. 42. 2 ad 4. Kilwardby explicitly cited the advantage of using relational terms such as ‘before’ and ‘after’ to talk of temporal elements because this avoided the need to specify what exactly was being referred to, de Temp. 6 [29] (14, 25 V.).

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recognize and deploy a distinction between instants and periods. They may have sometimes lacked a precise terminology in which to state the distinction, but that they possessed the concepts cannot be doubted. Contemporary philosophers have sometimes wondered whether postulating both instants and periods was metaphysically extravagant, and so there have been various reductive enterprises attempting either to reduce language about one of these temporal elements to language about the other, or even to try reducing the temporal elements to some further non-temporal kind of element. Whilst here the focus will be upon attempts to reduce one kind of temporal element to another, reductive strategies attempting to reduce temporal elements to non-temporal elements will be the focus of study in Chapter 4.50 In terms of reducing instants to periods, or periods to instants, thirteenth-century thinkers generally lacked the conceptual apparatus to make sense of the notion, and if confronted by it they would almost certainly have viewed the suggestion as proposing another species of atomism. We have already seen that Aristotle’s argument from velocities 50 Advocates of the reducibility of instants, to periods, or of the reducibility of periods to instants, typically fall into three basic types: those who appeal to the apparent Wndings of physics (H. Kragh and B. Carazza, ‘From Time Atoms to Space-Time Quantization’, 437–62), those who appeal to the supposed insights of psychology (C. D. Broad, ScientiWc Thought, 344–58; W. James, The Principles of Psychology, i. 605–42), or those who appeal to aspects of modern mathematical theories (G. J. Whitrow, The Natural Philosophy of Time, 200–5; W. H. Newton-Smith, The Structure of Time, 126–38; M. J. White, ‘On Continuity: Aristotle versus Topology’, 1–12). In this study I shall not be analysing the nature or coherence of these diVerent theories, merely using the categories and terminology which they develop, in order to better understand thirteenth-century thought.

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made versions of atomism seem unattractive to many thirteenth-century thinkers, and so it is that thirteenth-century thinkers seem largely to have felt content to simply state the irreducibility of instants to periods and periods to instants as a fact that did not need supporting argument or explanation.51 Where the issue of reductionism could, and perhaps should, have made more impact upon thirteenth-century thinkers was where it encountered the issues raised by supervenience. In order to account for a reduction of one kind of temporal element to the other, advocates must account for how it is that the very diVerent properties of extension and non-extensional boundaries both come into existence when ultimately there is only supposed to be the one kind of element. One of the most popular approaches to this problem is using the principle of supervenience. Using contemporary mathematical set theory, mathematicians have found that it can be fruitful to treat a continuum as if it were composed of a non-denumerable inWnity of non-extended points and so in order to explain the existence of both extensional and non-extensional elements, it has sometimes been hypothesized that extensional properties (temporal parts) come into existence by simply supervening upon the non-extensional elements (temporal boundaries).52 51 Theodoric, de Nat. et Prop. Cont. 1 (3, 252, 44–52). 52 A. Gru¨nbaum, Modern Science and Zeno’s Paradoxes, 127–8. M. White, The Continuous and the Discrete, 8. E. E. Savellos and U. D. Yalc¸in (eds.), Supervenience: New Essays, 1–16. Although popular, the superventionist thesis is nevertheless not without diYculties. Gru¨nbaum, for example, argues (in ‘A Consistent Conception of the Extended Linear Continuum’, 295) from the fact that ‘temperature’ is a property of a set of molecules, rather than

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Most thirteenth-century thinkers, with their primary focus upon physics rather than mathematical logic, would have found the idea of supervenience to be at best unconvincing if not downright incoherent. InXuenced heavily by Aristotle’s Physics, they construed continuity as a distinct species of contiguity and so insisted that continuous parts must have boundaries which touched and which thus enabled them to join in a continuous whole. As non-extended elements, by deWnition, had no parts, then this meant that they could have no boundaries. Lacking boundaries they could not meaningfully be said to lie next to each other, touching, and so they could not count as continuous. The only way two non-extended elements could be related contiguously would be if one were to be directly on top of the other, but in that scenario there would be no consequent supervenience of extension because the non-extended elements would simply fall on top of each other. No matter how many non-extended elements were added to the scenario the ultimate result would be the same, and so to the typical Aristotelian-orientated thirteenth-century thinker, supervenience could only appear as incoherent.53 being a property of individual ones, to the conclusion that we should deWne ‘length’ or ‘dimension’ similarly as a property not of points or instants but of sets of points or instants. But the diVerence is that temperature accrues to the set of molecules in virtue of a property which each molecule has—motion. On Grunbaum’s account, extension accrues to the set of points, not in virtue of any feature of the individual points, but in virtue of the sheer number. Without further argument it is diYcult to see why the sheer number of nonextensional elements should give rise to a property of extension. 53 Albert, de Caelo 3. 1. 2 (5.1, 204, 47 V.); 1. 2. 1 (5.1, 32, 87–92); 1. 2. 7 (5.1, 52, 48–58). Averroes’ treatment of this question is clearly guiding many thirteenth-century discussions, ‘Contiguatio rei secundum totum cum alia re

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Although the repudiation of supervenience was a widely held position amongst thirteenth-century thinkers, it wasn’t universally held. Grosseteste at least was willing to explore extensional properties arising from non-extensional particulars as a key part of his metaphysics of light. In the case of creation, for example, he believed that a case could be made for thinking of the diVusion of ‘continuous’ light as arising from the non-extensional ‘simple’ singularity of light with which the creation began.54 Even Averroes was willing to explore what it would mean to imagine a body as if it were composed of points, but as both he and later Albert the Great were particularly clear to point out, such reXections were based upon a theoretical exercise of imagination. Echoing Averroes’ own distinction, Albert summed up the attitude of most of his thirteenthcentury contemporaries when he indicated that he was perfectly willing to imagine lines and bodies and treat them as if they were made of series of non-extended points, but to go any further than merely imagining such scenarios secundum totum est superpositio; et ex superpositione non Wt magnitudo que ante non erat neque aliquid habens partes. Unde ex superpositione linee super lineam non Wt magnitudo in latitudine, cum non superponatur nisi ex parte latitudinis secundum quod est linea indivisibilis. Et similiter superpositio superWcierum non facit profundum. Et quia punctus est indivisibilis in omni parte, non facit aliquid habens partes; et continuum habet partes.’ In Phys. 6 [2] For further development of these approaches, J. E. Murdoch, ‘Superposition, Congruence and Continuity in the Middle Ages’, 422–34. 54 For Grosseteste on the expansion of light, de Luce (83). The relationship of this work, and the views expressed in it, to the rest of Grosseteste’s corpus has occasioned controversy, on which see C. Riedl, Robert Grosseteste, On Light: A Translation with Introduction, 3–8, and J. McEvoy, The Philosophy of Robert Grosseteste, 149–62, with alternative conclusions and perspectives in R. Southern, Robert Grosseteste, 134–40.

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was to commit the folly of thinking that the world actually conformed to such an imagination. It was a step too far. It was to confuse geometry with physics, or as we might say in a more contemporary idiom, it was to confuse the model with the reality which it was supposed to be describing.55

C O N C LU S I O N In this chapter we have seen that thirteenth-century thinkers distinguish between logically indivisible boundaries and divisible parts. As applied to time this distinction allowed them to identify and refer to two temporal elements, temporal parts and temporal boundaries. Thirteenth-century Latin-speakers had the beneWt of a broad temporal vocabulary including words such as ‘nunc’, ‘instans’, ‘momentum’, ‘periodus’, and ‘duratio’. Although each of these words have what appear to be obvious English translations, we saw that the medieval Latin terms often contained multiple nuances which were not always reXected in the typical English words used to translate them. Nevertheless some important terminological issues became apparent. We saw that the words ‘nunc’ and ‘instans’ were largely used to refer to indivisible temporal boundaries whilst the word ‘periodus’ was used to refer to temporal 55 Averroes, In Phys. 5 [29]. Albert, de Caelo 3. 1. 2 (5.1, 205, 8–62). For an introduction to the development of mathematical and physical models in the thirteenth and fourteenth centuries, G. J. Whitrow, The Natural Philosophy of Time, 182–5.

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parts. The word ‘momentum’ seems to have admitted of uses that would allow it to refer to either indivisible temporal boundaries, divisible temporal parts or even indivisible boundaries in a motion. Perhaps the most complex of these terms was the word ‘duratio’, which we saw to have two radically diVerent senses, depending on the nature of a particular thing’s existence (esse). Those particulars with successive existence consisting of part-following-part, had a duration which extended successively through time. But those particulars which lacked successive existence, having no parts and going through no changes, had an existence which was non-successive; thus giving rise to a non-successive notion of duratio. This will be of considerable signiWcance when we examine the notions of aeviternity and eternity in later chapters. In concluding our initial investigation of terminology the question was brieXy broached as to whether thirteenthcentury thinkers thought that non-extended instants or extended periods were such that either could be reduced to the other. Dismissing the mathematically based models and supervenience theses on which such contemporary reductionism is based, we saw that most thirteenth-century thinkers would not have found the reductionist thesis very feasible. This is not to say that they rejected all forms of temporal reductionism, for as we shall see in Chapter 4, they found the discussion of whether temporal elements could be reduced to non-temporal elements to be far more interesting and ultimately fruitful.

2 Temporal Simultaneity

Whilst medieval thinkers accepted that time could be analysed in terms of instants and periods, they were equally clear that it was the temporal relations of simultaneity, priority, and posteriority, holding between those instants and periods, which gave time its unique status and identity. During the next three chapters we shall be investigating this relational aspect of time. This chapter will look at the relational concept of simultaneity and the implications arising from medieval understandings of it. Chapter 3 will look at the (temporal) concepts of priority, posteriority, and causality, and Chapter 4 will be asking how well thirteenth-century views about temporal relations cohered with wider medieval theories of relations.1 1 On the role of temporal relations as constituting time, William of Auxerre, ‘Ubi est tempus, ibi est prius et posterius, et ita succesio et ordinatio’, Sum. Aurea. 2. 8. 2. 1. 5 (2.1, 184, 10-11). Orford, ‘successio autem instantis post instans facit tempus unde tempus . . . non est tempus nisi sit instans post instans’, Cor. Cor. Sciendum 1. 23 (105). Grosseteste ‘sine priori et posteriori non est possibile intelligere tempus’, Phys. 4 (87). Alexander, ‘ordo secundum tempus attenditur secundum istas differentias, prius, posterius, simul’, Sum. Theol. 1. 1. 2. 1. 4. 1 (1, 471). Avicenna, ‘tempus est collectio rerum que sunt momenta designata’, Suff. 2. 10. Aquinas, ‘tempus, quod est numerus prioris et posterioris, in quibus consistit tota successionis ratio’, In Sent. 1. 37. 4. 3.

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Conventionally, the English words ‘simultaneous’ and ‘simultaneity’ are used to translate the Latin words ‘simul’ and ‘simultas’. Whilst this is often an appropriate translation it is not always so, as the Latin words have a much broader set of connotations and implications than their English equivalents. Influenced no doubt in part by the Paraphrasis Themestiana, it was generally accepted by thirteenth-century thinkers that the word ‘simul’ could be used to describe togetherness in at least three contexts, giving rise to the tripartite distinction between a simultaneity of time, simultaneity of spatial locations, and a notion which we will return to as a simultaneity of nature.2 Although less explicit, the word ‘simul’ seems also to have acquired other nuances such that it could be used as a predicate to deny succession or change in both the divine and the created order. In this way we sometimes find the word ‘simul’ used as if it were a synonym of words such as 2 Paraphrasis Themestiana [167] (AL 1, 173, 2). Medieval translations of Aristotle, Averroes, and other texts emanating from an Arabic tradition often prefer to use ‘insimul’ rather than ‘simul’, e.g. Averroes, In Phys. 4 [105], [93]. Thirteenth-century language often suggests a debt to Avicenna, Suff. 2. 10, although it is probably Averroes, In Phys. 5 [22] who is being paraphrased by Albert in Phys. 5. 2. 1 (4.2, 422, 19–20). Ultimately all medieval sources are influenced by Aristotle’s discussion in Categories 13 (14B24–15A13) although in that text he merely distinguished between simultaneity of time and simultaneity of nature. Albert shows that thirteenth-century thinkers sometimes construed the notion of ‘simul’ as broader than this, ‘dicendum quod cum proprie dicitur simul dicit plura convenientia in unam naturam vel loci, vel temporis, vel alicuius adiacentis ad modum istorum’, Sum. de Creat. 2. 3. 2 ad 2 (Borg. 34, 347); 2. 5. 1 (Borg. 34, 365); ‘simul enim non convenit nisi his quae plura sunt, relatis per associationem ad unum tempus vel ad unum locum’, Sum. Theol. 5. 23. 1. 1. 1 ob. 8 (34.1, 122, 17–20). In Sent. 1. 9. B. 5 sed. con. 2 (Borg. 25, 279). See also Bonaventure, In Sent. 1. 37. 1. 1. 2 fund. 4.

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‘immutability’, (immutabilitas) and ‘instantaneous’ (in eodem instanti).3 Whilst recognized by medieval thinkers, the multiple senses and nuances of the word ‘simul’ have not always been recognized by contemporary thinkers and this 3 Bonaventure, ‘Ad illud quod obiicitur quod aeternitas dicit simultatem: dicendum quod simultas non dicitur ibi per positionem condurationis et coexistentiae diversorum durabilium, sed potius per privationem successionis in continuitate rei durantis; unde tota simul dicitur aeternitas quia in ea nihil alteri prorsus succedit, non propter hoc, quod in ea diversa et varia simul existant. Unde simultas nihil aliud dicit quam prasentialitatem summum et simplicem et indivisam . . . ’, Quaest. Disp. de Myst. Trin. 5. 1 ad 11. Albert, ‘simul autem removet successionem’, In Sent. 1. 8. A. 8 ad 9 (Borg. 25, 232); 1. 9. A. 3 (Borg. 25, 273); ‘simul autem excludit successionem’, Sum. de Creat. 2. 3. 2 ad 1 (Borg. 34, 346). ‘simul dicit associationem totius vitae in uno complexu primi simplicis quod est primum principium et causa vitae et esse quod in se complectitur omne principium, medium et finem esse et vitae omnium eorum quae sunt et vivunt’, Sum. Theol. 5. 23. 1. 1. 1 ad 8 (34.1, 124, 75–80). See also Aquinas, ‘Dicit ergo tota simul, ad removendum tempus’, Sum. Theol. 1. 10. 1 ad 5 and 1. 58. 2 and 1. 63. 8 ad 1. Kilwardby, de Temp. 17 [101], (34, 4–7). Note also Alexander of Hales, ‘nihil enim variabile est totum simul’, Sum. Theol. 1. 1. 1. 2. 4. 3 (1, 87) and his distinction: ‘simul aliquando dicitur per positionem, et tunc dicit convenientiam aliquorum secundum situm vel locum vel tempus . . . aliquando vero dicitur per privationem successionis’, Sum. Theol. 1. 1. 1. 2. 4. 1. 3 ad 4 (1, 88) where the later notion seems to be nothing but an ascription of a lack of succession to a particular. Even more revealing is a distinction which he offers elsewhere: ‘ . . . non est nota simultatis in tempore . . . sed similitudinis in ratione’, Sum. Theol. 2. 4. 2. 2. 2. 2 (2, 619), where he seems to be trying to articulate a distinction between a simultaneity in time and a non-temporal mental togetherness of particulars. Illustrating the antiquity of the notion, he bases himself explicitly on a quote from Gregory the Great, ‘simul videlicit non, unitate temporis, sed . . . simul per acceptam imaginem sapientiae’ (quoted ibid.). Focusing more particularly upon the angelic and divine contexts, Albert, ‘vera immutabilitas est vera aeternitas’, In Sent. 1. 9. A. 3 sed con. 1 (Borg. 25, 273); 1. 8.A. 8 ad 9 (Borg. 25, 232); Sum. de Creat. 2. 4. 1 (Borg. 34, 358). Bonaventure, In Sent. 2. 2. 1. 1. 3 conc. Note also the implications of Aquinas’ ‘Quamvis autem motus in suis partibus successionem habeat, tamen simul est cum causa movente’, In Post. Anal. 2. 10 [505]; and Grosseteste’s explanation of ‘tota simul’ as ‘non dicit simul in tempore aut instanti quia est ante instans et tempus; et pono huiusmodi simul super totalitatem essendi’, In Phys. 4 (96).

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has sometimes led to muddled interpretations and critiques of thirteenth-century thought.4 As Aristotle’s discussion of simultaneity in the Categories seemed to imply merely a distinction between the ‘simultaneous in nature’ and ‘simultaneous in time’, this came to provide an influential point of departure for many thirteenth-century explorations of the concept of simultaneity. Aristotle’s notion of ‘simul’ in nature had two elements. It was intended to be a relation describing particulars which implied each other’s existence, but the particulars had to be such that they were also not causally related to each other. The standard examples given by Aristotle, and repeated by medieval thinkers, were non-causal logical examples such as half and double. If an X is half Y then this logically implies that Y is double X. It is fairly clearly also the case that they are not causally related to each other. Neither the half nor the double causally brings about the other, they are just logical correlates springing into existence simultaneously when quantities are divided or added.5 4 Albert indicates that with so many nuanced uses of the word ‘simul’ there was serious risk of equivocation occuring in some of the arguments, ‘esse simul aeternitatis et aevi est aequivocum duplici de causa’, In Sent. 1. 9. A. 3 (Borg. 25, 274). As ‘simul’ is not just a temporal term, it is therefore not appropriate to critique the medieval notion of eternity as a ‘totum simul’ on the grounds that it allegedly uses a temporal term (simul) to define a nontemporal eternity (M. Kneale, ‘Eternity and Sempteritniy’, 227). It is also inappropriate to assume that the transitivity of temporal relations must apply to eternity because it is defined as a simul (A. Kenny, ‘Divine Foreknowledge and Human Freedom’, 264) and there is no basis for assuming that if God is simul then that must mean that events are temporally present to Him (A. Kenny, ibid., 261). 5 Philip the Chancellor, ‘Responsio autem est quod simul dicitur multipliciter. Est enim simul natura et simul tempore’. Sum. de Bono, 1. 3. 1 (1,

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Thirteenth-century thinkers seem to have largely accepted Aristotle’s position, often adding their own examples to illustrate it. Albert, for example, suggested a master–slave relation which combined the logical implications of the terms ‘master’ and ‘slave’ whilst also reflecting the fact that there was no causal relation between masters and slaves.6 Aquinas also had his own preferred example, one that can initially seem peculiar as he proposed a father–son relationship. Whilst a father and son did indeed have logical relations of dependence, the example is puzzling as fathers and sons are, nevertheless, causally related. It may be that Aquinas is subtly revising Aristotle’s notion, but it is more likely that Aquinas’ example suffers from the fact that there was no simple way of distinguishing words from ideas in medieval Latin. Rather than making a point about fathers and sons, he may well be making the more prosaic point that the words ‘father’ and ‘son’ are logically related without being causally related, and so there is no need to see his example as necessarily proposing a revision of Aristotle’s thought.7 113, 47–8). Bonaventure, ‘simul sint tempore et natura’, In Sent. 4. 17. 1. 2. 1 sed con. 6; ‘nec praecedit natura nec duratione aliqua’, Quaest. Disp. 5. 2 sed con. 2. See also Aquinas, In Sent. 2. 5. 2. 2 ad 1. Arisotle’s position was (in Boethius’ translation), ‘Naturaliter autem simul sunt quaecumque convertuntur quidem secundum subsistendi consequentiam, si nullo modo alterum alteri subsistendi causa sit’, Cat. [13] 14B24–9 (AL 1, 38, 16–21); ‘Simul ergo natura esse dicuntur quaecumque convertuntur quidem secundum essentiae consequentiam, nullo autem modo alterum alteri subsistendi causa est . . . ’, Cat. [13] 15A8–10 (AL 1, 39, 9–11). 6 Lib. de Praed. 4. 7 (Borg. 1, 235–6). In a related sense Albert, In Sent. 1. 9. B. 5 (Borg. 25, 278) and for simultaneity in species and genera, Phys. 4. 3. 17 (4.1, 291, 25). 7 Aquinas, ‘si enim unum in sui intellectu claudat aliud et e converso, tunc sunt simul natura: sicut duplum et dimidium, pater et filius et simila.

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Where the notion of ‘simultaneous in nature’ seems to have been of particular interest to thirteenth-century thinkers was in the doctrine of the Trinity, and its use here may even have been a factor influencing Aquinas’ use of the father–son relationship in order to illustrate the notion of ‘simultaneous in nature’. According to the (Western) doctrine of the Trinity, God exists as three distinct persons, the Father, Son, and Holy Spirit. Each person is equal in status and attributes, although the first person, the Father, has begotten (produced) the second person, and the Father and Son together have spirated (produced) the Holy Spirit. Over the centuries various ‘heresies’ had been formulated challenging aspects of this doctrine and one of the particularly serious heresies was Arianism. According to traditional Christian understandings of Arianism its fundamental error was in ascribing a subordinate status to the Son and Holy Spirit, thus implying that it was only the Father who was God in the full sense of the word. In order to avoid the subordination implied by Arianism, Christian theologians from Augustine onwards had believed that they must avoid any forms of expression which implied Si autem unum in sui intellectu claudat aliud et non e converso, tunc non sunt simul natura.’ Sum. Theol. 1. 13. 7 ad 6; and Quaest. Disp. de Pot. 7. 8 ad 1. Evidence supporting a possible modest difference of interpretation between Aquinas and Albert arises from the fact that Albert seems to have recognized the possibility of Aquinas’ merely logical reading of the relationship, but he seems to have thought that such a reading was so trivial as to be uninformative, ‘quia licet causa in quantum causa sit cum causato, tamen substantia causae necessario est ante id quod est causatum’, In Sent. 1. 9. B. 5 ob. 5 (Borg. 25, 278); Lib. de Praed. 4. 7 (Borg. 1, 236).

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superiority or priority of any kind to the Father. Maintaining this approach was of particular importance to medieval theologians.8 As standard formulations of Trinitarian theology portrayed the Father as begetting the Son, avoiding the ascription of any form of priority to the Father became a particularly significant imperative for medieval theologians. It was in this context that the notion of a simultaneity of nature would seem particularly attractive, especially when it was combined with Augustine’s distinction between an order of priority and an order of origin. Augustine’s distinction was intended to provide a way of distinguishing between causal scenarios in which the cause was in some unspecified sense prior to the effect, and causal orderings in which the cause was the actual origin of the effect, albeit an origin which was simultaneous in nature and so existed in no sense prior to the effect. The philosophical coherence of such a distinction was of much less concern to thirteenthcentury thinkers than the fact that this distinction enabled 8 Albert, ‘Unde Catholica fides confitetur Patrem nec secundum esse nec secundum intellectum praecedere Filium, nullo modo prioritatis, scilicet ordine, tempore, loco, dignitate, causa, vel intellectu.’ In Sent. 1. 9. B. 5 (Borg. 25, 280). The denial of a causal relation in the Trinity is because causation itself was thought to involve subordination, as Albert showed, ‘In quibuscumque causa prior est quam causatum, causa illa ab alio habet quod subsistit, et ab alio quod causa sit’, In Sent. 1. 9. B. 5 sed con. 1 (Borg. 25, 279); Sum. Theol. 9. 41. 2. 1 (34.1, 316, 86–7). See also Aquinas, ‘hoc nomen causae videtur importare diversitatem substantiae et dependentiam alicuius ab altero’, Sum. Theol. 1. 33. 1 ad 1 and ‘oportet ibi esse ordinem secundum originem absque prioritate. Et hic vocatur ordo naturae . . . ’, Sum. Theol. 1. 42. 3, and In Sent. 1. 20. 1. 3. See also Bonaventure, In Sent. 1. 12. 1. 1, and Peter of Tarentaise, In Sent. 1. 9. 2. 1.

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them to avoid Arian-sounding formulations in their descriptions of the Trinity.9 Whilst reflection on the notion of simultaneity of nature was important for theological reasons, it was reflection on Aristotle’s notion of temporal simultaneity which was of most significance for accounts of time. It was this notion, after all, which Aristotle had identified as the most proper and fundamental (simpliciter et proprie) type of simultaneity.10 In approaching this notion thirteenth-century thinkers seem to have realized that there was a distinction between simultaneity of instants and periods, but due to the degrees of terminological fluidity which we observed in Chapter 1, 9 Bonaventure notes that the need to avoid any ascription of priority to the Father entailed, ultimately, the impossibility of using causal language of Trinitarian persons. ‘Causa est cuius esse sequitur aliud, scilicet effectus: sed constat quod effectus sequitur causam, non ratione diversitatis, quia haec possunt esse simul; ergo ratione productionis. Ubi ergo est productio, ibi est antecessio et consecutio; sed ubi haec sunt, non est vera aeternitas.’ Quaest. Disp. de Myst. Trin. 5. 1 ob. 2. Henry of Ghent takes broadly the same approach, Lectura Ordinaria cap. 1 (36, 50, 78) as does Alexander of Hales, In Sent. 2. 1 [13] (6, 19–21). Thirteenth-century thinkers were absolutely clear in insisting on the simultaneity of nature of the Trinitarian persons, although as Bonaventure shows, it had to be a simultaneity that did not prohibit a priority of origin, ‘Simultas aeternitatis excludit ordinem prioris et posterioris, non tamen ordinem originis . . . ’, Quaest. Disp. de Myst. Trin. 5. 2 ad 2. Aquinas took a similar position, ‘neque enim prior tempore, cum filius sit aeternus; neque prior natura, cum patris et filii sit una natura’, Con. Err. Graec. 1. 2; Sum. Theol. 1. 42. 3 ad 2. Alexander of Hales seems to have diverged verbally in accepting that there could be an order of nature, as long as this ordering was understood to preclude temporal or causal overtones. Sum. Theol. 1. 1. 2. 1. 4. 2 and ad 2 (1, 473). For a fuller analysis of thirteenth century Trinitarian reflection, G. Emery, La Trinite´ Cre´atrice: Trinite´ et cre´ation dans les commentaires aux Sentences de Thomas d’Aquin et de ses pre´curseurs Albert le Grand et Bonaventure. 10 Aristotle, Cat. 13. 14B24–5 (AL 1, 38, 16–17 ff.).

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the expression of this distinction was not always particularly clear. Albert, for example, drew attention to the difference between simultaneity in time (in tempore) and simultaneity in a now (nunc), whilst Bonaventure explicitly cited the distinction as one between simultaneity in an instant (in . . . instanti) and simultaneity in an imperceptible part of time (in imperceptibili tempore).11 Focusing upon the concept of simultaneous periods, Aristotle and his medieval commentators developed a vocabulary which distinguished between the simultaneity of equal and unequal times. By equal times they meant periods of the same durational length; periods which were tokens of the same type period. By unequal times, they typically meant durations of different lengths such as an hour and a minute. When thirteenth-century thinkers identified periods as simultaneous they were careful to insist that it was only ‘unequal periods’ that they were referring to, which suggests that rather than being primarily a distinct notion of temporal simultaneity, talk of simultaneous (unequal) periods was instead a way of referring to nested periods which shared all the instants of one of the periods in common. This means that the most fundamental notion of temporal simultaneity for medieval thinkers was simultaneity at an 11 Albert, ‘vel in eodem tempore . . . (vel) in eodem nunc temporis’, In Sent. 1. 9. B. 5 sed con. 2 (Borg. 25, 279). Bonaventure, ‘Ad illud quod obiicitur, quod simul (angeli) ceciderunt, potest dici quod simul, non quia in eodem instanti, sed quia repente, quasi in imperceptibili tempore’, In Sent. 2. 5. 2. 2 ad 2. The formulation of a contrast between ‘time’ and ‘instant’ may well be influenced by Avicenna, ‘Remansit ergo ut eorum simul, sit illud simul quod est tempore, hoc est ut multa sint in uno tempore, aut in uno instanti quod est extremitas temporis’, Suff. 2. 10.

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instant, and that references to simultaneity involving periods, where they were analysed at all, tended to be taken as referring the simultaneity to the instants bounding, and thus constituting, the periods in question.12 In order to explain the notion of temporal simultaneity, Aristotle had provided a reductive analysis which thirteenth-century thinkers felt that they could use as the basis for their own understanding of the notion: Those things which are said to be simultaneous, strictly speaking and in the proper sense of the word are those which come into being at the same time, for neither is before or after. These are simultaneous in respect of time.13

Whilst undoubtedly appearing to offer an initially attractive reductive analysis of ‘simultaneity’, this account nevertheless had the unfortunate consequence of defining out of consideration the issue which contemporary philosophers refer to as the question of disunified time. In order to be able to consider a hypothesis of disunified times, it is essential to be able to hypothesize the existence of times which are 12 Aquinas, ‘Duae partes temporis quae sunt aliae ab invicem non possunt simul esse, nisi una contineat aliam, sicut maius tempus continet minus’, In Phys. 4. 15 and 6. 2. Bonaventure, ‘quae sunt simul sunt in eodem instanti’, In Sent. 2. 1. 1. 2 sed con. 4. See also Albert, Phys. 4. 3. 1 (4.1, 260, 45–88) and 4. 2. 7 (4.1, 246, 22–6); Grosseteste, In Phys. 4 (100). For the Aristotelian background to these formulations see Phys. 4. 10. 218A25–6 and Cat. 13. 14B24–6, although the most direct influence seems to be Averroes, as for example, In Phys. 4 [92]. 13 ‘simul autem dicuntur simpliciter et proprie quorum generatio in eadem tempore est: neutrem enim neutro prius est aut posterius; simul autem secundum tempus ista dicuntur’ Cat 13, 14b24–6 (AL 1, 38, 16–8). See also Grosseteste’s approach, ‘Esse namque cuius nulla pars habet illud simul esse cum alia esse temporale est’ In Phys 4 (96).

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neither before nor after each other, but which are also not simultaneous. By equating ‘not before or after’ with ‘simultaneous’, Aristotle has effectively made it impossible to formulate the question of whether there can be disunified times.14 It is not at all clear that medieval thinkers would have been able to recognize what contemporary philosophers mean by disunified time, so it is important to be clear about this notion before looking at medieval attitudes to it. Modern proponents of disunified time are typically claiming that it is possible for there to be a set of instants, i1, i2 . . . and a set of instants i1*, i2* . . . , such that the instants of each set are neither before nor after the instants of the other set; and yet contrary to what Aristotle suggests in the definition above, they are not simultaneous either. As each of these sets of instants would constitute a time, the proponent of disunified time is therefore claiming that it is possible to have two times (Time1 containing . . . i1, i2 . . . ; and Time2 containing . . . i1*, i2* . . . ) such that instants 14 There is some diversity of practice amongst contemporary philosophers concerning the most appropriate terminology in which to frame the question of disunified times. Some contemporary figures have talked of ‘extrinsic timelessness’ (B. Leftow, Time and Eternity, 22) but as the word ‘timelessness’ has traditionally been used to refer to a distinct notion of eternity it is doubtful whether that usage would aid clarity in this particular discussion. More typical descriptions have referred to the problem as whether there can be ‘disunified times’ or ‘multiple temporal streams’ or even just ‘multiple times’; and so it is those more typical formulations which I shall use henceforth. For an overview of the contemporary discussion of this matter, W. H. Newton-Smith, The Structure of Time, 79–95. See also the alpha and beta worlds of H. J. Nelson, ‘Time(s), Eternity and Duration’, 4–11. With a particular focus on using models of multiple times to explain notions of eternity, M. MacBeath, ‘God’s Spacelessness and Timelessness’. The coherence of the idea of disunified times has been challenged by, amongst others, R. Swinburne, Space and Time, 165–72.

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and periods of neither time are temporally related to each other. The instants of Time1 are temporally related to each other such that i1 is temporally before i2 and that the instants in Time2 are temporally related to each other such that i1* is temporally before i2*. What makes the times disunified, however, is the fact that the instants i1 and i2 are not temporally related with the instants i1* and i2*. The concept of temporal disunification can seem complex because it admits of various species of disunification. Two times could be described as disunified if it was the case that none of the instants of Time1 were temporally related to any of the instants of Time1*. But it is also possible to have partially disunified times if there are instants which are shared in common between the two times. Two disunified times could have a common ancestor, for example, if a single time had bifurcated or divided. What this would mean would be that instants i1 and i2 (of Time1) would be such that they had no temporal relations to i1* and i2* (of Time2), whilst there was yet a common ancestor ia which was temporally related both to i1 and to i1*. Another way in which two times might be partially temporally disunified would be if two times were to merge or come together so that they had a common successor instant. On this model instants i1 and i2 would again be such that they were not temporally related to the instants i1* and i2*, although there would be a common successor ib which was temporally after both i2 and i2*. Further models of partial disunification can be generated by varying the numbers of times involved and the number of bifurcations and mergings. The crucial factor in each case is

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the fact that just because instants exist does not entail that there are temporal relations between the instants. It is this claim, and the implication that there can be instants (and so times) which are not temporally related to each other, which constitutes the heart of the disunification position. Unfortunately it is precisely the claim that there can be instants which are not temporally related which the Aristotelian account of temporal simultaneity excluded. In Aristotle’s view there could only be a plurality of simultaneous periods, or ‘plura tempora’ as medieval writers sometimes referred to them, if the periods concerned were unequal and nested, such that one period was within the other. If the periods were equal in duration, then medieval thinkers thought that it was necessarily the case that the periods must reduce to one period, and so talk of a plurality of times would be incoherent. Starting from these assumptions and definitions it was almost impossible for thirteenthcentury thinkers to formulate the question which contemporary philosophers understand as the problem of whether time can be disunified. As Lombard’s Sentences introduced the issue of temporal unity in a peripheral way in book 2 distinction 2, most writers of the period were aware that temporal unity was an issue for discussion. Interest in the question varied significantly, from those who mention it in a perfunctory way when commenting on Lombard’s Sentences to those who raise it and discuss it at length in other works where they could just as easily have avoided mentioning the problem. Grosseteste, for example, in his commentary on the Physics did not raise the question of temporal unity at all. Albert, in

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his commentary on the Physics, acknowledges it as a question worth discussing but then, as a result of a not uncharacteristic digression, he seems to have forgotten to return to the issue. Similarly Pseudo-Aquinas introduces the problem and mentions it in passing in his de Tempore, but Kilwardby singled it out and considered the problem important enough to warrant spending almost a quarter of his entire de Tempore on the one single issue of temporal unity.15 Where thirteenth-century thinkers do comment on the issue of temporal unity they often seem unsure of whether the problem is one of explaining the assumed fact of temporal unity, or whether it is instead a problem of accounting for the necessity of temporal unity. In some discussions elements of both problems are so interwoven that it is not always clear whether a particular figure thought that time happened to be unified or whether they thought that time was necessarily unified.16 15 Albert indicates his interest in the question at Phys. 4. 3. 13 (4.1, 284– 6). The differing interest which the problem gave rise to may also be related to the intellectual aptitude of the author for, as Kilwardby points out, the issue was gradually coming to be seen as a ‘quaestio difficilis’, de Temp. 11 [44] (19, 2). 16 Earlier medieval writers such as Anselm seem to have assumed temporal unity as a fact, as for example in de Veritate 13 (Schmitt 1, 199, 22–7). Midthirteenth-century writers were undoubtedly influenced by Averroes’ view that multiple times were impossible, ‘Plura tempora esse insimul quod est impossibile’, In Phys. 4 [93], and so we begin to see explicit arguments developing. Albert identified a source of the impossibility of disunified times as arising from the logical implications of predicating ‘simultaneity’ of multiple times, ‘si plura sunt tempora, aut sunt simul aut non simul. Si simul sunt: sed simul sunt, quae sunt in eodem tempore, ergo tertium tempus est, in quo sunt simul. Et iterum illa tria sunt simul, aut non simul, et ita ibit in infinitum.’ Sum. Theol. 5. 23. 3. 2 (34.1, 138, 64–73). See also his Phys. 4. 3. 2 (4.1, 262, 28–35) and its most likely source in Avicenna, Suff. 2. 10.

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The four main sets of issues which repeatedly occur in mid-thirteenth-century discussions seem to have been established initially by Alexander of Hales, and they gave rise to four arguments or explanations as follows: [A] [B] [C] [D]

Temporal unity arises from the unity of number Temporal unity arises from the ‘exemplar cause’ of time Temporal unity arises from the ‘material cause’ of time Temporal unity arises from the unity of the subject of time.

[ A ] T E M P O R A L U N I T Y A R I S E S F RO M THE UNITY OF NUMBER The first argument [A] rests upon a geometrical analysis of time and tries to draw an analogy from the unity of numerical concepts to the unity of time. In Aquinas’ words, the argument was as follows: Some have said that there is one time of all temporal things because there is one number of all that is numbered (counted); since according to Aristotle time is a number.17 Aquinas takes a similar approach in Phys. 4. 15 [562] and 4. 23 [633], although his commitment to a version of the principle of the identity of indiscernibles in his theology (‘Si ergo essent plures dii oporteret eos differre.’ Sum. Theol. 1. 11. 3) raises the possibility that Aquinas may well have been additionally concerned about how multiple times would have been differentiated. For a fuller discussion of this complex set of issues see Capreolus’ fifteenth-century analysis in his Defensiones 2. 2. 2 (3, 145–6) and J. Broussard ‘Eternity in Greek and Scholastic Thought’, 86–8 and 138–43. 17 ‘Dicunt autem quidam esse unum tempus omnium temporalium propter hoc quod est unus numerus omnium numeratorum cum tempus sit

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The basis of the analogy underlying the argument rests upon the linguistic convenience deriving from Aristotle’s use of the word ‘number’ in order to describe time. As there can be different sets of three things, whilst the concept three remains a unity, so proponents of the argument seem to be claiming that time itself can be thought of as unified, because it is the conceptual frame in which all the sets of temporal things exist. This is a curious argument with a crucial flaw which became more and more evident to thirteenth-century thinkers as Aristotle’s treatise on time was understood better. The argument assumes a fundamental similarity between time and number as the basis for the analogy it appeals to; but for medieval thinkers time was not an abstract mathematical reality like the concept three. Following Aristotle’s own approach, time was generally thought to be a physical or natural reality existing in the world around us, gaining its very existence from the material world.18 numerus, secundum Philosophum.’ Sum. Theol. 1. 10. 6. See also his In Phys. 4. 17 and Bonaventure, In Sent. 2. 2. 1. 1. 2. Aquinas’ reference to Aristotle is to 220b8. The reference to ‘quidam’ (some people) seems to be taken from Aristotle and so referring to ancient philosophers rather than to contemporary thirteenth-century figures. 18 Aquinas, ‘Sed hoc non sufficit, quia tempus non est numerus ut abstractus extra numeratum sed ut in numerato existens: alioquin non esset continuus; quia decem ulnae panni continuitatem habent, non ex numero, sed ex numerato. Numerus autem in numerato existens non est idem omnium sed diversus diversorum.’ Sum. Theol. 1. 10. 6; In Phys. 4. 23 [633]; and In Sent. 2. 2. 1. 2. The Averroean argument which Aquinas finds so helpful was expressed in the syllogism, ‘Numerus non diversatur in specie per differentias substantiales ex numeratis; et omne, quod diversatur in specie, diversatur per differentias substantiales; ergo numerus non diversatur ex numeratis, sed tempus est numerus ergo tempus non multiplicatur in specie

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The first argument fails for Aquinas and his contemporaries because it is based upon the false premise implied in its mistaken notion of time. Nevertheless, there was an even more fundamental problem with the argument, an argument which thirteenth-century thinkers generally struggled to appreciate. As the analogy to numbered examples in the world indicates a reference to tokens of a single type, this meant that the argument was only referring to the unity of what Aristotle referred to as token equal periods. As the equality of the periods rests upon their identity of measure, so the argument is reducing what should be a topological question about temporal unity to the metrical domain, illustrating the difficulty which medieval thinkers had in keeping these distinct aspects of the problem clearly separated.

[ B ] T E M P O R A L U N I T Y A R I S E S F RO M T H E E X E M P L A R C AU S E O F T I M E The second argument [B] seems to have been preferred by Alexander of Hales, and in his version it read: there will be one time, not because of the unity of the things which are in time and measured by time . . . , but rather because of the per multiplicationem numeratorum.’ In Phys. 4 [134]. Albert takes a similar approach, distinguishing between numbered number and formal number, ‘inquantum est numerus numeratus qua et differt a numero formali’, Phys. 4. 3. 9 (4.1, 276, 34–5), italics mine. See also his Phys. 4. 3. 17 (4.1, 292, 43 f.).

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unity of the cause which causes the (temporal) duration from eternity . . . 19

According to this argument, temporal unity arises because of God’s causal power, creating time as the duration of temporal particulars. As there is just the one God, creating from a unified eternity, then so the causal influence which is propagated is unified, thus giving rise to a single unified time. This is not so much an argument for temporal unity, as rather an explanation for why a time which is assumed to be unified might indeed be so. As an argument to establish temporal unity, its limitations are immediately apparent. For as soon as one acknowledges that there can be a single God creating, in virtue of His unified causal power, a multiplicity of cats and dogs, how is it supposed to follow that the same causal influence must give rise to a single time? Pressing the point still further, Kilwardby adroitly pointed out that if the argument really did prove anything then it proved too much. If a single eternity caused a single time, then the single causal influence from God should ensure the numer19 ‘erit tempus unum, non ab unitate temporalium quae mensurantur tempore . . . sed ab unitate causae, quae est influentia seu virtus durationis ab aeternitate, secundum quod res sunt in participatione aeternitatis’, Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 102a). Aquinas cites a version of this argument, ‘unde alii assignant causam unitatis temporis ex unitate aeternitatis quae est principium omnis durationis’, Sum. Theol. 1. 10. 6. but this is not an entirely accurate summary of the sense of Alexander’s argument, for Alexander’s argument refers to the unity of the causal power of eternity, not the unity of eternity itself as Aquinas does. Kilwardby renders Alexander’s argument more accurately, ‘non ab unitate temporalis rei est unum set ab influentia una eternitatis que continuat et salvat esse motuum et mobilium’, de Temp. 13 [67] (26, 25–7).

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ical unity of creation. Yet the very fact that we do see a multiplicity of cats and dogs shows that this is not the case.20 These problems seem so obvious that it is surprising that Alexander himself failed to see them. In his defence, we need to be sensitive to the fact that he was to some extent ‘trailblazing’ by being one of the first thirteenth-century thinkers to explicitly address the problem of temporal unity, and he may well have been a little confused by elements of the Platonic environment which his citations of Boethius, Anselm, and Dionysius show that he was working within. For whilst concrete individual cats and dogs do indeed constitute a multiplicity of particulars, this multiplicity arises in the Platonic framework from the unified archetypes (or Forms) of ‘cat’ and ‘dog’. In approaching this problem from the Anselmian assumption of temporal unity, it may well be that Alexander thought that what needed explaining was the unity of the archetypal concepts, rather than the instantiation of those concepts. And in that respect an appeal to the divine causal unity as the crucial factor would make perfect sense. Unfortunately, if this was Alexander’s reasoning then it means that his argument suffers from the same fundamental problem as [A]: it is construing time as a conceptual reality rather than a physical reality and so all it has explained is the unity of the concept. Ultimately it offers no argument or explanation for why time itself should be unified. 20 ‘Set non video adhuc quomodo isti propter influentiam actiuam unam numero possunt dicere tempus unum numero, quia sic et omnia essent unum numero per eandem rationem.’ de Temp. 13 [68] (27, 3–5).

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[ C ] T E M P O R A L U N I T Y A R I S E S F RO M T H E M AT E R I A L C AU S E OF T I M E The third argument or explanation for temporal unity was also based upon the ‘principle’ of time, although in this case it appealed to what was taken as its fundamental or material cause: motion or change. It is this argument which Bonaventure preferred, and in his version it went as follows: And therefore (some) have said more profoundly that the unity of time is taken from the unity of the subject by which it is caused. The subject by which it is caused, however, is matter (considered) as mutable and thus as a being in potency. For matter as it is acquiring a form is changed and so it is a being in potency. And so time, more so than all other accidents, is associated with matter. As matter is one through its essence, differing through its esse, neither one by the unity of a universal nor singular, but in a middle way, so also time is in all things that are temporal.21 21 ‘Et ideo dixerunt tertii profundius, quod unitas temporis sumitur ab unitate subiecti, a quo causatur; subiectum autem, a quo causatur, est materia ut mutabilis, et ita ut ens in potentia. Nam materia, ut est in acquisitione formae, mutatur, et sic est ens in potentia; et ideo tempus maxime inter omnia accidentia se tenet plus cum materia. Sicut igitur materia una est per essentiam, differens per esse, una non unitate universalitatis nec singularitatis, sed medio modo, sic et tempus in omnibus temporalibus’. In Sent. 2. 2. 1. 1. 2 (2, 59). Whilst Kilwardby manages to accurately cite Bonaventure’s argument, de Temp. 13 [57] (23, 32), the version which Aquinas cites differs subtly, referring to prime matter, for example, instead of matter, ‘alii vero assignant causam unitatis temporis ex parte materiae primae, quae est primum subiectum motus . . . ’, Sum. Theol. 1. 10. 6. Although Aquinas might well be carelessly referring to Bonaventure’s argument, it is more probable that he is actually referring to the argument in Alexander of Hales’ Summa which does in fact refer to prime matter, ‘proprium subiectum . . . est materia prima quae est subiectum totius transmutationis, cuius

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Bonaventure has based his argument upon the indisputable Aristotelian identification of motion or change as the basis and cause of time. Recognizing that all changes occur as the result of potentiality, and that potentiality is the nature of matter, Bonaventure then moved to the conclusion that it must be the unity of matter which accounted for the unity of potentiality and thus of time. Bonaventure’s argument is an interesting one and has occasioned much reflection and comment over the centuries. In Aquinas’ opinion, however, the argument was fatally flawed in no less than three ways: (i) It is based upon a mistaken notion of time. (ii) It misunderstands the nature of matter. (iii) It begs the question at issue by assuming that matter is a unity. Focusing upon Bonaventure’s claim that the subject of time is matter considered as mutable, Aquinas’ first criticism is that Bonaventure has misunderstood what time is. With the reference to ‘mutable’, Bonaventure introduced a modal element which Aquinas believed had no place in an accurate Aristotelian account of time. We shall return to this question of modality in definitions of time in subsequent chapters, but for the moment we can concede the accuracy of Aquinas’ reading of Aristotle. For Aristotle, time was indeed the mensura propria est tempus . . . non est inconveniens ponere tempus unum ab unitate motus et subiecti materiae primae . . . ’ Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 103b). It has been suggested that there is a further argument for temporal unity in Albert the Great, one arguing from celestial matter (J. M. Quinn, ‘The Concept of Time in Albert the Great’, 47 n. 63). I have not been able to identify any such argument.

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numbering of actual change, not Bonaventure’s potential change, and so Aquinas is right to suggest that Bonaventure’s argument has started from a false understanding of Aristotle.22 This is not necessarily a fatal criticism, for we shall see that all thirteenth-century thinkers were adapting elements of Aristotle’s account of time to suit their own specifically Christian purposes and interests, particularly when it came to the subject of angels. Of much more significance, however, is the fact that Kilwardby managed to formulate the essence of Bonaventure’s argument without including the explicit appeal to modality. This shows that contrary to Aquinas’ view it was in fact possible to read Bonaventure’s general point within a broadly Aristotelian framework.23 Aquinas’ second criticism of Bonaventure engaged more directly with the concept of matter, taking issue with the whole thrust of the Bonaventurian argument by suggesting that matter was simply an inappropriate basis for temporal unity. Aquinas believed that any principle of temporal unity must be able to account for the fact that time, of its essence, contains a multiplicity of instants, whilst in its concrete existence it is a single unified reality. Matter, insisted Aquinas, is simply unable to explain this: 22 Aquinas, ‘tempus enim non mensurat variationem in potentia, sed variationem in actu’, In Sent. 2. 2. 1. 2. 23 Kilwardby, ‘Et sic patet quomodo a materia una per essentiam est motus unus per essentiam, et ab illo tempus unum per essentiam. Sic igitur patet quomodo tempus indeterminatum est unum per essentiam, multiplicatur tamen secundum esse, in qua multiplicatione recipit analogiam omnino sicut motus materialiter consideratus qui est eius causa.’ de Temp. 13 [66] (26, 18–22).

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time does not measure potential change but actual change; the act of change however, isn’t a unity in matter but rather a plurality, for only the first potency to change is a unity . . . In prime matter, according to its essence there is no multiplicity, only according to its esse (is there multiplicity and plurality), and in relation to that esse there is no unity amidst the plurality. Thus, time does not refer to matter on account of its essence, but only on account of its esse, accordingly as it (matter) is changed through motion. Thus from the unity of matter we can in no way derive the unity of time.24

At the heart of Aquinas’ criticism here is the allegation that Bonaventure has mixed up two different aspects of matter: its essence and its actual concrete existence. In its essence matter really does have a unity, but there is no plurality, for all there is in matter considered as an essence is its definition of ‘potentiality’ and its unified existence as potentiality. To identify the plurality of matter, it is necessary to focus on matter as it exists in the world around us. We see many different instantiations of matter, so matter in its existence (esse) has a plurality. But, stresses Aquinas, there is no single unity to all those instances of matter. Matter never exists as both plurality and unity. Yet, insisted Aquinas, time must have both unity and multiplicity in both 24 ‘tempus enim non mensurat variationem in potentia, sed variationem in actu; actus autem variationis in materia non est unus, sed plures: sed tantum prima potentia ad variationem est una . . . in materia autem prima secundum essentiam non est aliqua multitudo, sed solum secundum esse, et secundum hoc esse non est una in pluribus; unde nec tempus materiae secundum essentiam suam respondet, sed solum esse secundum quod variatur per motum; unde ex unitate materiae nullo modo potest esse tempus unum’, In Sent. 2. 2. 1. 2.

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its essence and its actual existence if it is to account for temporal unity, so ‘matter’ is simply unable to fulfil the role which Bonaventure asks of it. As far as Aquinas was concerned, Bonaventure’s argument had the same fundamental problem as Alexander’s in that it was not engaging with the proper notion of time, it was simply offering an explanation ‘secundum quid’; an explanation which merely explained one aspect of temporal unity.25 Although the precise point at dispute here is the basis for temporal unity, in reality this disagreement was actually a manifestation of a much more fundamental disagreement between Aquinas and Bonaventure, a disagreement about the nature of matter which spilled over into many areas of their philosophical theology including questions about the nature of souls and angels. Aquinas seems to have thought that matter considered as pure potentiality (its essence) only admitted of one potentiality, the capacity to receive the form of ‘quantity’, and this is why he insisted above that matter considered in its essence has no plurality. Bonaventure, however, disagreed strongly with this position and insisted that matter considered in its essence as potentiality contained an essential reference to a multiplicity of possibilities. If nothing else, stressed Bonaventure, there must be a fundamental plurality of options for prime matter in its ability to be actualized as either corporeal matter or spiritual matter. So although Bonaventure was willing to agree with 25 ‘ea quae sunt unum principio vel subiecto, et maxime remoto non sunt unum simpliciter, sed secundum quid’, Sum. Theol. 1. 10. 6. For a more detailed analysis of Aquinas’ argument and discussion of this criticism, see Capreolus’ (Latin) account in his Defensiones 2. 2. 2 (3, 145).

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Aquinas that matter does indeed exist in many distinct ways, he also wanted to stress that it possessed a necessary reference to plurality within its very essence. As Aquinas’ second criticism is based upon a more fundamental disagreement about the nature of matter, its effectiveness depended ultimately upon the arguments deployed in that more fundamental disagreement about the nature of matter. Yet that issue itself remained ultimately unresolved, and so Bonaventure and Aquinas do not seem to have been able to engage and resolve the matter as it related to time. Aquinas was effectively maintaining that Bonaventure’s argument assumed an inadequate notion of time, whilst Bonaventure was maintaining that Aquinas’ criticism was based upon an inadequate notion of matter. Aquinas’ third criticism was an epistemological challenge and went directly to the heart of Bonaventure’s argument by implying that he was making a crucially unjustified assumption. It’s all very well appealing to matter to explain temporal unity, but, asked Aquinas, what justification is there for assuming that matter itself is unified?26 Bonaventure does not seem to have directly addressed this issue, and neither do any of the later commentators on the debate. This may well be because, although Aquinas was raising a valid logical point, it was extremely difficult to make sense of what it would mean in a scholastic universe to talk of a disunified matter. Contemporary philosophers can at least formulate the question by appealing to the 26 ‘immo forte falsum, quod omnium mobilium sit materia una’, In Sent. 2. 2. 1. 2.

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notion of disunified spaces, but thirteenth-century thinkers did not have that option. It was therefore extremely difficult for them to conceive of a matter that could be distinct enough from their usual notions of matter to give rise to a notion of material plurality, whilst yet retaining enough in common for it to be an instance of ‘matter’. It was undoubtedly the realization of this problem that encouraged Aquinas to express the criticism so tentatively, suggesting merely ‘perhaps it is false’ (forte falsum) that matter is unified.27

[ D ] T E M P O R A L U N I T Y A R I S E S F RO M THE UNITY OF THE SUBJECT OF TIME The fourth approach to the question of temporal unity seems to have derived ultimately from Averroes. According to this approach, the question of temporal unity needs to be reduced to a question about the unity of the subject of time. Convinced by Aristotle’s argument in his Categories, 27 For the contemporary arguments in favour of a plurality of spaces, A. Quinton, ‘Spaces and Times’. Aquinas’ hesitation with this argument may well be due to the additional factor that it may find an echo in the writings of Siger of Brabant, who was widely considered at the time to be heterodox and yet also championed the possibility of a plurality of matter: ‘Utrum duae materiae possint esse simul. Videtur quod sic, quoniam duae formae possunt esse simul; quare et duae materiae. Probatio antecedentis, quoniam albedo et musica possunt esse simul, et etiam formae substantialis et forma accidentalis, sicut manifestum est. Quare, et duae materiae . . . ’, Phys. 7. 30 (15, 188). For an overview of the content and character of medieval discussions of the plurality of worlds, E. Grant, Planets, Stars and Orbs: The Medieval Cosmos 1200–1687, 150–68.

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medieval thinkers all tended to follow his assumption that time must be capable of being fitted into the analysis of reality that classified everything as either substance or accident. Within such a scheme, Aristotle was convinced that time could not be considered a substance, and so medieval thinkers had little hesitation in concluding that it must instead be an ‘accident’. As accidents were thought to necessarily inhere in a subject (a substance) in order to have existence, then so it was necessary to identify a subject or substance in which time could inhere. Aristotle himself does not seem to have developed the analysis of the appropriate subject, but Averroes had no hesitation in identifying the subject of time as the Primum Mobile.28 28 It is a central tenet of the Aristotelianism which thirteenth-century thinkers accepted that accidents cannot exist in the absence of the substances in which they inhere. Nevertheless a ‘miraculous’ exception was made in the case of the Eucharist. Aquinas, ‘Et ideo relinquitur quod accidentia in hoc sacramento manent sine subiecto. Quod quidem virtute divina fieri potest. Cum enim effectus magis dependeat a causa prima quam a causa secunda, potest Deus, quia est prima causa substantiae et accidentis, per suam infinitam virtutem conservare in esse accidens subtracta substantia . . . ’, Sum. Theol. 3. 77. 1. Albert, ‘Dicendum quod accidentia manent ibi sine subiecto . . . ’, In Sent. 4. 12. E. 16 (Borg. 29, 328); and de Sacramentis 5. 4 (26, 61, 76–9). William of Ockham, writing almost fifty years later, is clearly concerned about the postulation of miraculously existing accidents, but he feels constrained to defend the position because it has been authoritatively determined by the Church: ‘dico quod aliquando ponenda sunt plura miracula circa aliquid ubi posset fieri per pauciora, et hoc placet Deo. Et hoc constant Ecclesiae per aliquam revelationem ut suppono.’ Quodlib. 4. 30 (Opera Theologica 9, 450, 41–4). So although the existence of substance- or subject-less accidents was thought to be a miraculous possibility for God, thirteenth-century thinkers still treated hypotheses involving substanceless accidents as absurd when it came to describing natural non-miraculous realities such as time.

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The Primum Mobile has an essential part in medieval accounts of time, but its role is difficult to appreciate now that cosmological models have changed so significantly from the thirteenth-century models. Somewhat crudely, its role can perhaps best be appreciated by thinking of medieval models of the universe with the analogy of an onion. In the same way that an onion has layers of skins on top of each other, so the medieval models of the universe pictured the earth at the centre with various concentric crystalline layers surrounding it, each layer lying embedded inside another. The precise nature and number of these layers admitted of considerable medieval speculation and discussion, but their general existence and role was accepted and this gave rise to an overall model of reality similar to that represented in the illustration. Taking an almost clockwork view of the series of layers in the universe, it was thought that all motion began with the outermost layer, the Primum Mobile, which was set in a revolving motion by God. As the outermost layer turned, it then set the next layer beneath it in motion, and as that layer revolved then so it further set the layer beneath it in motion, and so on until all the layers were moving and motion had been transmitted ultimately from the furthermost layer to the earth and the life upon the earth.29 29 Ulrich on the Primum Mobile, ‘inquantum mobile est, . . . est ultimum quoad nos . . . a quo fluit duratio esse omnium inferiorum . . . ’, de Summo Bono 4. 1. 8 (4, 48, 134). For further information on medieval cosmology, T. Litt, Les Corps Ce´lestes dans L’Univers De Saint Thomas D’Aquin, 110–46; E. Grant, Planets, Stars and Orbs: The Medieval Cosmos 1200–1687, 308–15.

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EARTH

Averroes’ approach to temporal unity was relatively simple. By focusing upon the Primum Mobile he could argue from it as the basis of motion in the universe, via the assumption that motion was essential to the notion of time, to the conclusion that time and temporal unity could be reduced to the Primum Mobile itself. His argument was appealing to many medieval thinkers and was adopted

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widely, appearing in Albert, Thomas, Peter of Tarentaise, Richard Kilwardby, and many others.30 In Aquinas’ version of the argument it read: Time is one because of the unity of the motion of the Primum Mobile. Time is compared to this motion not in the way it is compared to all the other motions, as a measure is compared to what it is measuring, but (rather) it is as an accident in a subject.31

Despite the popularity of the approach, Bonaventure was concerned that it was over-simplifying the problem and so leading to an absurdity. 30 Albert, Sum. Theol. 5. 23. 3. 3 (34.1, 139–42). Peter of Tarentaise, In Sent. 2. 2. 2. 2; Kilwardby de Temp. 11 [51] (22, 1–3). Alexander of Hales’ text contains a reference to this approach, Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 103b). Roger Bacon can seem prima facie to be adopting a version of Averroes’ position (against Bonaventure’s) but whilst there is a superficial similarity of terminology he is in reality taking a rather more idiosyncratic (geometrical) approach to the problem. ‘Postremo res geometricae nobis ostendunt causam unitatis in tempore . . . respectu praesentis nullus motus habet dimensionem nec divisibilitatem et ideo non habebit unde excludat alium a praesenti. Et ideo infinitos secum potest pati praesentes; et ideo unum tempus praesens sufficit omnibus motibus praesentibus, et propter hoc habetur hic vera causa unitatis temporis, et non propter materiam.’ Opus Maius 4. 4. 14 (Bridges 1, 166). Bacon’s argument seems to be based on the assumption that objects with dimensions cannot occupy the same space, and so as time is a dimension then there cannot be two times in the same space. Expressed in this way his argument is an alternative more sophisticated version of Avicenna’s approach which attempted to reduce temporal unity to the space in which motion was occurring. ‘Non habent autem omnia unum tempus, nisi quemadmodum omnia habent unum locum’, Suff. 2. 10. 31 Aquinas, ‘tempus est unum ab unitate motus primi mobilis: tempus enim comparatur ad istum motum non tantum ut mensura ad mensuratum, sicut ad alios motus, sed sicut accidens ad subiectum, quod ponitur in definitione eius’, In Sent. 2. 2. 1. 2. In Phys. 4. 23 [630]–[637]. See also Albert, ‘tempus est in uno . . . quia causa omnium motuum est unus motus, scilicet motus primi mobilis’, Sum. de Creat. 2. 4. 2 (Borg. 34, 362). Peter of Tarentaise, ‘Tempus accidens est . . . unius subiecti quod est Primum Mobile’, In Sent. 2. 2. 2. 2. Kilwardby, de Temp. 11 [45] (19, 10–15).

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Some say that time is one in virtue of its subject, in which it first exists essentially (per se) and if it is removed, time also is removed. Thus they say that time is one because it is in the Primum Mobile. And if its motion were to cease, time also would cease. But this does not seem to be a sound argument because Augustine noted that even if the Primum Mobile were to cease, it would still be possible to move the potter’s wheel and it remains the case that the motion of the potter’s wheel would still be measured by time.32

Drawing on Augustine’s insights, Bonaventure was making use of what contemporary thinkers would refer to as a ‘thought experiment’. Averroes’ approach, he was suggesting, led to patent absurdities. If one imagined that the subject of time, the Primum Mobile, might cease to exist, then could we not still imagine motion taking place in the 32 ‘Dixerunt ergo aliqui, quod tempus est unum ratione subiecti, in quo primo est, et per se, quo remoto, removetur et tempus. Unde dixerunt, quod tempus est unum, quia est in primo mobili, cuius motu cessante, cessat et tempus. Sed illud non sufficit dicere, quia sicut dicit Augustinus, si cessaret motus primi mobilis, adhuc posset moveri rota figuli, et constat, quod mensuraretur ille motus . . . ’, In Sent. 2. 2. 1. 1. 2 (2, 59). Bonaventure also refers to free will as another case in point, ‘item, tempus est in affectionibus et cogitationibus liberii arbitrii, quod non subest motui caelesti’ (ibid.). The Augustinian argument which Bonaventure is referring to was stated as follows: ‘Cur enim non potius omnium corporum motus sint tempora? an vero, si cessarent caeli lumina et moveretur rota figuli, non esset tempus quo metiremur eos gyros et diceremus aut aequalibus morulis agi, aut si alias tardius, alias velocius moveretur, alios magis diuturnos esse, alios minus? aut cum haec diceremus, non et nos in tempore loqueremur aut essent in verbis nostris aliae longae syllabae, aliae breves, nisi quia illae longiore tempore sonuissent, istae breviore’, Conf. 11. 23 (29) (O’Donnell 158). Bonaventure’s overall position seems to draw upon Alexander of Hales’ texts, ‘Secundum etiam horum opinionem non est ponere tempus esse inprimo caelo mobili ut in subiecto, sed in prima materia; iuxta quorum positionem non est inconveniens ponere tempus unum ab unitate motus et subiecti materiae primae, etsi sint plures caeli.’ Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 103b).

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universe and would not that motion not require a time in which it takes place? As the postulation of (non-miraculous) accidents in the absence of their subject was an absurdity that even his critiques accepted, so Bonaventure was claiming that Averroes’ approach simply could not make sense of his thought experiment. Bonaventure’s challenge was particularly serious because it had a direct theological corollary. According to medieval understandings of eschatology, at some point God would destroy the physical world, including the Primum Mobile, yet sinners would be sent to an everlasting state of damnation, to be burned in sequential states of pain and agony. Suffering a series of burns and pains requires time, yet if time is treated as an ‘accident’ inhering in the Primum Mobile how could there be a time for the damned? With his thought experiment, Bonaventure was thus challenging the theological adequacy of approaches to temporal unity based upon Averroes. Faced with the theological consequences of the problem, Aquinas could not afford to ignore Bonaventure’s point, but he was equally reluctant to abandon the appeal to the Primum Mobile. Facing equally unpalatable choices he took the only way out by accepting that any motions or sufferings occurring in the absence of the Primum Mobile would be in time, but not in our time. They would be occurring in a time that had as its subject a different substance than the Primum Mobile.33 33 ‘si non esset hoc primum mobile, esset aliud, cuius tempus esset mensura’, In Sent. 2. 2. 1. 2 ad 4. If there were more worlds (i.e. not related to the Primum Mobile) there would be more times, ‘Si essent plures mundi,

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Pressing his critique still further, Bonaventure introduced a second thought experiment and asked what would happen if there were to be two Prima Mobilia. It would certainly no longer be coherent to talk of a single Primum Mobile as the (single) subject of time, and so, asked Bonaventure, surely it would not make sense to appeal to the Primum Mobile as the basis for temporal unity.34 Surprisingly, Aquinas does not seem to have engaged explicitly with the second thought experiment and this may well have been because he thought that it was incoherent. Familiar as he was with Aristotle and Averroes, he would have been aware of their arguments which showed that if there were more than one Primum Mobile that would entail a plurality of simultaneous and equal times. And that, as we have already seen, was generally considered to be impossible. In its Aristotelian context Bonaventure’s second thought experiment could thus be viewed as so incoherent as not to need a response.35 oportet esse plures primos motus, et plura tempora.’ In Sent. 1. 37. 4. 3. In so far as he addressed the point at all, Aquinas seems to have thought that the criteria for identifying the other subject(s) of time would be metrical, so that the subject of time in each case would be the most regular or perfect motion. This raises serious questions about the extent to which Thomas and fellow proponents of the Averroean approach to this problem were able to distinguish the distinctly topological issues which Bonaventure was challenging them on, from the metrical issues around which they were formulating their responses. 34 ‘si essent duo mobilia prima, adhuc unum esset tempus. Tunc non potest dici unum ratione subiecti, in quo primo esset, nec in quo primo appareret, cum utrumque esset aeque primum et evidens; nec ratione animae, quia tempus . . . est dispositio rei extra, non fictio animae’, In Sent. 2. 1. 1. 2 (2, 59). 35 For Aristotle’s original argument, de Caelo 1. 8 (276A18–279B4); Phys. 4. 10 (218B1–5). Averroes, ‘Si igitur essent plures coeli, tunc necesse esset ut

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Despite what was viewed as the absurdity of a plurality of Prima Mobilia, Albert was one of the few figures who was at least willing to engage with Bonaventure’s case and explore the implications of the example. In doing so, he made a rather surprising concession: [When] the first and proper subject is multiplied then the accident in that subject will also be multiplied, when [that] subject is the immediate recipient of the accident. Motion is such an accident because it is in the thing in motion and so when things in motion are multiplied then so it is necessary for motion to be multiplied. But time is not such an accident that it might exist essentially (per se) and immediately in the thing in motion, in so far as it is [actually] in motion; otherwise time would come (logically) before motion . . . Time, however, is in the thing in motion, through its motion, as the actual measure (number) of its motion; and so if there were two or three equal first motions then time would not be multiplied on account of this because the measure (number) of time would not be multiplied . . . 36 motus cuiuslibet eorum esset tempus, ex quo sequeretur plura tempora.’ In Phys. 4 [93]. The argument was paraphrased and developed by Albert, with the conclusion appended ‘et hoc est inconveniens’ Phys. 4. 3. 2 (4.1, 261, 83 f.); also Aquinas, In Phys. 4. 16 [566], 23 [633]. 36 ‘quia multiplicato subiecto primo et proprio multiplicabitur accidens, quod est in subiecto, quando subiectum immediate subicitur accidenti. Motus autem tale accidens est, quod est in mobili, et ideo multiplicatis mobilibus necesse est multiplicari motus. Sed tempus non est tale accidens, quod per se statim sit in mobili, ut mobile est, quia tunc tempus esset ante motum . . . tempus (autem) est in mobili per motum ut numerus motus existens, et ideo si duo vel tres essent aeque primi motus, non multiplicaretur per hoc tempus, quia nec numerus multiplicaretur’, Phys. 4. 3. 2 (4.1, 262, 9– 20). Alexander of Hales also seems to have believed that a plurality of Prima Mobilia (or Caeli) could be reduced to a single time (or perhaps more accurately a single measure), for ‘non esset unum tempus per essentiam, posset tamen esse unum per conformitatem sive indifferentiam participationis aevi et aeternitatis’, Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 103).

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In order to resolve Bonaventure’s challenge, Albert is suggesting a logical distinction between time and motion. When substances in motion are multiplied, then so is the number of the motions, but not so with time because it is not so fundamental as to be located ‘in’ the substance which is in motion. It has a derivative existence. As an account of the relationship between time and motion, there is much to be said for Albert’s approach, but it is clearly incompatible with the Averroean approach to temporal unity which bases itself fundamentally upon the identification of the accident time with its subject the Primum Mobile. Logically, Bonaventure is right, a plurality of subjects should entail a plurality of accidents, and so a plurality of Prima Mobilia should entail a plurality of times. In order to escape the implications of Bonaventure’s position, Albert has had to implicitly repudiate the Averroean appeal to the Primum Mobile as the subject of time, even though, verbally, he was still committed to it as providing the basis for temporal unity.37 One of the fundamental problems with Albert’s response is that, rather than providing an argument to address the topological problem of temporal unity, without realizing it he seems instead to be providing an argument for the unity of the temporal metric. This is why he seems largely unconcerned about the plurality of Prima Mobilia. For in so far as 37 Kilwardby also suggests that time can be a single (specialissima) accident within multiple subjects, de Temp. 13 [59] (24, 14–20), a position which bears similarities to Albert’s position, here, in his Commentary on the Physics. With further reflection Albert seems to have become concerned about the unAristotelian implications of his position so that when he returns to the topic in his later Summa Theologiae he takes care to stress the centrality of the Primum Mobile as the subject of time.

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they are all ‘Prima Mobilia’, then by definition they are all equally regular and so qualitatively identical. As metrical tokens of a more fundamental type measure, the mere fact of their plurality can then be viewed as irrelevant to the existence of a single temporal metric. Albert’s approach is an interesting one, but it is ultimately vitiated by the tendency to confuse topological and metrical issues, as he seems to have assumed that the topological question of temporal unity could be resolved by an appeal to issues relating to the temporal metric. The inability to sharply distinguish metrical and topological issues was endemic to the thirteenth-century discussions of the problem of temporal unity for, as Aquinas indicates, adherents of Averroes’ approach often appealed to the Primum Mobile in order to fulfil a topological function, but in reality the criteria for its selection were metrical: The reason for the unity of time is the unity of the first motion, which since it is the most simple (regular) it measures all the other motions. So time is compared to this motion not just as a measure to what it has measured, but also as an accident to a subject and in this way it receives unity.38

One of the few thinkers who began to appreciate that this sort of approach was at risk of confusing the distinct topological and metrical issues was Kilwardby. Rather than entering the debate on temporal unity by championing Aquinas’ 38 ‘Est ergo ratio unitatis temporis, unitas primi motus, secundum quem, cum sit simplicissimus omnes alii mensurantur. Sic ergo tempus ad illum motum comparatur non solum ut mensura ad mensuratum sed etiam ut accidens ad subiectum et sic ab eo recipit unitatem.’ Sum. Theol. 1. 10. 6. In Phys. 4. 23 [633]–[636].

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appeal to the Primum Mobile or Bonaventure’s appeal to matter, he seems to have appreciated that there were two very different sets of issues at stake in the dispute and so two rather different solutions were necessary. Agreeing with Aquinas, although without resolving Bonaventure’s arguments against the approach, he accepted that the Primum Mobile had a part to play in arguments about temporal unity but he insisted that it could only explain the unity of time qua ‘limited and determined’ (limitatum et determinatum), or as we might say now, as ‘measured’. The unity of time considered apart from its measure, or time qua ‘indeterminatum’, he thought should be explained by the argument from the unity of matter which Bonaventure championed. Although lacking the terminology to formulate the issue precisely, he was effectively offering a highly original reconciliation of the competing arguments by distinguishing between the unity of the metric, which should be explained by appeal to the Primum Mobile, and the topological unity of time, which was to be explained through the unity of matter.39 39 Kilwardby, ‘Patet igitur quod si consideretur tempus secundum esse limitatum et determinatum, ipsum est unum numero ab unitate unius individui subiecto, scilicet motus primi mobilis, et est in ipso sicut in subiecto.’ de Temp. 11 [51] (22, 1–3). ‘Et sic patet quomodo a materia una per essentiam est motus unus per essentiam, et ab illo tempus unum per essentiam. Sic igitur patet quomodo tempus indeterminatum est unum per essentiam.’ de Temp. 13, [66] (26, 18–20). A further example of the confusion caused by the failure to distinguish topological and metrical aspects of temporal unity arose when thirteenth-century thinkers posed the question of how uncaused acts of free will could be measured by the Primum Mobile, and so exist within a common time which only measured the motions which it caused (Bonaventure, In Sent. 2. 2. 1. 1. 2). Albert was so concerned about the causal role of the Primum Mobile interfering with free will that he was even ready to talk of multiple times, ‘Dicimus, quod plura sunt tempora; est enim quaedam mutatio quae non potest reduci ad motum coeli tamquam ad causam, sicut est mutatio potentiae intellectivae et voluntatis, et illa habet

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Whilst we have so far focused mainly upon the philosophical elements of the medieval discussion about simultaneity and temporal unity, we have begun to see that as soon as thirteenth-century thinkers tried to reconcile their Aristotelian world views with their theology it led to serious complications. We have seen, for example, that in order to accommodate theological views about damnation, Aquinas and many of his contemporaries were forced to accept a serial plurality of times. We shall see later that the attempt to fit angels into their world view caused even more difficulties. Without anticipating the precise details of the discussion, the crucial problem which Aquinas and his followers faced was that they felt constrained to posit both the existence of a continuous time for the physical creation, as well as the existence of a distinct discrete time for the angels. Despite all their verbal philosophical avowals, and best Aristotelian intentions, the demands of faith compelled them to commit themselves to plura tempora: a multiplicity of times.40 suum tempus . . . Alia autem omnia quae sunt sub motu coeli, habent tempus unum: omnis enim motus mensuratur per motum coeli tamquam per simplicissimum sui generis. Et similiter mensuratur per numerum motus coeli tamquam per extrinsecus adiacens, quod non est in eodem genere, quia esse in tempore, est esse in numero . . . .’ Sum. de Creat. 2. 5. 10 (Borg. 34, 385). Albert, ‘transitus per affecta vel concepta . . . ordinatur ad motum caeli non ut ad causam sed ut ad numerum . . . ’, Sum. Theol. 5. 23. 3 (34.1, 139, 20–2). 40 Richard Knapwell, ‘duplex sit tempus, unum scilicet continuum inter cuius quaelibet duo instantia cadit tempus medium, aliud tempus discontinuum inter cuius instantia non cadit tempus medium’, Cor. Cor. Quare 1. 23 (102) and in a rather stronger response to those who would cite Aristotle as opposing two times, ‘Illud etiam quod accipiunt de Philosopho nihil facit pro eis; planum est enim quod ut naturalis philosophus, in 4 Physicorum, non habuit de alio tempore quam de tempore continuo motum continuum

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Although Aquinas seems largely unconcerned about the problem, content to commit himself to what contemporary thinkers would view as a version of the plurality of times in his Summa Theologiae, whilst at the same time repudiating the idea in his commentary on the Physics, Kilwardby was clearly embarrassed about the implications of the position. Albert went a step further and actively tried to find a way of showing that the instants of the discrete time could be ordered to the instants of the continuous time, thus justifying the claim that there is still only one time. It may well have been the realization of the ineffectiveness of this approach and its danger of adversely reducing theological needs to pagan philosophical positions that prompted John Quidort to refer to such approaches as an ‘intolerable error’ that was ‘contrary to scripture’.41 sequente determinare; nec tempus non continuum quod est mensura actuum simplicium in substantiis separatis debebat in Praedicamentis explicare pueris. Signum ergo quod accipiunt nullum est.’ ibid. (105). See also William Macclesfield, Cor. Cor. Sciendum 23 (104). Aquinas seems to have contributed particularly strongly in popularizing the idea of a separate discrete time for angels. Earlier thirteenth-century theologians, such as Philip the Chancellor, talked more vaguely of the angels as ‘in tempore’ or ‘in infinitum duratione’ without feeling a need to distinguish that time from our time. Sum. de Bono 1. 4. 9 (1, 296, 164–5). Alexander of Hales illustrates the next evolutionary step in the idea, referring to the angelic duration as ‘like’ (quasi) time: ‘actionis angeli . . . non mensura ponetur tempus proprie nec aevum proprie, sed duratio quae est quasi tempus quantum ad aliquid et aevum quantum ad aliquid; quasi tempus quia ibi est quaedam variatio’, Sum. Theol. 1. 1. 1. 2. 4. 3. 3 ad 3 (1, 104). Aquinas’ position took it a step further by explicitly identifying at least one, and possibly even two, separate times for the angels, which when added to the cosmic time measuring the world resulted in a total of three times. For further details, J. MacIntosh, ‘St Thomas on Angelic Time and Motion’, 575. 41 If challenged about his apparently contradictory position Aquinas would probably have responded by claiming that his commitment to the unity of time (In Phys. 4. 23) was to be read as merely a commitment to

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Prompted by theological needs, thirteenth-century thinkers were thus gradually going beyond Aristotle to develop a metaphysical position of their own, one for which they were even struggling to develop their own distinct vocabulary. We can see this perhaps most clearly in the way that thirteenth-century thinkers tentatively explored ways of expressing non-temporal, non-simultaneous ‘togetherness’. Sometimes the word ‘simultaneous’ (simul) was deployed, on other occasions it was the word ‘with’ (cum), or even the the unity of continuous time, as the time which he postulates for the angels is a discrete time (Sum. Theol. 1. 63. 7 ad 4). Kilwardby refers to the issue of multiple times, ‘Sunt adhuc non nulli . . . dicentes scilicet quod sunt duo tempora quorum neutrum ad alterum reducitur.’ de Temp. 13 [71] (27, 17– 19). P. Osmund Lewry thought that this was a reference to Bonaventure’s position (27 notes on lines 17–22). But Bonaventure does not discuss the problem of reconciling angelic and continuous time with a denial of plura tempora and Kilwardby’s summary of Bonaventure’s position seems to occur instead at question 13 [57] (23, 31 f.). Kilwardby’s text at question 13 [71] has more in common with Albert’s position in his Sum. de Creat. 2. 5. 10 (Borg. 34, 385). By the time he wrote his later Summa Theologiae Albert was committed to trying to reconcile and reduce the two times to a single time, ‘Unde videtur esse dicendum quod non est nisi unum tempus, et quod transitus per affecta vel concepta spiritualis creaturae ordinatur ad motum caeli, non ut ad causam, sed ut ad numerum, quo nos mensuramus.’ Sum. Theol. 5. 23. 3. 2 (34.1, 139, 19–23). Whilst it was a thoughtful attempt to resolve the problem, and may even provide grounds for positing a single metric, his argument could not escape the crucial fact that the two times in question were thought to have the different topological properties of continuity and discreteness. Unless the topological properties of the angelic time were also viewed as being reducible to the topological properties of the continuous time, such an approach could never work, but if the properties were capable of being reduced then that was tantamount to denying the very existence of an angelic time. It is perhaps the realization of the difficulties of the position that encouraged John Quidort to dismiss all such efforts as ‘intolerabiliter erroneum et contra scripturam’, Cor. Cor. Circa (123, 74).

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word ‘when’ (quando), which was used to describe a nontemporal relation in which time itself, or another duration, was linked together with other particulars in a relation of nontemporal ‘togetherness’.42 Sometimes the relationship of togetherness is described as one of ‘coexistence’ (coexistentia),43 but one of the most widely used terms was ‘concomitance’ (concomitantia). This term was used by William of Auxerre, Aquinas, Bonaventure, Kilwardby, Peter of Tarentaise, Pseudo-Aquinas, Alexander of Hales, Albert the Great, and many others. Its 42 Albert, Phys. 4. 3. 16 (4.1, 289, 29–39); 6. 2. 8 (4.2, 480, 86). This terminology was well established and derived ultimately from Augustine’s reflections on creation, as Alexander of Hales’ formulation shows, ‘Creatio . . . non est sine tempore . . . non tamen est in tempore . . . nec cum tempora . . . .sed non sine tempore.’ Sum. Theol. 2. 1. 1. 1. 2. 2. 5 (2, 36). As Avicenna demonstrated, two particulars could only be temporally simultaneous if there was a third particular with respect to which the simultaneity was attributed, ‘omniaduo que sunt simul; in aliquo sunt simul’, Suff. 2. 10. For further details, T. Rudavsky, ‘Creation and Time in Maimonides and Gersonides’, 122–46. The implications of this argument were that if durations were to be identified as simultaneous that would have entailed a third duration with respect to which the simultaneity was predicated, and in the case of the simultaneity of durations this would have led to a vicious infinite regress, unless a simpler notion of togetherness or simultaneity could be developed. It is precisely that notion which Kilwardby is struggling towards when he wants to talk of instants of time and eternity being together (simul), ‘instans temporis est cum instanti aeternitatis . . . ergo sunt simul, quia sunt in simplici’, In Sent. 2. 4 (2, 19, 65–6). See also Albert, Phys. 8. 1. 13 (4.2, 574, 73) and Aquinas’ use of ‘quando’ for the Trinity, ‘Filius fuit quandoque fuit Pater. Et sic coaeternus Patri . . . ’, Sum. Theol. 1. 42. 2. 43 Tarentaise, ‘Illa enim substantia [i.e. Deus] potest designari per differentias temporum dupliciter, aut ut fluens cum illis, aut ut manens semper cum illis: primo modo dicitur Deus nec esse, nec fuisse, nec fore; secundo modo dicitur convenienter esse, fuisse, fore; nam primo modo designatur continentia, secundo modo coexistentia tantum.’ In Sent. 1. 8. 3. 1 ad 3.

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precise import is not always clear, but the occasion of its use is almost invariably to assert non-temporal togetherness between particulars in different durations, or even to assert non-temporal relations of togetherness between the relations themselves.44 44 William of Auxerre, ‘Ad hoc potest dici quod utrumque significat eternitatem, tamen in triplici habitudine at tempus, scilicet concomitantie, antecessionis et subsecutionis’, Sum. Aurea 1. 14. 4 (1, 274, 15–17); Kilwardby, de Temp. 17 [109] (36, 8–10); Alexander of Hales, Sum. Theol. 2. 1. 2. 2. 4. 1. 1. ad 6 (2, 87); Albert, ‘Angelus autem et aeviternum dicuntur esse in tempore sicut concomitantia tempus’, Sum. Theol. 5. 23. 3. 3. 2 (34.1, 141, 83–4); Pseudo-Aquinas, ‘Unde a parte aevi quod toti tempori nostro coexistit, et cuilibet eius instanti, inferri potest primum Angelum toti tempori nostro coexistere, . . . Tempus enim nostrum concomitanter se habet ad angelum . . . cui tempus nostrum est adiunctum’, de Inst. 4; Bonaventure, ‘esse simul in duratione est dupliciter: aut per mensurae concomitantiam, aut per mensurae unitatem et indifferentiam. Cum autem dicitur Deus, homo et Angelus esse simul; dicendum quod hoc dicitur per mensurae concomitantiam. Cum autem dicitur Petrus et Paulus simul sunt vel currunt, hoc potest dici per mensurae unitatem et indifferentiam’. In Sent. 2. 2. 1. 1. 2 ad 4 (2, 60). Tarentaise is hesitant, but he too is trying to distinguish between succession and co-presence, ‘Cum ergo quaeritur utrum coeperit esse Dominus ex tempore, distinguendum est: quia ly ‘‘ex’’ dicit ordinem, aut ergo notat consequentiam, Sic dico quod non coepit esse dominus ex tempore, aut concomitantiam solam, sic coepit esse Dominus ex tempore large accepto, id est cum tempore. Exemplum potest poni, dicitur enim: ex quo fuit lux, fuit splendor, et e converso; sed primo modo ly ‘‘ex’’ notat consequentiam, secundo concomitantiam.’ In Sent. 1. 30. 1. 5. Note also his ad 3. Aquinas, ‘Si autem significetur nunc aeternitatis, tunc dicitur Deus esse in illo sicut in mensura propria et adaequata; angelus autem et mobile, sicut in mensura excedenti. Si autem significetur nunc aevi, respondebit angelo sicut mensura adaequata, et deo secundum concomitantiam, et mobili sicut mensura excedens.’ In Sent. 1. 19. 2. 2 ad 1. For Aquinas ‘concomitance’ seems to imply an immediate togetherness, ‘dicendum quod cum dicitur quod intellectus agens est sua actio, est praedicatio non per essentiam, sed per concomitantiam; quia cum sit in actu eius substantia, statim, quantum est in se, concomitatur ipsam actio . . . ’, Sum. Theol. 1. 54. 1 ad 1; ‘Ad primum ergo dicendum quod rei eterne vel eviterne aliquid potest attribui dupliciter . . . Alio modo ratione mensure adiacentis vel subiacentis, id est ratione temporis; et sic attribuitur ei

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C O N C LU S I O N In this chapter we have focused upon the thirteenth-century views of ‘simultaneity’ and the implications of those views. We saw that the medieval Latin word ‘simul’ (simultaneous) had a wide set of meanings and uses, only some of which were reserved for discussions of temporality. Thirteenth-century thinkers clearly valued Aristotle’s insights and so the tendency was to follow his approach and understanding of temporal simultaneity, defining it in terms of temporal priority and temporal posteriority. Whilst this approach evidently had the attraction of being reductively simple, it also had the consequence of defining out of consideration the set of issues which contemporary thinkers refer to as the question of whether time can be disunified or not. Essential to formulating that question is the possession of a metaphysics and language which will make it possible to talk of instants which are neither before nor after each other, without that entailing that the instants are temporally simultaneous. fuisse per concomitanciam ad tempus preteritum, et futurum esse per concomitanciam ad futurum.’ Quaest. Quodlib. 10. 2. 1 ad 1. There are clearly similarities between the medieval notion of ‘durational concomitance’ and the notion of non-temporal ‘ET simultaneity’ developed by E. Stump and N. Kretzmann, in ‘Eternity’. It is difficult to believe that thirteenth-century thinkers would have been happy defining the relationship in terms of observers and observations, as Stump and Kretzman do, nevertheless the underlying intention of ET Simultaneity as a way of uniting distinct durations in a non-temporal way is clearly something that medieval thinkers would have had sympathy with. For a critical appraisal of ET simultaneity, J. Yates, The Timelessness of God, 126–30; B. Leftow, Time and Eternity, 167–80; R. Swinburne, ‘God and Time’.

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Although thirteenth-century thinkers were prevented from formulating explicitly the contemporary question of disunified times, they did nevertheless discuss their own problem of whether there could be a plurality of times. Taking its origin and formulation from Aristotle’s notion of time, it was not always clear to medieval thinkers what precisely a plurality of times would mean or amount to. Lacking the contemporary ability to define and discuss nontemporally related instants as constituting the distinct times, medieval thinkers often assumed that a plurality of times would amount to (temporally) simultaneous times, a notion which Aristotle had already repudiated as nonsensical. Starting, therefore, with Aristotle’s confident rejection of multiple times, we saw that medieval discussions of the question tended to assume the unity of time and focus on accounting for that unity, rather than arguing to it. On the one hand medieval discussions of the plurality of times are prone to be negative and dismissive, especially when explicitly drawing upon the Aristotelian philosophical tradition. Yet beneath the verbal repudiations, the metaphysical denials, and the confusion of metrical and topological issues, there was a very different distinctively theological agenda which was forcing thirteenth-century thinkers to take a very different and markedly un-Aristotelian approach to the entire question. It was clearly a source of embarrassment to many thinkers, but theological assumptions necessitated accounts of creation, angels, and damnation which, if they were to be fitted into a broader Aristotelian metaphysic, required the postulation of multiple durations and, as we saw Aquinas explicitly admit, multiple times.

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What this analysis of thirteenth-century accounts of temporal simultaneity and its implications shows is that there was a large degree of muddle present in thirteenth-century discussions, particularly revolving around what seems to have been a general inability to distinguish the topological and metrical issues of time. Of no less equal significance, however, is the way that faith and philosophy were pulling in different directions, directions which it seems thirteenthcentury thinkers were not always able to reconcile.

3 Priority, Posteriority, and Causality

In Chapter 1 we saw that for medieval thinkers time was composed of instants and periods which were temporally related to each other. In the previous chapter, we examined the temporal relation of simultaneity, exploring the implications of how that notion was defined. In this chapter, we shall turn our attention to the other two temporal relations, temporally before (temporal priority) and temporally after (temporal posteriority), examining the notions in themselves before turning to examine the related question of thirteenth-century attitudes to the causal theory of time. As we saw with the notion of simultaneity, thirteenthcentury accounts of temporal relations were much influenced by their authorities and the sources cited as the basis for their analysis. This was particularly the case with temporal priority and posteriority where the tendency was to try to synthesize the very diverse traditions and enumerations of senses of ‘priority and posteriority’ deriving from Augustine, Aristotle, Averroes, and many other key figures.1 1 Averroes, ‘dixit prius autem alterum altero quadrupliciter dicitur’, In Praedicamenta, Sermo de Priori (58C–F), although his actual distinction

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Inevitably this seems to have led to many thirteenth-century thinkers assuming that an analysis of terms such as ‘priority’ and ‘posteriority’ amounted simply to enumerating, classifying, and developing still further senses of priority.2 seems to be a fivefold one distinguishing between priority in time, priority by nature, priority by order, priority by dignity, and causal priority. As such the distinction seems to have much in common with Al Ghazali’s, ‘Ante vero sive prius dicitur prius tempore et hoc prius est magis in usu loquendi apud homines. Secundus est vel prius ordine, vel prius situ . . . vel prius genere . . . Tercius dicitur prius dignitate . . . .Quartus prius natura . . . . Quintus est prius essencia’, Algazel’s Metaphysics (Muckle 36, 4–21). The Augustinian analysis suggested four types of priority, ‘aeternitate, sicut Deus [praecedit] omnia; tempore, sicut flos fructum; electione, sicut fructus florem; origine, sicut sonus cantum’, Conf. 12. 29 (40) (181). Aristotle’s account is more complex. In his early Categories he seems to have viewed it as a distinct kind of priority, Cat. 1. 12 (14A26) whilst the latter works seem to indicate that he thought it could be reduced to other types of priority, Phys. 4. 10 (219A14); Meta. 5. 11 (1018B9 f.), 9. 8 (1049B4 f.). For more details, W. D. Ross, Aristotle’s Metaphysics, i. 316–18. J. J Cleary, Aristotle on the Many Senses of Priority, 21–63. 2 Albert, ‘In quibus est prius et posterius, hoc causabitur de necessitate ab intellectu, vel a tempore, vel a loco, vel a dignitate secundum mores vel naturam.’ In Sent. 1. 9. B. 5 sed con. 3 (Borg. 25, 279). Pseudo Siger, ‘prius et posterius possunt dupliciter considerari; nam cum ipsa dicant ordinem, poterunt dicere ordinem vel secundum naturam vel secundum successionem’. Phys. 8. 9 (15, 206). Bonaventure, ‘Dicendum quod prius dicitur multipliciter. Dicitur enim prius duratione, dicitur prius causalitate, dicitur prius origine, dicitur prius auctoritate. Et primis duobus modis prius nullo modo cadit in Deo; quia prius duratione contrarium est aeternitati, prius causalitate contrarium est esentiae unitati’. In Sent. 1. 12. 1. 1, although this is clearly not an exhaustive description because elsewhere he will talk of a priority ‘secundum rationem intelligeni’, In Sent. 1. 27. 1. 1. 2 fund. 2 and ‘aliquid est prius generatione et tempore; aliquid est prius complemento et definitione sive dignitate’, In Sent. 3. 34.1. 2. 2. He gives still further concepts of priority when discussing the notion of ‘ordo’. ‘Dicendum quod triplex est ordo scilicet secundum positionem, secundum antecessionem et secundum originem.’ In Sent. 1. 20. 2. 1 and 1. 40.1. 1 ad 3. Perhaps it was the increasing number of senses, and uses, that encouraged some writers to prefer occasionally more formulaic uses of ‘prius’ that attempted to abstract from the question of the nature of the priority, Aquinas, ‘prius est esse rei quam eius

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Despite what was often a very broad set of uses, thirteenth-century thinkers such as William of Auvergne, Philip the Chancellor, Alexander of Hales, Aquinas, Albert, Kilwardby, Bonaventure, Peter of Tarentaise, Siger of Brabant, and many others seem to have settled on a much simpler distinction between ‘priority in time’ and ‘priority in nature’, although as Albert’s distinction between ‘causal priority’ (secundum rationem causae) and durational priority (secundum rationem durationis) illustrates, the terminology was not always settled.3 agere’, In Sent. 3. 18. 1. 3 ob. 1; also Bonaventure, In Sent. 3. 18. 1. 1 sed con. 1; and Kilwardby, In Sent. 2. 4 (2, 17, 8, and 19, 55). 3 Aquinas, ‘esse est prius quam agere natura, non tempore de necessitate’, In Sent. 3. 18. 1. 3 ad 1; also Sum. Theol. 1. 55. 3 ad 1. Kilwardby, ‘mutabile prius est natura vel tempore quam mutatio’, In Sent. 2. 1 (2, 5, 51–2). Siger, ‘dicendum quod prius et posterius possunt dupliciter considerari: nam, cum ipsa dicant ordinem, poterunt dicere ordinem vel secundum naturam vel secundum successionem. Et tunc ad rationem: cum enim dicitur quod, si tempus factum est, non esse temporis prius est ipso tempore, dico quod hoc est verum de priori secundum naturam, non autem de priori secundum aliquam durationem temporalem. Et cum dicitur: prius et posterius non sunt sine tempore, dico quod verum est, prius scilicet et posterius secundum successionem.’ Phys. 8. 9 (Delhaye 206). Philip the Chancellor, ‘Preterea, non possumus ita dicere ex parte temporis sicut dictum est ex parte ipsarum creaturarum; nam in ipsis creaturis invenitur prius et posterius naturaliter, licet simul sint facte. Sed prius et posterius naturaliter non causat dierum multitudinem, sed prius secundum tempus.’ Sum. de bono, 1. 3. 3. (1, 123, 7– 10). Peter of Tarentaise, ‘Creator mundi aut praecedit mundum natura tantum, aut duratione: si natura tantum, ergo quandocumque fuit creator, fuit mundus; si duratione, cum prius et posterius in duratione causet tempus, ergo ante totum mundum fuit tempus.’ In Sent. 2. 1. 2. 3 ob. 4; and Alexander of Hales, Sum. Theol. 1. 1. 2. 1. 4. 2 (1, 473). Bonaventure, ‘Ad illud enim quod primo obiicitur, quod prius est esse quam agere; dicendum, quod illus habet veritatem, si intelligatur de prioritate quantum ad ordinem naturae. Si autem intelligatur de prioritate quantum ad durationem, non habet veritatem’. In Sent. 3. 18. 1. 1 ad 1; and ‘. . . duplex est ordo, videlicet secundum tempus et naturam, vel secundum naturam tantum’, In Sent. 3.

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Influenced undoubtedly by Averroes’ identification of temporal priority as the ‘core’ sense of Aristotelian priority, thirteenth-century thinkers tended to focus upon temporal or durational priority as the central sense of priority, but in doing so they tended to adopt the Aristotelian and Averroean reading of the notion which viewed it as a ‘metrical’ property rather than as a ‘topological’ one. Priority tended to be analysed as a matter of degree, in terms of the degree of proximity or distance between particulars. A relationship of priority was thus generally considered to exist where there were two particulars P and Q which were nearer to, or further away from, some marker or ‘principle’. In the case of time, the principle was usually the present time or date, so for a past P to be prior in time to a past Q was simply a matter of it being further away from the present. Medieval thinkers were generally clear that the date didn’t have to be the present one; other dates such as the foundation of Rome, the birth of Christ, or even the beginning of a battle could be chosen, and because the notion of temporal priority was fundamentally metrical, they would thus provide an equally sound basis on which to determine temporal priority and posteriority.4 3. 2. 3. 2 ad 4; and 2. 12. 2. 2. See also William of Baglione, De Aeternitate Mundi b and c (586); Albert, Sum. de Creat. 2. 3. 3 ad 6 (Borg. 34, 353); and William of Auvergne, De Trin. 1. 8 (52, 77–80). Henry of Ghent, ‘Dicamus ergo quia Deus creavit: id est produxit caelum et terram ex nihilo: id est post non esse absolute, non tamen posteritate naturae sive essentiae, sed durationis, non quo tempus sit prius, sed quod tempus incipiat esse, aeternitate praexistente duratione infinita’, Lect. Ord. Sup. Sac. Script. (50, 84–8). 4 Aristotle, Meta. 5. 11 (1018B9–29). Averroes, ‘dixit prius autem alterum altero quadrupliciter dicitur. Primo quidem atque famoso illorum modo

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We encountered the concept of priority of nature briefly in the previous chapter, when examining the notion of simultaneity of nature. As with simultaneity of nature there was basically a core twofold logical and causal notion attached to the concept. The prior in nature was that upon which other things (logically) depended, and that which in a sequence of causes was metaphysically prior or more perfect, such as a soul compared to a body. There are clearly similarities between the notion of prior by nature and the causally prior that contemporary philosophers might speak of. Causal agents upon whose agency an effect depends will often be characterized as prior by nature, but because this concept includes a relation of explicit logical dependence and metaphysical perfection, it cannot always crudely be equated with causal agency.5 dicitur, prius tempore; ut dicimus aliquem esse seniorem et antiquorem alio.’ In Praed. (58C–F). Albert, ‘In factis enim in praeterito quaedam dicuntur priora quae remotiora sunt ab ipso praesenti nunc.’ Meta. 5. 2. 11 (16.1, 247, 63–74 and 248, 7–9); Phys. 4. 3. 13 (4.1, 284, 40–8). Aquinas, In Met. 5. 13 [936–40]. Metrical analyses of priority were not confined to temporal priority as they appear also in accounts of spatial priority and even metaphysical priority. Bonaventure also seems to have introduced the notion of distances to his account of causal priority, ‘vera enim causa natura prior est, et ideo a sensibus nostris remotior’, In Sent. 4. 1. 1. 1. 2 ad 2. 5 Aquinas, ‘vel secundum ordinem causae . . . vel saltem ordine naturae’, Sum. Theol. 1. 55. 3 ad 1; ‘non enim semper necessarium est ut causa causatum praecedat tempore, sed quandoque sufficit quod praecedat natura’, In Sent. 3. 18. 1. 3 ad 3. Kilwardby, ‘Sicut enim intelligere et posse intelligere et vivere in aliis se habent secundum prius et posterius, quia quod intelligit, potest intelligere, et quod vivit, potest vivere, et non e converso, in Deo autem sunt id ipsum in re differentia solum ratione: sic creatio et creatibile in Deo sunt id ipsum nec praecedit creabile creationem natura vel tempore.’ In Sent. 2. 1 (7, 104–5). Sometimes the notion of ‘dependence’ is expressed as an ‘exigentia’ as in Bonaventure, ‘sed illud ad cuius exigentiam fit alterum, prius est’, In Sent. 2. 18. 2. 2 fund. 4.

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Nevertheless, one of the particularly interesting features about the notion of prior by nature is that it is often contrasted with prior in time. This conveys the implication that for medieval thinkers causal sequences and temporal sequences might not necessarily have been linked. If this was so then it raises the possibility that thirteenth-century thinkers might have had a distinct position on the question that contemporary philosophers have come to think of as the causal theory of time.

T H E C AU S A L T H E O RY OF T I M E The Causal Theory of Time is the attempt to explain temporal relations by reducing them to causal orderings. There are many different versions of the causal theory of time, all differing in details, but the central feature which both critics and proponents alike would identify as essential to a causal theory of time is its claim that the direction of temporal relations is identical to the direction of causal relations, so that temporal relations can be reduced to causal relations.6

6 Contemporary philosophers typically begin an analysis of causation by examining whether the relata of causal relations are events, substances, or even facts. For further details about these distinctions, see D. Ehring, Causation and Persistence, 71–90. For a more general introduction to causal theories of time see B.Van Fraassen, An Introduction to the Philosophy of Time and Space, 170–98. The literature on this question is vast. For a convenient summary of some of the key issues see the bibliography in M. Tooley, Time, Tense and Causation, 382–9.

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In order to explore the causal theory of time it is useful to distinguish the range of (temporal) ways in which a cause and effect may be causally related: (A) A cause acts to bring about an effect which is later in time (B) A cause acts to bring about an effect simultaneously (C) A cause acts to bring about an effect which comes to be earlier in time than the cause (D) A cause which is not located in time acts to bring about an effect in time (A) to (D) represent four distinct ways in which causes and effects can be temporally related. Only (A) is compatible with formulations of the causal theory of time. (B), (C), and (D) all subvert the relationship between temporal and causal direction. (B) makes the cause and effect (temporally) simultaneous whilst (C) locates the cause (temporally) after the effect and (D) simply denies that a cause has to have a temporal location at all. Each of (B), (C), and (D) are controversial and much discussed by contemporary philosophers, precisely because the truth of any one of them is enough to entail the falsity of the causal theory of time. Medieval thinkers had a much broader notion of causation than contemporary thinkers, so it is not always a straightforward matter to identify whether particular accounts of causation are instances of (A), (B), (C), or (D). Basing themselves upon Aristotle’s account of causes, they typically identified four distinct kinds of causes in each causal context: material causes, efficient causes, final causes, and formal causes.

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Material and efficient causes are relatively uncontroversial elements of a causal sequence and will be immediately recognized by contemporary philosophers. A material cause was the material which contributed to an effect, typically being the ‘substance’ or ‘stuff ’ out of which the effect came to be. In the case of making a cup of tea, the material cause would be the ‘water’ and the ‘tea’. The efficient cause was again simple enough to identify; it was the agent actually making the cup of tea. The notions of final and formal causation are more abstract and would not necessarily be recognized by contemporary thinkers as genuine elements of a causal sequence. A final cause was effectively thought of as the goal of the causal process, the factor which accounted for the causal process assuming the direction and course that it did. In the case of making a cup of tea the final cause would therefore be the notion of a perfect cup of tea existing in the mind of the maker and conditioning his or her actions so that the process would tend to actually produce a cup of tea. The formal cause was considered to be the aspect of the causal process that accounted for the effect assuming the precise nature that it did. The fact that ‘tea and water’ produced an actual drinkable cup of tea rather than a dark warm slop, would have been accounted for by medieval thinkers because the agent had the concept of ‘tea’ in mind and that concept acted as a form dictating the precise causal influence propagated—and so leading to it being a cup of tea that was produced. Final and formal causes can seem to merge and intertwine at times, especially in causal sequences involving agents

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where the final and formal causality can seem to reduce to mental states or aspects of intentionality. But it is essential to keep them conceptually distinct in temporal analyses of medieval language about causation, as they were sometimes depicted as exerting their causal influences in totally different temporal spheres. When the focus is upon final causes and goals of processes, the goal is something that the cause is tending towards and so it is not impossible that medieval expressions will seem to be locating the cause temporally after the effect, thus giving rise to an apparent example of (C). Where there is thirteenth-century language that seems to imply that causes exercise their causal influence temporally after the effect, we must thus check carefully to distinguish whether it is the final cause that is the focus of the discussion.7 Contemporary philosophers are generally less interested in what medieval thinkers referred to as final causes because it is the medieval notion of efficient causes that is considered to represent instances of causation in the proper contemporary sense of the word. In determining whether a putative example of causation is to count as an example of (A), (B), (C), or (D), it thus has to be the temporal location of the efficient cause which is crucial. Further complexity can arise in interpreting thirteenthcentury thinkers because in some contexts we can find 7 For further details on Aristotle’s notion of final causes, E. Gilson, From Aristotle to Darwin and Back Again: A Journey in Final Causality, Species and Evolution, 1–32; D. Des Chene, Physiologia: Natural Philosophy in Late Aristotelian and Cartesian Thought, 168–212; and W. Wallace, ‘Is Finality Included in Aristotle’s Definition of Nature?’ 52–70.

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almost textbook examples of what seem, on the surface, to be statements of the ‘causal theory of time’. Aquinas, for example, states: if we take this man who is now actually a man, prior to him in time there was a matter which was potentially a man. And similarly seed, which is potentially grain, was prior in time to what is actually grain. And ‘the thing capable of seeing’ i.e. having the power of sight, was prior in time to the thing actually seeing.8

Despite the apparent identification of causation and temporal orderings, Aquinas is not necessarily committing himself to the causal theory of time. In this passage his focus is upon the ‘stuff ’ out of which the effect comes to be. The point he is making is that in the analysis of changes, the matter out of which the effect comes to be cannot exist simultaneously with the effect itself because if both the prior and post-causal states of the matter had to exist simultaneously this would lead to a contradiction. In thirteenth-century terminology, the focus of this passage is upon material causes, rather than efficient causes, so, despite its apparent clarity on the matter, it is not necessarily expounding a thirteenth-century temporal theory of causation. 8 ‘Si enim accipiamus hunc hominem qui est iam actu homo, fuit prius secundum tempus materia, quae erat potentia homo. Et similiter prius tempore fuit semen quod potentia est frumentum quam frumentum actu, et visivum, idest habens potentiam videndi, quam videns in actu.’ In Meta. 9. 7 [1848]. Also, ‘Unde relinquitur, quod licet idem numero prius tempore sit in potentia quam in actu, tamen aliquod ens in actu secundum idem specie, est etiam prius tempore quam ens in potentia.’ ibid. [1848]. Albert glosses the priority in time as arising due to the prior visibility of the elements, Meta. 9. 4. 1 (16.2, 423, 32–47).

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Even where we are clear that thirteenth-century thinkers are focusing upon efficient causes, considerable ambiguity can still remain in the detail of their discussions. A cause and effect might both be said, for example, to occupy the same instant, and so an example of causation might initially seem to be an example of (B): an occasion of simultaneous causation. But the instant in common might well be the final instant of a prior period in which causal influence was propagated and the beginning instant of the period in which the effect came to be. If this were the case then, despite its prima facie similarities to (B), the causation would be an example of (A) because the cause and the propagation of its causal influence temporally precede the coming to be of the effect.9 9 Much of the complexity and confusion in medieval language about causation was occasioned due to the failure to distinguish between change in an instant and change during periods bounded by a common instant. This problem was often raised acutely in discussions of the doctrine of transubstantiation, where confusion could seem to lead to a contradition, ‘in qualibet mutatione instanea simul est verum dicere quod fit et factum est, quia in instanti non est accipere prius et posterius. Ergo cum transubstantiatio sit mutatio instantanea, simul verum est dicere quod fit ibi corpus Christi et factum est: ergo corpus Christi simul est ibi et non est’, Aquinas, Quaest. Quodlib. 7. 4. 2 ob. 4. Related issues arise in the similarly much disputed medieval question of creation, on which, Bonaventure, ‘sed creari rei est in instanti’, In Sent. 2. 1. 1. 3. 2 ob. 3. Generally, as Aquinas demonstrates, thirteenth-century thinkers were able to disentangle the issues of change in an instant and period, ‘Et pro tanto mutatio illa dicitur esse subito, vel in instanti, quia in ultimo instanti temporis, quod mensurabat motum praecedentem, acquiritur illa forma vel privatio, cuius nihil prius inerat; et in illo instanti dictur generatum esse’, In Sent. 1. 37. 4. 3; Quaest. Quodlib. 7. 4. 2 ad 4; Quaest. Disp. de Malo 4. 6 ad 13; In Phys. 8. 17 [1122]; and Albert, Phys. 8. 3. 6 (4.2, 633, 33–65). For further details on the specifically Eucharistic aspects of the debate, D. Burr, Eucharistic Presence and Conversion in Late Thirteenth

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One of the significant aspects of thirteenth-century thought is that the theories of causation appealed to are extremely rich. It is clear that in some instances medieval theories do indeed assume a temporal sequence between cause and effect,10 but in still other contexts the matter seems to be much less clear, especially in cases of putative simultaneous causation.

S I M U LTA N E O U S C AUS AT I O N Thirteenth-century figures used a variety of terms to refer to simultaneous causation. In some contexts they would simply refer to causation that was ‘simul’ (simultaneous), in

Century Franciscan Thought ; G. Buescher, The Eucharistic Teaching of William of Ockham. The most widely accepted solution to the problem of the supposed instant of change, when both prior and later states would be allegedly simultaneously present, was the claim that in all (substantial) changes there was a first instant of a new substance, but no last instant of the existence of the former ‘ingredient’ substances, just a last period. And so there could be no single instant at which the contradictory states could arise, Aquinas, ‘et sic non est ultimum instans in quo est panis, sed ultimum tempus’, Quaest. Quodlib. 7. 4. 2; also Robert Orford, Cor. Cor. Sciendum (106). 10 Aquinas, ‘Motus localis instantaneus esse non potest, sed tempore indiget.’ Sum. Con. Gen. 4. 63 [4000]; Philip the Chancellor, ‘Ergo in alio nunc erit in termino magnitudinis a quo movetur in alio nunc in quem. Ergo cum inter quelibet duo nunc intercidat tempus motus a termino in terminum, non erit in nunc . . . Et hoc planum est in alteratione; cum enim omne quod alteratur partim sit in eo a quo et partim in eo ad quem, hoc contingit tripliciter’, Sum. de Bono, 1. 1. 11 (1, 108, 61–73).

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other contexts they would use the words ‘instantanea’ (instantaneous),11 or even ‘subito’ (sudden).12 Unlike contemporary philosophical discussions of simultaneous causation, which largely revolve around consider11 Aquinas, ‘et simile contingit in omnibus operationibus instantaneis, quarum una est causa alterius, quod sunt simul tempore’, In Sent. 2. 6. 1. 2; ‘si sunt mutationes instantaneae, simul et in eodem instanti potest esse terminus primae et secundae mutationis’, Sum. Theol. 1. 63. 5; also Quaest Quodlib. 7. 4. 2 ad 3; and Quaest. Disp. de Ver. 29. 8. Bonaventure, ‘. . . motus, ratione praeparationis materiae, quae fit per dispositiones accidentles, et haec indiget successione et tempore; mutationis, ratione exitus in esse sive receptionis substantialis formae, quae fit in instanti . . .’, In Sent. 2. 1. 1. 3. 1; also Albert, In Sent. 2. 6. C. 3 (Borg. 27, 129). 12 Albert, ‘Si tamen non fieret vis in hoc et distinctio fieret de exitu potentiae ad actum, eo quod quaedam exeunt subito et in instanti, quaedam autem non subito et in tempore, et illa quidem, quae exeunt subito, non moventur, sed illa, quae exeunt in tempore, tunc satis convenienter posset diffiniri motus, sicut dicit Avicenna, quod ‘‘motus est exitus de potentia ad actum in tempore continuo, non subito’’.’ Phys. 3. 1. 7 (4.1, 163, 39–46); and again with an even more specific reference to the issue of simultaneous causation, ‘. . . materia susceptibilis est formae subito non interveniente tempore. Si ergo talis materia subiceretur motui, oporteret, quod omnis motus esset subito, quod falsum est . . . et sic creavit omnia simul . . .’, Phys. 5. 1. 3 (4.2, 408, 65–72); also Roger Bacon, Opus Maius, Perspectivae 1. 3 (2, 68). This technical sense of ‘subito’ seems to have developed during the thirteenth century. Earlier writers such as William of Auxerre, Sum. Aurea 2. 8. 2. 1. 1 (2.1, 175, 10), seem to have no appreciation of it and use the term interchangeably with ‘repente’ (quickly). Influenced by Alexander of Hales’ use it became popular by the latter half of the thirteenth century to distinguish these terms on the basis of the successiveness of ‘repente’ and the nonsuccession denoted by ‘subito’. Alexander of Hales, ‘differt dicere ‘‘subito’’ et ‘‘repente’’. ‘‘Subito’’ dicit instans; ‘‘repente’’ dicit tempus insensibile . . .’, In Sent. 2. 3 [33] (40, 1–3). Albert, ‘Repente autem fit, quod in se duo habet, scilicet brevitatem temporis, in quo fit, et insensibilitatem temporis, cuius quantitas sentiri non potest.’ Phys. 4. 3. 13 (4.1, 286, 30–2). Also Philip the Chancellor, Sum. de Bono, 1. 1. 11, 149–55). Aquinas seems unaware of, or perhaps uninterested in, this distinction. One of the few occasions he uses the terms ‘subito’ and ‘repente’ in the same sentence he comes close to simply conflating them, ‘. . . aliquod peccatum subito et quasi repente occurrit . . .’, Quaest. Disp. de Ver. 24. 12.

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ations of its logical coherence as a philosophical notion,13 thirteenth-century discussions focused upon instances and examples of where it was thought to be possibly occurring. In this context three examples stood out as requiring medieval discussion: (A) Illumination (B) Movement at an infinite velocity (C) The actions of angels and souls

(A) ILLUM INATION Commenting upon the notion of ‘illumination’, Bonaventure provided a particularly clear statement of its relationship to simultaneous causation: some corporeal things are such that in the first instant of their existence, they exercise their causal powers. (This is so) in the case of light which as soon as it exists, it illuminates. And (so) Augustine said that light and illuminating are coeternal, so that

13 For a summary of contemporary discussions about simultaneous causation, C. Bas Van Fraassen, An Introduction to the Philosophy of Time and Space, 44–57. Most arguments against the notion of simultaneous causation focus upon the incoherences which are supposedly entailed. It has been suggested, for example, that simultaneous causation must lead to the possibility of physically impossible states of affairs (R. Le Poidevin, Change, Cause and Contradiction: A Defence of the Tenseless Theory of Time, 92) and that the logical contingency of causal relations must mean that simultaneous causation would lead to logical contradictions (R. Swinburne, The Christian God, 82, and also D. H. Mellor, Real Time II, 108–10).

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if there were an eternal light, so there would be an eternal illumination.14

The widely held medieval position which Bonaventure summarizes is assuming that there can be a luminous body created at an instant i1 such that it exercises its causal powers in the very same instant in which it comes to be, i1. Adding the further assumption that the velocity of light is so great that it is propagated instantaneously, medieval thinkers therefore thought that not only could a luminous body come to be and act causally at an instant i1 but its very effect could come to be and start existing at i1, because the causality effecting it had been propagated instantaneously. It is not surprising that the empirical difficulties of measuring light would have led many thirteenth-century thinkers to assume that it was propagated instantaneously, but Albert at least seems to have thought that there was an additional argument from causal necessity which pointed to the necessity of the causal relations in illumination. Taking ‘illuminating’ as a necessary property of an ‘illuminator’ qua illuminator, he concluded that there could be no instant 14 ‘Aliqua creatura corporalis est, quae simul in eodem instanti est, et operatur, sicut lux statim cum est, lucet; et Augustinus dicit quod lux et splendor sunt coaeva, et si esset lux aeterna, splendor esset aeternus’, In Sent. 2. 3. 2. 1. 2 ad 3. See also Aquinas, ‘invenitur aliqua mutatio corporali in instanti, sicut illuminatio, et huiusmodi’, Quaest. Quodlib. 11. 4. 1 ob. 1. See also the ‘subitus’ ascent of bodies to heaven in an instant, In Sent. 3. 22. 3. 2b ob. 1; In libros de Sensu et Sensato 1. 16 [245]; and Quaest. Disp. de Ver. 29. 8 sed con. 8; Sum. Theol. 1. 63. 5; Sum. Con. Gen. 2. 19 [960]; Peter of Tarentaise, In Sent. 2. 6. 2. 1 ad 1; Albert, Phys. 4. 2. 7 (4.1, 249, 80 f.). Henry of Ghent, ‘et facta est lux, Dicit ergo ‘‘fiat’’ inquam; non per successionem et materiae successivam transmutationem, sed subito, quia nihil est, quod in materia eius potentiae possit resistere’, Lect. Ord. (36, 75, 50–5).

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between the illuminator being luminous and the illuminating of the effect. Otherwise, if there were an instant intervening, there would be the (absurd) possibility of there being a substance that could exist without its necessary property of ‘illuminating’.15 15 Albert, ‘Causa enim essentialis et univoca non videtur praecedere causatum suum secundum durationem, sicut luminosum coaequaevum est radio suo et pes in pulvere coaequaevus est vestigio. Illa autem, quae propter nimiam suam excellentiam nihil agit sibi univocum et extra omnem proportionem distat a quolibet suo causato, habet praecedere causatum, sicut praecedit dans aliquid datum suum.’ Phys. 8. 1. 12 (4.2, 573, 6–19). The impetus for viewing causal relations as necessary was taken as arising from Aristotle’s text, Post. Anal. 2. 12, on which see Albert, Meta. 2. 9 (16.1, 101, 19) and 8. 2. 1 (16.2, 414, 33); In Sent. 1. 8. A. 12 (Borg. 25, 236). Robert Kilwardby, In Sent. 2. 1 (7, 104). Due to the problems raised by Islamic Occasionalism (on which D. Salmon, ‘Algazel et les Latins’, 103–27; M. Fakhry, Islamic Occasionalism and its Critique by Averroes and Aquinas, 56–83, 139–208; R. Shanab, ‘Ghazali and Aquinas on Causation’, 140–50), thirteenth-century thinkers were keen to distinguish between a necessity influencing the cause to bring about the effect and the necessity we are discussing here, which was the necessity of the effect given the occurrence of the cause, an occurrence which may well have come about contingently. Aquinas differed from some of his contemporaries in concluding that simultaneity of causation was not required for causal necessity. For further details, W. Wallace, ‘Aquinas on the Temporal Relation Between Cause and Effect’, 569–84. Albert sometimes uses language which suggests an empirical basis for his belief in simultaneous causation, ‘Video in inferioribus quosdam gradus simultatis causae et causati; quaedam enim agunt quasi actione materiae, id est, quod in sua actione producendo species similes sibi, indigent materia quae recipiat, et ex qua ipsa species educatur de potentia ad actum, sicut elementa, et omnia illa indigent tempore in sua actione, ita quod actum ipsum non potest simul esse cum suo agente tempore. Video alia quae non agunt nisi actione formae suae, sicut lux in luminoso et similiter ea quae procedunt actu lucis, ut colores ad oculum vel ad speculum: et video, quod illa non indigent tempore, propter hoc quod praesentia eorum sufficit generationi et illorum generata sunt simul tempore cum ipsis.’ In Sent. 1. 9. B. 5 sed con. 4 (Borg. 25, 279–80), but the argument is from the conceptual nature of types of causation and so it is not a properly empirical argument.

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Albert’s argument is not particularly convincing because it slips and moves carelessly between the property of being luminous and the bringing about of the illumination in the effect. Roger Bacon pointed out this problem particularly well in noting that the argument fallaciously confused the illuminator qua illuminator and the illuminator qua illuminating. As he saw only too well, a temporal lapse between the cause’s transmitting of the effect and the effect’s becoming luminous would not mean that the substance itself had existed at any time without its necessary effect of ‘illuminating’, or, as we might more carefully say, without its necessary effect of ‘propagating illumination’.16

( B ) M OV E M E N T AT A N I N F I N I T E V E LO C I T Y The argument from infinite velocities to simultaneous causation took at least two distinct forms: an argument based upon ‘resistance to the cause’ and an argument based upon the ‘power of the cause’. The arguments, and indeed the discussion of this point, take their point of origin from Aristotle’s text, but the attitudes of medieval writers varied considerably. The argument from ‘resistance to the cause’ was relatively straightforward. It assumed that there was an inverse relationship between the velocity of causal propagation and the resistance of the medium in which it 16 Opus Maius, Multiplicatio Specierum 5. 3 (529). Bacon seems to have believed that the possibility of causation in an instant entailed the possibility of the existence of an instant without a time, something which he considered to be incoherent. Opus Maius, Perspectivae 1. 3 (2, 71).

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was propagated. Where there was no resistance this would therefore entail that the velocity of the causal propagation was infinite, as for example in a vacuum where, as Aquinas put it: If something is moved in a vacuum, it is moved in an instant because the medium does not resist the moving thing.17

Although this might seem an initially attractive position most thirteenth-century thinkers seem to have appreciated the absurdities that it led to, especially when reflection focused upon the case of the heavenly bodies. The heavenly bodies were thought of as objects rotating around the earth, impeded by nothing in their rotation and so effectively existing in a vacuum. This means that they should all have rotated at precisely the same infinitely fast rate, yet that was patently not the case.18 17 Aquinas, ‘Si fieret motus per vacuum oporteret aliquid moveri in instanti quia vacuum non resistit aliquo modo mobili’, In Sent. 4. 44. 2. 3c ob. 2; Quaest. Quodlib. 9. 4. 4 ob. 3, because, as he himself brings out, ‘poterimus universaliter accipere, quod in quacumque proportione medium, per quod aliquid fertur, est subtilius et minus impeditivum et facilius divisibile, in eadem proportione erit motus velocior’, In Phys. 4. 12 [529]. See also Philip the Chancellor, Sum. de Bono, 1. 1. 11 (1, 108, 64–9), and Albert, Phys. 4. 2. 7 (4.1, 245, 34–40), where he responds to critics of the idea, including Avicenna’s Suff. 2. 8 and Averroes’ In Phys. 4 [71]. Clearly formulated with instances of local motion in mind, the principle that the velocity of causal propagation was inversely related to the resistance of the medium was extended to quantitative and qualitative changes by postulating a puzzling notion of ‘intrinsic resistance’ and ‘distance’ which a cause had to overcome. Thus Aquinas, for example, in discussing a change from white to black, identifies the time taken for the change as arising due to the ‘intrinsic resistance’ of the whiteness, a resistance which is further supposed to vary as the whiteness itself does, In Sent. 4. 44. 2. 3c ad 3; and 4. 11. 1. 3b. 18 Aquinas, ‘Vacuum autem dividi non potest citius vel tardius: unde sequetur quod omnia aequali velocitate movebuntur per vacuum. Sed hoc

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It was to resolve problems such as these that Averroes had suggested that velocity had to be seen as more than just a function of an object’s relationship with a medium, it must also be seen as dependent upon the power of the agent that initiated the motion. This was an attractive solution to the problem and versions of it can be found reflected in Aquinas, Albert, and many other writers of the period. Unfortunately, when the nature of God was taken into account it gave rise to a different problem: As the mover is more powerful, then so the thing which is moved will move quicker. And so it is necessary that if [the mover] were infinite it would move [the moved thing] disproportionately fast, i.e. which is to move in no time at all.19 manifeste apparet impossibile’. In Phys. 4. 12 [539]. Philip the Chancellor, ‘Demonstratio est vacuum non posse moveri in tempore. Et ratio est quia vacuum non habet proportionem aliquam ad locum; quod enim movetur localiter movetur tardius aut velocius secundum resistentiam spatii per quod est motus et secundum dispositiones corporis moti quantum ad levitatem vel gravitatem. Ergo ex quo intelligentia nullam habet istarum dispositionum, per quam comparatur ad locum, non erit mobile in tempore sicut neque vacuum.’ Sum. de Bono, 1. 1. 11 (1, 108, 64–9). 19 Aquinas, ‘Relinquitur ergo secundum eius intentionem, quod potentia infinita corporis si esset, moveret in non tempore: non autem potentia incorporei motoris. Cuius ratio est, quia corpus movens aliud corpus, est agens univocum. Unde oportet quod tota potentia agentis manifestetur in motu. Quia igitur quanto moventis corporis potentia est maior, tanto velocius movet: necesse est quod si fuerit infinita, moveat improportionabiliter citius, quod est movere in non tempore. Sed movens incorporeum est agens non univocum. Unde non oportet, quod tota virtus eius manifestetur in motu, ita quod moveat in non tempore. Et praesertim, quia movet secundum dispositionem suae voluntatis.’ Sum. Theol. 1. 25. 2 ad 3; and In Phys. 4. 12 [534]–[536]; 8. 21 [1146]. Albert, Phys. 4. 2. 7 (4.1, 245, 34–40, and 246, 77– 90). Their discussion is heavily influenced by Avicenna, Suff. 2. 8, and especially Averroes, Phys. 4 [71]. For further details, J. A. Weisheipl, ‘Motion in a Void: Aquinas and Averroes’, 467–88.

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If infinitely fast motion followed as a result of a causal influence from an infinitely powerful cause, in the case of the heavenly bodies which had no medium to impede them and which were supposed to have been set in motion by God, this should have meant that they were rotating at an infinitely fast velocity. Aquinas, at least on some occasions, appreciated the absurdity of this conclusion and so when approaching the problem from the perspective of natural philosophy he had no hesitation in rejecting the possibility of an infinite cause moving the heavens infinitely fast. Yet when approaching the same question from the perspective of theology, where the issue is a problem for God’s omnipotence, he takes the much less satisfactory approach of insisting that God could move the heavens infinitely fast but simply chooses not to do so.20 In so far as the consideration of ‘infinite velocity’ influenced medieval attitudes to simultaneous causation there 20 Aquinas deals with the problem from the perspective of natural philosophy at In Sent. 3. 18. 1. 3 ad 4; In Phys. 8. 21 [1146]–[1149]. He states the problem in its theological form as follows, ‘Praeterea, Philosophus probat . . . quod si potentia alicuius corporis esset infinita, moveret in instanti . . .’, Sum. Theol. 1. 25. 2 ob. 3, and repeated at 1. 105. 2 ob. 3. The problem seems to arise in a particularly acute form because of the assumption that God brings about effects in an instant, ‘cum Deus in instanti operetur, natura vero successive’, Quaest. Quodlib. 9. 5. 1 sed con. 3. The most effective solution to the problem would have been to distinguish between cases of infinite velocity at an instant (instantaneous) and cases of infinite velocity at a period (where the causal influence would be propogated so fast that for any instant after the cause, the effect would be the case). Unfortunately, Aquinas and his colleagues do not seem to have realized that there was a significant difference between these scenarios, hence his failure to distinguish between creation at an instant and in a time, ‘si Deus in aliquo tempore vel instanti creaturam produxit’, Quaest. Disp. de Pot. 3. 14 ob. 6.

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seems to have been a significant degree of theological expediency forcing philosophical concessions of a particularly infelicitous nature.

(C) ANGELS AND SOULS A third area in which we can see thirteenth-century thinkers making use of the notion of simultaneous causation concerns angels and souls. We shall be focusing more particularly on the durational implications of angels and souls later, when we examine the notion of aeviternity. In the present context the focus will be merely the causal sequences attributed to them. One of the issues that was very important to thirteenthcentury thinkers was the recognition that simultaneous, or instantaneous, causation was the basic type of causation exercised by angels and souls. A particularly clear example of this can be seen in Tarentaise’s account of the angels’ fall: The interior spiritual motions of the angels are simple. And (as) many indivisible motions, of which one could be the cause of another, could exist simultaneously, in different respects (secundum diversa). Then (so) these four were simultaneous: the desire of Lucifer, his beckoning the others; their seeing him and their agreement with him.21 21 ‘Motus enim interiores angelorum spirituales simplices sunt: et simul secundum diversa plures motus indivisibiles, quorum unus esset causa alterius, esse potuerunt: unde simul fuerunt haec quatuor: appetitus Luciferi; nutus quidam ad alios; eorum visio; consensus utrorumque . . .’ Peter of

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Here Peter of Tarentaise is describing the transition of the angels from a good state to an evil state, a transition which was causally influenced by Lucifer, the leader of the evil angels. According to Tarentaise’s understanding there are basically four events which are simultaneous: (1) Lucifer chooses to be evil (2) He communicates his choice to the other angels (3) The other angels see and understand his choice (4) They agree with him and decide to follow him The question of what exactly occurred ‘simultaneously’ in the case of the angels was much debated by thirteenthcentury thinkers and there was widespread disagreement with the type of approach taken by Peter of Tarentaise. Aquinas, for example, insisted that there had to be a small period (mora) between the creation of the angels and their fall, but he wasn’t willing to call it a ‘time’, whilst Albert, sharing his basic intuition, seems to have been quite happy referring to the small period as a ‘time’.22 Tarentaise, In Sent. 2.6.2.1 (2, 58). Aquinas, ‘licet simul daemones peccaverint, tamen peccatum unius potuit esse aliis causa peccandi . . .’, Sum. Theol. 1.63.8 ad 1; 3.8.7 ad 2; In Sent. 2.6.1.2; Super Evang. Ioan. 8.6; Bonaventure, Hexaemeron 22 [3]. 22 Aquinas, ‘Unde nihil prohibet simul et in eodem instanti esse terminum creationis, et terminum liberi arbitrii’, Sum. Theol. 1. 63. 5; and ‘quidquid est in merito, est a Deo; et ideo in primo instanti suae creationis angelus mereri potuit’, ibid ad 3; and In Sent. 3. 18. 1. 3. Aquinas nevertheless insisted that a de facto small gap (a ‘mora’) must pass between the actual choice and the receipt of the consequences of that choice, whether it be a choice for good or for evil, ‘dicendum quod angelus est supra tempus rerum corporalium; unde instantia diversa in his quae ad angelos pertinent, non accipiuntur nisi secundum successionem in ipsorum actibus. Non autem potuit simul in eis esse actus meritorius beatitudinis, et actus beatitudinis . . .’, Sum. Theol. 1. 62. 5 ad 2.

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Although there was disagreement about the precise details of which angelic motions were simultaneous, thirteenthcentury thinkers all seem to have accepted that instantaneous changes do in fact occur, especially in the case of non-discursive intellectual operations, and they can be iterated into causal sequences which occur simultaneously. Aquinas summed up the position as follows: If local motion leads to alteration, it is not possible that in the same instant the alteration and the local motion should be terminated. But if there are instantaneous changes then it is possible for the first and second changes to terminate simultaneously and in the same instant; as for example happens when in the same instant in which the moon is illuminated by the sun, the air is illuminated by the moon. It is manifest that creation is instantaneous and similarly the free will in angels, for it doesn’t need discursive and successive reasoning . . . so nothing prevents both the terminus of creation and of free will being simultaneous and occurring in the same instant.23

23 Aquinas, ‘si motus localis sequitur ad alterationem, non potest in eodem instanti terminari alteratio et localis motus. Sed si sunt mutationes instantanae, simul et in eodem instanti potest esse terminus primae et secundae mutationis; sicut in eodem instanti in quo illuminatur luna a sole illuminatur aer a luna. Manifestum est autem quod creatio est instantanea et similter motus liberi arbitrii in angelis; non enim indigent collatione et discursu rationis, . . . Unde nihil prohibit simul et in eodem instanti esse terminum creationis, et terminum liberi arbitrii.’ Sum. Theol. 1. 63. 5. On the impossibility of a successive ‘motion’ (motus) in an instant, Aquinas, ‘in primo instanti quo res est, incipit illam actionem, non tamen illa actio est in illo instanti, sed in tempore . . . . Motus . . . not est in illo instanti, quia motus successivorum est’, In Sent. 3. 18. 1. 3. The simultaneity of intellectual operations was also applied to acts of self-consciousness, ‘simul dum aliquis sentit, sentit se sentire’, Aquinas, Quaest. Disp. de Ver. 29. 8 ad 4.

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This particular consideration of free will brings to the fore a serious problem of coherence with which models of simultaneous causation struggle. If, as thirteenth-century thinkers were willing to concede, acts of free will were instantaneous and could terminate simultaneously, then what was there to prevent someone willing p instantaneously and immediately willing not-p instantaneously so that p and not-p were the case simultaneously? It is not clear that medieval thinkers explicitly considered this question, but the development of the distinction between priority of nature and temporal priority may well indicate that they were at least broadly aware of the problem. One of the most standard objections to simultaneous causation is that it cannot account for causal direction and as a result of this it leads to contradictions. But if the separate elements of a simultaneous causal sequence could be privileged, with some being ‘prior in nature’ to others, then both these problems can be reduced, if not eradicated. This is such an apparently simple solution to the problem that it is not surprising that towards the end of the thirteenth century we start to find thinkers going so far as to distinguish between multiple ‘instants of nature’ which were able to contain a causal sequence within a single instant of time.24 24 The earlier thirteenth-century approach was simply to distinguish orders of nature and time. Aquinas, ‘esse est prius quam agere natura, non tempore de necessitate’, In Sent. 3. 18. 1. 3 ad 1; Albert, ‘duratio est consequens esse durans secundum naturam et non secundum tempus’, Phys. 8. 1. 12 (4.2, 573, 51–3). Bonaventure used slightly different terminology, distinguishing between an order of nobility and an order of duration, but we can see that the import was similar as the former notion seems to have assumed that the extremes were ‘simul’ whilst the latter did not. In Sent. 1. 40. 1. 1 ad 3. On the late-thirteenth-, early-fourteenth-century development of this

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In the three areas above, in which thirteenth-century thinkers discussed simultaneous causation we have seen that they approached each discussion with a presumption that simultaneous causation takes place. In the case of illumination the presumption was based upon the practical difficulties of measuring the velocity of light. In the case of infinite velocities and angelic willing the presumption was based upon a crude notion of infinity which treated it as a specific quantity. This meant that the concept of ‘infinitely fast’ was understood as entailing no quantity and so causal propagation was necessarily propagated instantaneously. Contemporary philosophers would not find any of these presumptions acceptable. We have empirical evidence about the velocity of light and we now know that it is propagated at a specific velocity. We also have a much more sophisticated understanding of infinity and can express notions of infinitely fast in ways that do not entail zero duration. Yet to do this is not to engage medieval philosophers in an argument about the coherence of simultaneous causation. They never asked the question whether simultaneous causation could occur. They were too busy taking its existence for granted.

distinction, S. Knuuttila and A. Inkeri Lehtinen, ‘Change and Contradiction: A Fourteenth Century Controversy’. Whilst this approach did at least provide a potential response to the problem that simultaneous causation could not account for causal direction (G. J. Whitrow, The Natural Philosophy of Time, 273), it did so only at the expense of creating a new and more perplexing problem of how exactly instants of nature were supposed to be explained, individuated, and related to instants of time.

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B AC K WA R D S C AU S AT I O N We have seen so far in this chapter that thirteenth-century thinkers were committed to simultaneous causation. This commitment shows that they rejected the causal theory of time’s insistence that a temporal sequence was reducible to a causal sequence. The question remaining now is the ‘extent’ of their rejection. Did thirteenth-century thinkers countenance the idea that causal sequences could run in reverse to a temporal sequence, thus allowing for backwards causation? When contemporary philosophers discuss the question of backwards causation it is customary to distinguish between backwards causation understood as changing the past, and backwards causation understood as bringing about the past. The former notion is asserting that a cause at i2 could bring it about that an E at i1 could be a not-E at i1, whilst the latter notion is simply asserting that the E at i1 is brought about by the cause at i2. Expressed in these terms, the latter notion of bringing about the past is decidedly ‘odd’, but the former notion of changing the past is patently contradictory, for it entails the conclusion that both E and not-E could exist at i1.25 25 On the distinction and the argument in favour of bringing about the past, M. Dummett, ‘Bringing About the Past’. Arguments against the notion divide into those that focus upon evidential problems in being justified in positing a case of backwards causation (A. Flew, ‘Can an Effect Precede its Cause?’), those that rule it out for ‘metaphysical’ reasons (W. L. Craig, ‘Temporal Necessity: Hard Facts/Soft Facts’, 83, although it is important to note that Craig bases his argument on the assumption of the truth of what we shall come to see later is referred to as an A-theory view of time), and those that rule it out on a priori logical grounds (R. Swinburne, The Christian God, 82, 86–8; D. H. Mellor, Real Time II, 106–8; G. Oddie, ‘Backwards Causation

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Medieval discussions do not seem to have recognized the distinction between changing the past and bringing about the past. The classic discussions of the issue tended to be almost entirely cases of changing the past, focusing in particular upon St Jerome’s fourth-century question about whether God’s omnipotence could extend to restoring a fallen virgin. Whilst some medieval figures were willing to extend God’s omnipotence over the powers of logic, the majority of thirteenth-century figures recognized that for God to change the past by restoring a virgin who had fallen, it would require a contradictory state of affairs to be the case, and so they ruled out the backwards causation which they assumed to entail such a contradiction.26 and the Permanence of the Past’). Notions of backwards causation need to be distinguished, further, from changing the truth value of propositions with a reference to a different time, on which see A. J. Freddoso, ‘Accidental Necessity and Power over the Past’, and W. L Craig, ‘Temporal Necessity: Hard Facts/Soft Facts’. There is a considerable literature on the question of backwards causation, references to which can be found in the works cited. 26 Aquinas was unimpressed by claims to extend God’s omnipotence to include a power over the past, insisting that things cease to be possible as they move into the past, ‘vel ex mutatione objecti, quod amittit rationem possibilis, quam prius habebat; potentia enim activa est respectu operabilis alicuius. Unde quando aliquid est iam determinatum ut sit praesens in actu, vel in praeteritum transiit, possibilis rationem amittit; et ideo dicitur quod deus illud facere non potest’, In Sent. 1. 44. 1. 4. In his later Summa, the impossibility is identified as arising due to a contradiction, ‘licet praeterita non fuisse sit impossibile per accidens, si consideretur id quod est praeteritum, idest cursus Socratis; tamen si consideretur praeteritum sub ratione praeteriti, ipsum non fuisse est impossibile non solum per se, sed adsolute, contradictionem implicans’, Sum. Theol. 1. 25. 4. Where Aquinas comes closest to accepting a version of backwards causation it is always causation involving non-efficient causes, as, ‘et sic passio Christi comparatur ad sacramenta sicut causa ad effectum. Sed effectus non praecedit causam.’ Sum. Theol. 3. 61. 3 ob. 1, to which he replies, ‘passio Christi est causa finalis veterum sacramentorum quae scilicet ad ipsum significandum sunt instituta’, ibid. ad 1.

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The issue of bringing about the past seems to have been a possible background consideration in discussions involving God’s grace and forgiveness, particularly as applied to people living earlier than Christ. Anselm, for example, had claimed that the Old Testament patriarchs were cleansed from their sins during their own lives (prior to the birth of Christ), in virtue of the future freely chosen sufferings of Christ. Whilst it is not entirely clear what exactly Anselm was committing himself to in advancing this claim, it does seem to involve an effect (the forgiveness of sin) occurring at a time where a significant element of the causal explanation is a contingent event occurring temporally later than that effect.27 A second aspect of this question concerned the specific case of the Virgin Mary and the doctrine of the Immaculate Conception. According to that doctrine, Mary was conceived without sin, but her sinlessness was supposed Similarly, ‘Nihil autem prohibet id quod est posterius tempore, antequam sit movere, secundum quod praecedit in actu animae: sicut finis, qui est posterior tempore, movet agentem secundum quod est apprehensus et desideratus ab ipso . . . Unde causa efficiens non potest esse posterior in esse, ordine durationis, sicut causa finalis . . .’, Sum. Theol. 3. 62. 6; also Sum. Con. Gen. 2. 16 [942]. Bonaventure, probing the issue of knowledge of future contingents considers, but rejects, the possibility that future contingents could cause knowledge prior in time to their occurrence, ‘et quia futurum contingens non habet esse nisi indeterminatum, ideo non potest intellectum iuvare ad certitudinalem cognitionem habendam de se’, In Sent. 2. 7. 2. 1. 3 ad 4. See also his In Sent. 1. 42. 1. 3, and Albert, In Sent. 1. 8. B. 13 (Borg. 25, 239). A range of medieval figures have been thought to take a contrary position on this question, including Peter Damian, Gilbert of Poitiers, William of Auxerre, Thomas Bradwardine, and Gregory of Rimini. For further details, T. Rudavsky (ed.), Divine Omniscience and Omnipotence in Medieval Philosophy; L. Moonan, ‘Why Can’t God Do Everything?’; W. J. Courtenay, ‘John of Mirecourt and Gregory of Rimini on Whether God Can Undo the Past’, 224–56. 27 Cur Deus Homo 2. 16 (2, 118, 5 to 120, 1).

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to be dependent upon Christ’s freely chosen (later) sufferings. Both Aquinas and Bonaventure were concerned about this account because it was difficult to see how Mary’s sinlessness could causally depend upon the contingent event of Christ’s freely chosen sufferings if she was born temporally before his birth.28 The doctrine of the Mass was another case where causal sequences seemed to diverge from the temporal ordering of events. Aquinas, for example was clear that the efficacy of the Mass was totally dependent upon Christ’s freely chosen death upon Good Friday. As such, His death is of course temporally before most celebrations of the Mass, apart from one exception. Ecclesial tradition, accepted by Aquinas and his contemporaries, insisted that the first mass was celebrated on Maundy Thursday, the day before Christ had freely chosen his sacrificial death on Good Friday. If that is the case then once again we have an event which is causally

28 Aquinas, ‘Beata Virgo contaxit quidem originale peccatum, sed ab eo fuit mundata antequam ex utero nasceretur.’ Sum. Theol. 3. 27. 2 ad 2; and ‘Et quamvis per fidem Christi aliqui ante Christi incarnationem sint spiritum ab illa damnatione liberati, tamen quod secundum carnem aliquis ab illa damnatione liberetur, non videtur fieri debuisse nisi post incarnationem eius . . .’, ibid. 3. 27. 3. For similar concerns amongst contemporaries, ed. L. Saggi, ‘Ioannis Baconthorpe, textus de Immaculata Conceptione’; ed. B. Hechich, De Immaculata Conceptione Beatae Mariae Virginis Secundum Thomam de Sutton O.P. et Robertum de Cowton O.F.M., 165 f. The doctrine of the Immaculate Conception seems to have occasioned more discussion at the end of the thirteenth, and beginning of the fourteenth century, where we can see Aquinas’ and Bonaventure’s concerns reiterated in authors such as Peter de Candida, de Conceptione Virginis 3. 2 ad 5 (328); Thomas de Rossy, de Conceptione Virginis Immaculatae (81–4); Andreas de Novo Castra, de Conceptionis Virginis Gloriosae 12 (223–5).

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dependent for its efficacy upon a contingent event occurring temporally later.29 It is difficult to be sure precisely how to interpret examples such as these, as thirteenth-century thinkers never identified them as raising questions about causal direction. We have seen already that of the many types of causality which thirteenth-century thinkers identified, it was the temporal location of the efficient cause which was essential in determining whether an example of causation would indeed count as bringing about the past. When it comes to theological examples involving the application of grace, or even instances of prophecy, it may well be the case that key aspects of the causal explanation need to be located temporally after the effects which they contribute to, but the efficient cause in each example would have been identified by thirteenth-century thinkers as God. God was thought of as acting outside of time and so as having no temporal relationship to the effects which were brought about. This means that the examples we have explored would not have been recognized by thirteenth-century thinkers as instances of bringing about the past. They would have instead been viewed as examples of the final type of causation which we need to examine, non-temporal causation.

29 Aquinas, ‘Et ideo, inquantum eius humanitas operabatur in virtute divinitatis, illud sacrificium erat efficacissimum ad delenda peccata’, Sum. Theol. 3. 22. 3 ad 1; ‘sacrificium autem, quod quotidie in Ecclesia offertur, non est aliud a sacrificio quod ipse Christus obtulit’, ibid. ad 2; ‘verum Christi sacrificium communicatur fidelibus sub specie panis et vini’, ibid. 3. 22. 6 ad 2; and on Aquinas’ identification of Maundy Thursday with the first Mass, ibid. 3. 81.

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N O N - T E M P O R A L C AU S AT I O N The final model of causation, non-temporal causation, exists where a cause lacking a temporal location brings about effects occurring in time. Contemporary philosophers have often focused upon this notion of causation, either as causing problems for the non-temporal God which they attribute to medieval thinkers, or else as providing solutions for medieval thinkers which would enable them to escape common philosophical problems.30 Although it seems initially logical to assume that thirteenth-century think who stress that God is ‘not in time’ would also stress that His causation cannot be in time, exegetes have never really probed the validity of this assumption. There are indeed examples of where it seems that a thirteenth-century thinker is trying to formulate a claim that would locate God and His causal activity outside of time, 30 Arguments against a non-temporally located cause either assume that it is impossible for such a cause to bring about any temporal effects at all (N. Pike, God and Timelessness, 104) or often attempt to identify specific actions which it is thought are impossible for a non-temporally located cause. Thus it has been suggested that a non-temporally located God could not ‘respond’ to prayer (N. Pike, God and Timelessness, 128) or ‘know’ or ‘love’ individuals in a temporal world (R. Sorabji, Time, Creation and the Continuum, 257–8); or even ‘forgive’, ‘warn’, or ‘punish’ (R. Swinburne, The Coherence of Theism, 228) as such actions must occur at specific times. But the proponents of nontemporal causation are not claiming that a non-temporal cause would bring about an effect without a temporal location. They are arguing that an effect would be brought about at a specific time whilst the cause has no temporal location at all. As long as the effect does indeed have a temporal location it is difficult to see why the absence of a temporal location for the cause should be as problematic as opponents of the notion seem to think it is.

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especially when the point at issue is the creation of time itself.31 But it is important to recognize that many thirteenth-century figures wanted to also assert a form of ‘togetherness’ between God and creation. We saw at the end of the last chapter, for example, that thirteenth-century thinkers could appeal to the terminology of ‘concomitantia’ to express relationships between durations and Aquinas was even willing to refer to God’s togetherness with creation as an example of ‘simultaneity’: And thus it follows that just as inferior agents which are causes of the coming to be of things, must exist simultaneously with the things which come to be, as long as they are coming to be, so also the divine agent, which is the cause of existing in act, is simultaneous with the existence of the thing in act. Hence if the divine action were removed from things, things would fall into nothingness, just as when the presence of the sun is removed, light ceases to be in the air.32 31 Albert, ‘Quod autem in divinis non possint causari prius et posterius secundum tempus . . . quia divina . . . nec tempore diffinita: ergo si est ibi prius et posterius, hoc erit secundum intellectum vel causam, vel dignitatem naturae vel morum’, In Sent. 1. 9. B. 5 (Borg. 25, 279). Bonaventure introduced a distinction between a principium originale and a principium initiale. According to this distinciton if a particular possesses a ‘principium initiale’ this entailed that it was durationally later than its cause. If however it possessed merely a ‘principium originale’ then Bonaventure felt that this was compatible with there being no temporal or durational element in the causation and this notion could therefore be applied to God. In Sent. 1. 8. 1 dub 7; also, Quaest. Disp. 5. 2 ad 6. 32 ‘Unde habetur quod sicut agentia inferiora, quae sunt causa rerum quantum ad suum fieri, oportet simul esse cum iis quae fiunt quandiu fiunt; ita agens divinum, quod est causa existendi in actu, simul est cum esse rei in actu. Unde subtracta divina actione a rebus, res in nihilum deciderent, sicut remota praesentia solis lumen in aere deficeret.’ In Phys. 2. 6 [195]. Note also Aquinas’ commitment to causal contiguity, In Sent 2. 2. 2. 2. 1.

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We have seen in the previous chapter that the word ‘simultaneous’ (simul) does not necessarily always have a temporal import, so this passage is not necessarily asserting a temporal simultaneity between God and creation. The atemporality which we shall later see that Aquinas ascribed to his God makes it difficult to draw the conclusion that Aquinas would want to be suggesting a straightforward temporal causal relation in this passage. Yet the language of ‘simultaneity’ indicates that he would not be entirely happy with a notion of causation that radically contrasted God with the temporal causation apparent in creation. It is difficult for us, at this point in the study, to be entirely sure what Aquinas is trying to affirm in this passage. It may be that he is merely using the unfortunate term ‘simultaneous’ because there are no more suitable terms which he can use to affirm a notion of ‘togetherness’ between God’s causation and His effects. If this is the case then it raises the possibility that God’s relationship to time and creation is considerably more complex than commentators on Aquinas typically appreciate. Although we can offer no final resolution of the matter at this stage of the study, we will be probing this issue through following chapters and offering an explanation in the final chapter.

C O N C LU S I O N In this chapter we have focused upon thirteenth-century views about the temporal relations of priority and posteriority. We began by examining essential terminology such as

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‘before’ and ‘after’ and we saw that there were a variety of temporal and non-temporal ways in which these terms could be used. The central question which we have investigated in this chapter has been the question of whether thirteenth-century thinkers would have accepted that temporal relations can be reduced to more fundamental causal relations. Thirteenthcentury accounts of simultaneous causation undermine this possibility, as the existence of simultaneous causation implies that causal orderings and temporal orderings could be, at least to some extent in thirteenth-century thought, uncoupled. The medieval identification of a non-temporal concept of prior by nature and a notion of instants of nature seems to indicate that rather than reducing temporal relations to causal sequences, they seem to have believed that, at least in some contexts, it was possible to identify what seem to be causal sequences within an instant. We saw this principle at its most extreme in the application of simultaneous causation to angels where they were thought to be capable of making decisions and influencing others, all in a single instant. There can be little doubt then, that for thirteenthcentury thinkers temporal and causal orderings were thought to be irreducibly distinct from each other. As part of our general investigation of causation and causal sequences we explored the notion of backwards causation. Although the majority of thirteenth-century thinkers are clear in dismissing the notion, we have seen that there are a few theological doctrines which seem to entail a causal explanation where key elements of the cause are temporally

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later than the effect. Whether this amounts to what contemporary philosophers would think of as backwards causation (in the sense of bringing about the past) is not entirely clear, as ultimately God was thought to be the agent at work in these examples and His causation was clearly not temporally later than the effects. When it comes to examining instances of non-temporal causation we looked briefly at God’s causation and the extent to which it is temporally related to its effects. We shall have to return to the specific issue of God’s relation to time in the final chapter, but at this point in our study it should be clear that divine causation would no more conform to a version of the causal theory of time, than any of the other notions of causation which we have examined in this chapter.

4 Relations and Reductions

We have seen that thirteenth-century accounts of time agree that time is composed of instants, periods, and the relations of temporally before, after, and simultaneous, which hold between the instants and periods. In the last two chapters we have been focusing upon the medieval understanding of ‘simultaneity’, ‘priority’, and ‘posteriority’; and through the examination of these concepts it has begun to become clear that thirteenth-century thinkers were committed to a reductive analysis of time. What precisely this means, and the implications which it had for thirteenthcentury thought, will be the focus of the following two chapters. This chapter will focus in particular upon relational aspects, examining how relational theories contributed to accounts of time and the extent to which temporal relationism cohered with wider thirteenth-century thought about relations.

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R E L AT I O N S A N D R E L AT I O N I S M Thirteenth-century reflection upon relations was relatively sophisticated, probably because theological needs had long before shown that a sound understanding of relations was absolutely essential for constructing a coherent account of the doctrine of the Trinity. Although there remained differences of nuance throughout the medieval period, especially in matters of classifying and categorizing relations, medieval accounts of relations were largely homogenous.1 Medieval thinkers took their point of departure from the fact that a relation was simply a referring of one thing to another. From this starting-point they distinguished four significant aspects of a relation: the subject (subiectum), the term (terminum), the relation (relatio) itself, and the foundation (fundamentum). Of these four notions, the first three are relatively straightforward. The subject, the subject1 Whilst Aquinas occasionally preferred to analyse the different categories of relation in terms of quantity, action, or passion (In Sent. 3. 5. 1. 1 sol. 1; Quaest. Disp. de Pot. 8. 1), Albert seems to have preferred a much broader analysis, Sum. Theol. 9. 38 (34.1, 288, 31–42). Nevertheless, the most common starting-point for many thirteenth-century thinkers was Aristotle’s distinction between causal, numerical, and psychological relations, Meta. 5.15 (1020B25–1021A11). By ‘causal’ relations he meant straightforward instances of the relations between causes and effects. Numerical relations were basically quantitative relations, involving ratios and sometimes instances of identity when the focus was upon identity as arising due to the oneness (in some respect) of particulars. Note, Aquinas, Sum. Con. Gen. 4. 14. Psychological relations were, as their name signifies, mental relations, involving examples of knowledge and intention. Psychological relations might well encompass causal and numerical relations in particular contexts where those relations involved a mental element.

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of-the-relation is the particular which is actually related to something else. The term is that which the subject is related to, whilst the relation is simply the reference of the subject to the term, the way in which the subject is being ‘referred’ to the term of the relation. The foundation of a relation was understood as the aspect of the term which accounted for the existence of a relation at all.2 If we take as an example of a relation, the relation of descent which Jesus had from Mary, then we will be able to see how these four aspects of an account of relations actually integrated into a single theory. In such a relation, Jesus would be the subject of the relation and Mary the term, as it is Jesus who is being referred to Mary. The relation itself is the type of referral that is being made and in this case it is the fact of Jesus’ descent from Mary. The foundation of the relation would be the aspect of Mary which accounts for Jesus having this relation of descent. This would be her motherhood, as it is the ultimate basis for Jesus’ relation of descent. 2 Aquinas, ‘relatio . . . consistit tantum in hoc quod est ad aliud se habere’, In Phys. 3. 1 [6]; In Sent. 1. 33. 1. 1 ad 1; Quodlib 12. 1; Quaest. Disp. de Ver. 21. 1 ob 9; Sum. Theol. 3. 2. 8 ob 1. Robert Kilwardby, ‘omne prius et posterius se respicientia ordinem habent . . . .Relatio est alicuius ad aliquid, ordo est relatio, ergo est ad aliquid’, In Sent. 2. 4 (2, 17, 6–14). Albert, Meta. 5. 3. 7 (16.1, 267, 40–3); Lib. de Praedic. 4. 2 (Borg. 1, 221–6); Sum. Theol. 9. 37 (34.1, 287, 48–70). Albert seems to have preferred to use the word ‘respectus’ instead of Aquinas’ ‘fundamentum’, as in Meta. 5. 3. 7 (16.1, 266, 79–83). For further details, A. Krempel, La Doctrine de la relation chez St. Thomas, 432 f. For an introduction to medieval accounts of relations, M. Henninger, Relations: Medieval Theories 1250–1325; and J. Hanagan, ‘The Contribution of Robert Kilwardby to Thirteenth Century Thought on the Doctrine of Relation’. Focusing more particularly on Aquinas’ theory, C. G. Kossel, ‘Principles of St. Thomas’ Distinction between the Esse and Ratio of Relation’, 93–107.

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So far the basic parameters of a medieval account of relations are relatively straightforward, but two further distinctions were introduced by medieval thinkers, that between real relations and relations of reason and that between mutual (mutuum) and non-mutual relations. The crucial distinguishing difference between a real relation and a relation of reason was the fact of whether the subject had a dependence upon its term. A child is dependent upon its mother and so medieval thinkers had no hesitation in labelling the relation between a child and its mother as a real relation. The mother, at least in respect of the existence of her motherhood, depends upon the existence of the child, and so she too has a real relation to the child. Where both the subject and term have a real relation to each other, then thirteenth-century thinkers described the relation as mutual.3 Not all relations are real relations because as far as medieval thinkers were concerned, not all relations denote a dependence. A typical example of the kinds of relations which they cited as involving a non-dependence would have included epistemological relations, those that hold between a knower and the object of knowledge. Whilst it is true that a knower depends upon the object of knowledge for his or her knowledge, the object which is known does not 3 Aristotle, Cat. 7 (7B15–8B13). The medieval terminology for this distinction varies from author to author. Bonaventure, for example, talks of a distinction between a relation ‘secundum esse’ and a relation ‘secundum dici’, In Sent. 1. 9. 1. 2 ad 4. Albert, instead, talks of a relation said ‘properly’ (proprie), which is distinguished from a relation said non-properly (non proprie) when one of the relations is merely one of reason. Sum. Theol. 9. 39. 1 (34.1, 294, 7–13).

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depend in any sense upon the knower, so an example such as this would be one in which the knower has a real relation to that which is known whilst the object of knowledge has just a relation of reason to the known. As one of the elements of the relation is not a real relation this meant that epistemological relations were classified as non-mutual.4 In order to fit temporal relations into this basic relational theory, thirteenth-century thinkers needed to address at least three questions. What precisely is the subject and term of a temporal relation? What is the foundation of the relation? And are temporal relations real relations or simply relations of reason? Medieval thinkers do not seem to have explicitly considered these questions, yet they provide answers to all of them within their wider discussions of time and temporal reduction.

4 Whilst one of the crucial distinguishing features of a psychological relation was that it was considered not always to give rise to a ‘mutual’ (mutuum) relation, Albert, Lib. de Praed. 4. 7 (Borg. 1, 234), it should not be assumed that only psychological relations support relations of reason. Both causal and numerical relations can also fail to be real relations, as for example when either the subject or term are the same thing, when the subject itself is a relation or when the term does not exist; as Albert points out, ‘Ea autem quae vere relativa sunt, ita quod utrumque ipsorum relationem importat ut exercitam, non omnino destruuntur altero mutato. Pater enim est, qui sui aliquid habet in filio, et ideo patre mortuo manet adhuc aliquid quo filius dicebatur ad patrem, et ideo filius non omnino cessat esse filius, sed cessat esse filius ex eo quod habitudo cessat, quae fuit inter patrem et filium, et hanc diximus esse in anima et non in re ipsa’, Meta. 5. 3. 7 (16.1, 266, 95 f.). For further details see Aquinas, Quaest. Disp. de Ver. 1. 5 ad 16; In Sent. 1. 26. 2. 1; Quaest. Disp. de Pot. 7. 11; Sum. Theol. 1. 13. 7.

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TEMPORAL REDUCTION Following Aristotle’s general approach, thirteenth-century thinkers were committed to a reductive understanding of time. They viewed time and the temporal relations constituting it as reducible in some sense to motion and the motion relations constituting the motions themselves. In some cases mid-thirteenth-century thinkers seem to have gone further and also believed that the very topology of time and motions could be reduced still further to the topology constituting the space in which motions were located. Reductive approaches that would reduce time to motion in crude simplistic ways had been firmly ruled out by Aristotle, on the basis that time and motion have very different kinds of properties. Motion, for example, has the property of being ‘in’ specific things whilst time is ‘equally everywhere and with everything’. Furthermore, he pointed out that motion can have variable velocities whilst time cannot. Whilst we can measure velocity and changes in velocity in terms of time, there is nothing comparable that we could use to measure the flow of time and any variation in that rate of flow.5 5 Aristotle, Phys. 4. 10 (218B9–12). On the medieval acceptance of this argument, Aquinas, In Phys. 4. 16 [568]. For the second argument, Phys. 4. 10 (218B13–18) and Aquinas’ comments at In Phys. 4. 16 [569]. Of Aristotle’s arguments the second seems to be appealing to implicit verificationist principles, for we can certainly make sense of the idea that time could pass faster, it would just mean that with all the processes in the world speeding up there would be no way of confirming that it was actually taking place. More worrying for the ultimate coherence of the arguments is the fact that this is supposed to be a topological question about the reducibility of time and yet Aristotle has introduced metrical considerations in order to resolve the matter.

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Whilst medieval thinkers accepted Aristotle’s position in this regard they were also aware of the need to incorporate time into his categorical framework. In that framework he divides reality into substances and accidents. Substances had an existence that we might spell out, somewhat simplistically, as independent. They could exist as real, concrete particulars in the world around us. Contrasted with substances were accidents which could only exist by inhering in a substance. Typical examples of substances might include a house or a horse whilst examples of accidents might include colours such as brown. Whilst a horse can exist in reality in its own right, a colour such as brownness can only exist as an aspect of a horse or a house, and so the accident brown must inhere in a substance. Leaving aside any philosophical problems with this distinction between substances and accidents, the key issue for medieval thinkers was that relations were accidents and so temporal relations had to be viewed as accidents inhering in some other substance. This had the effect of meaning that instants themselves could not be viewed as having a substantival existence and that questions about the existence of instants, periods, and indeed time itself had to be reduced to more fundamental questions about the ‘substance’ of time.6 6 Albert, Lib. de Praed. 4. 1 (Borg. 1, 149–303); 4. 10 (Borg. 1, 241); Aquinas, Sum. Theol. 3. 77. 2 ad 1; In Eth. Nic. 1. 6; In Sent. 1. 27. 1. 1 ad 2. The substantiality, or otherwise, of temporal elements has been a central issue disputed in the philosophy of time for several centuries. Advocates of time as a substance insist that the instants and periods constituting time can exist independently of change. This position is sometimes referred to as the ‘absolutist’ position, as ‘substantialism’ (P. Horwich, ‘On the Existence of Times, Spaces and Spacetimes’), and even as ‘super substantialism’ (J. Earmen, World Enough and Space-Time: Absolute versus Relational Theories of

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In order to accommodate time to the more fundamental ‘categorical’ framework, medieval thinkers such as Aquinas and Albert were content to follow Averroes’ identification of the Primum Mobile as the formal subject or material cause of time.7 This effectively made its motion privileged so that the Space and Time, 115). Its most historically significant proponents have been Newton (‘On Time’, 203–11) and S. Clarke (H. G. Alexander (ed.), The Leibniz–Clarke Correspondence, 30–6, 45–55). Relationists claim, instead, that periods should only be thought of as existing in virtue of the relations which hold between other substances and their changing states. This position is sometimes referred to as ‘reductionism’ (L. Sklar, Space, Time and Spacetime, 167–82, 191–4) and its most significant historical proponent has been Leibniz (Letters to Clarke, 3 sec. 6; 4 sec. 6, 13, 15; 5 sec. 52, 55–60, in H. G. Alexander (ed.), The Leibniz–Clarke Correspondence, 26–7, 37–8, 75– 9). For a general introduction to the concepts and issues, P. Turetzky, Time, 71–84. There have been attempts to reduce the relational–absolutist debate to a more fundamental debate about the nature of motion stages (J. Earmen, World Enough and Space-Time: Absolute versus Relational Theories of Space and Time, 91–110), and a further development has recently arisen in the suggestion that time might perhaps be better construed as a ‘property’ rather than as a substance or a relation (P. Teller, ‘Space-Time as a Physical Quantity’; L. Sklar, Space, Time and Spacetime, 167–82, 191–4). The fact that medieval thinkers were able to distinguish the basic relational and absolutist (substantivalist) positions is made clear by Avicenna, for example, who expresses the absolutist position as thinking that time was an ‘esse substantiam existentem per seipsam’, Suff. 2. 10. 7 Aquinas, In Sent. 1. 19. 2. 1; 1. 37. 4. 3; 2. 2. 1. 2; 4. 11. 1. 3; Sum. Theol. 1. 10. 6. Albert, Phys. 4. 3. 5 (4.1, 268, 16 and 266, 63); 4. 3. 17 (4.1, 290, 38); In Sent. 1. 30. B. 4 ad 1 (Borg. 26, 93); Meta. 5. 3. 1 (16.1, 257, 80). Ps. Aquinas, de Instan. 1; Siger of Brabant, Sup. Lib. de Causis 11 (62, 12–13). Albert even goes so far as to suggest that time should be defined in terms of the Primum Mobile, Sum. de Creat. 2. 3. 2 (Borg. 34, 345). Aquinas sometimes referred to the Primum Mobile as the ‘first motion’, In Phys. 4. 17 [576], and Albert occasionally referred to it as the ‘principle motion’, Phys. 4. 3. 5 (4.1, 267, 39– 48). Kilwardby refers to it as the ‘first heaven’ (primi celi), de Temp. 10 [39] (18, 3). Some modern commentators, especially those from a scholastic background, have struggled to make sense of references to the Primum Mobile. The tendency in such authors seems to be to simply ignore it, or to substitute terms such as ‘mobile’ or ‘mensura’, thus losing the fundamental

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very references to time were, in some sense, supposed to be reducible to the durational quantity of the motion of the Primum Mobile. This meant that references to instants, periods, and the temporal relations holding between them were to be thought of as reducible to the ‘moments’, motion stages, and relations holding between such motion elements, and the very question of whether something could be said to be in time or not could itself be reduced to whether it was related to the Primum Mobile.8 As Aquinas helpfully explained it: it must be known that there is one first motion which is the cause of all other motion. Hence, whatever is mutable in existence is sense of what thirteenth-century thinkers were trying to claim. See J. M. Quinn, ‘The Concept of Time in Albert the Great’, 34; J. Lottini, Compendium Philosophiae Scholasticae, i. 519; and I. Gredt, Elementa Philosophiae Aristotelico-Thomisticae, i. 242–9. The thesis that time can be reduced in some sense to the heavenly bodies has been labelled as ‘celestial reductionism’. On which, P. Ariotti, ‘Celestial Reductionism of Time: On The Scholastic Concept of Time from Albert the Great and Thomas Aquinas to the End of the Sixteenth Century’, 93. 8 Averroes, ‘Tempus igitur sequitur hunc motum: et iste motus accipitur in definition eius’, In Phys. 4 [132]. Aquinas, Sum. Theol. 1. 10. 6; In Sent. 1. 19. 2. 1; 1. 37. 4. 3; 2. 2. 1. 2; 4. 11. 1. 3; In Phys. 3. 2 [285]; 6. 2 [762]. Albert, In Sent. 1. 8. A. 12 (Borg. 25, 236). Ps. Aquinas, de Instan. 1. Theodoric, Trac. de Nat. et Prop. Contin. 4 (3, 266, 99–101). Kilwardby, de Temp. 2 [11] (9, 2– 14). It should be noted that the connotations of the Latin word ‘motus’ are much broader than that of the English word ‘motion’, being nearer to what we would think of as ‘change’. For ‘motus’ describes not only physical motion, but any actualization of a potentiality, whether it be qualitative or quantitative. On the issue of a relationship to the Primum Mobile as denoting a presence in time, see Alexander of Hales, ‘Notandum quod quorumdam est passibilitas a contrarietate principiorum intrinsecorum, et illa sunt corruptura; quaedam autem non, et illa non sunt corruptura. Passibilitas a contrarietate subiacet mobili continuo quod est in ratione duplicis continui, scilicet caeli; et quia virtus illius mobilis mediante motu influit super illud passibile,

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such because of that first motion, which is the motion of the first mobile object . . . time is consequent upon only the one first motion by which all other motions are caused and measured . . . 9

An appeal to the Primum Mobile was undoubtedly felt by many medieval thinkers to be helpful, not the least reason being that in virtue of its causal role a relation of dependence sicut motus mobilis non est totus simul, sed secundum prius et posterius cum successu, ideo actus et opera quae sunt in tali passibili, et in eis quorum hoc passibile est principium, sunt successiva vel habent diversos actus successive. Et hoc intelligendum de actibus illis quos habent mediante illo mobili, ut calere, frigere, sedere, currere, et consimilibus. In aliis autem quae sunt extra virtutem huius mobilis, non est actus vel operatio successiva, quantum est de se; nec etiam diversi actus vel diversa opera aut passiones successivae erunt, cum in quibusdam diversi actus, et in aliis diversae passiones secundum prius et posterius sunt sine tempore et successione.’ Glossa in Sent. 2, Appendix (423, 4–19). Note also Philip the Chancellor, ‘Prius enim et post non est in tempore nisi ex motu mutabilium, nunc autem in essentia mensura est immutabilium. . . . Ipsum vero nunc cum prius et posterius producit tempus, ita quod sicut in motu est id quod mutatur sic in tempore est ipsum nunc, et respondet tempus motui, nunc vero ei quod transmutatur respondet prout est principium futuri et finis preteriti. Quod si id quod mutatur sine mutatione acciperetur, acciperetur esse ipsius nunc sine respectu ad preteritum et futurum’ Sum. de Bono, 1.1.4 (1, 53, 44–57). 9 ‘sciendum est, quod est unus primus motus, qui est causa omnis alterius motus. unde quaecumque sunt in esse transmutabili, habent hoc ex illo primo motu, qui est motus primi mobilis . . . tempus non consequatur nisi unum primum motum, a quo omnes alii causantur et mensurantur’, In Phys. 4. 17 [574]. Albert, ‘tempus non est passio nisi unius mobilis per motum suum, et hoc est primum mobile; et hic motus percipitur in omni motu sicut causa in suo effectu . . . Si enim motus caeli non esset, non esset aliquid motus in inferioribus, sive in anima sive in aliis, qui faceret aliquam in inferioribus transmutationem’, Phys. 4. 3. 4 (4.1, 266, 85 f.). Aquinas refers, or alludes, to the causal role of the heavenly bodies at Quaest Disp. de Malo 16. 7 ob. 16; 16. 9 ob. 7; 16. 10 ob. 5; In Sent. 1. 37. 4. 3. Despite its causal role in motion, medieval thinkers were keen to stress that ‘free will’ was not subject to the Primum Mobile. See Albert, Sum. Theol. 5. 23. 2.2. B ad 5 (34.1, 130, 89–99), and Aquinas, Sum. Theol. 1. 115. 3–4.

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could be established between instants and periods, and the moments and motion stages which its motion gave rise to. With a relation of dependence, medieval thinkers were then able to view temporal relations as real relations and so they had a simple clear rationale for the existence of time as a reality rather than just a mental phenomenon. Even more fundamentally, from an appeal to the Primum Mobile medieval thinkers were able to provide a reductive explanation for the derivation and nature of the entire temporal topology. To cite Aquinas once again: everything which is moved is moved from something to something. But the first of all motions is local motion, which is motion from place to place in respect to some magnitude. But time is consequent upon the first motion. Therefore to investigate time it is necessary to consider motion in respect to place. Hence, since motion in respect to place is motion from something to something in respect to magnitude, and since every magnitude is continuous, then it is necessary that motion is consequent upon magnitude in continuity. That is, since magnitude is continuous, motion is continuous. And consequently time is also continuous.10

10 ‘omne quod movetur, movetur ex quodam in quiddam. Sed inter alios motus, primus est motus localis, qui est a loco in locum secundum aliquam magnitudinem. Primum autem motum consequitur tempus; et ideo ad investigandum de tempore oportet accipere motum secundum locum. Quia ergo motus secundum locum, est secundum magnitudinem ex quoddam in quiddam et omnis magnitudo est continua; oportet quod motus consequatur magnitudinem in continuitate, ut quia magnitudo continua est, et motus continuus sit. Et per consequens etiam tempus continuum est: quia quantus est motus primus, tantum videtur fieri tempus.’ In Phys. 4. 17 [576]. See also Alexander, ‘Et ad intelligendum hanc diversitatem, notandum quod successio ita causatur: in continuo est primum et ultimum, a quibus causatur prius et posterius in motu et tempore etc. Et est duplex continuum, vel unum

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Medieval attempts to reduce temporal properties to motion and to, more ultimately still, spatial properties, immediately fell into difficulties over the problem of changes and motions such as mental events, which do not occupy any spatial location. Amongst mid-thirteenth-century figures, Kilwardby seems to have engaged most vigorously with this problem and his solution was relatively simple. He went to considerable lengths to argue that all such changes do in fact fit a ‘spatial’ reductive model because they occur in substances which are themselves located in a spatial continuum.11 in ratione duplicis, scilicet spatii et continui quod movetur. Sit A, B, C, continuum quod movetur; sit D, F, G spatium. Partes mobilis dissimiliter se habent ad partes spatii, ut cum A est super F, non est super G, et tunc B est super D; et cum A est super G, B est super F, et C super D. Ex tali primo et ultimo in mobili et spatio provenit in motu successio; et in tempore, quia tempus est numerus motus secundumd prius et posterius. Unde in omni duratione vel mora est prius et posterius in successione, sed in illa quae est sic respectu duplicis primi et ultimi.’ Glossa in Sent. 2, Appendix (422, 22–34). For further examples, Aquinas, Quaest. Disp. de Malo 16. 4; Albert, Phys. 4. 3. 5 (4.1, 267, 37–48); ibid. (268, 13–15); Aristotle, Phys. 3. 7 (207B21–7); 4. 11 (219A10–220A24). For further detail on the specifically Aristotelian issues, E. Hussey, Aristotle Physics Books III and IV, xlii–xlvi, 142–59. At times the argument is stated in reference to ‘quantity’ rather than ‘continuity’, as Aquinas indicates, In Meta. 5. 13 [937], but the basic belief in the derivation of temporal properties from spatial ones remained, on which Kilwardby, de Temp. 3 (10. 10–12); Albert, Phys. 4. 3. 5 (4.1, 267, 37–48 f.). Aquinas, In Phys. 4. 17 [575]; and Bonaventure, In Sent. 2. 2. 1. 2. 1 11 For the statement of the problem, Aristotle, Phys. 6. 4 (235A17–18, 235B1–4, 236B2–8); Albert, Phys. 4. 3. 5 (4.1, 267, 55–64); 6 (4.1, 270, 76– 80); Aquinas, In Phys. 4. 17 [580]; 4. 18 [590]; Grosseteste, In Phys. 4 (87); Kilwardby, de Temp. 2 (9, 7–11). For Kilwardby’s solution, de Temp. 4 (10, 21 f.); and Albert, Meta. 5. 3. 1 (16.1, 256, 15–19). Kilwardby’s argument is not successful because in so far as the change is supposed to derive its ‘spatiality’ from the substance in which it takes place, this means that it is not deriving it from the topology of the spatial continuum, which is what

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Ultimately this position is difficult to sustain because all thirteenth-century thinkers were committed to the existence of non-material (and so non-spatial) souls and angels, which were necessarily thought to be able to be the subjects of a succession of changing states. There was no meaningful way in which they could always be related to the spatial topology, so there was no meaningful way to derive a topological structure, and hence a time itself with which to measure them. Rather than seeing this as a problem for their account of time, medieval thinkers seem, instead, to have drawn the opposite inference and concluded that such changes do not occur in time. To add to the difficulties of accommodating specifically Christian issues to the reductive model which medieval thinkers believed they had inherited from Aristotle, there was also the small matter that as Themestius, one of Aristotle’s own ancient critics had noted, in attempting to reductively explain a temporal ordering and the relations holding between the temporal elements by appealing to a spatial ordering and the relations holding between the spatial elements, there was a serious risk of begging the very question at issue. If a series of spatial points is identified, s1, s2, s3, . . . and a particular P is thought of as passing along those points, then unless we differentiate P’s position at those points with sequential (temporal) dates, it is difficult to see how we can get the concept of motion. Thus, to say medieval thinkers were trying to prove. If (per impossibile) a particular substance were to be atomic or consist of atomic parts then changes in it would be similarly atomic, regardless of the topological structure of the space in which the substance itself is located.

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that P moves from s1 to s3 is to say that it was at s1, and then afterwards it was at s2, and then still later it was at s3. But in expressing it this way, we have assumed the notion of a temporal ordering in order to explicate motion across a spatial continuum when that very motion is supposed to be giving us our notion of time. Both Aquinas and Albert explicitly acknowledge Themestius’ challenge, but they do not seem to have realized its full significance. They both treat him as if he has simply not understood Aristotle, and so they insist that it is the reduction to spatial magnitude, and in particular the Primum Mobile moving through that magnitude, rather than just the reduction to space, which ensures that there is no circularity. In doing so they seem not to have realized that Themestius’ challenge can be reformulated in terms of magnitudes so that the difficulty of explaining time, in terms of motion and the medium through which the motion takes place, remains.12 Whatever advantages accrued from reductive appeals to the Primum Mobile, there were clearly serious problems which it gave rise to. Besides the ones above which do not seem to have been fully appreciated by medieval thinkers, we saw in Chapter 2 that Bonaventure, at least, had expressed grave reservations about giving the Primum Mobile any role 12 Aquinas, In Phys. 4. 17 [580]; Albert, Sum. Theol. 5. 22. 2. 1 (34.1, 118, 70–3); Phys. 4. 3. 5 (4.1, 269, 53–8). Perhaps Aquinas and Albert were thinking that because the Primum Mobile has its own proper (circular) motion in virtue of its nature, then that would mean that it had an intrinsic orderliness to its motion regardless of the spatial structure. See Aristotle, Phys. 4. 1 (208B12–25) for tentative steps in that direction. Kilwardby seems unaware of (or uninterested in) Themestius’ point.

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at all as the subject of time. Not only was it always possible to think of that subject being destroyed and yet time continuing to exist, but from a more markedly theological perspective he was also worried about the fact that the book of Genesis asserted that the heavenly bodies (including the Primum Mobile) were not created until the fourth day of creation. If this were the case then it would entail that there was time prior to the creation of the Primum Mobile, otherwise there would be no meaningful sense in which the creation of the Primum Mobile could be said to have occurred on the fourth day.13 This is a serious problem as it cuts to the heart of the very nature of an Aristotelian account of time. Either there is a 13 There seems to have been some disagreement about the precise day on which the Primum Mobile was created. Figures such as Bonaventure preferred to view it as the fourth day, In Sent. 2. 1. 1 dub. 4, whilst Alexander seems to have thought it was created on the second day, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 1 (1, 106). Whatever the precise day the key problem remains, in Bonaventure’s view, that it makes little sense to offer a reductive explanation of time that reduces it to something that is created in time, ‘Dixerunt ergo aliqui quod tempus est unum ratione subiecti, in quo primo est et per se, quo remoto, removetur et tempus. Unde dixerunt, quod tempus est unum, quia est in primo mobili, cuius motu cessante, cessat et tempus.’’ Sent. 2. 2. 2. 1. 1. 2. Bonaventure’s argument is based upon Augustine’s insight, ‘cur enim non potius omnium corporum motus sint tempora? An vero, si cessarent caeli lumina et moveretur rota figuli, non esset tempus quo metiremur eos gyros?’ Conf. 11. 23 (29). For further details see Albert’s discussion, Phys. 4. 3. 3 (4.1, 264, 4–6); and Philip the Chancellor, ‘Tempus autem non est in principio temporis, quia successivum non est in sui termino’, Sum. de Bono, 1. 3. 5 (1, 129, 5–8); ‘quia firmamentum secunda die factum est quod est primum mobile’, ibid. 1. 3. 6 (1, 130, 8–10). The biblical argument against the Primum Mobile as the subject of time is also cited by Augustine. Basing himself upon the story of God stopping the rotation of the sun for a day (Josh. 10:12), he concludes that the passage of heavenly bodies cannot be responsible for the passage of time. Conf. 11. 23 (30).

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single subject of time which begins to exist when time itself begins to exist, so that all the temporal relations can inhere in it, or else the Aristotelian basis for the entire model of time collapses to leave temporal relations which need no substance in which to inhere. Aquinas, and colleagues who wanted to maintain the role of the Primum Mobile, tended to respond to the argument by insisting that, although it is indeed possible to imagine that for any motion in time, M1, it might not occur and a different motion M2 might occur instead, that does not necessarily mean that time cannot be reduced to a primary motion in which it can inhere as a subject. All it means is that the relation between time and that primary motion is contingent and that the motion which is the subject of time is the first motion which actually occurs. If the motion of the Primum Mobile, M1, had indeed failed to occur, but a different motion M2 had occurred, then there would be a different (although perhaps qualitatively identical) time in which M2 had been the principle motion and so therefore the causal subject of time.14 14 To counter the scriptural aspect of the problem there was a tendency to try to make sense of a ‘confused’ motion before the existence of the Primum Mobile which could provide a basis for time before the existence of the Primum Mobile. Note Henry of Ghent, ‘Dici ergo potest quod ante motum caeli fuit motus confusus elementorum in chaos confuso, sicut etiam posuit Plato ante mundi distinctionem, et illum necessario secutum est tempus confusum irregulare, quod regulato motu prius confuso per motum regularem caeli factum est regulare et sequitur motum caeli; et in illo tempore prius confuso potuit esse vera successio et ita distinctio vespere et mane secundum numerum horarum.’ Lect. Ord. (85, 59–65). This ‘confused’ motion would presumably have lacked a metric, so this position amounted to the claim that before the creation of the Primum Mobile time existed but only with a topology. Unfortunately this solution does not really resolve the

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Unconvinced by this approach, Grosseteste and Kilwardby took a very different approach. In Kilwardby’s words: motion can be imagined without any thought of the heavens because time is rather consequent (sequitur) upon motion in general, I say, as its subject, rather than the motion of the heavens.15

Verbally, Kilwardby is careful to accept that the Primum Mobile was ‘prior’ as long as it was understood that this meant that it was the most obvious instance of continuous motion.16 Beyond this verbal concession he and Grosseteste were actually subverting the entire Aristotelian basis on which they were trying to explicate their account of time. If the subject of time is to be the abstraction of ‘motion in general’ then it is no longer a substance, and the Aristotelian problem of what the subject of the temporal topology would have been and it gives rise to a new problem. If the Primum Mobile was supposed to have been created on a certain number of days after creation, how could there have been a specific number of days if time, at that stage, had no metric? 15 Kilwardby, ‘cum motus possit ymaginari sine ymaginari sine ymaginatione motus celi, quod tempus potius sequitur motum simpliciter quam solum motum celi—dico sicut subiectum.’ de Temp. 10 [40] (18, 10–12). Also, de Temp. 8 [35] (16, 14–15). One of the problems with medieval discussions of this issue is that they often seem unable to apply the distinction between motion and ‘a’ motion, although as we can see from Grosseteste, there does seem to have been a recognition that the distinction was significant, ‘item ad explanacionem diffinicionis temporis dicit quod motus secundum quod sumitur in diffinicione temporis non sumitur pro alico speciali motu, sed per motu simpliciter et in universali. Est enim tempus numerus motus simpliciter et non intendit diffinicio de alico speciali motu.’ In Phys. 4 (97). See also Aquinas, In Phys. 4. 23 [631–3]. 16 ‘Ad primum dicendum quod duplex est ratio; tum quia motus localis primus est, et ideo ei primo accidit tempus; tum quia motuum notissimus est quoad continuitatem esse per prius et posterius.’ de Temp. 4 (10, 17–20).

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categorical framework, in which the account of temporal relations is supposed to be explained, collapses.

A B S O LU T E O R R E L AT I O NA L T I M E ? There are at least four reasons which make it tempting to conclude that thirteenth-century accounts of time were ultimately relational accounts of time. In the first place, if there was a contingent relation between motion and time, as proponents of absolute time maintain, it would have made no sense for thirteenth-century thinkers to view the topological structure of time as arising from motion. If the relationship between time and motion is contingent, such that there could be a time without a motion, then this would have entailed, for thirteenth-century accounts of time, the possibility of the existence of a time without a topology, a notion which would have seemed as incoherent as talking of material objects which have no shape. Secondly, the much-debated question of whether or not time can exist in the absence of the Primum Mobile would have ceased to be a problem of significance for medieval thinkers if they had held any version of an absolutist thesis. Absolutist accounts claim that time can exist in the absence of any other particulars, including the Primum Mobile, so any commitment to absolutism would have entailed the acceptance of the possibility of time existing in the absence of the Primum Mobile. Although we have seen that some thirteenth-century accounts did indeed ultimately lead to

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the postulation of time in the absence of the Primum Mobile, such conclusions seem to have been more like ad hoc concessions forced by the complexity of arguments, rather than the considered views we would have expected if thirteenthcentury thinkers had indeed been committed to a version of absolutism. Thirdly, the way that time was defined introduced motion and change into the heart of its definition. We have seen already that, following Aristotle, time was typically defined by thirteenth-century thinkers as the ‘numbering of change’. Such a definition established an essential relationship between motion and change, a relationship which it is impossible to reconcile with the absolutist claim that there can be time in the absence of any other particulars.17 Fourthly, and somewhat pragmatically, there were also theological advantages to a relational account of time. Ancient philosophers had long criticized Christianity by suggesting that the doctrine of creation was incoherent because it entailed the existence of a lazy mutable God who had been doing nothing for ages before He got around to creating the world. By rejecting the coherence of the idea of time in the absence of change, Augustine had been able to provide a response to this criticism based upon the denial that there could be any ‘empty’ time before the creation, in which God could have been lazy. By the thirteenth century this response had become a classic ‘defence’, 17 Kilwardby, ‘tempus est numerus motus secundum prius et posterius, igitur ubi tempus, ibi prius et posterius est motus, et ubi non sunt ista, nec tempus’, de Temp. 1 [3] (7, 10–12). Aquinas, In Phys. 3. 2 [294]; 8. 2 [979],

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but it was one which rested on the assumption that time was ultimately relational.18 Whilst all these factors militate against viewing the medieval account of time as absolutist, we should not be too quick to conclude that it was simply relational. Rather than analysing time in terms of the traditional distinction between absolutist views of time and relational views of time, contemporary philosophers have suggested that we should also think in terms of models that would view time in terms of a modal-relational analysis. The modal relational account is distinct from substance models because it does not view instants as existing logically independently of motion or any other particulars, yet it cannot be reduced to a relational account because it affirms that there could be instants existing in the eventuality of an actual absence of motion, as long as there is a possibility of motion.19 [982]. Albert, In de Causis 2. 5. 20 (17.2, 185, 78–80). For the Aristotelian background, Phys. 8. 1 (251B21–219B2) and 4. 11(218B21). 18 Augustine’s central tenet is that time is a created entity and so owes its existence to God as much as anything else in the created world, Conf. 11. 13 (15) See also Aquinas, In Phys. 8. 2 [988]–[989]. Even as late as the debate between Leibniz and Clarke, a desire to avoid a version of this problem is clearly discernible in Leibniz’s position, H. G. Alexander (ed.), The Leibniz– Clarke Correspondence, 3 [6]. When examining the notion of ‘creatio ex nihilo’, Aquinas insisted that everything which has ‘being’ has been created, Sum. Theol. 1. 45. 1; 1. 46. 1 ad 6; and this applies to time, although accidents, amongst which time is classed, are more correctly said to be ‘concreated’, Sum. Theol. 1. 45. 4. See also Augustine, Conf. 11. 14.(17). Despite arguments to the contrary it has been suggested that Aquinas’ interest in the notion of ‘imaginary time’ might mean that he favoured a substantivalist account of time (Bas C. Van Fraasen, An Introduction to the Philosophy of Time and Space, 19). I shall suggest below that there are alternative ways of interpreting this notion. 19 On modal relationism, W. H. Newton-Smith, The Structure of Time, 38, 44–7; J. Butterfield, ‘Relationism and Possible Worlds’, 106; G. Forbes, ‘Time,

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Thirteenth-century writers never explicitly raise the question of modality in relation to temporal relations but there is evidence, especially in Albert’s work, that they were thinking about modal relations. In a particularly interesting discussion, Albert raised the question of whether a brother B1 can be said to have a relation of fraternity prior to the birth of his brother B2. Clearly, concludes Albert, there cannot be any actual relation of fraternity because there is no actually existing term to the relation (i.e. no brother) yet, he concludes, this does not mean that there is ‘entirely nothing’ in B1 prior to the birth of his brother.20 Events and Modality’, 80–99. Sometimes modal relationism has been referred to as a ‘liberalized relational account’ (P. Teller, ‘Substance, Relations and Arguments about the Nature of Space-Time’, 364). The coherence of modal relationism has been questioned because of its apparent surreptitious commitment to absolutist ‘possibilia’ (J. Earman, World Enough and Space-Time, 135). Responses range from the restatement of scientific theories in order to avoid any reference to absolutism (B. Mundy, ‘Relational Theories of Euclidean Space and Minkowski Space-Time’, 205–26), to more philosophical responses which accuse Earmen of begging the question at issue. Basically he believes that we can only have truths about how a particular would behave, if we have truths about how particulars do behave; and this he believes implies an absolutist notion of scientific laws and theories. Medieval thinkers would have taken a different view of the matter and said that behaviour is a result of a particular’s essence. If, per impossibile, a particular were to be frozen so that it could not exhibit any behaviour at all, as long as its essence remained, then there would continue to be truths about its behaviour. The debate about the coherence of modal relationism continues and it is now sometimes referred to as ‘a more modest version of absolutism’ (R. Sorabji, Time, Creation and the Continuum, 80). 20 ‘non nato fratre, sicut iam diximus, respectus est filii ad parentem, ut ad naturae originem, et ex hoc respectu in actu existente est potentialis convenientia ad id quod in origine est in potentia. Et haec potentia reducitur ad actum nativitate fratrum, et ideo non omnino nihil est fraternitas in fratre, qui prius natus est.’ Meta. 5. 3. 7 (16.1, 267, 21–7).

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Albert’s account is hesitant, but it is interesting precisely because he is trying to make sense of the idea of a relation that can exist in the absence of its term; it is a relation that would exist because of the possibility of the term, and so to that extent it would seem to be struggling towards a similarity with what contemporary thinkers mean when they talk of modal-relationism.21 Moving in a similar direction, but now applying it more explicitly to the case of time, Aquinas considered the problem of ‘rest’: Someone might say that although all bodies are capable of motion, they are not all actually in motion; for some are at rest. Thus it does not seem that time is in all things. To refute this, he (Aristotle) adds that time is together (simul) with motion, whether the motion be actual or potential. For everything that can be moved, but is not actually moved is at rest. And time not only measures motion, but also rest . . . Hence it follows that wherever there is actual or potential motion, there is time.22 21 Albert’s position was not fully worked out for he was unable to clearly identify what it was that could be attributed to the subject as the actual basis for the potential relation. (Although in this respect his problems are not really any different to those still besetting contemporary advocates of modal relationism, on which see C. A. Hooker, ‘The Relational Doctrines of Space and Time’, 129). It certainly could not be the full foundation (respectus), so he was left struggling to account for the basis of the relation in terms of the parents’ causal powers, Lib. de Praed. 4. 10 (Borg. 1, 242). Although ultimately lacking full coherence, Albert’s attempt to extend traditional Aristotelian relationism to encompass a modal element is a significant development and it is one that he kept returning to, Sum. Theol. 9. 39. 1 (34.1, 294, 39–40) and also Lib. de Praed. 4. 2 (Borg. 1, 226). 22 ‘Et quia posset aliquis dicere quod licet sint mobilia, non tamen omnia moventur, sed quaedam quiescunt, et sic tempus non videtur in omnibus esse: ad hoc excludendum subiungit quod tempus est simul cum motu, sive motus accipiatur secundum actum sive secundum potentiam. Quaecumque

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Here, Aquinas is introducing modality into his account of time in order to justify the common-sense conclusion that objects which are not actually in motion remain nevertheless in time. As their presence in time arises because of their capability of motion, what we might wonder would be the situation if the whole universe was to lapse into a temporary state of rest, frozen as it were but capable of motion at some (later) point? For thirteenth-century thinkers such a scenario of total rest would be unthinkable. To be in time was to be measured by some other motion, so quite simply the absence of other motions would make it impossible to contemplate the existence of anything like a time in which the universal rest could be said to be existing. The closest that thirteenth-century thinkers could get to considering such a scenario was contemplating Anaxagoras’ claim that there could have been universal rest prior to the beginning of motion. But that claim was considered by Aquinas as absurd because the transition from universal rest to motion would itself be a motion, and so Anaxagoras’ position would entail the absurdity of motion before motion.23 enim sunt possibilia moveri et non moventur actu, quiescunt. Tempus autem non solum mensurat motum, sed etiam quietem . . . Unde relinquitur quod ubicumque est motus, vel actu vel potentia, quod ibi sit tempus.’ In Phys. 4. 23 [626]. 23 For a contemporary formulation of universal rest as an argument against the relational account of time, S. Shoemaker, ‘Time Without Change’. On the medieval view of universal rest, Averroes, ‘quiescens non est in tempore, secundum quod est quiescens . . . res non est in tempore nisi sit mota’, In Phys. 4 [118] and also ibid. [106]. For Aquinas’ rejection of Anaxagoras’ viewpoint, In Phys. 8. 2 [976]–[978]. He and almost all of his contemporaries would have insisted strongly that creation is not a motion, otherwise arguments against Anaxagoras would have meant that creation

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I M AG I NARY T I M E We have seen that whilst thirteenth-century thinkers were unable to develop any explicit account of modal relationism in relation to time, there were nevertheless incipient developments towards a version of modal relationism. One of the potentially most interesting developments in this regard involved the notion of imaginary time. Imaginary time is a puzzling notion as it seems to be an account of time which can be imagined as existing in the absence of any other substances or actual changes. The precise origins of the notion are unclear. Averroes, in his treatise on time, appeals on several occasions to the implications of ‘imagining’ an instant, and this undoubtedly contributed to the positive reception which imaginary time seems to have received. But it is probably Maimonides who has most directly influenced the reception of the idea. Confronted by an objection to the idea of ‘creatio ex nihilo’ he had responded: every thing other than God . . . was brought into existence from non-existence by God . . . He brought into existence out of nothing all the beings as they are, time itself being one of the created things. For time is consequent upon motion, and motion is an accident in what is moved. Furthermore, what is moved . . . is itself created in time and came to be after not having been. When one says that God ‘was’ before he created the world . . . and when one imagines the infinite duration of God’s existence before the

itself would have been logically impossible: a conclusion vigorously repudiated by medieval thinkers, on which see Tarentaise, In Sent. 2. 1. 1. 2.

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creation of the world, this is due to supposing or imagining a time, not due to the true reality of time [which did not exist then]. For time is indubitably an accident [and in the absence of creation there would have been nothing for it to be an accident of].24

The point at issue in this paragraph was not so much a philosophical one about creation or the nature of God. It was rather an issue of semantics and how the word ‘was’ could be ascribed to God, prior to His creation of matter and the things in motion on which the existence of time was supposed to depend. When Augustine considered the question, he had simply dismissed the idea of there being a ‘prior to time’ in which God could exist—unless the priority was honorific or ‘ontological’ and was just a linguistic way of spelling out God’s excellence. Maimonides, however, took a rather different approach, effectively suggesting that the notion of ‘prior to time’ had a genuine import because it was possible to ‘imagine’ a time prior to the existence of time. It is not entirely clear why Maimonides felt that he needed to introduce such a puzzling idea as imaginary time, and even less clear why Albert and Aquinas followed him and reiterated the concept within their own accounts of time. Precisely how the notion should be interpreted seems to have been unclear even to thirteenth-century figures. Albert, for example, seems, at times, to have thought of a mental

24 Guide of the Perplexed, 2. 13. Translation quoted from A. Hyman and J. Walsh (eds.), Philosophy in the Middle Ages, 391. For Averroes, see his appeals to imagination at In Phys. 4 [125] and [106]. For an analysis of ‘imaginary’ as appearing in expressions of ‘imaginary space’, E. Grant, Planets, Stars and Orbs: The Medieval Cosmos 1200–1687, 177–85.

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extension as simply a model of ‘eternity’.25 Aquinas, however, seems to have thought of it as a time, but his understanding of it seems to have developed and changed. In his early Commentary on the Sentences he dismissed the notion as ‘sophistical’—probably because its implied commitment to the idea of a time without motion is utterly incompatible with a relational account of time. Yet fifteen years later when he considers the notion again in his Summa Theologiae and Commentary on the Physics he has become much more positive towards the idea: In a similar way the first now which is the beginning of time is not preceded by a time existing in nature, but only in our imagination. And this is the time which is designated when it is said that the first now is a beginning of time before which there is no time.26 25 Albert, ‘Ad omnia autem ista solvitur, quod est extensio esse. Et haec necessario extensum agit in quantitatem. Et est extensio secundum intellectum, quae est acceptio per intellectum esse stantis et indivisibilis, non deficientis in aliquo tempore vel in aliquo loco. Et illa extensio extensum non agit in aliquam quantitatem, quia non est in eo, sed in intellectu . . . Et talis protensionis vel potius ipsa protensio aeternitas vocatur’. Lib. de Causis 2. 1. 8 (17.2, 70, 65–71). 26 ‘Similiter etiam primum nunc quod est principium temporis, non praecedit tempus in rerum natura existens, sed secundum imaginationem nostram tantum. Et hoc tempus designatur, cum dicitur quod primum nunc est principium temporis, ante quod nihil est temporis . . .’ In Phys. 8. 2 [990]. See also Albert, ‘Et est extensio secundum intellectum, quae est acceptio per intellectum esse stantis et indivisibile, non deficientis in aliquo tempore vel in aliquo loco.’ In de Causis 2. 1. 8 (17.2, 70, 65–71). On Aquinas’ earlier rejection of the notion as ‘sophistical’ (sophistica ratio) see In Sent. 2. 2. 1. 2. See also, Quaest. Disp. de Pot. 3. 17 ad 20; Sum. Theol. 1. 46. 1 ad 6 and ad 8. But contrast Aquinas’ position with Henry of Ghent’s in which he effectively rules out any notion of a time as prior to time, ‘Dicamus ergo quia Deus creavit: id est produxit caelum et terram ex nihilo; id est post non esse absolute, non tamen posteritate naturae sive essentiae, sed durationis, non quo tempus sit prius, sed quo tempus incipiat esse, aeternitate praexistente

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Aquinas does not explain why he changed his mind on this question, but he must have thought that it was important to do so, for the notion of an imaginary time is difficult, if not impossible, to reconcile with Aristotle’s insistence of relating the existence of time itself to actual motion. The most probable reason for his change of mind must be that he became more appreciative of how Maimonides was using the concept in order to address theological objections about the idea of creation; and as it was theological concerns that were driving his interest Aquinas was less worried about the issue of how imaginary time would cohere with Aristotle’s wider philosophical views on time. Thirteenth-century thinkers were aware of a variety of viewpoints about the question of creation, including a significant number of arguments which purported to demonstrate that creation could never have happened. Amongst those arguments there were two which stood out as particularly significant; what we might call a ‘semantic’ argument and a ‘logical’ argument. The semantic argument seems to have been of interest to Maimonides and can be found stated particularly clearly duratione infinita. Et dico ‘‘post non esse’’ ad differentiam productionis personarum divinarum. Dico ‘‘absolute’’ ad differentiam productionis ex materia praecedente, qualem posuit Plato. Dico ‘‘posteritate durationis’’ non solum naturae; ad differentiam productionis mundi quam peripatetici posuerunt ab aeterno. Dico ‘‘non quo tempus sit prius’’ ad differentiam productionis rerum per propagationem ex materia sive a Deo immediate, sive a causis naturalibus.’ Lect. Ord. 1 (36, 50, 84–94). Although Aquinas subtly avoids any commitment to earlier patristic sources on this question it is worth noting that there was a well established tradition which he would have been aware of, according to which certain aspects of creation had been produced prior to time. Isidore, ‘fecit deus duo, scilicet angelicam naturam et informem materiam, ante omne tempus’, de Differentiis 2. 11 [30].

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in Bonaventure. According to this argument, if time had a beginning then it must have begun either in an instant or in a period. But, an extended period, a time, cannot exist in an instant so it would make no sense to talk of a time as beginning to exist in an instant. If time had a beginning, then, so this argument maintained, it must have begun in a period. Yet a period necessarily contains parts such that some are prior to the others and so if time began in a period then there would be time prior to time, which is absurd. So, concluded the argument, time necessarily could not have had a beginning and it must therefore exist uncreated.27 The second argument against creation was a tense logical argument which seems to have been promoted particularly by Averroes. According to that argument, the crucial issues were the logical implications of words such as ‘instant’ and ‘now’. In Averroes’ usage, an ‘instant’ (now) was a boundary lying between periods, so for any instant cited it must be a necessary truth that there was a period lying either side of that instant. To reinforce the point Averroes had appealed to tense logic. For any instant that we take as the beginning of the world, he urged, it would have been true prior to that instant that time will exist. And so, he concluded, a future tense implies a time, so there must exist time before the 27 ‘Si tempus producitur, aut in tempore, aut in instanti. Non in instanti cum non sit in instanti: ergo in tempore: sed in omni tempore est ponere prius et posterius and praeteriturm et futurum: ergo si tempus in tempore fuit productum, ante omne tempus fuit tempus, et hoc est impossibile: ergo’, Bonaventure, In Sent. 2. 1. 1. 2.

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world and before any other origin which one cares to cite as the beginning of time.28 Arguments against the creation, or beginning, of time were of particular concern to thirteenth-century thinkers, as they were viewed as an instance of the heretical rejection of ‘creatio ex nihilo’. Standard attempts to reduce the force of such arguments typically focused upon stressing the created physical nature of time, especially in virtue of its relationship to the Primum Mobile, as that helped to align time with the other elements of creation which needed a causal explanation.29 28 Averroes, ‘(si) tempus enim non fuit ante mundum . . . tunc tamen verum fuit ante mundum futurum esse tempus; sed futurum dicit tempus, ergo tempus fuit ante tempus’ (quoted and commented upon by Albert, Phys. 4. 3. 13 (4.1, 285, 26–9); 4. 3. 3 (4.1, 264, 65); 4. 3. 4 (4.1, 266, 84). Aquinas, Sum. Theol. 1. 46–7. For details about medieval versions of Averroes’ problem, R. C. Dales, Medieval Discussions of the Eternity of the World, 81–4. For a contemporary restatement of Averroes’ position, R. Swinburne, Space and Time, 172, and The Christian God, 94. Siger of Brabant gives a slightly different, but related version of the argument, ‘Intelligendum, secundum Commentatorem, quod instans de necessitate est finis unius temporis et etiam principium alterius, quia impossibile est imaginari instans absque hoc quod sit finis unius et principium alterius. Et huius ratio secundum ipsum est quia instans est aliquid temporis; tempus autem habet esse in successione et fluxu quodam; et ideo instans quod est in tempore est continuativum duorum temporum . . . .’ Phys. 8. 10 (Delhaye 207). As Henry of Ghent noted only too clearly, the Averroean position amounted to a serious heresy, ‘Ista expositione excluditur error aliquorum haereticorum ponentium mundum non semper fuisse, sed aliquando incepisse, et ponentium cum hoc tempus mundum praecessisse, et in aliquo ipsius mundum incepisse.’ Lec. Ord. 1 (36, 41, 16–19 f.). 29 Ulrich, ‘dicimus motorem cum mobili incepisse, et cum his incepit motus circularis motore influente suam in dextram partem mobilis tunc et non prius, et ideo nihil fuit ante hoc de motu. Et cum hoc motu dicimus incepisse tempus in primo suo nunc, quod concreatum fuit cum illa parte caeli a qua motus incepit . . .’ de Summo Bono 4. 1. 8 (4, 49, 179 to 50, 185). Note Tarentaise’s attempt to link a physical notion of time with the idea that

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Engaging more directly with the kinds of arguments that worried Maimonides, and the kinds of arguments that convinced Averroes that creation was impossible, medieval thinkers developed sophisticated models of time. They compared time to geometrical models in order to show that in precisely the same way that a geometrical point could be understood to have no line before it and only a line after it, so time itself could be imagined as starting in an instant and continuing its existence thereafter.30 there could still nevertheless be a ‘before’ time, ‘dico ergo quod aevum tempus proprissime dictum praecedit dignitate seu electione et duratione, quia tempus illud non fuit ab initio creationis, sed a motu primi mobilis’, In Sent. 2. 2. 2. 3. Where medieval thinkers explicitly cited ‘time’ amongst the principles of the universe, they also stressed that it had to be created. See Philip the Chancellor, ‘Et dicendum est quod omnia creata erant simul; dico de illis quatuor [scilicet angeli, celum empyreum et materia quatuor elementorum et tempus]. Et quod obicitur de initio temporis, dicendum est quod illus non est nisi defectus aut discontinuitas ex parte ante et ita non est creatura. Et cum dicitur illa creata esse post principium temporis, non sic ponitur quod post aliquam creaturam. Si vero esset aliquid dictum secundum positionem, dicendum est quod tempus ratione sui initii simul dicitur creari cum aliis, cum tempus per se non fuerit nisi secunda die.’ Sum. de Bono, 1. 3. 6 [1, 130, 16–21]. Albert, Sum. Theol. 5. 23. 2. 2. B ad 5 (34.1, 130, 86–9). Aquinas cites Genesis (1:1) and Apocalypse (10:6) as scriptural evidence that is supposed to support the view that time is finite and bounded at both ends, Quaest. Disp. de Malo 16.4. On the doctrinal implications of denying a beginning to time see also his comments, Sum. Theol. 1. 61. 2; de Aetern. Mun. [7]. Also Albert, Sum. Theol. 5. 23. 1. 2 (34.1, 129, 7–12). 30 Aquinas, In Phys. 8. 2 [983]; Pseudo Siger, Phys. 8. 6 [201]; 8. 10 [207]. Kilwardby indicates an awareness of a similar argument at de Temp. 15 [84] (31, 16–17) and even Bonaventure, writing twenty years earlier than Aquinas and Siger, proposed a similar argument, although he does not use the appeal to imagination or geometry, In Sent. 2. 1. 1. 1. 2. On time beginning in an instant, Alexander of Hales, ‘Credendum est tempus in principio mundi factum esse, sed hoc dicitur ratione ipsius nunc temporis’, In Sent. 2. 2 [7] (17, 4–6). Aquinas, ‘Nihil autem est temporis nisi nunc. Unde non potest fieri nisi secundum aliquod nunc: non quia in ipso primo nunc sit tempus,

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One of the key issues raised by Averrores, as far as Aquinas was concerned, was providing a non-problematic content to the use of the tenses and terms which seemed to imply an extension ‘before’ creation. For many of his colleagues the way forward lay in making such terms honorific so that they denoted the immutability of a God who was ‘prior’ in the sense of ‘superior’ to a mutable creation.31 sed quia ab eo incipit tempus.’ Sum. Theol. 1. 47. 1 ad 3. Philip the Chancellor, ‘Sed questio est utrum tunc in principio tempus creetur aut post. Si in principio temporis, esset successivum in sui initio; si vero post, ergo principium temporis precedit tempus; ergo illa que sunt illi coequeva. Ergo principium temporis fuit ante celum et terram, quia hec sunt tempori coequeva’. Sum. de Bono, 1. 3. 6 (1, 130, 12–16). Although the point is not always made explicit, thirteenth-century thinkers seem to be treating Averroes’ arguments as actually begging the question at issue. For unless one assumes that there is in fact a period prior to any other period—i.e. the unboundedness of time— then it will not follow that a tensed proposition about the future entails the existence of a period, as Averroes claims. For a contemporary defence of this approach, W.H. Newton-Smith, The Structure of Time, 97–101. 31 Albert, ‘esse autem intelligentiae vel Angeli sit cum aeternitate; esse autem animae sit post aeternitatem inferius et supra tempus. Unde dicit ibidem, quod anima est in horizonte aeternitatis et temporis creata, ita quod inferior sit aeternitate, et superior tempore . . . Unde verum est, quod Deus est ante aevum, et secundum rationem causae, et etiam secundum durationem; intelligentia autem est cum ipso et in ipso: quia aevum est mensura ipsius esse durantis, et ante tempus, non secundum durationem, sed secundum rationem causae: quia propinquior est aeternitati intelligentia, quam anima, . . . Secundum hunc modum prioritatis dicitur etiam anima ante tempus, quod per se est mutabilium; anima autem nec penitus est mutabilis, nec penitus immutabilis; et ideo ante tempus et circa aevum est . . .’ Sum. de Creat. 2. 3. 3 ad 6 (Borg. 34, 353). See also Aquinas, Sum. Theol. 1. 61. 2, and Ulrich, de Summo Bono 4. 1. 8 (4, 47, 112–15). Aquinas considered reinterpreting language of temporal priority into priority of nature, Sum. Theol 1. 46. 1 ob. 8, but he was clearly unconvinced that this could provide an entire solution to the problem, ‘dicendum quod Deus est prior mundo duratione. Sed ly prius non designat prioritatem temporis, sed aeternitatis. Vel dicendum quod designat aeternitatem temporis imaginati, et non realiter existentis.’ Ibid. ad 8. See also Peter of Tarentaise, In Sent. 2. 1. 2. 3 ad 4.

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Aquinas rightly recognized that this approach did not really engage with the heart of Averroes’ critique, so when he returned to this issue in his later works he decided that he needed to appeal to imagainary time as the way of explaining any import in language about time that seemed to imply the existence of time before the creation of time. Where there were such logical implications he could now assert that they merely referred to an imaginary time and the time before creation which they seemed to imply was just a mental construct. Imaginary time is a puzzling idea. Lacking any reference to motion, it is difficult to see how it could count as a time at all within an Aristotelian framework. But it is equally difficult to see how it could represent a commitment to an absolute time, the idea of a temporal duration which would exist in the absence of any motion. If Aquinas did have absolutist leanings then his imaginary time would have become a real time, as it would have been a duration that could exist as a time in the absence of any physical world and motion, and as such it would not have presented a solution to the problem he was grappling with. It would, in fact, have conceded the very point that Averroes was challenging. Averroes was insisting that there could be no beginning to time, so it was absolutely essential for Aquinas to insist that imaginary time had no real existence and that the only sense in which it preceded the real time that we experience now was as a logical fiction or as a mental extrapolation. As far as Aquinas was concerned, real time, the time we experience now, had to have a beginning and what it was that made imaginary time just a mental phenomenon was precisely its failure to be related to physical motion.

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Perhaps it would be tempting to think of imaginary time as a version of a modal relational concept of time, but this is also an implausible interpretation. According to a modalrelational account of time the mere possibility of motion would be enough to generate an actual time, and so an imaginary time in which it was possible to think of actual motions occurring would become a real time and it would once again undermine Aquinas’ attempts to repudiate Averroes’ arguments. Aquinas’ appeal to imaginary time is ultimately difficult to reconcile with his own Aristotelian-based accounts of time, and it is difficult to interpret in terms of any of the contemporary discussions about relational and absolutist models of time. The basic contours of what we might term his philosophy of time has most in common with what we would think of as a relational theory of time. Rather than constituting an additional feature to his philosophy of time, the introduction of the idea of imaginary time is more plausibly accounted for as an idiosyncrasy prompted by theological concerns about the notion of ‘creatio ex nihilo’, an idiosyncrasy which he was ultimately unable to reconcile with his broader philosophy of time.

C O N C LU S I O N This chapter has focused on thirteenth-century views about temporal relations. It has shown that although medieval thinkers used differently nuanced terminology,

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a broadly shared approach to a theory of relations became apparent. Applying this theory of relations to the case of time generated serious difficulties. Relations were considered by thirteenth-century thinkers to be accidents, and so temporal relations needed a substance in which to inhere. This substance was considered by many thirteenth-century thinkers to be the Primum Mobile, but such an identification was deeply problematic even within the framework of medieval thought. Besides the problem of identifying a substance for time, it is not at all clear that the wider aspects of an account of temporal relations could be accommodated within the confines of the medieval theory of relations. To posit a relation, for example, thirteenth-century thinkers needed to identify a subject of the relation, a term (the thing to which the subject is related), a relation (the relatedness of the subject and the term), and a foundation (what it was about the term that gave rise to the relation). Attempting to apply this model to time means that each instant would have to be both a subject and a term. An instant i1, for example, would be the subject of the relation of temporally before i2 whilst it would be the term of the relation when we consider i2 as the subject of a relation of temporally after i1. As relations are supposed to be accidents inhering in a substance, this approach would tend to substantivalize the instants and thus undermine the otherwise relational account which we have seen that thirteenth-century thinkers were trying to be committed to. If we press the point further and ask what the foundation of temporal relations is supposed to be, then at that

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point medieval thinkers would appeal to their reductionist approach and direct us to motions and the ‘moments’, or motion boundaries, which they contained. In so doing, however, they would be admitting that there is not really a foundation for each of the temporal relations as such, so temporal relations themselves would have to be viewed as reducible to the more fundamental motion; as would the dependency relation which we have seen was essential for a relation to be ‘real’ rather than simply ‘rational’. And yet we have seen that Aristotle and his medieval commentators were extremely reluctant to accept that time, and the temporal elements and relations which constituted it, could be so reduced. In analysing medieval accounts of relations we explored the question of contemporary interest about whether medieval theories of time should be viewed as absolute (substantival), as relational, or as modal relational. The evidence overwhelmingly suggested that thirteenth-century accounts should be interpreted as instances of a relational model, but there were nevertheless tantalizing glimpses of potential modal developments in some of Albert’s work. One of the most perplexing aspects of thirteenth-century reflection was Aquinas’ interest in the notion of imaginary time. I have suggested that this notion cannot easily be integrated into his wider philosophical reflections on time and that it must therefore be viewed as representing a theologically motivated incursion; an incursion that ultimately further undermined the coherence of his account of temporal relations.

5 The Reality of Time

This chapter will be exploring a set of related themes and questions, focusing upon the central issue of the reality of time. As well as examining the question of thirteenthcentury views about the mind-dependence of time, we shall also be examining their views about the reality of temporal becoming and flow, so that we can establish how thirteenthcentury views can be represented in terms of the contemporary debate about whether time is best thought of in terms of flowing (A theory) or static (B theory) models.

EXPERIENCING TIME When considering the reduction of aspects of time to aspects of motion, Aristotle considered the interesting case of individuals whose experience of time was interrupted: When we ourselves do not suffer changes in our mind, or notice alterations, then it does not seem to us that time exists, just as it did not seem so to the fabled sleepers in . . . Sardinia. When they woke

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up they joined up the earlier instant to the later one making it one, removing the time in between because they hadn’t noticed it . . . it is manifest that there is no time apart from change and alteration.1

Aristotle seems to be suggesting in this passage that if there could be a situation where people failed to experience change or motion, that would suggest that time was not passing for them. Perhaps he is influenced towards this conclusion by the verificationist worry of what it would mean to talk of specific amounts of time in the absence of perceived measures of time, but the overall direction of his comments would seem to be implying that the experience of time was crucial for its actual existence.2 Thirteenth-century thinkers certainly read the passage in this way and were not slow in repudiating what they considered to be its mistake. As Kilwardby caustically commented, surely the role of perception and experience is to help us know time not make it.3 1 Aristotle, ‘cum enim nichil ipsi [tempora] mutamus secundum intelligentiam aut latet transmutantes, non videtur nobis fieri tempus, sicuti neque in Sardo qui fabula certo dormire . . . Cum expergescantur copulant enim primum nunc posteriori nunc et unum faciunt, removentes propter insensibilitatem medium. Tamquam igitur si non esset laterum nunc sed idem et unum, non esset tempus, sic et quoniam latet alterum esse, non videtur medium esse tempus. Si iam et non opinari esse tempus tunc accidit nobis, cum non diffinimus nec unam mutationem, sed in uno et indivisibili videtur animae manere, cum autem sentimus et determinamus, tunc dicimus fieri tempus, manifestum est quod non est sine motu nec mutatione tempus.’ Phys. 4. 11. 218B22–34 (AL 7. 1.2, 173, 5–17). My italics above. For further development of the issue see also Averroes’ discussion, In Phys. 4 [130]. 2 On Aristotle’s possible verificationist concerns, R. Sorabji, Time, Creation and the Continuum, 74–8. 3 ‘non . . . facimus tempus per nostram diffinitionem vel numerationem, sed per hoc cognoscimus illud’, de Temp. 14 [77] (29, 18–21).

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A further way in which experience and mind-dependence sometimes crept into accounts of time arose from the very definition which Aristotle himself had given of time, viewing it as the ‘numbering of change’. Numbering implies a numberer, so medieval thinkers frequently had to face the question of whether the definition of time implied the necessary precondition of an existing mind if time itself were to exist. This is perhaps most clearly shown in Averroes, who understood Aristotle to be arguing that in the absence of an actual numberer (soul), there would not be an actual time. There would be just a potential time, an un-numbered (unmeasured) duration of motion. Using the terminology of matter and form, or material and formal elements, this position was echoed by many of the thirteenth-century thinkers such as Aquinas, who argued explicitly in his earlier Commentary on the Sentences that in the absence of a numbering soul, time existed merely ‘materially’. It was the soul that gave it formal existence (or at least gave the formal temporal metric an existence) and so, as far as Aquinas was concerned, the soul was necessary for the full proper existence of time.4 Albert took a rather different approach. Whilst he was happy to concede that actual numbering required an actual soul, he went on to suggest that there must also be a further 4 Averroes, ‘et si anima non erit, et secundum quod prius et posterius sunt in eo numerata in potentia, est tempus in potentia: et secundum quod sunt numerata in actu, est tempus in actu’, In Phys. 4, [131]; Aquinas, ‘ex quo patet quod illud quod est de tempore quasi materiale, fundatur in motu, scilicet prius et posterius; quod autem est formale, completur in operatione animae numerantis; propter quod dicit Philosophus quod ‘‘si non esset anima, non esset tempus’’ ’, In Sent. 1. 19. 2. 1; Albert, Phys. 4. 3. 9 (4.1, 275, 39–41); also J. Broussard, ‘Eternity in Greek and Scholastic Thought’, 141.

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‘principle’ of number in the actual motion; a formal element which meant that there was something to be counted existing independently, whether or not there was a soul to do the actual counting. The existence of this formal element, in his opinion, ensured that there was no need to talk of the soul ‘making’, or ‘constituting’, time, as Kilwardby had put it.5 As time passed, Aquinas seems to have become unhappy with his former position in his Commentary on the Sentences, and so almost twenty years later when he came to write his Commentary on the Physics, he too had changed his mind: but for slightly different reasons than Albert. Reflecting on the fact that it is possible to talk of ‘sensible’ things (things capable of being sensed) in the absence of a ‘senser’, he was willing to allow that there could be countable things in the absence of a counter, and in doing so he showed himself willing to use a modal analysis that Albert consistently showed himself reluctant (or unable) to make use of: it must be realised that if there are numbered things, then there must be number. Hence, both numbered things and their number depend on one who numbers. Now the existence of numbered things does not depend on an intellect unless there is some intellect which is the cause of things, as is the divine intellect. However, their existence does not depend on the intellect of the 5 Albert’s refinement is to view the soul as having an efficient, rather than formal, role in the numbering process, ‘ergo ad numerare tria exiguntur, scilicet materia numerata et numerus formalis et anima efficienter et non formaliter numerans; ergo si non sit anima, adhuc numerus est secundum esse formale et secundum materiam numeratam’, Phys. 4. 3. 16 (4.1, 290, 2– 11). Grosseteste makes a similar point but refers to the soul’s aptitude to count. ‘Numerus enim secundum quod ponitur in diffinicione temporis non dicit actualem numerationem, sed aptitudinalem ab anima.’ In Phys. 4 (104).

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soul. Only numeration itself, which is an act of the soul, depends on the intellect of the soul. Therefore just as there can be sensible things when no sense power exists, and intelligible things when no intellect exist, likewise there can be number and numerable things when no one who numbers exists.6

Although it made sense to relate the question about the existence of time to the existence of sense perception objects in the absence of a perceiver, there was nevertheless a crucial dissimilarity between sense perceptible things and particulars such as time and motion. Whilst sense perceptible things can exist at an instant and can be grasped by a single intellectual act, time and motion must, of their very nature, exist sequentially and extensionally. This means that, unlike sense perceptible things, they cannot exist at the present instant and so cannot be grasped in the present instant by the same kind of single undivided intellectual operation. 6 Aquinas, ‘positis rebus numeratis necesse est poni numerum. Unde sicut res numeratae dependent a numerante ita et numerus earum. Esse autem rerum numeratarum non dependent ab intellectu, nisi sit aliquis intellectus qui sit causa rerum sicut est intellectus divinus; non autem dependet ab intellectu animae. Unde nec numerus rerum ab intellectu animae dependet, sed solum ipsa numeratio, quae est actus animae, ab intellectu animae dependet. Sicuti ergo possunt esse sensibilia sensu non existente, ita possunt esse numerabilia et numerus non existente numerante.’ In Phys. 4. 23 [629]. For further details about Aquinas’ change of mind, J. Quinn, ‘The Doctrine of Time in St. Thomas Aquinas: Some Aspects and Applications’, 315–16; and J. Weisheipl, The Development of Physical Theory in the Middle Ages, 45. For Albert’s views on modal relations see his In Sent. 1. 8. A. 12 (Borg. 25, 235). He insists, for example, that measures only exist if the measured things themselves exist, ‘mensura non est nisi mensurati’, In Sent. 1. 8. A. 8 (Borg. 25, 229). Aristotle’s original argument occurs at Phys. 4. 14 (223A21–9) and there remains considerable contemporary disagreement about what point he was trying to make. For further details, R. Sorabji, Time, Creation and the Continuum, 90–5.

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Instead, implied Aquinas, their existence must almost be inferred by a mind, rather than merely observed: nor is anything concerning motion actually found in things except a certain indivisible part of motion, which is a division of motion. But the totality of motion is established by a consideration of the soul which compares a prior disposition of the mobile object to a later one. Therefore time also does not have existence outside the soul except in respect to its own indivisible part. For the totality of time is established by the ordering of the soul which numbers the before and after in motion.7 7 ‘Sed motus non habet esse fixum in rebus, nec aliquid actu invenitur in rebus de motu nisi quoddam indivisibile motus, quod est motus divisio; sed totalitas motus accipitur per considerationem animae comparantis priorem dispositionem mobilis ad posteriorem. Sic igitur et tempus non habet esse extra animam nisi secundum suum indivisibile. Ipsa autem totalitas temporis accipitur per ordinationem animae numerantis prius et posterius in motu.’ In Phys. 4. 23 [629]. See also Aquinas, ‘Sicut igitur, si non esset aliud et aliud nunc, sed idem et unum, non esset tempus medium; sic et quando latet diversitas duorum nunc, non videtur tempus esse medium. Si ergo tunc accidit non opinari tempus, cum non percipimus aliquam mutationem, sed homini videtur quod sit in uno indivisibili nunc; tunc autem percipimus fieri tempus, quando sentimus et determinamus, id est numeramus, motum aut mutationem; manifeste sequitur quod tempus non sit sine motu, neque sine mutatione.’ In Phys. 4. 16 [570]. Pseudo-Aquinas takes a similar position, ‘Et ideo anima in suis cogitationibus percipit successionem continuam, et apprehendit prius et posterius in ea, et in hoc consistit ratio temporis . . .’ de Instan. 1 [314]. Bonaventure does not discuss this problem, but his stress upon the need for the soul to hold a plurality of instants, as a condition for the existence of time, suggests he would hold the same basic view as Aquinas, see his Quaest. Disp. de Myst. Trin. 5. 1. Sylvester Ferrariensis, the fifteenthcentury Thomist commentator, took Aquinas to be claiming, ‘Unde remoto opere animae, est quidem in re illa entitas quae est tempus: sed non habet complete rationem temporis, quia non habet actualem divisionem et separationem et consequenter non est actualiter numerus.’ Commentaria in Sum. Con. Gen. 1. 15 (Leonine edn. 13, 43). Ferrariensis seems not to appreciate that Aquinas’ position has developed between his earlier and later works and so he thinks that his final position is roughly similar to his earlier one, that a

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In reflecting on this problem Aquinas seems to be struggling to relate three distinct sets of issues and problems. In the first place, and particularly in his earlier works, he was influenced by Averroes’ view that time could only exist partially (materially) in the absence of a soul numbering or measuring time. We could almost express that early position as the view that time has a topology independently of a mind, but it receives its metric only when a mind exists to measure it, and it is only when time has both a topology and a metric that it exists in its full sense. When he revisits this issue almost twenty years later, he has moved away from that view but was instead juggling two totally different sets of considerations, considerations which ultimately pull in diametrically opposite directions. On the one hand, he wants to affirm the mind independence of reality and so he is inclined to accept that time can exist in the absence of a soul or mind. Even when a soul does not exist to carry out measurements, it remains the case that time’s topology is derived from the Primum Mobile and because its motion represents a process, as we shall see in Chapter 6, that necessarily meant that it had a metric too, albeit one that can only be recorded by a mind. However, whilst he seems to have been more open to the mind-independence of time in consideration to arguments about measurement, he nevertheless seems to have become concerned about the implications of the argument for the nature of time. Material objects that can exist independently soul or mind is required in order to ‘complete’ time. Although Aquinas may indeed be open to allowing a role to the soul or mind, as we shall see below, it has little to do with ‘completing’ or ‘measuring’ time.

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of a mind can exist at an instant. Even if their existence is typically over periods, they are still such that they can be said to be existing at an instant such as the present instant. Time (and motion) are crucially dissimilar. Their very nature requires extension over more than a single instant, but as all that ever exists is the present instant, this would seem to require a soul to hold at least another instant in mind in order to create a sense of time. Aquinas’ ambiguity and ambivalence about the minddependence of time arose largely because he was not entirely sure how to address this distinct problem of how, given the nature of time, it could be said to exist at all. The classic focus for considering this issue arose as a result of what I shall call Aristotle’s Paradox.

A R I S TOT L E ’ S PA R A D OX Aristotle’s paradox is a problem which he introduces in Book 4 of his Physics and, although he states it in different ways, the force of the paradox remains the same. The paradox starts from the assumption that time is composed (componere) or constituted (constituere) by continuous periods. By adding the additional assumption that it is only ever the present instant which actually exists, the paradox proceeds by insisting that no period can exist in the present instant and so no periods can exist at all. In Aquinas’ version the paradox concluded: Anything that is composed of things which do not exist cannot itself exist or have any substance. But time is composed of things

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which do not exist. For one part of time is the past which does not exist, and the other part is the future which does not yet exist. And from these two things the whole of time, given as infinite and perpetual, is composed.8

The formulation of the paradox, and the acceptance of its force, involves a commitment to what has come to be known as ‘entitism’; the view that it is possible to talk of instants as particulars and make sense of individual instants having, in some sense, an existence. The relational implications which we saw in the last chapter that thirteenth-century thinkers were committed to, provided a degree of inoculation to the quasi-substantival assumptions behind entitism, and perhaps for that reason later medieval thinkers were less interested in the problem. The interest for earlier thirteenth-century thinkers arose because the problem was raised by Aristotle and left hanging without any apparent solution being provided in his text.9 8 ‘Omne compositum ex his quae non sunt, impossibile est esse, vel habere aliquam substantiam. Sed tempus componitur ex his quae non sunt; quia temporis est aliquid praeteritum, et iam non est, aliud est futurum et nondum est, et ex his duobus componitur totum tempus, infinitum et perpetuum positum. Ergo impossibile est tempus aliquid esse.’ In Phys. 4. 15 [559]. Also Albert, Phys. 4. 3. 1 (4.1, 259, 57 f.). For a much longer analysis identifying five distinct versions of this paradox, see Albert, Sum. de Creat. 2. 5. 1 (Borg. 34, 364–6); and for a version based on the property of extension, rather than, as here, ‘existence’, see Aquinas, In Meta. 5. 15 [977]. For Aristotle’s arguments, Phys. 4. 10. 218A1–3, 218A3–5, 218A8–30; Categ. 6. 5A26. Aquinas, In Phys. 4. 15 [560]. The use of the verb ‘constituere’ seems to be a preference of the Latin translations of Aristotle. Patristic sources tend to use in its place ‘facere’ and its cognates, see Pseudo-Bede, de Divisionibus Temporum (PL 90, 653–4). 9 On ‘entitism’, J. Zupko, ‘Nominalism meets Indivisibilism’; and for later medieval rejection of it, Scotus, Opus Oxon. 2. 9. 2; as also, in the next century, Burley, Chatton, and Henry of Harcley, on whom see J. E. Murdoch,

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One of the earliest responses to the paradox was probably Augustine’s. Although medieval thinkers such as Kilwardby read him to be responding to Aristotle, it is not clear that Augustine was actually writing with the text of Aristotle’s Physics in mind. Nevertheless, Augustine was clearly aware of the kinds of concerns that Aristotle had identified and his response to the paradox is relatively simple. He accepted the broad outlines of the paradox and concluded that time could not be a ‘real’ phenomenon. Instead, it was to be viewed as simply a mental or intellectual phenomenon, a ‘distension’ (distensio) of the soul in which the present instant is just the boundary of our awareness of the past and future. For Augustine the present instant is held in the mind and joined to successive instants in order to generate a sense of extensional periods, and so time.10 Whilst writers such as Grosseteste were sympathetic to the broad contours of Augustine’s approach, neither Albert nor Aquinas were happy with the way that it conceded the ‘William of Ockham and the Logic of Infinity and Continuity’, and C. G. Normore, ‘Walter Burley on Continuity’. Contemporary sympathies would generally favour the non-entitist position, viewing instants as logical fictions, on which see G. J. Whitrow, The Natural Philosophy of Time, 157, and B. Russell, Logic and Knowledge, 63. On the question of whether Aristotle ever resolved the paradox, E. Hussey, Aristotle, Physics, Books III and IV, 139–40; and with a different nuance, N. Kretzmann, ‘Aristotle on the Instant of Change’, 91–114. 10 Kilwardby, de Temp. 1 [4] (7, 15–17). Kilwardby’s view that Augustine was responding to Aristotle’s paradox is not unreasonable as we know from Augustine himself that he was familiar with Aristotle’s Categories: Conf. 4. 16 (28), and there are actually echoes of Aristotle’s paradox to be found in his own work, Conf. 11. 14 (17). For other medieval commitments to an Augustinian approach on this question see Grosseteste, In Phys. 4 (95). Avicenna also seems to take a similar approach to Augustine, Suff. 2. 10.

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point at issue, viz. that time does not exist in the present instant. In their opinion, the reality of time could be established by exploring the implications of reducing it to motion. Often Aquinas talks of the reduction to motion as providing the solution to the problem, but that cannot be quite right. If the problem really is how an extensional time can exist at the present instant, appealing to motion is not going to solve the problem, as exactly the same question will arise as to how an extensional motion can exist at the present instant. In order to establish some sense in which the motion can be existent it is necessary to reduce the matter still further to the subject of the motion, and in the case of time that is, as we saw in the last chapter, the Primum Mobile. Although the Primum Mobile could not be thought of as moving in the present instant, the reality of the periods which its motion was thought to generate would be entailed by the fact that the Primum Mobile was existent in the present instant with a nature that entailed the natural flowing motion, which was thought to be observed in the rotation of the heavenly bodies.11 11 We shall examine the notion of the ‘flowing now’ in the next section, and how it was thought to generate time. At this point it is only necessary to note that it was the flowing now which was thought to generate time, and that the flowing now could be reduced to what Albert terms a ‘flowing moment’. This seems to have been an analogous non-extensional ‘present state’ of the motion of the Primum Mobile. Albert, ‘Cum autem in motu et in tempore sint indistincta, quia in motu non est nisi momentum currens et in tempore non est nisi nunc fluens.’ Phys. 4. 3. 6 (4.1, 270, 29–33). Ps.-Aquinas seems to think that the existence of the present instant is enough to justify the existence of time, because it is the ‘substance’ of time, de Instan. 3 [323]. On the appeal to motion, albeit with only a loose reference to the potentiality of motion as a way of addressing the issue of how motion can be said to exist (in the present instant), Aquinas, ‘tempus est simul cum motu, sive motus

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This approach does not entirely resolve the problem because it still remains the fact that there is no sense in which an extensional particular such as time can be said to actually exist in a non-extensional present instant. For this reason, Aquinas and Albert continued to maintain that there was a role for the mind. Even if the reality of time could be established by reducing questions about it to questions about the motion of the Primum Mobile, it remained the case that the only way in which a period could be said to be present in an instant would be if it were held in a mind which was itself present in the instant in question.12 accipiatur secundum actum sive secundum potentiam. Quaecumque enim sunt possibilia moveri et non moventur actu, quiescunt. Tempus autem non solum mensurat motum sed etiam quietem, . . . Unde relinquitur quod ubicumque est motus, vel actu, vel potentia, quod ibi sit tempus.’ In Phys. 4. 23 [626]. 12 Albert, ‘Nunc enim est quod adiacet ei quod fertur in motum secundum acceptionem animae. Sed id quod fertur in motum, numquam accipitur stans hic vel ibi in tota magnitudine, per quam movetur, sed semper accipitur partim hic et partim ibi, ut protensum de ubi in ubi et iteratum per totam magnitudinem, per quam movetur. Anima ergo accipiens ipsum, secundum id quod adiacet ei, secundum id quod movetur, accipit nunc ut fluens de priori in posterius continue.’ Sum. Theol. 5. 22. 1 (34.1, 115, 47–55). See also Kilwardby, de Temp. 1 [9] (8, 17–21). For further details on Aquinas’ position and the way he seems to move closer to Albert’s in his latter works, see P. A. Redpath, ‘The Ontological Status of Time’, 13–14. One of the ways in which thirteenth-century thinkers could have resolved Aristotle’s paradox would have been to deny its assumption that existence must amount to existence at the present instant. If they had developed, instead, a notion of existence which amounted to existence over a period bounded by the present instant, then this would have enabled them to affirm the existence of an extensional time without having to appeal to a mind in which it could exist. Discouraging them from taking this kind of approach was both their attraction for simultaneous causation, which we saw earlier, and their accounts of particulars such as angels, which we shall see later involved existence at a nonextensional instant.

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THE REALITY OF TEMPORAL BECOMING: T H E A A N D B T H E O R I E S OF T I M E A final area where issues of mind-dependence and the reality of time could arise for medieval thinkers was in considering the nature of temporal becoming. In order to understand temporal becoming it is important to distinguish between two sets of terms which we can use to describe temporal orderings. These two sets, and the accounts of time they give rise to, have traditionally been referred to as the A and the B series accounts of time.13 On the A series account of time, temporal items such as instants and periods, or even substances and events located at temporal references, can be said to be past, present, and future. According to this model, the status of instants and the events or substances located at those instants is forever changing, as those that are future become closer to the present, before becoming actually present and then finally slipping away into the past. It is for this reason that the A series is sometimes referred to as a ‘dynamic’ or a ‘flowing’ series and the account of time that it gives rise to is referred to as an account of temporal becoming or a tensed theory of time.14 13 J. McTaggart, ‘The Unreality of Time’. 14 Strictly speaking the word ‘tensed’ refers to more than just tenses. We can characterize an A series account of time with verbs such as ‘will be’, ‘is’, and ‘was’, but we could also use adverbs such as ‘tomorrow’, ‘today’, and ‘yesterday’. It should be noted that the A series account is sometimes referred to as a ‘token reflexive’ account of time. There is contemporary disagreement about whether ‘pastness’, ‘futureness’, and ‘presentness’ should be interpreted

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The A series is to be contrasted with a second series of temporal terms which are purely relational, such as ‘earlier than’, ‘simultaneous with’, and ‘later than’. This B series is sometimes referred to as a static series because particulars located within it are static, that is they never change in relation to each other. If the death of Albert is later than the death of Aquinas then the relation between those events is static; Albert’s death is always going to be later than Aquinas’ death. This contrasts with tensed references to events in Albert’s life which change as time itself changes. It is not always going to be the case, for example, that Albert’s death is going to be ‘in the future’ or ‘in the past’. Subsequent to his death his death will no longer be in the future, and prior to his death it was not in the past. But given the respective dates of their deaths, both before and after Albert’s death it was an unchanging fact that Albert’s death is later than the death of Aquinas. Sometimes it is thought that advocates of the B theory are denying ‘temporal becoming’, and not accepting that things happen; but that is a far too crude analysis of their position. Instead, advocates of the B theory accept temporal becoming but, as they believe that the relationships between events are static and unchanging, they view ‘becoming’ as something which is simply a mind-dependent phenomenon.15 as relations or as properties. For further details see R. Le Poidevin and M. MacBeath (eds.), The Philosophy of Time, 33; R. Swinburne, ‘Tensed Facts’, 119; R. Gale, The Language of Time, 240. 15 Sometimes the B theory of time is referred to as a ‘stasis theory’ (A. Padgett, God, Eternity and the Nature of Time, 74). On the problems with B-theory accounts of ‘becoming’, see A. Gru¨nbaum, ‘The Status of Temporal Becoming’, 322–54. Some critics of the B series reject it precisely

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Whilst the question of A and B theories of time is still of considerable importance to contemporary thinkers, the issues have been broadened recently to include a discussion of A and B sentences, and A and B facts, where A sentences and facts are simply those which are tensed and B sentences and facts are those which are not tensed. In all these cases the question of interest to contemporary philosophers is not so much the issue of mind-dependence, but rather the more fundamental reductive question of whether the A or B theory can be reduced to each other. Advocates of reducing B series to A series typically argue that what it is that makes a sentence such as, ‘It’s raining now,’ true is the tensed fact that it is now in fact raining. But advocates of the B series have replied by insisting that what it is that makes such sentences true is the tenseless (timeless) fact of rain simultaneous with the utterance of the A sentence. And so defenders of the A series have been forced to develop accounts of tensed truth which cannot be reduced to timeless tenseless truths.16 because it can seem to imply that time is a mind-dependent illusion, on which see, W. Hasker, ‘Concerning the Intelligibility of the claim ‘‘God is Timeless’’ ’, 190. 16 Advocates of the B theory have identified at least four reasons for preferring it to A-theory accounts of time. The A theory entails a contradiction (J. MacTaggart, ‘The Unreality of Time’). All A-theory facts or truth conditions can be reduced to B-theory ones, and so A-theory facts or truth conditions become redundant (D. H. Mellor, Real Time, 29–73). Temporal becoming is irrelevant to physical theories (A. Gru¨nbaum, ‘The Status of Temporal Becoming’, 322–54) and the Special Theory of Relativity requires it (R. Weingard, ‘Relativity and the Reality of Past and Future Events’, 119–21). For a general apology for the B theory see Hector-Neri Castan˜eda, ‘Omniscience and Indexical Reference’. 203–10. Apologists for the A series, such as N. Kretzmann, ‘Omniscience and Immutability’, 409–21, and R. Swinburne, ‘Tensed Facts’, 117–30, take the view that the B series is seriously

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The position of thirteenth-century thinkers in relation to this contemporary debate is neither straightforward, nor entirely clear. They did not typically appreciate the distinction between A and B theories and so, where they raise issues which are of relevance to the contemporary debate, they often do so partially and in passing, rather than attempting to present anything like a complete and consistent treatment of the matter. Nevertheless, it has been argued that there are aspects of thirteenth-century thought which seem to entail a commitment to the B theory of time and the notion that ‘temporal flow’ or ‘becoming’ is mind-dependent. This is particularly the case with medieval treatments of divine omniscience, where it has been suggested that the medieval assumption seems to be one which views God as timeless and omnisciently knowing all events and facts in a single immutable act of knowing. Such a view of God would be very difficult to make sense of unless medieval thinkers accepted a B-theory approach to time, one that entailed that all events and facts have a single (timeless) relationship to each other which could be grasped in a single act of knowing.17 deficient as an account of time, as it is unable to do sufficient justice to the significance of the present. For an overview of the debate, see A. Padgett, God, Eternity and the Nature of Time, 82–121. The most comprehensive treatment of the issues is to be found in the two treatises by W. L. Craig, The Tensed Theory of Time: A Critical Examination, and The Tenseless Theory of Time: A Critical Examination. 17 D. Lewis, ‘Timelessness and Divine Agency’, 143–59. In an interesting development J. C. Yates, The Timelessness of God, 296, offers an attempt to defend an A-theory view of time with timelessness. W. L. Craig has argued that Aquinas, at least, commits himself to a B-theory account in explaining divine relations to the world, but commits himself to an A-theory account in

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Further evidence of a possible commitment to a B-theory, tenselessness account, is evident amongst those Aquinas refers to as ‘Nominales’. Prompted by the theological need to make sense of divine knowledge about matters which change, there was a tendency to treat sentences such as ‘Christ is born’ and ‘Christ will be born’ as making the same (tenseless) claim about the world. Aquinas rightly draws attention to the incoherence involved in this approach, since it seems to ignore the obvious fact that such different sentences have clearly different truth conditions. It is difficult to know for sure precisely how we should interpret the position of the Nominales. Rather than committing themselves to the crude absurdities which Aquinas points to, they may instead have been trying to formulate an account of A facts and A sentences which could be reduced spelling out the natural order, see W. L. Craig, ‘Aquinas on God’s Knowledge of Future Contingents’, 33–79; ‘Was Aquinas a B-Theorist of Time?’ 475–83; and The Problem of Divine Foreknowledge and Future Contingents From Aristotle to Suarez, 118. His interpretation is challenged by Theodore Kondoleon, ‘God’s Knowledge of Future Contingent Singulars: A Reply’, 117–39. Aquinas’ position is considerably more complicated than it might initially seem, because although he uses the metaphor of God ‘seeing’ all the events of time, his actual position is that God does not depend on events for His knowledge. His knowledge is causal and events depend for their existence on being known by God. See also Albert for a similar account, In Sent. 1. 38. A. 1. Bonaventure sees God as merely ‘co-operating’ with good acts, i.e. as not knowing their outcome from being their cause, In Sent. 1. 37. 1. 1, a position which Tarentaise seems to share, In Sent. 1. 38. 1. 1–2, but which Aquinas rejects as heretical (semi-Pelagian), instead reiterating the fact that God must know the future through ‘causing’ it, Sum. Theol. 1. 14. 8; 1. 14. 13. Once the causal role of the knowledge is stressed, it becomes less apparent that omniscience considered on its own must entail either an A- or a B-theory account of time, although consideration of the additional factor of divine immutability would seem to rule out any changing knowledge that included tensed facts.

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to B-theory facts and sentences, in which case their position would have been infelicitously stated but nevertheless trying to use the distinction between A- and B-theory terms to offer an account of omniscience.18 Despite the specific needs occasioned by reflections upon the problem of omniscience, the overwhelming impetus of thirteenth-century accounts of time seems to be in an A-theory direction. We have seen earlier, for example, that temporal relations of before, after, and simultaneous were understood as having an essential reference to the (ever changing) present instant. But perhaps the clearest evidence of medieval commitment to the A theory arises from the way in which they viewed the Primum Mobile’s role in relation to temporal flow. It is clear in medieval accounts that the actual generation of time was thought to arise from the flowing now (nunc fluens) which, as it flows from the future into the past, generates a time which Albert was quite willing to talk of as ‘not existing yet ’, prior to the movement of the flowing now.19 18 Aquinas, ‘dicendum quod antiqui Nominales dixerunt idem enuntiabile esse Christum nasci et esse nasciturum et esse natum; quia eadem res significatur per haec tria, scilicet nativitas Christi; et secundum hoc sequitur quod quidquid Deus scivit sciat’, Sum. Theol. 1. 14. 15 ad 3. 19 Terminology for the flowing now was fluid. Albert at times refers to it as a flowing instant, Sum. Theol. 5. 22. 2. 2 (34.1, 119, 30–1) and flowing point, Sum. Theol. 5. 22. 1 (34.1, 116, 43). On the role of the flowing now, Albert, ‘sicut tempus est numerus motus, ita nunc est unitas eius quod fertur, unum existens in toto motu, Et sicut id quod fertur, agit motum, ita nunc agit tempus; . . . id quod fertur, agit motum, et est notius motu, eo quod ipsum est substantia permanens in seipsa, motus autem non . . . Id autem quod fertur agit motum per hoc, quod fluit a priori in posterius in spatio, et numerus partium motus est tempus, et unitas eius in toto motu est nunc quod est idem in substantia propter incorruptibilitatem et invariabilitatem mobilis

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In order to understand the notion of the flowing (or continuous) now it was felt important to distinguish it from the terminal now (nunc terminans), which we analysed in Chapter 1, as simply the unchanging boundary of a period. Whilst a boundary date such as 1 January 2000 will always bound the same period, the continuous now is constantly changing as the present itself changes. In determining the relationship between both notions of the now, thirteenthcentury thinkers generally viewed the flowing now as having a logical primacy such that it actually generates the terminal nows or boundary instants of periods.20 sive eius quod fertur secundum subiectum, et est secundum esse diversum, inquantum fluit a priore in posterius, cuius causa est renovatio situs in eo quod fertur, uno existente secundum subiectum.’ Phys. 4. 3. 7 (4.1, 272, 63– 77); ‘nunc transiens facit tempus’, Meta. 5. 3. 2 (16.1, 260, 43); ‘tempus enim in praeterito non est. Futurum autem in futuro nondum est. Acceptum autem in nunc esse temporis non habet, sed substantiam imperfectam quod esse temporis non accipit nisi in fluxu de praeterito per praesens in futurum. Qui fluxus ab eo quod abiit in non esse, incipit, et terminatur in id quod nondum est.’ (Italics mine) Lib. de Causis 2. 4. 7 (17.2, 161, 70–6); Sum. Theol. 5. 22. 2. 2 (34.1, 119, 23–4). Aquinas, Quaest. Disp. de Ver. 29. 8 ob. 6. On the origins of the notion, Boethius, de Trin. 4. 4; Aristotle, Phys. 4. 10–12. As well as identifying the role of the flowing now as having a crucial role in generating time, Albert also claimed that the continuity of the flowing now explained the topological property of temporal continuity, Sum. Theol. 5. 22. 2. 2 (34.1, 119, 31); Phys. 4. 3. 6 (4.1, 270, 31–2). See also Theodoric, Tr. de Nat. et Prop. Cont. 3 (3, 258, 84–90). The flowing now of time was generally contrasted with the standing now (nunc stans) of eternity, ‘Nunc autem temporis propter relationem quam habet ad prius et posterius, magis est in se varium et diversum quam nunc stans et non movens se’, Albert, In Sent. 1. 9. B. 5 (Borg. 25, 279); Phys. 4. 4. 2 (4.1, 295, 48); Sum. Theol. 5. 22. 2. 2 (34.1, 119, 54–6). Aquinas, Sum. Theol. 1. 10. 1. Bonaventure, In Sent. 2. 1. 1. 1. 2 ad 3. Alexander, ‘et est nunc temporis, quod est fluens a praeterito in futuram’, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 1 (1, 106). 20 Albert, Sum. de Creat. 2. 3. 2 (Borg. 34, 341); Sum. Theol. 5. 22. 1 (34.1, 116, 46–8); 5. 22. 2. 2 (34.1, 119, 27–30); Phys. 4. 3. 7 (4.1, 271, 58–60); 4. 3.

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In order to spell out how a flowing now can generate time, thirteenth-century thinkers often appealed to an analogy popularized by Avicenna. This analogy compared time to a geometrical line. As a line is generated by drawing a writing implement across a medium, so the analogy suggested that time itself was generated as a result of the movement of the flowing now.21 Avicenna’s analogy certainly possessed value. We can indeed imagine a point moving across a page and thus producing a line but, as Albert himself points out, it is frivolous (frivolum) to assert that moving geometrical points really make lines. For a start, there is no such thing as a moving geometrical point. Any talk of a writing implement making a line is a distinctly non-geometrical example because the point of such an implement must actually possess a quantity, 8 (4.1, 275, 40–3); In Sent. 1. 8. B. 13 (Borg. 25, 239); Meta. 5. 3. 2 (16.1, 260, 47–8). Bonaventure proposes a similar analysis in terms of the essence and esse of time, ‘dupliciter est loqui de tempore: aut secundum essentiam, aut secundum esse, Si secundum essentiam, sic nunc est tota essentia temporis et illud incepit cum re mobili, non in alio nunc, sed in se ipso quia status est in primis, unde non habuit aliam mensuram. Si secundum esse, sic coepit cum motu variationis, scilicet nec coepit per creationem, sed potius per ipsorum mutabilium mutationem, et maxime, primi mobilis’, In Sent. 2. 1. 1. 1. 2 ad 4. See also Siger of Brabant, Sup. Lib. de causis II (63, 21–6); Aquinas, In Phys. 4. 18 [583], [585]. It has been suggested that if Aristotle’s ‘now’ was always the same then this would entail the simultaneity of all time (N. Kretzmann, ‘Aristotle on the Instant of Change’, 106) but using the distinction between a continuous now and a terminal now we can see that it is only the terminal now which would be the same. The flowing now is ever-changing. For more details, E. Hussey, Aristotle, Physics Books III and IV, pp. xliv–xlvi. 21 Ps.-Aquinas, ‘Sciendum est ergo quod sicut punctus se habet ad lineam, ita se habet ‘‘nunc’’ ad tempus. Geometrae autem imaginantur punctum per motum suum causare lineam.’ de Instan. 2 [320]; also see Aquinas, In Sent. 1. 37. 4. 3; Albert, Phys. 4. 2. 6 (4.1, 242, 65). For Avicenna’s analogy, Suff. 2. 12.

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otherwise it would make no mark at all. Further, real lines (as opposed to geometrical lines) come into existence as the result of the movement of a real substance upon a medium like paper. If Avicenna’s analogy was to have any practical value it was necessary to clarify how precisely the flowing now could be identified with a substance and medium in order to generate time.22 We saw in the last chapter that there was a clearly marked tendency in medieval accounts to follow what they took to be the Aristotelian approach of reducing questions about the temporal topology to questions about the Primum Mobile. This reductive approach tended to be applied also to the question of the flowing now, which thirteenth-century thinkers seem to have thought could be identified, in some sense, with the Primum Mobile itself. One of the consequences of this is that as the Primum Mobile was thought to rotate around the earth, moving through the medium of space, so the very topology of time seems to have been treated, albeit hesitantly and not always clearly, as if it could be reduced to the topology of the motion of the Primum Mobile, which itself could be derived from the topology of the space it was moving through.23 22 Albert, ‘quidam dicunt de motu puncti, quod motu suo constitutit lineam et linea motu suo superficiem . . . penitus est frivolum, quia punctus non movetur et similiter nec linea . . . Talia ergo dicta sunt secundum imaginationem solam et non secundum rei naturam.’ Meta. 5. 3. 2 (16.1, 260, 15–24). 23 Albert, ‘oportet quod nunc quod constituit tempus et est substantia temporis, sit fluens et fluxu suo temporis successionem constituat’, Sum. Theol. 5. 22. 1 (34.1, 115, 28–40); In Sent. 1. 30. B. 4 (Borg. 26, 93). On the identification of the Primum Mobile with the flowing now see Albert, Sum. de Creat. 2. 3. 2 (Borg. 34, 347); Phys. 4. 3. 10 (4.1, 277, 72 f.); 4. 3. 13 (4.1, 285, 56–

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As the Primum Mobile was considered to be the substance that was the ‘subject’ of time, there can be little wonder that medieval thinkers felt tempted to try to identify, in some sense, the flowing now with the Primum Mobile. In doing so they clearly interpreted language about the flowing now to have more than merely metaphorical import, although precisely what it would have meant for such language to have more than metaphorical import was left unhelpfully vague. Although it is difficult to clarify the import of their language we can sum up graphically what seem to have 9); 4. 3. 17 (4.1, 292, 9–20); Grosseteste, In Phys. 4 (105); Siger, Sup. Lib. de Causis 11 (63, 28–31). On the topological significance of the medium of motion, Aquinas, ‘divisio motus sumitur ex divisione spatii vel ex divisione mobilis’, In de Trin. 5. 3 ad 5. See also Albert, Phys. 4. 3. 5 (4.1, 267, 59–64); 6. 2. 2 (4.2, 467, 19–20) and referring to ‘that which moves through the medium,’ Bonaventure, In Sent. 2. 2. 1. 2. 1; Albert, Sum. Theol. 5. 22. 1 (34.1, 116, 43–52); Phys. 4. 3. 7 (4.1, 272, 49–53); 6. 3. 4 (4.2, 494, 51–62); Meta. 5. 3. 1 (16.1, 260, 58–61); Aquinas, In Phys. 4. 1 [406]. It is not always clear precisely what the authors of these texts are referring to. Whilst sometimes they refer explicitly to the Primum Mobile, at other times they refer more vaguely to merely ‘that which moves’. This may well be because Averroes had explicitly referred to the Primum Mobile and used its motion as the basis for his claim that time was circular and so beginningless and uncreated. Thirteenth-century thinkers would understandably have wanted to avoid identifying themselves with such a position. For further details, B. S. Kogan, ‘Eternity and Origination: Averroes’ Discourse on the Manner of the World’s Existence’, 222. Although there does seem to be a tendency to reduce the topology of ‘our time’ (as Ps.-Aquinas refers to it, de Instan. 4 [332]) to the topology of motion and then to space, it would be wrong to conclude that this is a necessary feature of all times. Thirteenth-century thinkers accepted, for example, that angels could be involved in motion and although, as we shall see later, Aquinas (amongst others) thought that there might even be a special discrete time to measure their motions, the topology of such a time could not be reduced to a spatial topology as the angels were thought of as necessarily not having spatial locations at all. Aquinas, ‘et praeterea contingit quod quando corpus est in medio instanti, angelus in nullo loco sit, cum non sit necessarium eum semper esse in loco’, In Sent. 1. 37. 4. 3 ad 7.

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Flowing through space Spatial topology

Primum Mobile

Identified (in some sense)

Identified (in some sense)

Flowing The (flowing) now

Temporal topology

been the assumptions behind discussion of the Primum Mobile, and flowing now (as above). The overall picture remains vague and unclear, as the relationship between the key elements of this model was simply not explained by thirteenth-century thinkers. We have already seen that there was a tendency to relate, or equate, the Primum Mobile and flowing now in some sense in medieval thought, although precisely what that meant is difficult to understand. There was a similar level of confusion concerning the relationship between spatial and temporal topology, where we have seen that there was a willingness to consider the nature of the temporal topology as being determined by the spatial topology. Whilst the details of such a model remain puzzling and ultimately unclear, it is precisely the kinds of relationships denoted by this model which lie behind, and explain, the kinds of medieval utterances which we have been exploring. The significance of this model should not be underestimated, particularly for the question of temporal becoming

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and the reality of time. The existence and motion of the Primum Mobile is clearly not mind-dependent so this model provides a way of establishing the reality of time. It does so, however, by appealing to the ongoing process of the Primum Mobile’s motion, which is equally clearly understood to involve genuine A-theory temporal becoming, rather than B-theory relations, or a merely psychological analysis of becoming. Part of what it means to talk of the motion of the Primum Mobile and the temporal becoming that it gives rise to, is the recognition of the reality of the ever-changing present as the focal point around which is constructed the Aristotelian account of time which thirteenth-century thinkers developed.24 At the heart of thirteenth-century natural philosophy is a clear commitment to the reality of temporal flow and 24 Note Albert’s appeal to a clearly A-theory account, ‘concedimus . . . quod ‘‘quando’’ causatur a tempore secundum differentias ipsius; et ideo ‘‘quando’’ aliud est praeteritum, aliud futurum, aliud praesens, et ‘‘quando’’ preteritum sequitur suum tempus et ‘‘quando’’ futurum praecedit suum tempus, et ‘‘quando’’ praesens cum suo tempore est. Et ex hoc ipso patet, quod ‘‘quando’’ magis causatur a substantia temporis secundum quod accipitur in ipsius temporis partibus, quam ab ipso tempore’, Sum. de Creat. 2. 5. 11 particula 3 (Borg. 34, 387). A common corrollary to this is the significance which thirteenth-century thinkers give to the reality of the process of ageing, on which see Alexander of Hales, Glossa In Sent. 2, appendix (423, 1–3). For the significance of the present to medieval thinkers see Kilwardby, ‘presens enim est quia pre sensu est, futurum et praeteritum per respectum dicuntur ad praesens’, de Temp. 13 [60] (24, 23–4). The appeal to senses seems to derive from Isidore, ‘praesens dictus quod sit prae sensibus’, Etym. 10. 1 [207]. It might seem initially that this represents a pyschological account of the present such as might be proposed by an advocate of the B theory who wanted to deny the reality of an ever-changing present and instead reduce its existence to a matter of awareness on our behalf. That would be reading too much into what is ultimately merely an attempt to provide an etymology for the Latin word ‘praesens’. The appeal to ‘sense’ is not so much an attempt to

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temporal becoming. Nowhere is this clearer than in accounts of time, where the significance of the A-theory emphasis is clearest. We saw earlier that in relation to God and the question of omniscience, some commentators believe that thirteenth-century accounts seemed to be presupposing a possible B-theory analysis which would enable temporal events to have a single temporal relationship to each other; a relationship which could be known by God timelessly. As we have yet to address the question of God’s relationship to time we are not yet in a position to draw firm conclusions about whether any medieval models of divine omniscience do indeed require a B theory of time. If subsequent investigation should show that this is the case then it will mean that there was an underlying tension between a philosophical commitment to an A-theory account of time and theological commitment to a B-theory account.

C O N C LU S I O N In this chapter we have explored the question of whether thirteenth-century thinkers such as Aquinas and Albert explain the present, as rather an attempt to explain our relationship to the present. The present is that which we sense directly. In passing it should be noted that A-theory accounts were not thought to merely apply to time. Note Bonaventure’s account of the angels, where he seems to be introducing A-theory concepts, ‘quidam dicunt quod duratio aevi est simplex et tota simul, non habens praeteritum et futurum: nihilominus Ipsum aeviternum habet praeteritam et futurum quantum ad affectiones’, In Sent. 1. 8 dub. 5 (1, 163).

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viewed time as having its own existence in reality, or whether they considered it instead to have an existence which depended upon a mind. The answer we have reached is that there is an ambiguity lying at the heart of their thought on this matter; an ambiguity which sometimes expressed itself in affirmations that stressed the mind independence of time and yet which at other times seems to imply a role, albeit a limited one, for a mind. The two areas where this ambiguity becomes visible are: when they were considering the question of whether time exists in the present instant, and in relation to their views about the reality of temporal becoming. The apparently simple question of whether or not time exists was a particularly difficult one for thirteenth-century thinkers to respond to. Due to the way that the question was raised in Aristotle’s Physics, the question actually asked was whether time exists in the present instant. As time is extended and the present instant is non-extended, thirteenth-century thinkers could see no way in which time could be said to exist in the present unless the role of a mind was introduced; a mind which can hold a period in its mind, and can do so at the present instant. Whilst this might seem at first glance to amount to a claim that time is mind-dependent, instead this response has an ‘ad hoc’ character dictated by the specific way in which the question was raised in the problem which we referred to as Aristotle’s paradox. The overwhelming thrust of Aquinas’ and Albert’s thought is to stress the reality and mind independence of time; a position which they believed they could justify by appealing to the reductive analysis of time which

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we saw in the last chapter. According to that reductive account, time could be reduced, in some sense, to the motion of the Primum Mobile and so questions about the reality of time could be reduced to questions about the reality of the Primum Mobile and its motion. As the Primum Mobile’s existence was clearly not dependent upon any minds, appealing to a reductive analysis of time thus gave a clear basis for an account of time that was non-mind-dependent. Introducing the Primum Mobile to the discussion raised the further question of whether thirteenth-century thinkers viewed ‘temporal becoming’ as real, or as merely mind-dependent. Contemporary philosophers explore this question by asking whether time can be analysed in purely ‘B-theory’ terms so that events are viewed as having a ‘static’ relationship to each other, with all events capable of being described as ‘before’, ‘after’, and ‘simultaneous’ with each other. In contrast to this approach, there is an alternative way of viewing time in A-theory terms, according to which events can be viewed as ever-changing, as existing in the future and then in the present and finally in the past. It is clear that thirteenth-century thinkers took the reality of change very seriously and there can be little doubt that in relation to their natural philosophy they were thoroughly committed to what we now view as an A-theory account of time. Complications arise when we also consider their views about divine omniscience and the fact that they seemed to view God as capable of knowing all truths in a single nonsuccessive act of knowing. This account would seem on the surface to presuppose a B-theory account of time where all truths can indeed have a single unchanging relationship to

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each other and so it would appear that there is the possibility of a tension in their thought between their commitment to an A and B theory account of time. Determining the full extent of this tension will only be possible later, once we have clarified further issues such as God’s relationship to time.

6 On Measurement and Numbering

Previous chapters have been exploring the topological implications of the medieval acceptance of Aristotle’s definition of time as ‘the numbering of before and after in motion’. This chapter will be focusing upon the metrical implications of the definition and how they fit into the wider medieval account of time.1 A metric is simply a measure of distance, and so an investigation of the metrical implications of this definition is just an exploration of the issues to do with distance between instants and/or periods. The importance of the metric for medieval accounts of time arises for at least two different reasons. In the first place, contemporary exegetes have urged that Aristotle’s account of time is ultimately just an account of a temporal metric and, as medieval thinkers are largely following Aristotle, this approach would imply that metrical issues should play a correspondingly large part in their own accounts of time. Secondly, 1 For Aristotle’s definition, ‘hoc enim est tempus: numerus motus secundum prius et posterius’, Phys. (Vetus) 4. 11. 219B1 (AL 7.1.2, 175). On its reception and use note Aquinas, Sum. Theol. 1. 10. 1.

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metrical issues are important because we have already seen that medieval thinkers found it extremely difficult to distinguish the topological and metrical properties of time and so there was a constant tendency in medieval thought to confuse them.2 Medieval reflection on measurement began with two specific terms: ‘numbering’ (numerans) and ‘measuring’ (mensurans). Both terms can be found in the Latin translations of Aristotle’s works and were used to demark distinct ways of quantifying different kinds of particulars. Discrete quantities such as coins were considered to be numbered (or counted), whilst continuous quantities such as lengths of cloth were considered to be measured. When it came to measuring time, thirteenth-century thinkers often distinguished between ‘number’ (numerus), and ‘numbered number’ (numerus numeratus), where the word ‘number’ was used in a looser way to refer to a type period such as an hour’s length and the phrase ‘numbered number’ referred to tokens (or instances) of the type; what we might even refer to as enumerated applications of the measure.3 2 It has been suggested that assigning a metric to time is more than just assigning a measure to temporal extent, as it involves the systematic assignation of dates to instants (W. H. Newton-Smith, The Structure of Time, 144). But assigning dates to instants must either depend upon the topological ordering of those instants, in which case it will depend upon topological properties of time; or it will arise from the distance between the instants, in which case the issue at stake is metrical. For an account of Aristotle’s concept of time that analyses it as fundamentally an account of a temporal metric, see M. White, The Continuous and the Discrete, 50. 3 Although there was an ultimate Aristotelian origin for the distinction, many medieval thinkers preferred to attribute the distinction to a scriptural origin, ‘omnia in mensura et numero et pondere disposuisti’, Wisd. 11:20. See Philip the Chancellor, for example, Sum. de Bono, 1. 3. 7 (1, 131, 2 f.); and

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Despite the semi-official nature of a distinction between the terms ‘discrete’ and ‘continuous’, it is clear that medieval thinkers felt at liberty to use the words in a more casual way, and so we often find references to non-extended durational entities such as God, eternity, and an instant, which are spoken of as measured, or not measured, rather than being referred to in the more proper way as numbered, or not, as the case may be. The most likely reason for this medieval looseness of expression was that they had inherited an alternative Platonist way of using the word ‘measure’ which they were trying to integrate into their otherwise Aristotelian uses of the terms.4 Bonaventure, In Sent. 1. 3. 2. 2. For a contemporary way of phrasing the same basic distinction, H. E. Kyburg, Theory and Measurement, 253. On the use of Aristotle’s distinction see Aquinas, In Meta. 10. 2 [1938]; In Sent. 1. 8. 4. 2 ad 3; In Phys. 4. 17 [581]; Albert, Phys. 4. 3. 9 (4.1, 275, 51–61); Sum. Theol. 5. 23. 1. 2. 2. A (34.1, 129, 31–3); Grosseteste, In Phys. 4 (90); Kilwardby, de Temp. 5 [20] (11, 14–19). One of the ancient commentators, Simplicius, had expressed concern about Aristotle’s account of time because the fact that it involved both measuring and numbering could be taken as implying that it was both continuous and discrete. Using the language of ‘number’ and ‘numbered number’ Aquinas’ response was basically to distinguish between a type period (such as an hour) which is measured and the tokens of that type which are the discrete counted elements. Aquinas, In Meta. 10. 2 [1939–40]. This account is the basis for his otherwise puzzling comment that even a foot can be said to be an indivisible entity. Its indivisibility arises when it is considered as a token rather than as a type, In Meta. ibid. [1950] and also Kilwardby, de Temp. 6 [26] (13, 23–9). For more detailed accounts of measurement theory, see also Giles of Rome, Quaest. de Mens. Angelorum and Richard of Middleton, In Sent. 2. 2. For an account of medieval measurement theories with further background details, B. I. Mullahy, ‘Thomism and Mathematical Physics’, 322–62; R. Dalbiez, ‘Dimensiones Absolues et Mensures Absolues’; G. Isaye, ‘La the´orie de la mesure et l’existence d’un maximum selon Saint Thomas’. 1–36. 4 On the use of ‘mensura’ for non-divisible measures note Ps.-Aquinas, ‘illud enim instans est mensura etiam primi mobilis secundum quod est

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A typical example of this occurs with the distinction which Albert cites, between measurement by position and measurement by nature. The notion of a measure by nature clearly finds its origin in the Platonist tradition and amounted to measuring the ontological perfection of a particular. To take a substance such as a dog and measure it by nature, it was necessary to compare that particular dog with the archetypal dog; the definition and standard of perfection against which all dogs had to be compared. When it came to applying the notion of measurement by nature to qualities such as goodness then it was God who was the supreme measure against which all other substances would be compared and measured. In some instances eleventh- and twelfth-century thinkers even extended the notion to include examples in which different substances such as a man and a horse were compared to each other to determine which had the higher degree of ‘being’ (esse) and so which was the ontologically most superior. permanens . . . instans quod est mensura ipsius mobilis sequens ipsum est unum secundum rem’, de Instan. 2; and Aquinas, In Sent. 1. 19. 2. 2; 1. 8. 4. 2 ad 3; 1. 24. 1. 2 ob 4; 2. 2. 1. 1 ad 3; 3. 23. 1. 1; Quaest. Disp. de Pot. 7. 10; 9. 5 ob 12; Sum. Con. Gen. 1. 28; Sum. Theol. 1. 10. 4 ad 3; 1. 13. 5 ob 3; Quaest. Disp. de Ver. 23. 7; In de Div. Nom. 4. 3; 4. 5 [1]. Also Albert, Sum. Theol. 5. 22. 1 (34.1, 116, 16–20); and 5. 23. 3. 3. 1 (34.1, 139, 54–63). In Sent. 1. 8. A. 8 (Borg. 25, 229). For further details, A. G. Molland, ‘Continuity and Measure in Medieval Natural Philosophy’, 139. With a particular focus on the more ‘Platonist’ use of terminology see Gilbert of Poitiers, In de Trin. 1. 4 [83] (132, 95–8), which has clearly influenced Albert, Sum. Theol. 5. 22. 2. 2 (34.1, 119, 59–69), and Aquinas, In Sent. 2. 2. 1. 1 ad 3. Albert evidently considered measurement to be an important enough issue to warrant a separate treatment in his projected Scientia Astronomiae, which he refers to, Phys. 4. 3. 17 (4.1, 292, 42) but which he never completed.

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When it came to applying the concept of measure by nature to time and other durations, the key issue at stake was establishing whether there were any criteria that indicated ontological superiority for particular durations, or particular substances. When we come to look at the criteria of temporality in Chapter 7 we shall see that, amongst other factors, immutability was often cited as a factor that denoted ontological superiority, and that as a result of this any particular possessing this attribute was generally considered to be superior to time. Applying the concept of measurement by nature to time therefore resulted in the identification of an ontological hierarchy of particulars, such that the extent to which particulars manifested qualities such as mutability or immutability would determine which duration could be said to measure their nature.5 Measurement by position, or mathematical measure, as Aquinas referred to it, is the measure of a particular’s quantity or size, as we might put it today. It is this notion of measurement that contemporary philosophers would typically recognize, and it is this one that we shall focus on when examining the notion of a temporal metric. In order to apply the notion of mathematical measure, medieval thinkers tended to distinguish between an intrinsic 5 Aquinas, Super ad Rom. 1.3. See also the way Averroes is quoted and used by Ps.-Aquinas, de Instan. 5. Albert takes a similar approach, Phys. 8. 1. 1 (4.2, 549, 45–51) and distinguishes between at least three types of measurement, In Sent. 1. 8. A. 9 sol. (Borg. 25, 233). Medieval thinkers do not always clearly distinguish how they are using the word ‘measure’ and this often leads to a syncretistic approach in which they were attempting to blend the Platonist approach into a more physical account of measure, as Aquinas illustrated when he attempted to apply a Platonic adage about God exceeding the ages, to a basically Aristotelian notion of God’s relation to time, De Div. Nom. 5. 1.

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(intrinseca) and an extrinsic (extrinseca) measure. In Aquinas’ words: It must be said that there are two kinds of measure. Those which are in a subject as an accident are intrinsic measures, and there are as many such measures as there are things being measured; as for example there are as many lines measuring the length of objects as there are objects. There is also, however, an extrinsic measure and this is not necessarily measured when there is more than one thing being measured. It is in one object as an accident to which all the others are compared and thus measured, as many reams of cloth are measured by one basic unit. And in this way many motions are measured by the Primum Mobile, the number of which amounts to time.6

What this passage demonstrates clearly is that the notion of intrinsic measure arises primarily as an exigency of Aristotle’s categorical theory. Because being a measure is a property, it must inhere in a subject, so the particular in which a measure inheres is labelled the intrinsic measure of that particular measure. If thirteenth-century thinkers had been confronted with the contemporary measurement 6 Aquinas, ‘dicendum quod mensura est duplex. Quaedam intrinseca, quae est in mensurato sicut accidens in subiecto: et haec multiplicatur ad multiplicationem mensurati; sicut plures lineae sunt quae mensurant longitudinem plurium corporum aequalium. Est etiam quaedam mensura extrinseca; et hanc non est necesse multiplicari ad multiplicationem mensuratorum, sed est in uno sicut in subiecto ad quod multa mensurantur, sicut multi panni mensurantur ad longitudinem unius ulnae: et hoc modo multi motus mensurantur ad numerum unius primi motus, qui numerus est tempus.’ In Sent. 2. 2. 1. 2 ad 1. See also his accounts, In Sent. 1. 8. 4. 2 ad 3; In Phys. 3. 5 [322]; Quaest. Disp. de Ver. 1. 5. Bonaventure makes basically the same distinction but refers to ‘inside’ (intra) and ‘outside’ (extra) measures, In Sent. 4. 49. 2. 3. 1 ad 4.

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scale of metres they would have assumed that there must be some substance in which the measure metre inheres as the subject of the measure. As it is the standard metre in Paris which is used to determine the length of a metre, that standard metre would therefore be considered, in medieval terminology, the intrinsic measure of a metre.7 The notion of extrinsic measure is simply the basic idea of measuring. X is an extrinsic measure of Y if, in the case of solid substances, X is a ‘measuring rod’; or, in the case of processes, X is a periodic process (a clock) which can be used to quantify and measure the actual length of Y. In order to carry out measurements it would be necessary to establish, first, a type measure such as an hour or a metre. In order to apply that measure to concrete instances of measurement there would need to be a substance in which that measure inhered as the intrinsic measure. Once that intrinsic measure was determined, or recognized, tokens of that type measure could then be applied to distances or lengths of time, as an extrinsic measure, in order to generate a measurement of the distance or duration in question.8 As the language of intrinsic and extrinsic measures has found a place in contemporary discussions of measurement theory, it is important to note that the contemporary distinction differs from the medieval one. Whilst the medieval and contemporary notions of an extrinsic measure are rela7 Aquinas, ‘ulna comparatur ad virgam ligneam sicut ad subiectum, ad pannum autem qui per eam mensuratur sicut ad mensuratum tantum’, Quaest. disp. de Spir. Creat. 9 ad 11. 8 Kilwardby, de Temp. 5 [24] (13, 13–15); 6 [27] (14, 4–9); [28] (14, 12– 24). Albert, Phys. 4. 3. 17 (4.1, 291, 50–64); Sum. de Creat. 2. 3. 2 (Borg. 34, 349); Aristotle, Phys. 4. 221A1–4, 219A2–220A23.

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tively straightforward, and merely denote the use of rods or processes to measure a substance or process, the concepts of intrinsic measurement diverge significantly. According to the contemporary distinction an intrinsic measure of an X is a measure provided by smaller units which constitute the larger entity X, where being constitutive means simply being such that the existence of the X depends upon the existence of the smaller sub-units. A hydrogen molecule, for example, depends upon the existence of both the hydrogen atoms constituting it, and on this account it could be measured intrinsically by simply using the atoms as measuring units.9 According to the medieval use of language, sub-units constituting an X would not be intrinsic measures of the larger entity, the sub-units would instead themselves be tokens of a type sub-unit, and that type sub-unit would be an extrinsic measure of the X. The only intrinsic measure of X would be, on the medieval understanding, the particular identified as the standard measure, or subject, of the measure X. Actual measurement requires a measure, and one that is appropriate, or as medieval thinkers put it ‘homogenous’, 9 For the contemporary distinction, A. Gru¨nbaum, Philosophical Problems of Space and Time, 505. It is also important to ensure that the medieval distinction between intrinsic and extrinsic measures is not confused with a further distinction made by medieval thinkers between intensive and extensive measures. A quantity of heat in, for example, a piece of wood can be measured either according to the physical extent that it is present in the wood, i.e. the dimensions of the ‘hot bit’, and this was what was referred to as an extensive measure. The heat could also be measured according to its intensity, which would be measured by using a thermometer and gave a measure that would have been referred to as the intensive measure. For more details see Aquinas, Quaest. Disp. de Virt. in Com. 11 ad 10; Sum. Theol. 1. 42. 1 ad 1.

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‘adequate’ (adaequata), or ‘of the same definition’ (ratio) as that which is to be measured.10 Two issues arise here: issues which were noticed and commented upon by medieval writers. First, as substances differ, so too will the kind of measure that is appropriate to them. Clearly one cannot measure wind speed with a ruler, or length with a thermometer, so these different kinds of quantities need different kinds of measures. But how are we supposed to distinguish which substances are measured by which measures? Aristotle and his medieval commentators proposed a relatively simple answer: identifying membership of a common genus as the criterion for two things being measured by the same measure.11 Secondly, when talking of a type, or kind, of measure, it is often the case that there are many ways of going about making a measurement. In order to actually carry out a measurement we need to adopt something as the privileged measure which we are going to use to measure the distance or duration that needs to be measured. To put this in medieval terms, we would need to identify a substance or process which can count as the ‘intrinsic measure’. In order to do this there would need to be clear criteria which would 10 Aquinas, Lib. Post. Anal. 1. 36. 11; Quaest Disp. de Pot. 7. 7 ad 1; In Sent. 1. 35. 1. 4 ad 2; Albert, In Sent. 1. 8. B. 13 quaest. 2 (Borg. 25, 239). 11 Aristotle, Meta. 10. Medieval thinkers sometimes talk of similarity of esse rather than genus membership as the key defining criterion, but as the types of esse determine the genera this means that the distinction is fundamentally the same as the one that Aristotle was proposing. See Aquinas, In Sent. 2. 2. 1. 1; Sum. Theol. 1. 10. 5; 1-2. 96. 2; Sum. Con. Gen. 3. 61; Quaest. Quodlib. 7. 4. 2 ob. 2; 7. 10. 2 ad 3. Bonaventure, In Sent. 2. 2. 1. 1; Albert, Sum. Theol. 5. 22. 1 (34.1, 116, 10–13).

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help identify the privileged measure and we would need to be clear about what precisely we mean when we talk of a measure as privileged. Taking the later question first immediately brings us to the contemporary debate between objectivists and conventionalists. Objectivists typically assert that the privileged measure is a true measure, giving true readings about the extent of duration or distance which is being measured. Conventionalists deny this, holding instead that a privileged measure does not so much give a true measure as merely provide an account of extension which is always relative to the conventions used in making the measurement.12 As medieval thinkers never directly confront these questions, it is difficult to be sure precisely where they would stand in the debate. Nevertheless, there is a certain amount of evidence which would support a generally objectivist position. Albert, for example, indicates that he is well aware of the fact that there is some convention in the way 12 The objectivist position is sometimes referred to as realist and the conventionalist position as anti-realist. For an overview of the contemporary debate and its contours, B. Ellis, ‘The Ontology of Scientific Realism’, and C. Swoyer, ‘The Metaphysics of Measurement’, 235–90, and more generally D. Armstrong, Universals and Scientific Realism, ii. 1–5. On objectivism and its contemporary formulations, H. C. Byerly and V. Lazara, ‘Realist Foundations of Measurement’, 10–23; C. Swoyer, ‘Realism and Explanation’; B. Mundy, ‘The Metaphysics of Quantity’; and E. Brian, ‘Comments on Swoyer and Forge’. For specifically conventionalist formulations, H. Kyburg, ‘A Defence of Conventionalism’; W. H. Newton-Smith, The Structure of Time, 164. A Classic defence was initially provided by B. Ellis, Basic Concepts of Measurement, before he changed his position and in the articles cited above repudiates conventionalism. Many contemporary philosophers prefer to speak of privileged measures as a way of stating their positions without having to commit to either the conventionalist or the objectivist position.

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we label measures. To use a contemporary example, we can see this in the way that some people prefer to talk of an inch whilst others will talk of 2.54 centimetres. Despite his recognition of such a level of convention, both Albert and Aquinas are still perfectly happy to talk of ‘true’ measures, with Aquinas even going so far as to explicitly distinguish between truths of appearance and truths of fact.13 Having decided to measure something, the crucial question for thirteenth-century thinkers was how should they pick the particular which was to count as the privileged measure, or as they themselves put it, the ‘first member’ of the genus in which the particular to be measured was located.14 Aristotle himself had suggested six basic criteria: simplicity, perfection, most power, finiteness, being a certain (certa) quantity and being a ‘minimal part’ (minimum) of that which is to be measured. Although medieval thinkers such as Aquinas and Albert do not always explicitly cite all six criteria in each discussion, they do, over the course of their works as a whole, cite or refer to all of the criteria at varying points.15 13 Albert, In de Caelo 2. 2. 6 (5.1, 137–42). Aquinas’ position is that incompatible theories (i.e. the Ptolemaic and Aristotelian) can account for astronomical observations and so both can be truths of appearance, although this does not mean that they are both truths of fact, as he makes clear, In de Caelo 2. 8 [368]. They both contrast this with the case of the Primum Mobile where its regularity is both a truth of fact and a truth of appearance. For further details, S. Leggatt, Aristotle: On The Heavens I & II, 10–41. 14 Aquinas, Sum. Theol. 1-2. 19. 9; 1-2. 90. 1; Sup. Lib. de Causis [16]; In de Div. Nom. 5. 1; Quaest. Disp. de Pot. 1. 4 ob. 2. 15 Aquinas, In Sent. 1. 8. 4. 2 ad 3; 1. 24. 1. 1; 2. 2. 1. 2 ad 3; 3. 37. 1. 4 sed con 2; Sum. Theol. 1-2. 19. 4 ob 3; 1-2. 91. 3 ob 3; 1-2. 96. 1 ad 3; In Lib. Post. Anal. 1. 36 [318]; Quaest Quodlib. 2. 3. 5; 5. 3. 2; Quaest. Disp. de Vir. 5. 3;

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As there is a certain amount of overlap amongst Aristotle’s terms, we can divide the criteria for a measure into two broader categories: metaphysical requirements and epistemological requirements. Albert, at least, seems to have thought that a particular’s capacity to fulfil the epistemological requirements depended upon its prior ontological status and its capacity to fulfil the metaphysical requirements, so it would be appropriate to begin with the metaphysical requirements.16 Talk of simplicity and perfection clearly falls within the first category of metaphysical requirement: picking out the properties which would ensure that a substance or process was the most appropriate for measuring other members of the genus. The requirement of ‘most power’ also falls within this first category, because, for medieval thinkers, the power which a substance had was a function of its metaphysical perfection. In the case of measuring periodic processes over time, this would clearly entail picking out a process which kept a basic congruence between its parts. The last three of the Aristotelian criteria also lay down epistemological requirements. The claim that a measure must be ‘certain’ or ‘most certain’ was simply the (epistemological) requirement that of all the things that it is measuring, we have a clearer knowledge of the appropriate property in the measure. If that were not so we would not be able to Albert, Sum. Theol. 5. 22. 2. 2 (34.1, 119, 59); Phys. 4. 3. 9 (4.1, 275, 48–56); In Sent. 1. 9. A. 3 quaest 2 (Borg. 25, 274). 16 In Phys. 4. 3. 17 (4.1, 292, 1–8).

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use it as a basis of comparison and so measurement of the particulars of which it is used. In a similar way, the criteria of ‘finiteness’ is another way of insisting upon the fact that we have epistemological access to the measure. There would be no point, for example, in appealing to an infinite measure, for there would be no way that we could manipulate it and use it in any meaningful way to measure other particulars and processes. The appeal to minimal parts was also an epistemological criterion as it was an attempt to avoid measurement inaccuracy. Insisting that the privileged measure must have minimal parts was an attempt to avoid the problem of there being bits that were left over when the measure was used to measure particulars and processes. The larger the units, the more likely it was that the units would be an inexact measure, so the appeal to minimal parts was an attempt to ensure the best fit between measure and measured particulars or processes. Albert, at least, seems to have felt that it was useful to distinguish between what he termed a ‘minimum by position’ and a ‘minimum by nature’. He took a minimum by position to be the smallest (arbitrary) part of an extended thing, whilst a minimum by nature was taken as similar to what we have seen to be the contemporary notion of an intrinsic measure, a smallest constitutive element, something so small that it might well be impractical to use it in day-to-day measures. Thus, measurement of particulars for Albert was a case of taking a minimum by position and repeatedly and consecutively applying that measure to the particular to be measured until a final number of applica-

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tions was arrived at. That would constitute the measure of the object.17 When it came to making a measurement thirteenth-century thinkers typically stressed that it was necessary to identify the genus of the thing to be measured and then to take the first member of that genus as the intrinsic measure: a member picked out according to epistemological and metaphysical requirements, and so worthy of being used to measure the other members of that genus. As an account of measurement this account is deceptively simple, especially when we come to the question of measuring things which do not seem to be in a single shared genus or kind. It’s all very well taking the most perfect jug to measure the quality of jugs produced on a production line, but what happens, for example, when it comes to measuring the speed of a horse and of a car? Problems of identifying a common genus must have been familiar to medieval thinkers as they all agreed that the Primum Mobile was the measure for time, but also accepted that it was made of a unique non-changeable stuff and so almost literally ‘sui-generis’. How could such a particular be in the same genus as the physical particulars which it was supposed to measure?18 Albert and Aquinas seem to have been aware of this problem and, although Aquinas does not seem to have found 17 Sum. Theol. 5. 22. 2. 2 (34.1, 119, 60–4); ibid. (34.1, 119, 67–8). For similar accounts see also Grosseteste, In Phys. 4 (88–9), and Aquinas on minima in motions, In de Caelo 2. 6 [356]. 18 On the Primum Mobile as the measure of time, Albert, In Sent. 1. 8. B. 13 quaest 2 (Borg. 25, 239).

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a satisfactory account of the matter, Albert at least was keen to explore a solution using a distinction between ‘univocal’ and ‘non-univocal’ measures. Univocal measures, he believed, were genus-specific measures. This meant that they could only measure members of the same genus, whilst nonunivocal measures were those that could measure members of different genera.19 With this distinction Albert was then able to explain how we can compare things in different genera. We compare them in virtue of other similarities which are non-genusspecific, producing in the process a kind of semi-genus from which we take as our measure the member which best exemplifies the property to be measured: the property which is common between the diverse members of the genera. Thus, although the Primum Mobile is indeed unlike the other substances in the world, in virtue of its being in motion it can be put into a semi-genus of ‘things in motion’, and thus can provide a non-univocal intrinsic measure of their motion.20 19 Albert, ‘unumquodque mensuratur duplici mensura, scilicet univoca, secundum quod unumquodque mensuratur sui generis proximo ut unitates unitate, equi autem equo; et sic necesse est, quod mensuretur tempus totum a quodam tempore finito et certo nobis. Mensuratur etiam unumquodque non univoca mensura, et hoc dupliciter, scilicet essentialiter, scilicet quando per quantitatem mensurae accipimus quantitatem mensurati, sicut mensuramus per ulnam pannum et cado oleum et lagena vinum.’ Phys. 4. 3. 17 (4.1, 291, 50–64). Aquinas shows that he was aware of the problem, but without offering any solution, at Sum. Theol. 1-2. 19. 4 ad 2. 20 Albert, In Sent. 1. 9. A. 3 (Borg. 25, 275); 1. 8. B. 13 quaest. 2 ad 1 (Borg. 25, 241). But Albert is not always verbally consistent. On at least one occasion he attributed to the ‘perfection’ of the Primum Mobile the fact that it is a measure, implying that it would only be a measure if it were the most perfect member of its genus. Phys. 8. 3. 9 (4.2, 640, 84–90).

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THE P R I M U M M O B I L E A S T H E P R I V I L E G E D CLOCK Having established that thirteenth-century thinkers thought that it is the Primum Mobile which is the measure of all motion within the world, it still remains to ask why should that particular motion be singled out? The answer to this question lay in the fact that it was considered to fulfil the two criteria for being the most metaphysically perfect and the most epistemologically accessible member of what we might refer to as the semi-genus of things in motion. Its motion is clearly evident to the senses because it is sensed in all the other motions which it causes, so it definitely fulfils the epistemological requirements.21 As regards its metaphysical perfection or regularity, Aristotle and his heirs had found at least seven arguments to support it. Aquinas, attempting to structure Aristotle’s discussion of the issue, reduces the arguments to what he considered were the four crucial issues: (1) The impossibility of irregularity in circular motion (2) The impossibility of irregularity in infinite time (3) The impossibility of the Primum Mobile being caused to be irregular (4) The impossibility of the Primum Mobile’s motion being irregular.22 21 Aquinas, In Phys. 4. 17 [574]; 4. 23 [635]. 22 On Aristotle’s arguments, de Caelo 2. 6; Aquinas, Sum. Theol. 1-2. 34. 4 ad 2; 1-2. 91. 3 ad 3; 1-2. 97. 1 ad 2; In de Caelo 2. 6 [356]; 2. 9 [379]; In Phys. 4. 23 [11]; Albert, Phys. 8. 3. 9 (4.2, 638, 41). For a discussion of Aristotle’s seven arguments, S. Leggatt, Aristotle: On the Heavens I & II, 234–7. Albert

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The first argument represents a claim that the circular nature of the Primum Mobile’s motion rules out the possibility of irregularity. Irregularity, suggests Aristotle, involves acceleration and the notion of acceleration requires a particular to reach a top speed. But if reaching a top speed is to occur then it must occur at either the beginning, middle, or end of the motion. In Aristotle’s opinion, however, a circular motion does not have a beginning, middle, or end, so necessarily it cannot accelerate or decelerate.23 It is difficult to see how this argument could have been considered convincing unless perhaps a commitment to objectivism influenced its reception. In an infinite circular motion it may well be the case that we cannot identify any true beginning, middle, or end of the motion, and so, to an objectivist way of thinking, it may have seemed that no true measurement could be taken. But, regardless of the objectivist and conventionalist disagreements about the nature of measurement, it should be clear that in the case of circular motion it is not necessary to identify a true beginning or end in order to make a measurement; all that is needed is an

adds further arguments based upon contemporary linguistic assumptions, In de Caelo 2. 2. 6 (5.1, 141, 64 f.). The recognition of the need for arguments to establish the Primum Mobile’s regularity seems to have arisen gradually. Alexander of Hales was content merely to state its regularity, ‘sicut omnia temporalia, quantum ad esse et operationem, in quantum huiusmodi, dependent a primo motu; propter quod et eorum motuum est regula tempus unum, scilicet illud quod est numerus primi motus.’ Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 103b). Aquinas, however, summarized and explored the arguments, In de Caelo 2. 8–9. 23 Albert, de Caelo 2. 2. 5 (5.1, 137, 31–72); Phys. 8. 3. 9 (4.2, 641, 1–9); Aquinas, de Caelo 2. 8 [372].

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arbitrary point in the circular motion which can be used as the point from which measurements will be taken. The second argument against irregularity is more an assumption than an explicit argument. Aristotle and his medieval heirs believed that in infinite time, particulars must at some point follow their nature. As the nature of the Primum Mobile entailed its regularity, this meant that, given the infinite time which Aristotle believed to have elapsed, even if there had been irregularity there would also (necessarily) have to be regularity. This would imply that acceleration or deceleration would be necessary, as the change from regularity to irregularity (or vice versa) would involve a change in velocity. Drawing on the previous argument, it was then claimed that there could be no measurement of the Primum Mobile’s acceleration or deceleration and so it was simply not meaningful to ascribe irregularity to the motion of the Primum Mobile.24 The third argument was based upon the assumption that irregularity, if it occurred, must be caused. In the case of irregularity in the motion of the Primum Mobile, Aquinas believed that there could only be two factors which could be causally relevant: the Primum Mobile itself or its mover. One of the cornerstones of Aristotelian cosmology was the assumption that heavenly bodies such as the Primum Mobile were causally inert and substantially unchangeable, so it was difficult for medieval thinkers to see how irregularity could arise due to any change in the Primum Mobile itself. Yet 24 Aristotle, de Caelo 2. 6 (288B22–4); Aquinas, In de Caelo 1. 4 [45], [49]. Albert, de Caelo 2. 2. 6 (5.1, 141, 9–12).

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irregularity in its mover, God, was even more inconceivable, and so Aquinas felt confident in concluding that there was a clear a priori argument against its motion exhibiting anything less than perfect regularity.25 Besides the a priori argument, medieval thinkers also believed that they had a sound empirical basis for rejecting the possibility of variation in the Primum Mobile’s motion; a basis grounded in the fact that there was no evidence of the Primum Mobile itself, or its relationship to other heavenly bodies, changing over past times.26 Unfortunately these arguments for the Primum Mobile to be considered as the privileged clock are vitiated at every step by a cosmology which we now know to be utterly false. Nevertheless, what these arguments show is that thirteenthcentury thinkers were aware of the need to identify a privileged clock and that by focusing upon regularity they were approaching the problem in a similar way to contemporary philosophers. When it comes to identifying a privileged clock, contemporary philosophers take regularity as the key criterion and usually determine it in terms of a motion’s capacity to reduce laws of motion to a unique simplest form. If there were two (non-linearly related) motions M1 and M2, then the most regular motion would be the one that made it 25 In de Caelo 2. 8 [373]. 26 Glossing Aristotle’s argument, Albert and Aquinas noticed that our experience of non-variance is really based on perceptions of the motions of the stars, but as their motion is caused by the Primum Mobile then that was thought to be enough to give us epistemological access to the Primum Mobile’s motion. Albert, de Caelo 2. 2. 6 (5.1, 139, 38–52); Aquinas, de Caelo 2. 9 [374].

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possible to state laws of nature in their simplest form. Whilst Aquinas indicates similarities of approach in his insistence that a measure should reduce complexity to simplicity, the fact that thirteenth-century thinkers were unable to clearly identify and cite what would later be thought of as laws of nature, meant that there were no practical tests which could be used to compare the regularity of the Primum Mobile with other motions. This was all the more so as thirteenthcentury thinkers viewed the Primum Mobile as the cause of all the other (observable) motions.27 27 For a contemporary account of regularity, R. Swinburne, Space and Time, 70. For Aquinas’ approach, In Meta. 5. 8 [872]; 10. 2 [1945]; Sum. Theol. 1-2. 91. 3 ad 3. It is worth noting that early twentieth-century scholastic commentators tried to update medieval texts by substituting the motion of the earth for references to the Primum Mobile. Thus Iosephus Gredt, for example, ‘Tempus primarium est numerus numeratus motus telluris. Motus enim telluris est maxime sensibilis omnibus (tamquam motus apparens solis) et valde regularis’ Elementa Philosophiae Aristotelico-Thomisticae, i. 248 [299]. Contrasted with the earth are clocks, which is where time is located in a secondary sense. Whilst this approach is typical of the neo-scholastic attempt to salvage a Thomistic philosophy for the modern world, it achieved its goal by radically misunderstanding the role which the Primum Mobile was thought of as playing in medieval measurements of time. According to the thirteenth-century view, time existed in the Primum Mobile as in a subject and as an intrinsic measure. It was because of the causality which the Primum Mobile exercised over natural processes on earth that they could be taken as instantiating the temporal measure (as numbered number) and so used as secondary more convenient ways of measuring time. Not only is it difficult to apply any of the Aristotelian Thomistic arguments for the perfect regularity of the Primum Mobile to the earth, but even if they could be applied, the essential relationship of cause and effect which thirteenth-century thinkers thought of as existing between the Primum Mobile and all other motions, could clearly not be applied to the relationship between the earth and clocks. So whilst thirteenth-century thinkers could base an argument for the congruence of natural processes (which could count as clocks) upon the causal influence that all were in receipt of, there can be no such basis in neoscholastic attempts to retrieve a Thomistic cosmological model of time.

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D O E S T H E P R I V I L E G E D C LO C K ‘C O N S T I T U T E ’ T H E M E T R I C O R ‘ EV I D E N C E ’ I T ? Once it was clear what criteria were appropriate for identifying the privileged clock, the next questions for thirteenth-century thinkers were about its role, in particular whether the privileged clock constitutes the metric, or merely gives evidence of it, and whether possessing a metric (or multiple metrics) is a necessary or contingent property of time. Beginning with the first question, it is important to note that the measurements provided by the privileged clock can be related to talk of temporal distances in two fundamental ways. They can either be taken as evidence of temporal distance or as constitutive of temporal distance. That is to say, we can ask whether there is a metric independent of the privileged clock, one that is somehow accurately recorded by the privileged clock, or we can ask whether the metric is simply whatever the privileged clock reads, so that there would (necessarily) be no possibility of divergence between the privileged clock and metric. Medieval thinkers do not discuss this question directly, so it is difficult to be sure how they would have responded to it. As we know that thirteenth-century figures were not always rigorous in their use of expressions such as ‘measure’ and ‘number’, the mere use of such terminology in definitions of Although neo-scholastic arguments might have the advantage of being reliant on a less mythical cosmology than thirteenth-century positions, they seem to have bought their cosmological advantage at the price of their internal coherence.

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time certainly cannot be taken as evidence that time was thought to have a necessary or essential metric.28 Although unaware of the problem as raised by contemporary philosophers, medieval comments about the Primum Mobile do provide some interesting glimpses into what their overall position on the question might have been. Albert, for example, explicitly took it to be the common view of his predecessors that if the Primum Mobile, the privileged clock, were to speed up then so would the rate of changes in the world. This meant, as Oresme concluded in the fourteenth century, that it was impossible, almost by definition, to observe discrepancies in the readings of the temporal metric taken from the Primum Mobile. What this begins to suggest is that the privileged clock must be constitutive of the metric, rather than merely evidential, for changes affecting the clock seem to also affect the metric, making it impossible to observe the changes.29 Perhaps the single most interesting piece of evidence to support this constitutive reading is provided by the way that thirteenth-century thinkers appealed to the Primum Mobile as the basis for distinguishing between different notions of time. Following what seems to be broadly Alexander of Hales’ position, Bonaventure stated that the word ‘time’ could be used in three ways: 28 On time as a numbering see Grosseteste, Hexaemeron 5. 12 (172, 21–2). For ‘looser’ definitions of time as just a measure, Grosseteste, In Phys. 4 (88), and Kilwardby, de Temp. 5 [25] (13, 18–19). See also Albert, Sum. Theol. 5. 23. 3. 3. 2. 1 (34.1, 141, 63–5), and Bonaventure, In Sent. 2. 2. 1. 1. 2. 29 Albert, In Sent. 2. 1. B. 10 (Borg. 26, 24). Nicholas Oresme, Le liver du ciel et du monde 2. 14 (421–3).

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when used as a measure of any coming-about when used as a measure of any change at all, especially of those that occurred before the Primum Mobile existed when used as a measure of the motion of the Primum Mobile, as the distinction is customarily made.30

30 Bonaventure, ‘tempus, dicitur tripliciter: communissime, communiter et proprie. Communissime: dicitur mensura exitus de non-esse in esse. Communiter, dicitur tempus mensura cuiuslibet mutationis, maxime illius quae fuit ante primum mobile. Tertio modo dicitur proprie mensura motus, primi mobilis ut communiter consuevit distingui.’ In Sent. 2. 1. 1 dub. 4; see also 2. 2. 2. 1. Bonaventure is not altogether consistent in how he states this distinction, sometimes stating the ‘proprie’ sense as, for example, ‘tempus uno modo dicitur proprie et sic dicit mensuram rei mutabilis, in quantum mutabilis, tamen sub ratione continui’, In Sent. 1. 37. 2 dub. 3. For further discussion of Bonaventure’s distinction(s) see, P. L. Veuthey, S. Bonaventurae Philosophia Christiana, 213. Bonaventure’s distinction seems to be based upon Alexander’s broader one which Alexander stated as: ‘Tempus dicitur communiter et improprie, communiter sed minus proprie, et proprie. Communiter et improprie dicitur tempus unum nunc primo; communiter minus proprie nunc post nunc; proprie vero tempus extensio continua secundum praesens a praeterito in futurum. Primo modo tempus non est tempus, sed temporis initium, secundum modo tempus est numerus secundum prius et posterius, tertio modo tempus est continuum secundum continuitatem motus secundum prius et posterius et medium quod est terminus praeteriti prioris et futuri posterioris . . . secundo modo respicit mutationem quae est de uno esse in aliud sine continuo’. Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 1 (1, 105). Peter of Tarentaise offers another version of the distinction, In Sent. 2. 2. 12. 2, which also seems to draw upon Alexander. Philip the Chancellor, writing at the beginning of the century, seems unaware of the distinction, although cognizant of the general point that the distinction is intended to convey, ‘Et dicendum est quod tempus accipitur dupliciter. Vel mensura motus primi mobilis, et secundum hoc ante omne tempus illa duo facta sunt secundum illam sententiam que dicit non omnia simul fieri, quia firmamentum secunda die factum est quod est primum mobile et ita motus et sic tempus. Si vero tempus dicatur mensura eius quod mutatur de non esse in esse, tempus est coequevum predictis et precedit firmamentum et ita tempus stricte; cum illis enim exit de non esse in esse.’ Sum. de Bono, 1. 3. 6 (1, 130, 6–11).

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It is probably no coincidence that we can detect the influence of earlier writers behind Bonaventure’s distinction, as a prime reason for developing distinctions during this period was the need to reconcile competing authorities and interpretations. But, a no less important factor lying behind the development of this distinction was the difficulty that theologians were having in making sense of how there could be time before the Primum Mobile and time after its destruction. We have already seen earlier some of the problems which arose in relation to questions about the origins of the universe and the need to identify a time prior to the existence of the Primum Mobile. But there were also important questions arising about the eventual fate of the universe. Basing themselves on a scriptural warrant, medieval thinkers were firmly convinced that one day God would end creation by destroying the physical world and assigning the souls of people to an eternal destiny. The existence of an eternal destiny gave rise to questions about whether there would be a time to measure that destiny, whether it was eternal beatitude in heaven or eternal damnation in hell. The need for a time was more explicit with damnation, as damnation was thought to Albert’s thoughts on this issue developed. He began by attempting to state the distinction as one between the ‘time of the philosophers’ and the ‘time of the theologians’, Sum. de Creat. 2. 5. 2 (Borg. 34, 369), which seems to be a distinction between ‘time’ used in what was to become the first and third senses in his later definition, which was itself modelled more closely on Alexander’s approach. Sum. Theol. 5. 23. 3.1 (34.1, 136, 52–63). For the further development of the distinction in the fourteenth century, Walter Burleigh, Sup. Octo Lib. Phys. 4. 3. 2, but see especially John Marbes, who seems to have believed that there were as many times as motions, but only one universal fundamental time which is given by the Primum Mobile: Johannis Canonici, Quaest. Sup. Octo Lib. Phys. 2.

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involve burning processes with pain and suffering, and it was difficult to see how there could be such processes in the absence of time. But the key problem was how there could be time at all in the absence of the Primum Mobile.31 One of the roles of Bonaventure’s distinction was clearly to address issues such as this. His third notion of time is the classic Aristotelian account which we have been exploring so far. It is indexed to the Primum Mobile, from which it acquires its topological and metrical properties, and so it is referred to as the ‘proper’ account of time. The more interesting distinctions are the first two notions, which seem to be accounts of time which make no reference to cosmological features such as a Primum Mobile. These notions of time represent ways of talking about a time which would be applicable, as the second account makes explicitly clear, in situations prior to the existence of the Primum Mobile. The first account is even broader still, allowing for a notion of time to be applied to any situation 31 Medieval thinkers were committed to Aristotle’s belief that the Primum Mobile could never naturally cease: Albert, Phys. 8. 3. 9 (4.2, 638–41); Aquinas, In de Caelo 1. 4 [41], and so it was agreed that any final destruction would only be as a direct result of God’s actions. There was general agreement about the nature of damnation, Bonaventure, In Sent. 4. 50. 1. 2. 3; Alexander, Sum. Theol. 1. 1. 1. 2. 4. 2. 4 ad 15 (1, 98–9), but there was much less agreement about whether the blessed needed a time and, if so, what its nature should be. Alexander, probably influenced by Richard of St Victor’s view, In Apoc. 3. 7 (PL 196, 790A) that the angels and saints will cease to exhibit ‘variatio’ in heaven, quotes an anonymous opinion that such a time would have no extension (‘simul protenditur cum aeternis’) Sum. Theol. 1. 1. 1. 2. 4. 1. 1. 2 (1, 86); 1. 1. 2. 3. 4. 3. 4. 2 (1, 108–9). Aquinas, however, was convinced that there would still be a need for a time for the blessed, ‘quamvis post resurrectionem non sit tempus quod est numerus motus caeli, tamen erit tempus consurgens ex numero prioris et posterioris in quolibet motu’, In Sent. 4. 44. 2. 3 ad 5.

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in which there are changes or transitions occurring between non-being and being (esse). These accounts are interesting because they seem to imply that there can be time existing in the absence of the Primum Mobile, and so they seem to assume that time can exist without the metric provided by the Primum Mobile. If this is so, and if these other uses of ‘time’ are meant to indicate alternative instances of time, then it would seem to suggest that the Primum Mobile is constitutive of the temporal metric because when the metric provided by the Primum Mobile is no longer present then there is a different time, constituted in its difference purely and simply in virtue of the fact that it has a different metric. Whilst this distinction between senses of ‘time’ is interesting, it is also extremely puzzling. It is not at all clear whether the distinction is meant to pick out different times or a single time with different properties. What is particularly puzzling, however, is that the philosophy of time which we have been investigating seems to assume that the topological properties of time arise from the topological properties of the motion of the Primum Mobile. Lacking any reference to the Primum Mobile, it is therefore not clear how the ‘most common’ and ‘common’ uses of ‘time’ could refer to a time that is existing in any sense at all. Perhaps it was concerns such as these that encouraged Aquinas to ignore the distinction between senses of time. It is extremely unlikely that he could have been unaware of it, yet when discussing time before the Primum Mobile he seems to deliberately avoid using any distinction between different senses or notions of time. Instead, his preferred

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solution is to talk of a single time which gains its metric from whatever process is the most simple.32 Aquinas’ approach still faces the difficulty that it seems to ignore the question of how time would get its topology in the absence of the Primum Mobile. When commenting on the angels he seems to have thought that the topological properties of their time arose from the same source as their metrical properties, as we shall see when we examine the angelic time later. It is probable, therefore, that Aquinas would have assumed that time would get its topological properties from whatever motion or process it inhered in as a subject and was measuring. For Aquinas, as for his colleagues, the distinction between topology and metric was not one that they could easily make and so they tended to assume that the subject of the metric determined and constituted not only the metric, but also the topology of time.

IS POSSESSING A METRIC AN ESSENTIAL P RO P E RT Y O F T I M E ? A question sometimes raised by contemporary philosophers is whether time can exist without a metric. A time without a metric would still possess a topological structure with 32 Aquinas, ‘dicendum quod, si motus firmamenti non statim a principio incoepit, tunc tempus quod praecessit, non erat numerus motus firmamenti, sed cuiuscumque primi motus. Accidit enim tempori quod sit numerus motus firmamenti, inquantum hic motus est primus motuum; si autem esset alius motus primus illius motus esset tempus mensura’, Sum. Theol. 1. 66. 4 ad 3.

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instants temporally related to each other but it would lack a metric and so there would be no truth about the distance between the instants. Whilst thirteenth-century thinkers did not explicitly consider the case of a time existing without a metric, their reflections on the nature of the privileged clock indicate the contours of how they would probably have treated this question. We have seen that the privileged clock was considered to be constitutive of the metric, rather than as merely evidence of a metric. As a result of this, some medieval thinkers went so far as to talk of the existence of another time, or another sense of time when the privileged clock of the Primum Mobile was not existing. Despite their language, as they were lacking the terminology to distinguish between a metric and a topology, when medieval thinkers talked of a different time they were not necessarily affirming that there must be a different topology. When talking of a different time, thirteenth-century thinkers may well have been merely trying to say that the metric was different. Aquinas’ discussion of time before the Primum Mobile indicates precisely this emphasis. He seems to have assumed that time always has a metric but that the actual privileged clock itself can change. In cases where the Primum Mobile was absent, he still referred to time as measured and assumed that, of whatever motions were present in such a time, there would be a simplest and most regular one which could provide a privileged clock. The distinction between the senses of time provided by Bonaventure and Alexander makes the same basic assumption. Although they considered scenarios in which the

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Primum Mobile might be absent, all of their distinctions between different notions of time assume the core idea that time is a measure (mensura). Even in Bonaventure’s loosest sense of ‘time’, where the word is used in its ‘most common’ sense to refer to any kind of transition from nonbeing to being, the focus is still upon the fact that time is a measure. This suggests that thirteenth-century thinkers had an operating assumption that time must always be a measure. It was simply inconceivable to them that there could be a time that either lacked a measure, or had two different but equally valid measures. Whilst this may seem to align them with a particular side of the contemporary debate about whether possessing a metric is an essential property of time, the reality of the matter is that they simply could not formulate the question within their own conceptual framework and so they were never able to give the matter the careful consideration that surrounds the contemporary discussion of this issue.

C O N C LU S I O N In this chapter we have examined thirteenth-century views relating to issues of measurement and, in particular, temporal measurement. We have seen that thirteenth-century thinkers distinguished between a variety of ways in which the word ‘measure’ (mensura) could be used; distinguishing between Platonic senses which were typically used

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to compare particulars in relation to their ontological perfection, and Aristotelian senses of the word ‘measure’ which were used to give an account of what we think of as the metric of time. When it came to applying measurement theory, we have seen that thirteenth-century thinkers would typically distinguish between the intrinsic and extrinsic measure. The intrinsic measure was the ‘subject’ of a particular kind of measure; the perfect standard which was the actual measure used in measuring other particulars of that same kind. When it came to carrying out actual measurements the extrinsic measure was the ruler or clock, or other type of measure, which was an instance of the perfect standard laid down by the intrinsic measure, and which could then be used in concrete practical situations to carry out actual measurements. In the case of time, we have seen that thirteenth-century thinkers generally agreed that the Primum Mobile was the intrinsic measure of time. It qualified in this respect because, in their opinion, it met the metaphysical and epistemological requirements so that it was the most apparent, most perfect, and most regular motion. In examining thirteenth-century accounts of measurement, we have looked at several questions that are of interest to contemporary philosophers. In the first place we looked at the debate between objectivists and conventionalists over whether measurements should be thought of as objectively true or as simply truths that are relative to particular standards or conventions of measurement. Although this is not a question that thirteenth-century thinkers explicitly

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considered, I suggested that their general approach was one that implied a preference for the objectivist approach on this matter. Having examined that question we next considered two further issues: the question of whether the measure provided by the Primum Mobile should be thought of as constituting (rather than merely providing evidence for) the metric of time and the question of whether thirteenthcentury thinkers believed that possessing a metric was an essential property of time. As thirteenth-century thinkers do not typically consider these kinds of questions, it is difficult to be sure precisely how they would have responded to either. Nevertheless, in examining a distinction between the senses of time, a distinction developed initially by Alexander of Hales but used widely in the thirteenth century, we found that thirteenthcentury thinkers seemed to believe that the absence of the Primum Mobile entailed that time itself must be different in some sense. It was not always clear from the texts whether this difference was thought of as a difference of metric or as a difference of topology. It is probable that many medieval thinkers were not even clear in their own minds about the precise import of this distinction. One of the potentially clearest accounts, however, is provided by Aquinas. Although he chose not to use Alexander’s distinction he was nevertheless clear in stating that time in the absence of the Primum Mobile takes its metric from whatever other process or motion is now the most regular. This would seem to suggest that the Primum Mobile is being viewed as constitutive of the metric, rather than as merely evidencing the metric.

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The question of whether time must necessarily possess a metric is a harder question to derive a medieval response to. The fact that thirteenth-century thinkers almost always describe time as a measure (mensura) probably indicates that they were unable to separate the idea of time from the idea of measurement and so the suggestion that there could be a time without a metric would probably have seemed inconceivable to them. As they never considered the question explicitly it is difficult to settle the matter for sure. It has been suggested, as we saw at the beginning of the chapter, that Aristotle’s notion of time is basically that of a metric rather than of a topology. Whilst this may well be the case for Aristotle, the situation for thirteenth-century thinkers was a little more complex. They do have what amounts to a topology for time and they do consider questions which we now classify as topological but, because they lack the distinction between a topology and a metric, they are almost entirely incapable of keeping the issues distinct in their discussions. We have seen this particularly clearly in the case of the Primum Mobile, which had both a topological and a metrical role, even though the basic discourse used to refer to it was largely metrical. The medieval failure to distinguish considerations of measurement and topology led to confusion in their own thought and ultimately continues to make it difficult for contemporary philosophers to fully appreciate the distinct elements of medieval philosophies of time.

7 Time and Atemporality

In the previous chapter we saw that thirteenth-century figures were often inclined to use the word ‘time’ (tempus) in a variety of ways. In this chapter we shall be examining the criteria which medieval thinkers used to determine whether a particular should be located in time, and if so which particular notion of time it should be identified with. Having clarified these factors, we shall then go on to examine the thirteenth-century terminology and phrases which were used to suggest that particulars were outside, beyond, or existing alongside time. Whilst all thirteenth-century figures were happy to talk of particulars as existing ‘in tempore’ (in time), very few seem to have asked whether the word ‘in’ conveyed anything of philosophical import. Aquinas noticed that the word ‘in’ was not being used univocally when it was used in expressions such as ‘in time’ and ‘in place’, but he does not seem to have felt that this was a significant issue. Bonaventure seems to have been even less concerned about a precise use of terminology and was content to treat the expressions ‘in tempore’ (in time) and ‘sub tempore’ (beneath time) as equivalents.1 1 Aquinas, In Phys. 4. 16 [567]. Bonaventure, In Sent. 2. 7. 2. 1. 2 ad 3–4.

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As a result of this relaxed usage, thirteenth-century accounts of time often presuppose a difference between temporality and non-temporality, but they rarely clarify precisely what the determining factors were. Different accounts stress different nuances, and so it is possible to identify some nine factors, in thirteenth-century accounts of time, as factors which were thought to determine the temporality of the particulars they were attributed to: [1] [2] [3] [4] [5] [6] [7] [8] [9]

the possession of change and succession suffering from the ‘ravages of time’ having a common measure being measured by the Primum Mobile having a causal relationship with the Primum Mobile being spatial having a duration bounded by further periods being created having a first instant of existence.

The fundamental basis determining the ascription of temporality was, for medieval thinkers, change and successiveness, as the first criterion lays down. Things were in time to the extent that they were in motion and so subject to the successive actualization of potentialities.2 Particulars such as 2 Kilwardby, ‘tempus vero est talis esse quantitas sive duratio, mensurans ipsum dum continue transit futurum per presens in praeteritum’, de Temp. 16 [94] (32, 25–7). Bonaventure, In Sent. 1. 30. 1. 1; Albert, ‘sic large sumpto tempore, omnis creatura temporalis est et in esse, et in posse, et in agere’, In Sent. 1. 8. A. 12 (Borg. 25, 237) and ‘omnis creaturae sit per tempus mutari: et ita convenit ei praeteritum et futurum’, ibid. (Borg. 25, 235). See also his Sum. de Creat. 2. 3. 2 (Borg. 34, 349); In Sent. 1. 9. A. 3. 2. 4 (Borg. 25, 274). Phys. 4. 4. 4 (4.1, 298, 33).

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God, angelic esse (existence) and logical truths were generally thought of as admitting of no successiveness and change and so, as a result of this failure to meet the first criterion for temporality, they were deemed to be non-temporal.3 Although this seemed a simple and straightforward factor accounting for temporality, complications arose when the question was asked whether the (unchanging) essences of temporal things should be thought of as themselves temporal. Albert seems to have felt that because the essences were ‘joined or related to change’, then they should be considered temporal; but Kilwardby was unhappy with that approach, as it effectively amounted to claiming that unchanging essences constituted an exception to the general rule that associated temporality with explicit change and succession. Ultimately, as Ulrich was to state particularly clearly, the solution to the problem lay in distinguishing between the unchanging essence and the changing actualization of that essence, the ‘esse’; so that whilst the essence must be considered eternal because it failed to meet the requirements for change and succession, the esse of temporal particulars would remain firmly temporal in virtue of its mutability.4 3 Siger de Brabant, ‘sicut motus consequitur tempus, ita immutabilitatem aeternitas consequitur’, Sup. Lib. de Causis 9 (58, 8–14); 11 (62, 12–17). Albert, In Sent. 1. 9. A. 1 (Borg. 25, 272). Accounts of time that identified temporality with mutability were well established prior to the thirteenth century as can be seen in Hugh of St Victor ‘(esse) . . . temporis est subiacere mutabilitati, et pati vicissitudinem . . . extra tempora enim aeternitas erit, et mutabilitas non erit’, In Ecclesiasten, Homilia 13 (PL 175, 207). Aquinas, Sum. Theol. 1. 10. 3; 1. 53. 3; Albert, Sum. Theol. 5. 23. 1. 1. 2 (34.1, 126, 7–11). 4 Kilwardby, de Temp. 16 [95] (33, 3–6); Albert, In Sent. 1. 9. A. 3 ad 4 (Borg. 25, 275). Ulrich, ‘corruptibilia habent quandam vitae successionem, quia licet vita secundum essentiam una sit per totum periodum viventis,

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The question of rest raised similar problems. A particular at rest is not in motion, so the question arose as to whether it should be considered temporal whilst at rest. Although Aristotle’s response to the problem is not clear, Albert and his colleagues had little hesitation in concluding that particulars at rest remained ‘aptum natum moveri’ (by nature capable of being in motion) and so they were still actually being measured by the Primum Mobile, even whilst at rest. This meant that they should still be classed as temporal.5 A second factor implying temporality arose from the fact that particulars in time should suffer from the ‘ravages of time’. Moving beyond the mere fact of change, this criterion laid down that particulars which are measured by time should suffer decay during their existence. Taking their point of departure from Aristotle, thirteenth-century thinkers such as Aquinas, Albert, and Bonaventure claimed that time was a ‘per se’ cause of decay and corruption in the world; not because of any power of its own but rather because of the essentially mutable nature of the kinds of tamen, quia secundum esse est in materia habente, ideo sic continue fluit et variatur secundum successionem’, De Summo Bono 2. 4. 2 (2, 121, 10–17). 5 Albert, Phys. 4. 3. 11 (4.1, 280, 50); 6. 2. 11 (4.2, 484, 35–48); Aquinas, Sum. Theol. 1. 53. 3; Quaest. Disp. de Malo 16. 4; Kilwardby, de Temp. 20 [130] (41, 10). On the question of whether the Primum Mobile could be considered at rest if it were to cease moving, Aquinas concluded that it could not because if it were to cease moving there would be no time (in the proper sense) in which it could be said to be at rest, Quaest. Disp. de Pot. 5. 5 ad 10; Albert, Phys. 4. 3. 13 (4.1, 285, 18). Aristotle’s account of rest was not only unclear, it also seems to have been inconsistent. At Meta. 7. 7 (1032b2–6) he identifies time as an accidental measure of rest, whilst at Phys. 4. 12 (221b25–8) he contrasts what time measures accidentally with both motion and rest. For more details see J. Callahan, Four Views of Time in Ancient Philosophy, 69.

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particulars which time measured. This meant that temporality was identified clearly with corruption and decay.6 The third indicator of temporality arose from the extent to which a particular shared a common measure with other particulars which were in time. It was only possible to share a measure between particulars which were in the same genus, and so this criterion for temporality amounted to a metaphysical requirement determining temporality according to the genus membership of particulars. Radically different particulars, such as God, angels, souls, and heavenly bodies could not share a genus with physical, temporal particulars, and so, as we shall see in more detail in the next chapter, this criterion of temporality had the implication of entailing that they could not be temporal.7 6 Albert, ‘dicitur quod ‘‘temporale’’ dicitur multis modis: dicitur enim temporale quod subiacet et facit subiacere temporis variationi: et sic tempus dicitur esse causa corruptionis, quia per motum et mutationem facit distare quod est’, In Sent. 1. 14. B. 10 sol (Borg. 25, 399); and ‘Necesse est etiam, quaecumque sunt in tempore, aliquid pati a tempore.’ Phys. 4. 3. 10 (4.1, 279, 42–57 and 4.1, 287, 42); also, In Sent. 1. 8. A. 12 (Borg. 25, 236). Alexander, ‘tempus sit causa corruptionis et inveterationis, hoc non habet virtute propria, sed ex conditione rei quae mensuratur tempore’, Glossa In Sent. 2, Appendix (425, 6–8). Aquinas, In Phys. 4. 20 and 4. 23 [631]; In Sent. 2. 9. 1. 1 ad 2; 4. 50. 2. 2. 1 ad 3. Ps.-Aquinas, de Temp. 3; Bonaventure, In Sent. 2. 7. 2. 1. 2. Thirteenth-century thinkers seem to believe that the identification of temporality with decay arises from Aristotle, de Int. 1. 13 (22b32), although Albert also cites an influence from Priscian, ‘Tempus est mensura motus mutabilium rerum’, quoted at Sum. Theol. 5. 23. 1. 1. 1 (34.1, 124, 10–15). Note also Averroes arguing from this principle to the non-temporality of non-changeable substances, ‘res aeternae non sunt in tempore . . . tempus non operatur in eis; sed omnia quae sunt in tempore, tempus operat in eis: ergo res aeternae non sunt in tempore’, In Phys. 4 [117]. 7 Aquinas, ‘Modus igitur substantiae intelligentis est quod esse suum sit supra motum, et per consequens supra tempus.’ Sum. Con. Gen. 2. 55 [1308]. On measuring the angels see Aquinas, Quaest. Quodlib. 5. 4. 7; Albert, Sum.

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A fourth factor implying temporality seems to have been derived from the requirement that a temporal particular needs to be measured by the Primum Mobile. We saw in the last chapter that the word ‘time’ is used in its most proper sense when it refers to a duration which has its metric determined by the Primum Mobile, so this fourth criterion is not so much laying down a criterion for temporality as instead laying down a condition for a particular type of temporality. Particulars which failed to meet this criterion would fail to be in time in the most proper sense of the word, but they would not necessarily fail to be in time at all. The fires of hell represent a good example in this respect. They were widely thought to continue in existence after the destruction of the Primum Mobile and even though such an existence could not be temporal in the most proper sense of the word, the mutable nature of ‘fire’ was taken as nevertheless entailing that the fires of hell remained a temporal phenomenon in some wider sense of the word.8 A fifth factor implying temporality takes its point of departure from the Primum Mobile again, insisting that everything which is to count as being in time should be causally influenced by the Primum Mobile. The implication of this, as Siger and Bonaventure drew out, was that particulars which were not causally influenced by the Primum Mobile would be eternal or aeviternal and thus not count as temporal. AccordTheol. 5. 22. 1 (34.1, 116, 10–20). Philip the Chancellor seems to have allowed for a looser notion of being in time which could be used of a particular which although lacking succession or change could still in some sense be measured by time, Sum. de Bono, 1. 4. 9 (296, 155–70). 8 Bonaventure, In Sent. 4. 50. 1. 2. 3; 4. 44. 2. 2. 14. 1 ad 1.

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ing to this criterion only the mutable and the ontologically inferior can be in time, for it is only substances such as those which can be causally influenced by the Primum Mobile.9 A sixth factor implying temporality, and one that Aquinas seems to have taken as a necessary condition, was that temporal particulars should be spatial. This condition arose once again because of the common measure and common genus which temporal particulars were thought to necessarily possess and share. As the temporal particulars which we are familiar with are material, Aquinas took this as implying that all temporal particulars would be in the same common genus and so would necessarily be material and spatial.10 Whilst the requirements for common genus membership might indeed support such an approach we shall see in the next chapter that there are circumstances where Aquinas and his colleagues wanted to talk of non-spatial angels as being measured by a time. This suggests that spatiality is linked to temporal existence only in the case of time considered in its most proper sense. Spatiality cannot be thought of as a necessary condition for temporality where we are considering broader senses of ‘time’, such as those which are not measured by the Primum Mobile. 9 Albert, ‘in omni motu deprehenditur motus caeli sicut causa in suo effectu, et ideo tempus relinquitur esse in motu caeli’, Phys. 4. 3. 16 (4.1, 290 49–51); ‘tamen omnia ordinantur ad motum primi mobilis, qui causa est et numerus omnium motuum temporalium’, Sum. Theol. 5. 23. 2. 2. 2 (34.1, 134, 20–2). Aquinas, ‘secundum rationem divinae providentiae, hoc in rebus omnibus invenitur, quod mobilia et variabilia per immobilia et invariabilia moventur et regulantur’, Sum. Theol. 1. 113. 1; 1. 115. 3; In Sent. 1. 8. 3 ad 3. Quaest. Quodlib. 5. 4. 7; Siger of Brabant, Sup. Lib. de Causis 12 (65, 61–3). 10 Aquinas, ‘tempus non mensurat nisi quae aliquo modo sunt in loco, quia tempus consequitur motum localem’, Sum. Con. Gent. 2, 96.

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A seventh factor indicating temporality was that a particular must be ‘contained’, ‘excelled’, or ‘exceeded’ by time. This principle derived ultimately from Aristotle’s stipulation that a measure must be greater than what it is measuring, if it is to count as a measure at all.11 In order to be contained by the measure of time, the Primum Mobile, this principle was widely thought to mean that temporal particulars must necessarily have a beginning and an end to their existence. Particulars lacking either of these boundaries were therefore thought of as not properly temporal. Logically necessary truths (and logical impossibilities) were widely thought to have neither a beginning nor an end and so, as they could not be exceeded by the measure of time, they were considered to fall outside of time. Naturally immortal angels were also considered to have no end to their existence and so to be incapable of being exceeded by the measure of time, with the implication that they too fell outside of time in its most proper sense.12

11 Averroes, ‘Omne quod est in tempore, est in eo ut numeratum in aliquo numero, numerus excedit ipsum in duobus extremis: ergo omne quod est in tempore, tempus excedit ipsum in duobus extremis’, In Phys. 4 [117]; Philip the Chancellor, ‘si velimus ponere mensuram excellentem, sicut tempus est mensura excellens rerum que fiunt in quadam parte temporis . . .’, Sum. de Bono, 1. 1. 4 (1, 52, 7–14), and also Sum. de Bono, 1. 1. 4 (52, 7–10); Albert, In Sent. 1. 8. A. 12 (Borg. 25, 236); Aquinas, In Phys. 4. 20 [602]; Bonaventure, In Sent. 1. 37. 2. 1. 1 con 2; 2. 2. 1. 1. 1 ad 2. Theodoric of Freiburg, Tr. de Mensuris 2 (3, 216, 49–51; 3. 221. 222–5). 12 Aquinas, ‘omne quod quandoque est, et quandoque non est, subiacet tempori. Sed angelus est supra tempus ut dicitur in libro de Causis. Ergo angelus non quandoque est et quandoque non est, sed semper.’ Sum. Theol. 1. 61. 2 ob. 2; 1. 50. 1 ad 2; In Phys. 4. 20 [611]; Albert, Phys. 4. 4. 1 (4.2, 294, 31–40). Bonaventure, In Sent. 2. 2. 1. 1 fund. 4.

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An eighth factor implying temporality was that a particular should be created. This criterion derived ultimately from patristic authors such as Augustine and Jerome. As patristic authors tended to cast their discussions of temporality in terms of a distinction between the durations of time and eternity, it was natural for them to link the distinction between created and uncreated with the distinction between time and eternity, assuming that temporality and createdness were necessarily related as facets of nature. By the time of the thirteenth century it was customary to distinguish between three durations: time, eternity, and aeviternity, therefore it was no longer possible to map the distinction between createdness and uncreatedness onto durational distinctions in a simple and straightforward way. As we shall see in the next chapter, aeviternal beings were also thought of as created but not temporal and so, as reflection on the nature of aeviternal beings progressed during the thirteenth century, it became more difficult to maintain that createdness implied temporality.13 A ninth factor which was thought to imply temporality can be identified in debates about the status of the soul. We shall return to this issue in the next chapter, but because souls were substantially unchanging, there was a general reluctance to consider them temporal. We saw above that thirteenth-century figures tended to identify mutability and 13 Where authors do seem to assume a relationship between createdness and temporality it is often difficult to disengage the extent of their own commitment to the position from the commitment which is evident in their authorities and which, as Albert shows, there was a consequent reluctance to be seen to undermine. In Sent. 1. 8. A. 12 (Borg. 25, 235).

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temporality and so the lack of change evidenced by souls could be taken as suggesting that souls were non-temporal. If this conclusion was accepted, then that led to the peculiar situation where a human being’s body was temporal and the soul non-temporal. It was in order to address this particular question that Bonaventure and Albert appealed to what we might consider a ninth indicator of temporality, the suggestion that something could count as temporal if it was unchanging but had at least a ‘beginning’ of its existence in time. Whilst this approach might seem to resolve the puzzle of a human composed of a temporal body and nontemporal soul, it wasn’t actually very informative. Appealing to a beginning-in-time as a way of explaining and justifying the attribution to a soul of existence-in-time, was not very illuminating, as it presupposed the very concept of temporality that was unclear and in need of explanation in the case of a soul.14 By now it should be clear that although we can find at least these nine indicators of temporality in medieval thought, their existence represents not so much components of a theory of temporality as rather an assortment of ad hoc 14 Bonaventure, ‘uno modo dicitur temporale quod habet initium et variationem et actum in tempore; et hoc modo dicitur temporale quod subiacet tempori et est corruptibile et variabile. Secundo modo dicitur temporale quod habet initum essendi in tempore, sed non variationem, ut anima. Tertio modo dicitur temporale quod habet initum in tempore, sed actum extra tempus et supra tempus elevatum’. In Sent. 1. 14. 1. 1 ad 5; 2. 30. 1. 1 fund. 4. Compare this with Albert, ‘Dicimus, quod ‘‘temporale’’ dicitur multis modis: . . . Dicitur etiam temporale, cuius ortus est in tempore, etiamsi non varietur secundum suum esse cum tempore: sicut creatio huius animae in tempore est, quae tamen in tempore non corrumpitur’ In Sent. 1. 14. B. 10 (Borg. 25, 399).

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principles and competing authoritative dictums. Of these factors, we have seen that [6]–[9] are basically ad hoc principles derived from authorities or specific considerations; [3]–[5] represent, on the other hand, criteria for a specific narrower notion of a time where the particulars are in a common genus which have a metric provided by the Primum Mobile. This account of time is one which we saw in the previous chapter was referred to as the most proper notion of time. It is only when we come to the factors implying temporality denoted by the first two principles, [1]–[2], that we come to anything which could be thought of as offering a fundamental account of what medieval thinkers believed it meant to be temporal. According to those indicators temporality in its broadest sense is to be attributed to a particular when it exhibits succession and experiences decay or corruption.15 It should immediately be clear that even in its broadest sense the medieval account of what it is to exist in time is much narrower than many contemporary philosophical ac15 Alexander of Hales indicates that in contexts involving resurrected bodies, it is possible that some thirteenth-century thinkers wanted to separate the notion of time and corruptibility, as such bodies were thought to be substantially incorruptible, ‘Similiter in illis quae puniuntur: non enim insimul, sed secundum prius et posterius, sunt in calore et frigore. Ergo videtur quod ibi sit tempus et quod cadunt sub tempore quae huiusmodi passionibus puniuntur. Sed hoc non potest esse, quia tempus non est nisi corruptibilium; ergo, cum illa non sint huiusmodi, tempore non debent mensurari. Item, omni corruptibilitate remota, removetur tempus; sed post finem naturae removebitur omnis corruptibilitas; ergo post finem naturae non erit tempus, ergo neque prius neque posterius.’ Glossa in Sent. 2, appendix (420, 10–19). See also Albert on the saints in heaven who exhibit ‘variatio’ rather than successive ‘motus’, Sum. de Creat. 2. 4. 1 ad 1 (Borg. 34, 359).

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counts. As we have seen earlier, many contemporary philosophers would claim to be able to make sense of time in the absence of succession or decay, and so for them an unchanging immutable particular could well count as existing in time, even though for medieval thinkers such a particular would be not in time. What this means is that when we come to compare and contrast contemporary and medieval approaches to the question of temporality we must remember that there are at least three very different notions of time that need to be taken account of. There is a very narrow medieval notion of being in a time which has a metric determined by the privileged clock of the Primum Mobile, there is a broader medieval notion of being in time because a particular is in successive states (involving corruption), and then there is a modern, broader sense of temporality, which can be ascribed wherever it would make sense to affirm temporal relations, even if the particular of which the relations are affirmed is undergoing no change or succession. When it came to explicitly excluding particulars from accounts of time we can find at least three expressions which were widely used by thirteenth-century writers to affirm what we might term atemporality: (1) supra tempus (above time) (2) extra tempus (outside time) (3) cum tempore (with time). Although thirteenth-century thinkers do not spell out precisely what they mean by these expressions we can see that the word ‘supra’ is being used to denote an ontological superiority. To affirm that a particular is ‘supra tempus’ is to

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affirm that it is ontologically superior to particulars within time and that as a result of this fact it cannot meet the criteria for being in time. As thirteenth-century thinkers rarely distinguish between broad notions of temporality and accounts of time in its most proper sense, it is not always clear whether ‘supra tempus’ is to be taken as meaning that a particular fails to meet the criteria to be in the metricated most proper concept of time, or whether it fails to meet the criteria to count as temporal at all.16 16 Aquinas provides a particularly clear illustration of the way that substances were thought to be ‘supra tempus’ because of their failure to exhibit motion or change, ‘Modus igitur substantiae intelligentis est quod esse suum sit supra motum, et per consequens supra tempus. Esse autem cuiuslibet rei corruptibilis subiacet motui et tempori.’ Sum. Con. Gen. 2. 55 [1308]. One of the key implications of being ‘supra tempus’, as Alexander of Hales noted, was that particulars exhibited an ontological perfection that prevented them from being ordered, Glossa in Sent. 2, appendix (422, 4–10). This meant, according to Bonaventure, that God could be described as ‘supra’ creation, In Sent. 2. 1. 1. 3. 1, a position Peter of Tarentaise shared, In Sent. 2. 1. 2. 2. In a similar way Bonaventure depicted the intellectual part of the soul as ‘supra’ the rational part, In Sent. 2. 2. 2. 1. 2 sed con. 4, whilst Aquinas noted that an angel’s knowledge was ‘supra’ human knowledge, Sum. Theol. 1. 57. 2, and that divine gifts from God were ‘supra’ temporal realities, In Sent. 4. 49. 1. 2. 3; Sum. Theol. 1. 10. 5 ad 5; Sum. Con. Gen. 3. 60. Kilwardby concluded from God’s perfection that there were even senses in which God must be ‘supra’ eternity, ‘Aliquando enim ponitur aeternitas pro aevo, . . . Et dicit quod supra aeternitatem est Deus, id est supra aevum, quia constat quod supra veram aeternitatem non est.’ In Sent. 2. 10 (40, 42 f.). Compare Albert, ‘Supra enim aeternitatem est esse, quod secundum se stans est et indeficiens ante omne aevum et in omni aevo et post omne aevum secundum intellectus protensionem’ Lib. de Causis 2. 1. 9 (17.2, 71, 64–70) and Sum. de Creat. 2. 3. 2 (Borg. 34, 341). Albert provides a similar account of God’s being neither ‘in’ nor ‘with’ the aevum because of his causal superiority, Sum. de Creat. 2. 3. 3 ad 6 (Borg. 34, 353). Terminology in the period seems to have exhibited a degree of looseness. Alexander of Hales seems to prefer the word ‘ultra’ to ‘supra’ but uses this term in the same way as other figures use ‘supra’, Sum. Theol. 1. 1. 1. 2. 4. 2. 1 ad 2 (1, 90). Albert seems to have assumed that ‘supra’ and ‘ante’ were interchangeable, ‘esse autem animae sit . . . supra tempus . . . Secundum

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The confusion engendered by failure to distinguish between the different notions of time is particularly evident in discussions involving angels. As a result of their radical nonphysicality, Aquinas had no doubt that angels could not share a genus with any material substances and as a result of this they had to be classed as ‘supra tempus’. Yet despite this he was insistent that the angels exhibited a successiveness in their operations and so, despite being ‘supra tempus’ there was still a sense in which they shared a temporality.17 God was also clearly identified as ‘supra tempus’, but in doing so most thirteenth-century thinkers were careful to stress that it was because God failed to meet any of the criteria of temporality. God’s transcendence was such that He was ‘supra’ all senses of time and even, in Philip the hunc modum prioritatis dicitur etiam anima ante tempus, quod per se est mutabilium; anima autem nec penitus est mutabilis, nec penitus immutabilis; et ideo ante tempus et circa aevum est’, Sum. de Creat. 2. 3. 3 ad 6 (Borg. 34, 353). See also John Peckham’s account of God as ‘ante tempora’, De Aeternitate Mundi (3 and 31). 17 The precise basis for excluding the angels from time varied. Aquinas affirms at times that their ‘supra’ temporality status arose from their not being exceeded by time, ‘omne quod quandoque est, et quandoque non est, subiacet tempori. Sed angelus est supra tempus . . . Ergo angelus non quandoque est et quandoque non est, sed semper’, Sum. Theol. 1. 61. 2 ob. 2; Sum. Con. Gen. 3. 61. Bonaventure, however, thought that the crucial issue was that they admitted no ‘succession’ in their substance, In Sent. 2. 7. 2. 1. 2 ad 3–4. The ambiguity of the phrase ‘supra tempus’ is illustrated clearly in Aquinas’ claims that, ‘dicendum quod angelus est supra tempus quod est numerus motus caeli, quia est supra omnem motum corporalis naturae. Non tamen est supra tempus quod est numerus successionis esse eius post non esse, et etiam quod est numerus successionis quae est in operationibus eius.’ Sum. Theol. 1. 61. 2 ad 2, and ‘dicendum quod substantia et operatio daemonis est quidem supra tempus quod est numerus motus caeli, tamen in eius operatione adiungitur tempus, secundum quod non omnia simul actu intelligit.’ Quaest. Disp. de Malo 16. 7 ad 3.

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Chancellor’s opinion, ‘supra semper’, because he was beyond the limitations associated even with words such as ‘always’.18 From this analysis of the expression ‘supra tempus’ it can be seen that this expression was merely a generalized way of affirming that something did not meet some, or all, of the criteria to be in time. Affirming that a particular was ‘supra tempus’ could mean anything from affirming that it was temporal but not subject to a particular metric, to affirming that it did not exhibit succession or decay. The second expression which needs to be examined is ‘extra tempus’ (outside of time). When thirteenth century thinkers claimed that a particular was ‘extra P’ they were typically claiming that it lay beyond the causal influence of P. To be ‘extra tempus’ was simply a matter of being such that time could not be said to act on a particular, causing it to age, decay, and fall into corruption. As with the expression ‘supra tempus’, it would seem that unchangeability was the key criterion in classifying particulars as ‘extra tempus’ and so unsurprisingly we find God, angels, and souls all described as ‘extra tempus’.19 18 Aquinas, Sum. Theol. 1. 14. 13 ad 3; Philip the Chancellor, Sum. de Bono, 1. 2. 1 (1, 60, 86). In order to stress the fact that eternity does not meet the requirements for temporality Alexander of Hales even went so far as to talk of eternity exceeding time, ‘sed istud dicitur ratione durationis aeternitatis excedentis tempus’, Sum. Theol. 1. 1. 1. 2. 4. 2. 1 ad 2 (1, 90). Aquinas similarly talks of God as ‘supra aeternitatem’ when he wants to distinguish the superiority of God from angels which can be said to ‘participate’ in eternity in virtue of their metaphysically superior status to material particulars, ‘Sed Deum convenit laudare communiter et per aevum et per tempus; quia Ipse est causa et temporalium et aeternorum et est supra aeternitatem et tempus, prout aeternitas et tempus intelliguntur participata a creatura.’ In de Div. Nom. 10. 3 [875]. 19 Aquinas, ‘Deus est omnino extra ordinem temporis, quasi in arce aeternitatis constitutus, quae est tota simul, cui subiacet totus temporis decursus secundum unum et simplicem eius intuitum’, de Interpetatione 1. 14 [195];

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The third medieval expression indicating atemporality is ‘cum tempore’ (with time), which was used to refer to particulars which could not be said to exist ‘in’ time, but which nevertheless needed to be thought of as having temporal characteristics. There were broadly two ways in which a particular could have temporal characteristics and yet fail to count as properly temporal. In the first place it might be successive and mutable but equal in its extensional duration to time, so that it could not fulfil the criterion of being contained by time. Classic examples of this were thought to include the existence of the world and the existence of temporal durations, both of which were successive but which were thought to be necessarily coextensive with time. As a result of this their existence was often referred to as occurring ‘with’ time.20 Albert, In Sent. 1. 14. B. 10 (Borg. 25, 398–9); Alexander of Hales, Glossa in Sent. 2, appendix (422, 15–16). The central role that causal influence has, in determining the scope of ‘extra’, is particularly clear in the discussion of whether a particular could be ‘extra’ God, which Albert and Aquinas both answered negatively because they took it to be raising the possibility of there being particulars beyond God’s power. Albert, Sum. de Creat. 2. 3. 1 (Borg. 34, 338); Aquinas, Super 1 ad Corinthios 15. 1. The language of ‘extra tempus’ was not peculiar to thirteenth-century authors as it can be found in related forms in twelfth-century writers such as Hugh of St Victor, ‘temporis est subiacere mutabilitati, et pati vicissitudinem . . . extra tempora enim aeternitas erit, et mutabilitas non erit’, In Epist. ad Tim. (PL 175 207). Besides the role of mutability as defining what was to be thought of as ‘extra tempus’, Bonaventure also seems to have been influenced in his usage by the container model of temporality, which attributed existence in time only to those particulars which could be viewed as being exceeded by time. When it came to relating God to space, he seems to have used precisely the same argument to conclude that God could not be ‘in’ space, ‘nec ex hoc sequitur quod separetur a loco sed superexcedat omnem locum’, In Sent. 1. 37. 2. 1. 3 ad 2 and ad 3. See also Aquinas, Quaest. Disp. de Ver. 2. 12. 20 Bonaventure, ‘differt incipere ex tempore et in tempore et cum tempore, quia ex dicit ordinem et ita praesupponit tempus tanquam anterius; et

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The second way in which succession and extension were often separated from time was when it occurred in particulars which were ontologically more perfect than the physical particulars measured by the Primum Mobile. Where this issue became particularly significant was with angels, souls, and even God, all of which were considered unchangeable although capable of interacting with the world to bring about continuous effects which were in time. When the effects existed in time, questions naturally arose as to whether the cause could be located in time, but with the metaphysical perfection of the cause excluding a simplistic ascription of temporality, medieval thinkers seem to have found it convenient to talk instead of the cause’s existence as occurring ‘with’ time.21 ideo nihil coepit ex tempore nisi quod sequitur tempus. In tempore dicit temporis existentiam; sed tempus non fuit in sui initio, cum sit successivum. Ideo quae sunt aequalis durationis cum tempore non coeperunt, nec ex tempore, nec in tempore, sed cum tempore’. In Sent. 1. 30 dub 2 resp. Illustrating the fluidity of usage, Tarentaise takes a slightly different approach identifying ‘cum tempore’ with an extended sense of ‘ex tempore’, as in ‘Cum ergo quaeritur utrum coeperit esse Dominus ‘‘ex’’ tempore, distinguendum est: quia ly ‘‘ex’’ dicit ordinem, aut ergo notat consequentiam. Sic dico quod non coepit esse dominus ex tempore, aut concomitantiam solam, sic coepit esse Dominus ex tempore large accepto, id est cum tempore. Exemplum potest poni, dicitur enim: ex quo fuit lux, fuit splendor, et e converso; sed primo modo ly ‘‘ex’’ notat consequentiam, secundo concomitantiam.’ In Sent. 1. 30. 1. 5 resp. Ulrich, ‘Sic ergo dicere mundum aeternum, quod non fuerit tempus ante mundum nec post ipsum futurum sit, sed semper cum tempore fuerit mundus et futurus sit.’ de Sum. Bono 4. 1. 8 (4, 49, 147–50). For the patristic background note John Peckam’s use of Augustine, de Aeternitate Mundi ad 7 (13). 21 Knapwell, ‘Quod vero Philosophus insinuat quod tempus . . . mensurat motus animae nostrae, concedi debet; et hoc quia motus animae nostrae ratione corporis conveniunt in continuitate cum motibus corporum, per se vel ad minus per accidens; planum est enim quod potentiae organicae ipsius

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C O N C LU S I O N In this chapter we have examined the factors which encouraged medieval thinkers to consider something as existing ‘in time’, as well as examining the expressions which they used to refer to particulars which they considered to exist outside of time. We have found that there were at least nine factors which thirteenth-century thinkers were inclined to identify as implying temporality, factors which actually identified two broadly different kinds of time. There was time in its most general sense as simply a duration in which particulars undergo successive states and experience decay, and then there was a more precise, or more proper, sense of time in which the changing states of particulars were thought to be measured by the metric determined by the Primum Mobile. When thirteenth-century figures spoke of particulars as existing ‘outside’, ‘above’, or ‘with’ time they were intending animae habent in operando actum sive motum continuum, utpote materialem; actus vero potentiae intellectivae, licet sit in se simplex et immaterialis, tamen non est omnino sine illis inferioribus materialibus, quia non est sine phantasmate, et per consequens est cum continuo et tempore.’ Cor. Cor. Quare 1. 23 (106); Ulrich, ‘sempiternum est semper durans cum tempore’, de Sum. Bono 4. 1. 8 (4, 48, 146–7). Sometimes ‘quando’ (when) was used by medieval figures in a similar sense to ‘cum’, as in ‘angelus enim et corporalis creatura non est in eodem tempore, quamvis habeat esse quando tempus est’, Cor. Cor. Circa (125, 21). The convenience of being able to distinguish ‘in’ and ‘with’ encouraged Albert, at least, to extend and apply the use of ‘cum’ to eternity, especially when angels needed to be associated with eternity, but could not be said to exist ‘in’ it, as their metaphysical status was so much lower than that of God, ‘esse autem intelligentiae vel angeli sit cum aeternitate’, Sum. de Creat. 2. 3. 3 ad 6 (Borg. 34, 353). See also Peter of Tarentaise, ‘Quidquid aeternum est simul, est cum toto tempore’, In Sent. 1. 9. 4. 1 con. 3.

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to exclude such particulars from the scope of ‘time’, but they were not always clear about which account of time they were referring to. And so it was perfectly possible for medieval thinkers to affirm that a particular undergoing successive states was not in time, when what they were really trying to affirm was the weaker claim that such a particular was simply not measured by the Primum Mobile. Although unmeasured, such a particular would nevertheless still count as being in time in the broader sense of the phrase and so thirteenth-century language has the seeds of considerable confusion in this matter of what constitutes existence in time. Further complexity arises when we bear in mind that the thirteenth-century notion of being-in-time, even at its broadest, still represents an account of time according to which particulars can only count as being in time when they are fundamentally related to process. Whilst some contemporary philosophers would share elements of this approach, others would view the ascription of temporality as dependent upon temporal relations, rather than processes or succession as such. This means that besides the confusion internal to medieval accounts of existence within time, there is a further level of difficulty when it comes to translating such language into contemporary idiom. The import of this will become clearer in the next chapters as we begin to look at some of the particulars which thirteenth-century thinkers understood as existing outside of time.

8 Sempiternity, Angelic Time, and the Aevum

Having now examined the significant features of temporality and the language used to affirm existence within and without time, during the next three chapters we shall be focusing on atemporal issues, especially the particulars and durations which medieval thinkers affirmed as not existing in time. These chapters will look at the concepts associated with the Latin terms: ‘sempiternitas’ (sempiternity), ‘perpetuitas’ (perpetuity), ‘aeviternitas’ or ‘aevum’ (aeviternity) and ‘aeternitas’ (eternity), concluding with an examination of thirteenth-century views about God’s relation to time. In attempting to relate medieval discussions to contemporary discussions, one of the factors which complicates matters is that contemporary philosophers have introduced an analysis of atemporality of which medieval thinkers were unaware. Contemporary philosophers distinguish between ‘everlastingness’ and ‘timelessness’, where a particular or duration P is everlasting if (and only if) for all instants i, P exists at each i, whilst a particular, or duration, P is timeless

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if (and only if) it exists, but for all instants i, P does not exist at any instant i.1 In order to take account of what we saw earlier to be medieval reflections involving the notions of disunified temporal streams, it will be helpful if we were to distinguish between absolute and relative notions of everlastingness and timelessness. A particular or duration would be absolutely everlasting if it existed at all the instants of all durational streams, whilst it would be relatively everlasting, or everlasting with respect to a duration, if there was a duration such that it existed at all the instants of just that single duration. In a similar way a particular or duration would be absolutely timeless if it existed, but existed at none of the instants of 1 The definition of ‘timelessness’ and its cognates is intended to convey what I take to be the ‘traditional’ understanding of the term as exemplified in works such as N. Pike, God and Timelessness, 6–16; B. Leftow, Time and Eternity, 20–1; and W. L. Craig, ‘God, Time and Eternity’, 501–3. Alternative understandings exist. Some philosophers have suggested that the term ‘timelessness’ can be used to denote ‘an isolated, static instant’ (E. Stump and N. Kretzmann, ‘Eternity’, 429–58; R. Swinburne, The Coherence of Theism, 223), a notion which has also been referred to as a ‘degenerate duration’ (B. Leftow, Time and Eternity, 54). Other philosophers have suggested that the notion of ‘timelessness’ can be used to refer to a metricless duration (A. Padgett, God, Eternity and the Nature of Time, 19). Still others have suggested that the adequacy of a definition of the concept should be determined, in part, by its capacity to resolve the problem of God’s knowledge of future contingents (W. Hasker, God, Time and Knowledge, 146). Generally, there has been greater philosophical unanimity concerning the understanding of the term ‘everlastingness’, and the definition given here is intended to convey the notion as exemplified by, amongst others, N. Wolterstorff, ‘God Everlasting’, 79–83. Although there remain many contemporary defenders of the notion of timelessness, including amongst others, B. Leftow, Time and Eternity, 267– 83; P. Helm, Eternal God, passim; J. Yates, The Timelessness of God, 131–64, the coherence of the notion has been questioned by, amongst others, N. Pike, God and Timelessness, passim, and R. Swinburne, The Coherence of Theism, 223–8.

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any existing durational streams; whilst it would be relatively timeless, or timeless relative to a particular duration, if it was the case that it existed but existed at none of the instants of just that duration. The implication of this distinction is that a particular can be everlasting relative to some durations and timeless relative to others. This can be seen if we distinguish two temporal streams, S1 and S2 such that S1 contains an ordered series of instants i1, i2, . . . and S2 contains an ordered series of instants i1*, i2*, . . . If we further imagine a particular, P, such that it existed at the instants i1, i2, . . . of S1, whilst it did not exist at any of the instants i1*, i2*, . . . of S2, then P would be everlasting relative to S1 and timeless relative to S2.2 During the next three chapters we will be investigating how, if at all, the concepts of timelessness and everlastingness apply to the particulars that thirteenth-century thinkers identified as atemporal. In this chapter, the focus of our investigation will be examining the import and content of the terms ‘sempiternitas’, ‘perpetuitas’, and ‘aeviternitas’ or ‘aevum’. 2 The language of absolute and relative timelessness and everlastingness is not generally used by philosophers, probably because the problem of God’s relationship to time is generally not discussed in relation to the hypothesis of alternative temporal streams. Nevertheless, aspects of the notions can be seen embedded in works such as K. Ward, Rational Theology and the Creativity of God, 166, where it is suggested that God could create different temporal streams which would all be simultaneous to Him, and so He would be ‘absolutely everlasting’. The overall coherence of this particular model is in question. A divine simultaneity across differing temporal streams would seem to make the streams simultaneous with each other and so force their reduction to each other, unless there was some other factor to account for their distinct identities.

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S E M P I T E R N I TA S A N D P E R P E T U I TA S The words ‘sempiternitas’ and ‘perpetuitas’ are usually rendered in English with the terms ‘sempiternity’ and ‘perpetuity’, terms which are generally used to depict an everlasting mode of existence, amounting to existing at every instant of a duration.3 The content of the Latin terms is more complex. Although the word ‘sempiternitas’ expresses a conceptual construct derived from the adverb ‘semper’, meaning ‘always’, Alexander of Hales nevertheless suggested that it had two main usages: a use to indicate that a substance or state endures through all time, and a use to indicate that a substance or state has no limits.4 3 On the use of the English terms, E. Stump and N. Kretzmann, ‘Eternity’, 429–58. 4 Sum. Theol. 1. 1. 1. 2. 4. 1. 1. 1 (1, 85); 1. 1. 1. 2. 4. 3. 1 ad 2 (1, 100). Later he distinguishes these two uses, the former being attributed to Augustine and the non-extended limitlessness notion to Anselm (the quote which he believes is from Augustine is actually from Boethius’ de Trin. 4), Sum. Theol. 1. 1. 1. 2. 4. 4. 1 (1, 111). Alexander goes on to suggest that there is a distinction between the limitlessness uses as they are predicated of the differing durations of time, aeviternity, and eternity and so, in his opinion, it is possible to talk of something as simul without thereby necessarily using the word univocally. The criterion of univocity is genus identity, which according to medieval thought cannot occur between substances and particulars in different durations. Sum. Theol. 2. 1. 2. 2. 4. 1. 1 ad 5 (2, 87). Alexander is indebted to twelfth-century thinkers, in his development of a limitlessness predication of ‘semper’, particularly Gilbert of Poitiers, In de Trin. 1. 4 [71] (129, 17–20); Hugh of St Victor, de Sacramentis 1. 2. 10 (PL 176, 210C); In Ecclesiasten, Hom. 13 (PL 175, 207D); Richard of St Victor, de Trin. 2. 2 (PL 196, 903A). This usage can also be found in Augustine, de Lib. Arb. 2. 8 [21], and especially de Civ. Dei 12. 16.

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Alexander’s first usage seems to be straightforward and amounts to ascribing an existence such that it occurs at all the instants of a duration. This, we have seen, amounts to an instance of what contemporary philosophers would view as everlastingness. The second notion differs subtly and is not necessarily a temporal or atemporal concept at all. It ascribes, instead, a property of having no limits. If time were thought of as infinite, then it would be possible for both of Alexander’s notions to come together in the case of a substance that existed through all time, limitlessly. But, because thirteenth-century thinkers believed that they had sound theological reasons for believing that time had a beginning and an end, then, as Ulrich of Strasbourg indicated, this was taken as suggesting that the latter notion of limitlessness had a logical and ontological priority over the property of simply existing at every instant.5 Taking up Alexander’s initial thoughts on the matter, Aquinas suggested that it was important to distinguish two ways in which limitlessness might be ascribed to something that was said to exist ‘semper’ (always): There are two ways in which something could be ‘always and everywhere’ (semper et ubique). In one way it is as extended to all time and places—as God is. In a second way because a thing has nothing that limits it to any one particular time or place—as prime matter for example.6 5 Ulrich suggested that to exist ‘semper’ was to exist uncaused and to have existence of oneself (ex se), De Summo Bono 2. 4. 2 (2, 120, 3–4). Aquinas refers to this property as ‘necessary existence’, on which, P. Brown, ‘St. Thomas’ Doctrine of Necessary Being’, 157–74. Note also Albert’s tendency to equate ‘necesse’ and ‘aeternum’, Sum. Theol. 5. 23. 1. 1. 1. (37.1, 123, 57–9). 6 Aquinas, ‘dicendum quod aliquid esse semper et ubique potest intelligi dupliciter. Uno modo, quia habet in se unde se extendat ad omne tempus et

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According to Aristotle, one of the factors determining whether something could be in time, or not, was whether there were instants lying beyond the limits of the existence of the substance, or particular, in question. As Aquinas shows in the example above, both God and Prime Matter were such that neither could admit of instants beyond their duration, and so both technically fell outside of Aristotle’s account of time. God possesses limitless power and so exceeds time because there are no instants to which He and His power does not extend. Prime Matter is at the other extreme by being causally inert, so inert that it doesn’t exist at any instants at all and therefore as it cannot be located at any particular instants, this means that there cannot be (further) instants which lie outside of its existence.7

ad omnem locum, sicut Deo competit esse ubique et semper. Alio modo, quia non habet in se quod determinetur ad aliquem locum vel tempus: sicut materia prima dicitur esse una, non quia habet unam formam, sicut homo est unus ab unitate unius formae, sed per remotionem omnium formarum distinguentium.’ Sum. Theol. 1. 16. 7 ad 2. See also Aquinas, In de Caelo 1. 21 [215]; Sum. Theol. 1. 61. 2 ob 2; 1. 50. 1 ad 2. 7 On the criterion of being exceeded by time in order to be ‘in time’, Aquinas, In Phys. 4. 20 [602]. Aquinas is clearly drawing upon Aristotle and is probably influenced also by Boethius, De Trin. 1. 4. A similar approach is evident in the work of Averroes, In Phys. 4 [120] and Albert, Sum. Theol. 5. 23. 1. 1. 2 ad 7 (34.1, 127, 1–3). Albert stressed that the limitlessness defined as a property of ‘sempiternitas’ entailed that a particular was not subject to corruption, de Caelo 1. 3. 7 (5.1, 69, 53), and so angels and incorruptible heavenly bodies could be identified as being in ‘sempiternitas’. Ulrich went so far as to refer to them as ‘semper et simul’, de Summo Bono 4. 1. 8 (4, 45, 42). Thirteenth-century thinkers also viewed necessary truths as existing ‘semper’ rather than in time, because like God they had no boundaries to their existence. For further details, C. H. Kneepkens, ‘From Eternal to Perpetual Truths: A Note on the Medieval History of Aristotle De Interpretatione Chapter 1 16a18’, 181.

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Although both Prime Matter and God were thought to exist ‘semper’, Aquinas’ distinction between them is interesting because he seems to be viewing them as examples of what we might think of as timeless and everlasting existence. Prime Matter is identified as not existing at any instant and so it seems similar to the contemporary notion of timelessness. God on the other hand, and by contrast with Prime Matter, exists such that his power extends to every instant. If ‘power extending to’ were to be explicated as ‘existing at’ this would amount to a simple and straightforward ascription of everlastingness to God. Such an analysis would, of course, be highly controversial, as traditional readings of Aquinas have always assumed that he believed God’s existence was timeless. At this stage in our investigation it is too early to attempt to settle the matter one way or the other and so we shall return to this particular question of God’s relationship to time in the final chapter. The key issue at present, as we focus upon the word ‘sempiternitas’, is to note that Aquinas seems to be using ‘sempiternitas’ in a way that is compatible with both a timeless and an everlasting notion of existence. This is because he, like his contemporaries, was thinking principally in terms of limitlessness, rather than durational properties when using terms such as ‘semper’ and ‘sempiternitas’.8 8 Ulrich, ‘semper habet se eodem modo, cum probatum sit ipsum esse immutabile’, de Summo Bono 4. 1. 2 (4, 11, 245); Aquinas, ‘Ly semper designet permanentiam aeternitatis’, Sum. Theol. 1. 42. 2 ad 4. Sensitive to Aristotle’s criterion of being exceeded by time in order to be in time, Ulrich talks of sempiternal things as being with time, ‘sempiternum est semper durans cum tempore’, De Summo Bono 4. 1. 8 (4, 48, 146–7). Alexander tried to distinguish senses of ‘semper’ by appealing to what he seems to have taken as the

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Even where ‘semper’ and ‘sempiternitas’ are used to pick out examples of durational limitlessness, the particular content of claims can be obscured by the fact that medieval thinkers tended to conflate two distinct forms of limitlessness: beginninglessness and endlessness. Some particulars, such as incorruptible bodies, might be limitless and so sempiternal in virtue of being endless. Other particulars such as God were sempiternal in virtue of possessing a double limitlessness, possessing neither a beginning nor an end. What this brief analysis of the Latin term ‘sempiternitas’ shows, is that its meaning is broader than the English term ‘sempiternal’ as it has ‘limitlessness’ implications that the English term does not have. Whilst it will be accurate to render ‘sempiternitas’ with ‘sempiternity’ in some contexts, it is important to be aware that there may well be other contexts where it would be positively misleading to draw the extensional durational implications associated with the English term. Turning to the word ‘perpetuitas’, Alexander of Hales saw that there was a tendency to treat it as a synonym with ‘sempiternitas’, especially when the quality prompting the

more fundamental notions of time, aevum, and eternity, ‘Et illud, ‘‘semper’’ colligitur ex universitate particularium temporum. Secundo modo dicitur anima semper esse. Tertio modo dicitur Deus semper esse. Et est primum semper temporis, secundum semper aevi, tertium semper aeternitatis’, In Sent. 2. 1 [14] (8, 2–6). William of Conches seems to have used ‘semper’ to rule out the limitations of senses, Glossae Super Platonem 32 (172–3). On the non-applicability of tenses to a ‘semper’ God in twelfth-century thought, see also Peter Lombard, Sententiae 1. 8; and Robert of Paris on the sentence: ‘fuit quando non fuit tempus’, Summa ‘Breve sit’ (73–4); and L. M. de Rijk, ‘On Ancient and Medieval Semantics’, 1–62.

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usage was the limitlessness of a particular.9 Nevertheless, there was also a tendency apparent in some writers which stressed that the term was distinct and that it had its own content. In perhaps the most ambitious attempt to suggest a distinction Gilbert of Poitiers proposed a tripartite distinction: Sempiternitas has Perpetuitas has Eternity has

a collectio with a collatio a collectio without a collatio neither a collectio nor a collatio.10

This distinction was clearly familiar to thirteenth-century thinkers as Albert, for example, quotes it without explanation. Perhaps even more significantly for him, he quotes it without feeling that it needs any comment.11 Central to this definition is the distinction between the terms ‘collectio’ and ‘collatio’. It is much to be regretted that none of the central thirteenth-century figures seem to have provided an analysis of these terms. Nevertheless, Albert does refer to the key terms in a discussion, suggesting an identification of the term ‘collectio’ with the ever-changing flowing now, and a use of the term ‘collatio’ to refer to the set of prior and posterior locations of that flowing now. If Albert is using the terms in a technical way then this could 9 Alexander, Sum. Theol. 1. 1. 1. 2. 4. 1. 2 (1, 87); 1. 1. 1. 2. 4. 3. 4. 2 ad 5 (1, 108). William of Baglione focuses on the immutability of the particulars in question, ‘in perpetuis non differt esse et posse’, Quaest. de Aetern. Mundi 11 (584). By the thirteenth century Albert is explicitly referring to the limitlessness, ‘infinitus’, of the particular as the key issue, Lib. de Causis 2. 3. 1 (17.2, 139, 48). 10 In Lib. de Trin. (PL 64 1289). 11 Sum. Theol. 5. 23. 1. 1. 2 (34.1, 125, 71–3). Grosseteste also refers to a collatio as an element in time, In Phys. 4 (96) but it is not clear that he is consciously echoing Gilbert’s definition.

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well indicate that the terms are being used so that a ‘collectio’ refers to a set of ever-changing present instants, whilst ‘collatio’ refers to the temporal duration, the period, between two fixed instants. In the absence of any more explicit evidence such a reading must be considered tentative at best, as must the peculiar results of applying it to Gilbert’s distinction. When applied to his account it generates a distinction between sempiternitas as an extended duration with an ever-changing (tensed) present and perpetuitas as a nonextended duration but one that can still be referred to as possessing an ever-changing (tensed) present.12 Whilst the incoherence which this analysis would attribute to Gilbert might also explain why Gilbert’s distinction was not more widely used by thirteenth-century thinkers, a more prosaic explanation of its non-use might simply be that thirteenth-century figures could not understand what he was trying to get at. Where Gilbert’s distinction may have some explanatory power is in helping us to understand why Bonaventure introduced a notion of an extended aevum as a duration which possessed no ‘newness and oldness’. Aquinas dismissed the concept as incoherent, but Bonaventure may well have been influenced in his development of this concept by the fact that it constituted an implicit fourth element to Gilbert’s tripartite distinction, as it amounted to 12 Albert, ‘Sempiternitas enim dicitur, quam facit nunc sese movens indeficienter et sine fine collectio ipsius ‘‘nunc’’ collatione prioris et posterioris’, quoting Gilbert, Sum. Theol. 5. 23. 1. 1. 2 ad 7 (34.1, 127, 1–3) and reflecting a usage that we can find also in Avicenna, ‘tempus est collectio rerum que sunt momenta designata’, Suff. 2. 10. Aquinas seems to confirm that a collatio has extension and so cannot be present in an instant, ‘sic est ibi aliqua collatio, quae non potest esse in instanti’, Quaest. Disp. de Ver. 29. 8 ad 4.

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a notion of the aevum as a collatio (extension) without a collectio (tenses).13 It is difficult at this distance to be sure precisely how Gilbert’s distinction should be interpreted. The important fact for us is that thirteenth-century thinkers seem to have been none the wiser. Philip the Chancellor seems to have ignored it totally and suggested distinguishing between perpetuitas and sempiternitas on the basis that perpetuitas was the state of mutable particulars ‘equal to time’, whilst sempiternitas was the state of immutable particulars. Theodoric of Freiberg took yet another approach, suggesting that the word ‘sempiternitas’ was to be used to refer to the universe and the word ‘perpetuitas’ to refer to coextensive particulars which possessed an ontological priority to the universe. Aquinas, on the other hand, seems to have ignored the issue and let pass the question of whether there is a sustainable distinction between the terms ‘sempiternitas’ and ‘perpetuitas’.14 Ultimately, it is difficult to find any clear and generally accepted thirteenth-century distinction between the terms ‘sempiternitas’ and ‘perpetuitas’. Perhaps most revealingly of all, thirteenth-century thinkers seem to have had few concerns about using these terms and their cognates, both 13 ‘Alii vero assignant differentiam inter haec tria per hoc quod aeternitas non habet prius et posterius, tempus autem habet prius et posterius cum innovatione et veteratione, aevum autem habet prius et posterius sine innovatione et veteratione. Sed haec positio implicat contradictoria’. Sum. Theol. 1. 10. 5. 14 Philip the Chancellor, Sum. de Bono, 1. 1. 3 (1, 49, 46–9; 1, 50, 92) and de bono naturae intellectualis creaturae 9 (1, 297, 175–82); although Philip is not consistent, as he will sometimes use the terms interchangeably, ibid. 1. 4. 9 (1, 297, 193–8). Theodoric, de Mensuris 2 (216, 57–63).

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synonymously and interchangeably as they discussed angels, saints, perpetual motion, and God. As with the word ‘sempiternitas’ and its cognates, where issues about its application crop up there are invariably matters relating to ‘limitlessness’. This means that in precisely the same way that we need to take care interpreting ‘sempiternitas’ we must also conclude that the term ‘perpetuitas’ (and its cognates) cannot be viewed as merely amounting to what contemporary philosophers would think of as a notion of everlastingness.15

A EVI T E R N I TA S / A EV U M The words ‘aeviternitas’ and ‘aevum’ seem to have entered medieval lexicons as alternatives to ‘aeternitas’ for translating the Greek word ‘aeon’ (eternity). They occur in transla-

15 Aquinas, ‘duplex est perpetuitas vel perpetua durabilitas: una quidem per modum aeternitatis, alia vero per modum totius temporis, et differunt hae perpetuae durationes tripliciter. Primo quidem quia perpetuitas aeternalis est fixa, stans immobilis; perpetuitas autem temporalis est fluens et mobilis, . . . secundo quia perpetuitas aeternalis est tota simul quasi in uno collecta; perpetuitas autem temporalis habet succcessivam extensionem . . . tertio quia perpetuitas aeternalis est simplex tota secundum seipsam existens; sed universalitas sive totalitas perpetuitatis temporalis est secundum diversae partes sibi succedentes.’ Sup. Lib. de Causis 30. Alexander, ‘Quod ergo de se habet, hoc non est nisi mensurare opera et motus secundum prius et posterius; et ideo, cum non est amplius talis materia, adhuc est tempus, sed non sicut est respectu horum inferiorum. Et tempus, hoc modo sumptum, est illa duratio, quae alio nomine potest dici perpetuitas.’ Glossa in Sent. 2, Appendix (425, 9–23). For examples of synonymous and interchangeable usage,

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tions as diverse as biblical texts, philosophical writings, and patristic sources. Whilst medieval figures were content to use the terms ‘aeviternitas’ and ‘aevum’, Albert and Kilwardby both noted that their authorities provided little by way of explicit analysis of what they meant and of how they should be distinguished from ‘aeternitas’. As a result of this, there was a tendency in some writers to treat the terms as synonyms of ‘perpetuitas’ and ‘sempiternitas’.16 Aquinas, Sum. Theol. 1–2. 5. 4; 1–2. 31. 2; Sum. Con. Gen. 2. 55 [1299]; In de Caelo 2. 8 [372]. Albert, Sum. Theol. 5. 23. 2. 2. 1 (34.1, 133, 32); de Caelo 2. 2. 6 (5. 1, 141, 12–16). Kilwardby, In Sent. 2. 10 (39, 21). Richard of St Victor, De Trin. 2. 2 (PL 196, 902C). Ulrich, de Summo Bono 2. 4. 3 (2, 125, 59). Boethius’ casual usage of these terms at De Trin. 1. 4 undoubtedly contributed to the tendency to use the terms synonymously, especially as Albert explicitly refers his usage to that text at Sum. Theol. 5. 22. 1 (34.1, 115, 14– 21). The importance of limitlessness as the key import of ‘perpetuitas’ is illustrated by the fact that in 1277 Bishop Stephen Tempier included amongst the 219 propositions that he condemned, proposition 25 which claimed that God could confer the property of perpetuity (perpetuitas) upon other substances (H. Denifle and E. Chatelain (eds.), Chartularium Universitatis Parisiensis, i. 545). If the matter had simply been whether God could create something which could have the property of perpetuitas, and exist at every instant of time, it would have been relatively uncontroversial. What worried Tempier was the stronger thesis that God could confer limitless existence on substances, implying thereby that they had no beginning and so undermining the doctrine of creatio ex nihilo. On this see Aquinas’ usage, de Sub. Sep. 9, and Bonaventure’s discussion of different lengths of perpetuity in respect of the saints, In Sent. 2. 2. 1. 3. 16 Occurrences of the terms can be found in the Latin Vulgate, Ecclus. 1:1; in philosophical tracts such as Chalcidius’ commentary on Plato’s Timaeus (38A), Timaeus a Calcidio Translatus (30); and in patristic literature, Augustine, ‘An aeterna tempora aevum significavit, inter quod et tempus hoc distat, quod illud stabile est, tempus autem mutabile’, In 83 Quaest. 72. See also Isidore, Etym. 5. 29; 5. 38 [4]. For comments on the lack of authoritative analysis of the terms, Albert, Sum. de Creat. 2. 4 (Borg. 34, 357). Kilwardby, In Sent. 2. 10 (2, 40, 39–41). Alexander provided one of the earliest attempts to sum up how the term ‘aevum’ was being used, ‘Notandum autem quod nomen aevi dicitur multipliciter. Aliquando enim aevum accipitur pro omni

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Nevertheless there were two authoritative sources which significantly influenced medieval thought about the aevum: the writings of Proclus (P) and Dionysius (D). Amongst their writings there were two sentences which stood as

duratione quae non est tempus . . . . Aliquando vero pro tota duratione temporis . . . .Aliquando totam durationem temporis, quae apud nos est, aevum appellat . . . Aliquando vero pro antiquitate temporis . . . Aliquando pro magna parte temporis . . . Aliquando vero pro periodo sive duratione rei alicuius, secundum quod tota vita alicuius hominis appellatur suum aevum. Aliquando vero accipitur secundum proprium modum, secundum quod aevum est duratio rei habentis esse post non esse, sed non vertibilis in non esse, ut in perpetuis.’ Sum. Theol. 1. 1. 1. 2. 4. 3. 1 (1, 100). See also Kilwardby, In Sent. 2. 10 (40, 42 f.) and Theodoric of Freiberg, de Mensuris 2 (3, 221, 215–17; 3, 219, 46–50). Aquinas seems to have viewed the development of a distinction between aevum and eternity as arising because of a misunderstanding of the Greek language. ‘Dicendum quod ex ignorantia linguae graecae provenit quod communiter apud multos aevum ab aeternitate distingueretur, ac si distingueretur anthropos ab homine. Quod enim in graeco dicitur aevum, in latino aeternitas; et sic etiam Dionysius . . . pro eodem utitur aeternitate et aevo. Sed quia nominibus utendum est ut plures; si utrumque distinguamus ab invicem aevum nihil aliud erit quam aeternitatis participatio ut scilicet esentialis aeternitas ipsi Deo attribuatur aevum autem quasi participata aeternitas substantiis spiritualibus, quae sunt supra tempus.’ Quaest. Quodlib. 5. 4. 1. For examples of ‘aevum’ used interchangeably with ‘perpetuitas’, see Alexander, ‘Primo, cum nos videamus in aeviternis quod quaedam prius recipiunt perpetuitatem, quaedam consequenter.’ Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 101); Albert, Sum. Theol. 5. 23. 1 (34.1, 130, 177–8); In Sent. 1. 8. A. 12 sol. (Borg. 25, 237); Bonaventure, In Sent. 2. 2. 1. 1. 1 fund. 3 and 6. Kilwardby, In Sent. 2. 10 (2, 39, 21); 2. 12 (2, 151). For examples of ‘aevum’ used interchangeably with ‘sempiternitas’, Philip the Chancellor, Sum. de Bono, 1. 4. 9 (1, 297, 193–8). The concept of limitlessness at the heart of the definition is particularly clear in Isidore’s definition, ‘aevum est perpetua aetas cuius initium inveniri non potest’, Etym. 5. 29; 5. 38 [4]; and the everlastingness notion is clear in Kilwardby’s use of ‘aevum’ interchangeably with time, In Sent. 2. 10 (143); and Bonaventure’s reference to it as a ‘broad sense of time’, In Sent. 2. 2. 1. 1. 1 ad 2. William de la Mare went so far as to identify it with ‘eternal times’, In Sent. 2. 2. 1.

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having a particular relevance for discussions about eternity and the aevum: (P) the relationship of time to the temporal thing is as that of aeviternity to the aeviternal thing, and eternity to the eternal thing (D) the defining characteristic of the aevum is ancientness and invariability, and to be measured whole, by a whole17 Whilst (P) and (D) clearly influenced many thirteenthcentury thinkers, it was not always appreciated that there are subtle differences between the content of these claims. Dionysius seems to have viewed the aevum as an extended changeless duration, one which bears some similarities with a Newtonian absolute time, but Proclus seems to have taken an altogether different approach. He suggested that aeviternity acquired its character from the particulars of which it was predicated, particulars which in some cases could be simple and non-extended, thus implying a nonextensional duration. In an oft-quoted passage, Proclus summed up his position by proposing that: 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 17 Proclus, ‘quod est aeternum aeterno, hoc et est aeviternum aeviterno, et tempus temporali’, quoted by Albert, at In Sent. 1. 8. A. 8 (Borg. 25, 231). Dionysius’ text is from de Div. Nom. 10 [3] (PG 3; 937C). There were at least two translations of this text circulating in the thirteenth century, ‘proprietas aevi est antiquum et invariabile et totum secundum totum metiri’, and ‘proprietas aevi est antiquum et immutabile et universale metiendo’. On the relationship between the translations see Albert, Sum. Theol. 5. 23. 2. 1 (34.1, 131, 33–6).

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[momentum] of time, there is another middle [kind of existence] where the substance is in the moment [momentum] of eternity (i.e. the aevum) and the operations are in the moment [momentum] of time.18

At the heart of Proclus’ approach lay the distinction between substantial and operational changes, a distinction between changes which involve the destruction or mutation of a substance qua that substance, and (accidental) changes to the substance which arise as a result of operations such as exercising volitional and mental acts, and which arise even as a result of movement between places.19 Proclus’ tripartite distinction begins with an eternal substance which admits of no substantial or operational changes and so possesses the property of natural immortality. As it also lacks locational changes and mental or volitional acts, it also possessed the property of immutability. In contrast to this are temporal substances which experience both substantial changes and changes of mental, volitional, and movement acts. Such substances undergo destruction and, in virtue of their tendency to change locations and experience mental and volitional acts, they are also mutable. Finally, suggests Proclus, there is a class of aeviternal beings 18 ‘inter rem cuius substantia et actio est in momento aeternitatis, i.e. mensurantur aeternitate, et inter rem cuius substantia et actio sunt in momento temporis existens est medium, et est illud cuius substantia est in momento aeternitatis (i.e. aevi) et operatio est in momento temporis’, Liber de Causis 31. This distinction was widely used by medieval thinkers as Albert indicates, Sum. de Creat. 2. 3. 1 ad 2 (Borg. 34, 339); In Sent. 1. 8. A. 8 (Borg. 25, 230); Sum. Theol. 5. 23. 2. 1 (34.1, 132, 35–8). 19 Alexander of Hales, Sum. Theol. 1. 1. 2. 3. 4. 1. 1. 2 (1, 85); Albert, Sum. Theol. 5. 23. 2. 1 (34.1, 133, 51–8; 34.1, 130, 77–83); Philip the Chancellor, Sum. de Bono, de bono naturae intellectualis 1. 2. 1 (60, 82). Aquinas refers to

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which have a natural immortality, like an eternal being, but also experience the mutability consisting of the locational changes and mental and volitional acts which are associated with temporal beings. Medieval thinkers were generally indebted to Proclus’ approach, and tended to identify at least three kinds of particulars as falling in the ‘in-between’ category of aeviternal existence: angels, heavenly bodies (such as stars and planets), and resurrected bodies.20

substances incapable of substantial changes as having ‘permanentia essendi’, In Sent. 2. 2. 1. 2 ad 2. Albert refers to them as having a ‘necessitas essendi’, In Sent. 1. 9. A. 3 ad 1 (Borg. 25, 275). On the mutability of operational changes, Sum. Theol. 5. 22. 2. 1 (34.1, 117, 80–2); Ulrich of Strassburg, De Summo Bono 2. 4. 3 (125, 38–41). Theodoric, at least, refers to these changes as accidental changes, De Mensuris 7 (3, 238, 52). Although mental acts were theoretically mutable operational changes, the situation is complicated in the case of the angels because their acts of knowing and loving God seem to have been thought of as not admitting change. Alexander, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 2 ad 2–3 (1, 107–8); Aquinas, Sum. Theol. 1. 10. 3; Sum. Con. Gen. 3. 60; Quaest. Quodlib. 5. 4. 7. Aquinas uses the fact that there are unchanging operations in the angels to justify predicating ‘aeternum’ of them, Quaest. Quodlib. 5. 4. 1; Quaest. Disp. de Pot. 4. 2 ad 19; In Sent. 2. 2. 1. 1 ad 4; 4. 49. 1. 2. 3; Sum. Theol. 1. 10. 5 ad 5. Clearly sensitive to using ‘aeternum’ of aeviternal beings, he sometimes talks of the aevum as analogously equivalent to eternity, In Sent. 1. 19. 2. 1 ad 3. Although note Bonaventure’s strong disagreement with this, In Sent. 2. 1. 1. 1. 2. 20 Alexander of Hales, ‘perpetua, ut animae, angeli et materia, habent omnino absolutum modum essendi et non dependent ab invicem; ergo habent omnino disparatam durationem; sed duratio cuiuslibet est aevum’, Sum. Theol. 1. 1. 1. 2. 4. 3. 2 (1, 101). Albert, Sum. Theol. 5. 22. 2. 1 (34.1, 118, 16–20); 5. 23. 2. 1 (34.1, 131, 63–9); Theodoric, De Mensuris 4 (3, 231, 106– 25); Aquinas, In Sent. 2. 2. 1. 2 ad 2, and note also his ‘Quaedam vero recedunt minus a permanentia essendi . . . Sicut patet in corporibus caelestibus, quorum esse substantiale est intransmutabile . . . Et similiter patet de angelis . . . Et ideo huiusmodi mensurantur aevo’, Sum. Theol. 1. 10. 5. Philip the Chancellor seems to have taken a slightly different approach on the

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In addition to these aeviternal beings, thirteenth-century thinkers generally wanted to identify the human soul as aeviternal for, like angels, souls were thought to be naturally indestructible and yet admitting of mental and volitional acts. However, in contrast to angels, souls were also recognized as forming body–soul composites with the thoroughly temporal matter that constituted human bodies. This factor clearly worried some thirteenth-century thinkers, so that whilst Aquinas and Theodoric, for example, were happy to talk of the soul as aeviternal, Bonaventure insisted that it should only be thought of as aeviternal when its bonds to the human body are released.21

T H E NATU R E O F T H E A EV U M In the preceding chapters we have seen that despite whatever problems there were in the detail of their accounts, medieval question of the heavenly bodies, ‘item, omnia contenta sub firmamento quod movetur sunt in tempore. Ergo si illud movetur, sempiterne substantie que ab illo continentur proprie erunt in tempore et non in evo’, Sum. de Bono, 1. 2. 2 (1, 63, 59–61). For a fuller account of the heavenly bodies, J. L. Russell, ‘St Thomas and the Heavenly Bodies’, 27–39, and more broadly still, Thomas Litt, Les corps ce´lestes dans l’univers de Saint Thomas d’Aquin. 21 Theodoric, Tr. de Mensuris 3 (3, 227 62–6); Aquinas, ‘anima mensuratur tempore secundum esse quo unitur corpori; quamvis prout consideratur ut substantia quaedam spiritualis, mensuretur aevo’, Quaest. Disp. de Pot. 3. 10 ad 8; de Sub. Sep. 19 [113] (118); Robert Orford, ‘anima secundem se est supra tempus’, Cor. Cor. Sciendum (106). He believes this view can be found in Aristotle, Phys. 4. 11. See also ‘mens autem humana secundum se quidem est supra tempus’, Cor. Cor. Quaestione (118). For Bonaventure’s position, see, In Sent. 2. 17. 1. 3.

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thinkers nevertheless shared a basic model of durations which they used to explicate a notion of time. According to that model, time was a duration that was constituted by, and derived its topological structure from, its now. The now of time, or flowing now, as it was sometimes referred to, was thought of and explained reductively by associating it with the Primum Mobile, in which it was said to ‘inhere’ like an accident in a subject. In a way that must remain far from clear to us, the flow of the Primum Mobile was thought to explain the flow of the now, so that the ordered motion stages (moments) and constitutive motion segments in the Primum Mobile’s motion constituted the instants and periods of time. One of the particularly interesting elements in thirteenthcentury thought is the fact that writers clearly felt the need to explicate the duration of the aevum in language similar to that which they had used when discussing the duration of time. In the same way that temporal topology and its very existence was fundamentally based upon a ‘nunc constitutivum’, so too was the aevum.22 In the same way that time was explicated as an accident, so too was the aevum.23 Furthermore, in precisely the same way that medieval figures went on to explicate a temporal metric which was based upon the nature of the subject of time, so too we find the language of 22 Albert, ‘videtur, quod nunc aeviternitatis, ipsius aeviternitatis constitutivum, sit nunc indivisibile per substantiam, protensum autem, secundum quod adiacet potentiae sive potenti’, Sum. Theol. 5. 22. 2. 1 (34.1, 118, 5–10). 23 Alexander, ‘Ex accidentibus autem propriis est aevum aeviternis et tempus temporalibus.’ Sum. Theol. 1. 1. 1. 2. 4. 3. 1 ad 4 (1, 101); Albert, Sum. de Creat. 2. 3. 2 (Borg. 34, 348). Note also his discussion of the unity of the aevum considered as a measure, Sum. Theol. 5. 23. 2. 2. 2 (34.1, 134, 60–81).

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measures applied to the aevum, and the identification of the subject of the aevum as the privileged substance which is to provide the intrinsic measure of the duration.24 24 Alexander, ‘Nomen ergo aevi potest accipi communiter et proprie: Proprie enim est aevum, secundum B. Dionysium, inalteratum et secundum totum esse mensurans. Et secundum hoc aevum est mensura aeviterni . . .’ Sum. Theol. 1. 1. 1. 2. 4. 3. 3 ad 2 (1, 104); Albert, In Sent. 1. 8. B. 13 ad 2 (Borg. 25, 240–1); Aquinas, ‘dicendum quod creaturae spirituales . . . quantum vero ad eorum esse naturale, mensurantur aevo’, Sum. Theol. 1. 10. 5 ad 1. One of the factors which encouraged thirteenth-century thinkers to stress metrical aspects of the aevum, was the perceived implication in Dionysius’ account that the aevum had existed for longer than time, see Albert, Sum. Theol. 5. 23. 2. 2. 1 (34.1, 133, 59–64). In Sent. 1. 9. A. 3 ad 1 (Borg. 25, 275). Where it was felt necessary to measure the aevum against time, as Tarentaise shows, this tended to lead to the assimilation of the topological structures of the two durations, as the aevum was effectively, conceptually, laid alongside time in order to facilitate the measurements and comparisions: ‘Resp(ondeo): Loquendo de plus and minus a parte aevi secundum se, non est ibi plus et minus: sed per comparationem ad tempus cui coexistit est ibi assignare plus et minus’. In Sent. 2. 2. 2. 1 ad 5. It should be noted that there were considerable disagreements about precisely what it meant to measure the angels and even about what precisely was being measured. As a result of this there was a well established diversity of opinion running through thirteenthcentury thought about whether a single ‘aevum’ measure would suffice or whether more were required. The majority opinion preferred a single aevum as Alexander, Sum. Theol. 1. 1. 1. 2. 4. 3. 2 ob 3 (1, 101) and Albert, Sum. Theol. 5. 23. 2. 2. 2 (34.1, 134, 82–91) show. Aquinas refers this conclusion to the application of Aristotle’s axiom that substances within a single genus have a (single) common measure, ‘quia cum unumquodque mensuretur simplicissimo sui generis . . . oportet quod esse omnium aeviternorum mensuretur esse primi aeviterni, quod tanto est simplicius, quanto prius’, Sum.Theol. 1. 10. 6; ‘Et quia semper illud quod est simplicissimum est mensura in quolibet genere, . . . ideo necesse est ut duratio simplicissimi aeviterni sit aevum omnium aeviternorum; et ita simplicissimum aeviternum est subiectum aevi.’ Quaest. Quodlib. 5. 4. 1. Bonaventure used the same arguments which we saw him use against the Primum Mobile, as the basis for temporal unity, and argued that there must be a plurality of aeva, In Sent. 2. 2. 1. 1. 2. For a more detailed examination of the issues, see Scotus’ lengthy discussion in his Lectura, In Sent. 2. 2. 2. 1. 3 (Vat. 17, 131–40) and Cajetan’s commentary on Aquinas’ discussion in the Leonine Opera Omnia (4, 105–6).

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One of the most significant medieval disagreements about the nature of the aevum was over whether it should be thought of as extended or not. Dionysius’ widely used definition made use of the language of ‘ancientness’, thus seeming to imply an extensional existence, but Proclus’ definition suggested that the nature of the aevum should be identical to the non-extensional particulars which it measured. As might be expected, when faced by differing authorities, medieval views diverged, giving rise to a broadly Franciscan school stressing the extensionality of the aevum and a broadly Dominican approach stressing the non-extensionality of the aevum.25 Bonaventure’s (Franciscan) preferences for an extensional aevum seem to have ultimately been based on his fear that the transcendence of God would be undermined by a nonextensional aevum. Unless the aevum was considered to be 25 Although it is convenient to refer to a broadly Franciscan and Dominican approach to this question, the reality of medieval debate meant that viewpoints occasionally crossed the boundaries between the religious orders. Ulrich of Strasbourg, a Dominican, for example, seems to have thought that the aevum could measure the (extensional) existence of the world, ‘sed mensura esse divini est aeternitas, mensura autem durationis mundi est aevum vel tempus, quae ab aeternitate causantur’, de Sum. Bono 4. 1. 8 (4, 47, 117 f.). In an attempt to distinguish notions of the aevum Albert suggested that extensional and non-extensional notions could be distinguished by referring to a common and proper sense of the word ‘aevum’, ‘Et dicunt, quod aevum accipitur duobus modis: communiter et proprie. Proprie invariabile est penitus et invariabilium. Communiter autem dicit extensionem communicantem tempori, et sic aliquo modo variabilium est secundum actionem.’ Sum. Theol. 5. 23. 2. 2. 1 (34.1, 133, 84–9). The distinction does not seem to have been as widely accepted as the equivalent temporal distinction which we saw earlier, probably because advocates of an extensional aevum and advocates of a non-extensional aevum would both have wanted their own particular usage to count as the proper sense of ‘aevum’.

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extensional he felt that it, and the particulars measured by it, would become indistinguishable from the non-extensional eternity which he was committed to, and from the nonextensional God which was at the heart of that eternity. That, in his opinion, would have amounted to equating God and His creation. Whilst often agreeing in principle with him, later Franciscans such as John Pecham went on to sharpen the debate further by also developing a logical basis for their position. According to this approach, unless the aevum was extended then the theological necessity of predicating sequentially contrary properties of the angels would entail a contradiction, as the properties would have to be possessed by the angels ‘at the same time’.26 Advocates of an extensional aevum, such as Bonaventure, seem to have viewed it as if it were a Newtonian absolute time. The duration possessed instants, and so durational relations of before and after, but there could be no motion or, as Bonaventure himself put it, there could be no ‘newness and oldness’.27 26 Bonaventure’s concerns about the aevum seem to have arisen because he assumed that ascribing to it the property of being ‘simul’ would have entailed that it was uncreated. In Sent 2. 2. 1. 1. 1 fund. 3 and 6; 2. 12. 1. 1. 3; although he does not refer to him by name it is more than likely that Bonaventure’s formulation is drawing upon Richard of St Victor’s notion of a ‘successio et nulla decessio: et sic quaedam immutabilitas’, In Epist. ad Tim. 3 (PL 176, 603B–C). See also Roger Bacon, Opus Maius 4. 4. 14 (Bridges 166). Pecham’s argument occurs at Quodlibeta 2. 10 (99, 37–42). Roger Marston offers a different version of the same basic argument, insisting that angelic properties can only be possessed across periods, Quodlibeta 3. 2 (317, 18–30). 27 Bonaventure, In Sent. 1. 8. 1. 5. It is probable that his formulation of this position is influenced by Alexander of Hales, ‘Item, eorum quorum est passibile principium duplex est diversitas. Quorumdam enim est deperditio

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It is difficult to make sense of a concept of an absolute duration in medieval thought, especially when we bear in mind the care which medieval thinkers took to explicate a firmly relational notion of time. As the aevum cannot admit continua sine restauratione; et illa, ex quo facta sunt, incipiunt inveterascere. Et talium est tempus mensura secundum prius et posterius [in] succedendo; et cum haec veterascunt in tempore, et in talibus passiones quae fiunt non sunt in duratione sua novae vel quasi de novo factae. Aliorum autem est continua deperditio, sed restauratio fit in eis. Et hoc dupliciter; scilicet quandoque maior vel aequalis ipsi deperditioni; et talia, quam cito fiunt, veterascunt sed non senescunt. Quandoque fit minor restauratio, [et] tunc senescunt. Et talia mensurantur a tempore seundum prius et posterius in succedendo; et cum haec inveterascunt et senescunt in tempore, et passiones et actus in eis non sunt in duratione sua novi vel quasi de novo facti. Et talia, si sunt animata quae tempus non sentiant, ut illa quae non habent memoriam, sentiunt in se passionem semper quamdiu durat, quasi novam. Si autem tempus sentiunt, non; sed sicut in esse suo inveterascunt, et in sentiendo. Unde in quorum sensu vel cognitione cadit successio, non tantum sicut apprehensa, sed sicut ratio vel dispositio ad apprehendendum passiones et durationes passionum, hoc accidit, quod non sentiunt quasi novam semper, quamdiu durat, passionem. In illis vero in quibus non est istud passibile principium, inveteratio non est aut senium in sua duratione, et in talibus successio, si cadit in cognitionem eorum, cadit sicut res cognita, et non sicut ratio aut dispositio cognoscendi alia. Unde non congnoscunt in collatione prorioris et posterioris et in successu; et talia passiones in eis factas, quamdiu durant, sentiunt novas vel quasi de novo factas, et non inveteratas. Alexander of Hales, Glossa In Sent. 2, Appendix (423, 20 to 424, 12). See also Kilwardby, ‘instans autem aevi nullum habet fluxum penitus’, de Temp. 17 [106] (35, 3); and Aquinas, Sum. Theol. 1. 63. 7 ad 4. The extensionalists often prefer to use the word ‘mora’ of it, as Robert Orford: Cor. Cor. ‘Sciendum’ 23 (104–7). Attempting to mediate, Albert suggested that the aevum could be thought of as a ‘mora’ because we can intellectually extend the duration when thinking about it, ‘anima accipiens aeviterno adiacens nunc et protendens ipsum per indeficientiam ad omne tempus et temporale facit continuam moram quae dicitur aeviternitas’, Sum. Theol. 5. 22. 2. 1 (34.1, 118, 92 f.). It has been noted that Scotus’ views on time share similarities with aspects of the Newtonian absolute time (P. Ariotti, ‘Celestial Reductionism’, 113) and this may well be due to his reflections on Bonaventure’s attempts to formulate a notion of the aevum.

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of the possibility of motion, it is not even possible to explain it in virtue of modal relationism, so Bonaventure’s notion of the aevum does not appear to cohere with what we have seen to be the wider medieval philosophy of time. Thirteenthcentury critics of Bonaventure’s position seem to have been less concerned with the issue of background coherence, however, as they were more troubled by its internal coherence. Aquinas, for example, attacked the notion as simply contradictory because, on his reading of it, it was implying that there could be a succession without a before and after within that succession.28 Although Aquinas’ reading of Bonaventure clearly indicates an incoherence, there is an alternative way of interpreting Bonaventure’s position. If we were to take Bonaventure’s distinction between ‘newness and oldness’ and ‘before and after’ as a primitive attempt to differentiate (respectively) an A- and B-theory of temporal language then it could be the case that he was struggling to articulate a distinction between time and the aevum. This is because time is to be analysed as a relational duration which can only be described in A-theory terms and concepts, whilst the aevum is to be viewed as a non-relational (absolute) duration which can only be analysed in B-theory terms and concepts. 28 Aquinas, ‘Sed haec positio implicat contradictoria. Quod quidem manifeste apparet si innovatio et veteratio referantur ad ipsam mensuram. Cum enim prius et posterius duratione non possint esse simul, si aevum habet prius et posterius oportet quod priori parte aevi recedente posterior de novo adveniat, et sic erit innovatio in ipso aevo sicut est in tempore.’ Sum. Theol. 1. 10. 5. Thomists have followed Aquinas on this point as Cajetan indicates, In Prim. Par. Sum. Theol. 10. 5 (Leon. 101–4), and as more recent defenders continue to stress, J. Broussard, ‘Eternity in Greek and Scholastic Thought’, 70.

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Whilst this interpretation preserves Bonaventure’s position from a charge of internal incoherence, it does so only by overthrowing what we have seen in earlier chapters to be the relational basis upon which medieval philosophies of time were based. So ultimately, even if Bonaventure’s account can be rescued from charges of internal incoherence it cannot be shown to cohere with the wider philosophical basis upon which medieval accounts of time rested. Contrasting with the broadly Franciscan tradition was what we might think of as the broadly Dominican commitment to a non-extensionalist account of the aevum. Drawing explicitly upon Proclus’ methodology of deriving the nature of the aevum from the aeviternal particulars, Albert noted that: Since the Aevum is a measure of those things which have a beginning and yet are unchangeable and without succession, it would seem that the aevum is totally extensionless (totum simul).29

Although there were verbal disagreements about whether the aevum should be described as ‘totum simul’ or simply as ‘simul’, there was nevertheless a broad consensus amongst many thirteenth-century figures that the aevum was necessarily non-extended.30 29 ‘cum aevum sit mensura eorum quae habent principium, et incorruptibilia sunt, et tamen quae omnino sunt sine successione, videtur quod aevum sit totum simul sicut est aeternitas’, Sum. de Creat. 2. 4. 1 (Borg. 34, 358). Even advocates of an extensional aevum, such as Bonaventure, conceded that the substances within the aevum were non-extended, In Sent. 2. 2. 1. 1. 3. 30 Albert, Sum. de Creat. 2. 4. 1 (Borg. 34, 358); Sum. Theol. 5. 23. 2. 2. 1 (34.1, 133, 90 f.); In Sent. 1. 9. A. 3. 2 (Borg. 25, 273); and ibid. ad 1 (Borg. 25, 275). Albert justifies the non-extensionalist position by pointing out that in order to have an extended duration there would have to be a moving subject

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In order to appreciate why thirteenth-century figures felt that this had to be the case, it will be useful to distinguish between intrinsic and extrinsic successiveness. A particular is intrinsically successive if it is extended and has ordered successive or continuous parts. A table, or an hour, for example, would be intrinsically successive in this sense. Extrinsic successiveness would be exemplified by particulars which are ordered to each other. A traffic cone within a line of cones, or a car in the middle of a traffic jam would be extrinsically successive because in each case it would be related successively to other particulars. The Proclan position, as understood by thirteenth-century thinkers, seems to assume that a lack of intrinsic successiveness must entail a lack of durational extrinsic successiveness. Having made this assumption they concluded that a non-extended angel must exist in a non-extensional duration. No argument was ever advanced to justify such a claim, and more seriously there is a direct counterexample of the duration, Sum. de Creat. 2. 4. 1 (Borg. 34, 358). For Aquinas’ position, In Sent. 2. 2. 1. 1 ad 5; de Sub. Sep. 9 (57); Sum. Theol. 1. 10. 5; Quaest. Disp. de Ver. 8. 14 ad 12. Alexander had shared the same position but had been cautious about the implications of using the phrase ‘totum simul’ for angels, Sum. Theol. 1. 1. 2. 3. 4. 1. 3 (1, 87) and (1, 104). ‘Totum simul’ is the phrase used by Pecham in his refutation of the non-extensionalist position, Quodlibeta 2. 10 (99, 37–42) and it is used by Theodoric, Tr. de Mensuris 2 (3, 224, 269–99), 3 (3, 227, 60–1), and 4 (3, 227, 62–6). See also Philip the Chancellor, Sum. de Bono, de bono naturae 4 (54, 59). Robert Orford, Cor. Cor. Sciendum (104). For Albert’s reference to the aevum as a ‘nunc stans’, Sum. Theol. 5. 23. 2. 1, ad 7 (34.1, 132, 75–7). Some commentators have described Aquinas’ view of the aevum as an account of a ‘quasi-temporality’ (W. L. Craig, ‘Divine Timelessness and Personhood’, 112; and see also B. Leftow, Time and Eternity, 236); but this description would be more appropriately applied to the extensional (broadly Franciscan) view of the aevum, rather than to Aquinas’ non-extensional view.

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provided by consideration of the nature of an instant. An instant is a non-(intrinsically)-extended entity which, in the case of time, exists in the (extrinsically) extended duration of time. If a non-extended instant can exist in an extended duration then we might well wonder why a non-extended aeviternal particular cannot also exist in an extended duration. Perhaps it was the needs of their theology and more particularly its ontological requirements, which stressed the differences of substance and measure between angels and physical particulars, that prevented thirteenth-century thinkers from seeing this particular problem. If so, it also generated significant problems for them when it came to explaining precisely how the now of the aevum was to be individuated. This was a problem confronting proponents of both extensional and non-extensional accounts of the aevum, but the problem had a particular edge for advocates of a nonextensional aevum. The problem arose, as Albert explained, because a now could only have two properties: either it was moving or it was standing. Unfortunately, these properties were the defining characteristics (respectively) of the now of time and the now of eternity.31 If the now of the aevum was said to be moving then that reduced the aevum to a time. But if it was identified as not moving then that had the result of collapsing the now of the aevum (and the aevum itself) into the now of eternity, and 31 Albert, ‘Non enim potest intelligi nunc nisi stans vel non-stans, quia inter contradictoria non est medium; nunc autem stans aeternitatem facit . . . non stans autem facit tempus.’ Sum. Theol. 5. 23. 2. 1 (34.1, 132, 9–11).

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that had the very undesirable implication of associating God and aeviternal beings into a single class of beings. As we noted earlier, Aristotle’s theory of measurement insisted that genus likeness was the basis for applying a common measure so anything that implied the aevum and eternity were identical would have amounted to making the heretical claim that God and aeviternal beings could share a genus. Although the problem of individuating the now afflicted both extensional and non-extensional accounts of the aevum, the problem for extensionalists was distinguishing it from the now of time, whilst the problem for nonextensionalists was distinguishing it from the now of eternity. It was the particularly serious consequences of this latter problem that made it more of a pressing concern to advocates of a non-extensional aevum, especially when it was exacerbated by describing both the now of the aevum and the now of eternity as ‘totum simul’.32 The standard response to this problem, labelled by Albert as the ‘common view’ (communis usus), was to focus upon non-durational properties such as limitlessness, as providing the key difference between the durations and their nows.33 32 Albert, ‘sit totum simul sicut est aeternitas’, Sum. de Creat. 2. 4. 1 (Borg. 34, 358). 33 Alexander, ‘Est enim ‘‘nunc’’, quod non incepit esse et quod immutabiliter manet in esse, et est ‘‘nunc’’ aeternitatis; et ‘‘nunc,’’ quod incipit esse, sed non mutatur nec fluit in esse; et tale est nunc aevi, et dicitur hic fluxus successionis variabilis et non continuationis esse sive durationis; et est ‘‘nunc’’ quod incipit esse et mutatur et fluit in esse: et tale est ‘nunc’ temporis Sum. Theol. 1. 1. 2. 3. 4. 3. 1 (1, 100); also, Philip the Chancellor, Sum. de Bono 1. 1. 3 (1, 51). Albert, ‘Ergo sicut esse differunt, ita mensurae differunt. Sicut ergo propriam mensuram habet esse, quod nec incipit nec desinit,

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Aquinas in his early Sentences accepted this approach, but by the time that he came to reconsider the question in his Summa Theologiae, he was more sensitive to modal issues and was convinced that ‘having a beginning’ was not a sound basis on which to distinguish between beings or their durations. Instead, he suggested that the key difference between the now of eternity and the now of aeviternity must be due to the fact that the now of aeviternity was related or joined to change (adiunctum) whilst the now of eternity was in no way related to change.34 Ultimately, it is far from clear that this modified approach really resolves the problem. On the one hand, his distinction between the aeviternal now and the eternal now seems too ambitious, for as we shall see in the next chapters there are very real contexts in which God and eternity needed to be related to change. But perhaps more worryingly his solution seems to be extremely vague at the crucial point. He has proposed what is effectively a ‘relational’ response: arguing that it is the et propriam esse, quod incipit et desinit, ita propriam habebit esse, quod incipit, sed non desinit, et hanc dicimus esse aevum vel aeviternitatem.’ Sum. Theol. 5. 23. 2. 1 (34.1, 132, 39–48); and In Sent. 1. 9. A. 3 ad 4 (Borg. 25, 275). 34 Aquinas’ early position, In Sent. 1. 19. 2. 1 ad 5; 4. 49. 1. 2 ad 3. His later position, ‘Sed horum differentiam aliqui sic assignant, dicentes quod aeternitas principio et fine caret; aevum habet principium, sed non finem; tempus autem habet principium et finem. Sed haec differentia est per accidens . . . Est ergo dicendum . . . aeternitas sit mensura esse permanentis . . . Quaedam autem sic recedunt a permanentia essendi, quod esse eorum est subiectum transmutationi . . . et huiusmodi mensurantur tempore . . . Quaedam vero recedunt minus a permanentia essendi, quia esse eorum nec in transmutatione consistit, nec est subiectum transmutationis; tamen habent transmutationem adiunctam . . . . Et ideo huiusmodi mensurantur aevo.’ Sum. Theol 1. 10. 5 (my italics). Note also Albert’s attempt to move beyond the common view (communis usus). He is probably influenced by Aquinas’ ‘transmutationem adiunctam’ to offer his own ‘nunc indivisibile per substantiam, protensum autem secundum quod adiacet potentiae’, Sum. Theol. 5. 22. 2. 1 (34.1, 118, 7–10), my italics.

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aeviternal now’s relation to change that distinguishes it from the ‘now’ of eternity. But on the crucial issue of what this relation to change is, and how such a relation might fit into what we have seen earlier was the medieval account of relations, Aquinas is utterly silent. Nor is it clear what he could offer by way of elucidation. Although there must remain serious concerns about the coherence of the notion of an unextended aevum, thirteenth-century advocates felt that they could at least respond adequately to their own contemporary critics. We have seen earlier, for example, that Pecham claimed that the notion entailed contradictions when different logically incompatible properties were ascribed to aeviternal beings. Aquinas felt that this was not the case because although he was affirming the existence of a non-extensional aevum, he and his fellow non-extensionalists were also proposing that there was a further extensional duration, a duration which was distinct from time, and it was that duration which could possess instants at which the changing mental acts and operations of the angels could be located.35

ANGELIC TIME Aquinas seems to have popularized the notion of ‘angelic time’ and it was enthusiastically taken up by many of his contemporary non-extensionalists.36 35 Aquinas, Sum. Theol. 1. 63. 7 ad 3; and referring to it as a ‘time’, Quaest. Disp. de Pot. 3. 19 ob 5. 36 Aquinas was clearly indebted to Alexander, particularly his notion of a ‘saeculum’, ‘est primo duratio uno modo se habens, in qua nihil sequitur, et

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In proposing an angelic time Aquinas was mindful of his more general account of time which, as we have seen previously, identified a subject and derived the topological properties of time from the nature of that subject and its motion. As angels had such a very different nature to the physical particulars measured by time, this meant that their angelic haec est aevum; consequenter est duratio, in qua aliquid consequitur, sed tamen sine continuatione, et hanc dicunt saeculum’, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 2 (1, 108). Alexander also ruminated about an angelic ‘tempus vel aliquid ad modum temporis se habens’, Sum. Theol. 1. 1. 2. 4. 3. 3 ad 2 (1, 104); ibid. ad 3; and referred to it as ‘like a time’ (quasi tempus). He even went so far as to notice that it ‘non habet rationem continuantis’, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 2 (1, 107). A further reason for postulating a separate time for the angels lies in the fact that it was widely thought that scripture (Rev. 10:6) taught that the time which material substances existed in would end. As the angels are immortal and will endure for ever, so thirteenth-century thinkers concluded that they must have their own distinct time which will endure with them. For a particularly clear example of this reasoning, John Quidort Cor. Cor. Circa (123, 74–81). Sr. M. Jocelyn, ‘Discrete Time and Illumination’ (52) has argued that the development of an angelic time arises because if they were to be located in a continuous time this would have to be quantitative and so imply ‘matter’ which would undermine the spirituality of the angels. But this seems unlikely, for as we shall see, the angelic time is itself quantitative, albeit a discrete quantity. It is also unlikely that the development of an angelic time was based upon authorities, for although patristic and twelfth-century thinkers had spoken of the angels and souls as in time (Augustine, ‘Mutari autem animam posse, non quidem localiter, sed tamen temporaliter, suis affectionbus quisque cognoscit’, De Vera Religione 10 [18]; De Gennesi ad Litt. 8. 20. 39; Ep. 18. 2; and Hugh of St Victor, De Sacramentis 1. 3. 16 (PL 176, 222). In Epist. ad Timotheum 3 (PL 176, 603) ), the time that they are referring to seems to be our (continuous) time, the time which the material universe exists in. On the reception of the notion of angelic time, see William Macclesfield, Cor. Cor. Quaest. 23 (115); Richard Knapwell, Cor. Cor. Quaere 23 (102). Theodoric of Freiberg seems to have attributed a metric to the angelic time in order to avoid the fallacy that souls created later than other souls would have existed for the same amount of time. Tr. de Mensuris 4 (229, 28–37). For a particularly clear summary of Aquinas’ position, Ioannis a S. Thomae: In Summam Theologicam D. Thomae, Cursus Theologicus 2. 10. 10 (123). For Bonaventure’s view, see In Sent. 1. 37. 2 dub. 3.

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time must have a rather different topological structure too. According to Aquinas, It is true that there is time between two instants whatsoever in so far as time is continuous. Aristotle proves this. But in the angels who are not subject to the heavenly motion which measures a continuum through time, time is said of them on account of a succession of intellectual acts . . . In a first instant all were good, but then in a second instant the good and the bad were distinguished.37

This is a remarkable but important claim because Aquinas is distinguishing between the standard continuous time which derives its topological structure from the continuity of motion of the Primum Mobile, and an angelic time which is discrete because its subject is a discrete series of (nonextended) intellectual acts. One of the puzzling things about Aquinas’ position is that in order to propose a discrete angelic time he had to reject Aristotle’s arguments against a discrete time; arguments which we saw in Chapter 1 that he actually used to justify stating the continuity of time. 37 ‘dicendum quod inter quaelibet duo instantia esse tempus medium habens veritatem inquantum tempus est continuum, ut probatur in 6 phys. Sed tamen in angelis qui non sunt subjecti coelesti motui, qui primo per tempus continuum mensuratur, tempus accipitur pro ipsa successione operantium intellectus . . . Et ideo in primo instanti omnes fuerunt boni, sed in secundo fuerunt boni a malis distincti’, Sum. Theol. 1. 63. 7 ad 4. See also Quaest. Disp. de Malo 16. 4; In Sent. 2. 2. 1. 1 ad 4; and ‘Tempus autem motus angeli potest esse non continuum; et sic angelus in uno instanti potest esse’, Sum. Theol. 1. 53. 3 ad 3. Robert Orford stresses that the basis for multiple times lies in the fact of the metaphysical chasm of incommensurability which exists between angels and physical particulars, ‘cum igitur motus angeli et motus corporales non sint commensurabiles . . . oportet ponere quod habeant diversa tempora pro mensuris suis’, Cor. Cor. Sciendum (106).

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Faced by theological needs, he is once again adapting Aristotle’s philosophy, arguing now that all that Aristotle’s arguments have shown is that time must be continuous when measured by a continuous motion. Albert was clearly worried about this ad hoc imposition into the common Aristotelian philosophical framework,38 but it was Pecham and his fellow extensionalists who challenged its coherence. By way of a response to Aquinas all that they felt that they needed to do was to reiterate Aristotle’s original argument for the continuity of time and explicitly apply it to the case of an angelic time: They say that there is a continuous time . . . and another time which is discrete, composed of instants which . . . [are constituted by] the instantaneous angelic operations. But against this, imagine if we take one discrete instant ‘a’ in which an angel was good and another ‘b’ in which it was bad. Instant ‘a’ is simultaneous with 38 It appears that Albert modified his views from his early Summa de Creaturis and Commentary on the Sentences, where he evidently believed that there was only one time, and so he was forced to reinterpret Augustine’s words about the angels being in a time by talking of two senses of time, Sum. de Creat. 2. 4. 1 (Borg. 34, 361); In Sent. 1. 8. A. 12 (Borg. 25, 237). By his later Summa Theologiae he seems to have moved closer to Aquinas’ position, ‘Est enim tempus, per quod deus movet creaturam spiritualem, . . . quae non movetur nisi secundum affectiones et conceptiones, in quibus nihil est continuans. Et est tempus, in quo movetur corpus de forma in formam vel de ubi in ubi in quo aliquis est continuans’, Sum. Theol. 5. 23. 3. 1 (34.1, 137, 89– 94), and he is willing to accept that it cannot be reconciled with Aristotle’s position, ‘Et haec distinctio satis probabilis est, sed naturali philosophiae non concordat.’ Sum. Theol. 5. 23. 3. 1 (34.1, 138, 86–7). He is nevertheless clearly worried about the coherence of Aquinas’ views with the wider philosophical framework for discussions of time and so even in his apparent acceptance of Aquinas’ position he effectively hedges his position by also talking of the angelic actions as existing within a continuous time, although one that is not ordered causally to the Primum Mobile, ibid. (34.1, 139, 19–25).

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another instant of continuous time . . . which we can call ‘c’; and similarly instant ‘b’ is simultaneous with another instant of the common time ‘d.’ Either ‘c’ and ‘d’ are one and the same instant or they are two . . . If they are two instants then . . . [as Aristotle’s argument tells us] . . . between any two instants there falls a time in between.39

It is difficult to see how Aquinas might respond to this argument, especially when we bear in mind that there was a significant range of instances in which he actually wanted to allow for aeviternal beings interacting in a continuous process. Aquinas accepted, for example, that aeviternal beings such as the heavenly bodies rotated continuously in the heavens and that angels could bring about effects which occur in the physical world in continuous time. Angelic knowledge was another case in point. All medieval thinkers believed that a knowledge of future contingents was a divine privilege because it was only possible in virtue of God’s unique knowledge of His own essence. Angels, therefore, could only know future contingent events as and when they occurred. But if this was so, it would mean that they would be continuously acquiring new knowledge and so, as Pecham postulated, it would be possible to establish a 1:1 relationship between the instants of continuous time at 39 Pecham, ‘dicunt quod est tempus quod est continuum et mensura continui et tempus aliud quod est discretum et compositum ex instantibus quod mensurat operationes angelorum instantaneas . . . Sed Contra: Accipiamus unum instans temporis discreti in quo fuit bonus et dicatur a, et aliud instans in quo fuit malus, et dicatur b. A instans est simul cum aliquo instanti temporis continui, quia etiam aeternitas Dei est simul cum tempore, sit c. Item b est simul cum aliquo instanti illius communis temporis; sit d. Aut ergo c et d sunt unum instans aut duo . . . Si duo, sed inter quaelibet instantia illius temporis cadit tempus medium . . .’ Quodlib. 2. 10 (99, 25–35).

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which free non-determined events take place, and the instants of the angelic time at which a knowledge of those events becomes possible to the angels.40 Ultimately Aquinas’ position was in difficulties; difficulties which even his most eloquent later exponents were never entirely able to appreciate or resolve. It would be wrong to think that his position was more or less coherent than that of his extensionalist opponents. Attempts to make sense of the aevum exercised all sides in the debate, although in different ways. Aquinas can be accused of introducing an ad hoc incoherent notion of an angelic discrete time, but Pecham and the extensionalists can be accused of introducing an ad hoc notion of an extensional aevum; one that they never seem to have managed to distinguish clearly from the duration of (continuous) time. Faced by these problems and their intractable nature it should come as no surprise that less than fifty years later Ockham was to have no hesitation at all in rejecting the notion of the aevum and instead affirming that the angels were measured by time.41 40 For Aquinas on angelic actions, Sum. Theol. 1. 52. 1. It should also be noted that aeviternal particulars such as the heavenly bodies were necessarily moving in a continuous motion as they were believed to be rotating around the earth. Albert, In Sent. 1. 8. A. 12 (Borg. 25, 237); 1. 8. B. 13 quaest. 2 (Borg. 25, 239). Aquinas, Sum. Theol. 1. 10. 6 ad 2. On the matter of future contingents, ‘licet intellectus angeli sit supra tempus . . . .cum sit successio in intellectu angeli, non omnia quae aguntur per totum tempus, sunt ei praesentia’, Sum. Theol. 1. 57. 3 ad 2; Quaest. Disp. de Malo 16. 4; Pecham, Quodlib. 4. 20 (221, 42). 41 Ockham, ‘dico quod angeli mensurantur per tempus et non per aevum, quia aevum nihil est’, In Sent. 2. 11 (5, 236, 18–20). Amongst the 1277 condemnations was a condemnation of those who said that time and the aevum ‘non sunt in re’ asserting that they are only ‘in apprehensione’, Prop. 200 (H. Denifle and E. Chatelain, Chartularium Universitatis Parisiensis, 554).

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C O N C LU S I O N This chapter began to explore the language of atemporality by examining the terms ‘sempiternitas’ and ‘perpetuitas’ and by investigating the notion of ‘aeviternitas’ (also referred to as the ‘aevum’). It seems that the terms ‘sempiternitas’ and ‘perpetuitas’ are often used interchangeably as they were basically used to refer to limitless particulars and their durations. Medieval figures recognized two types of limitlessness: durations which had no end and durations which had neither a beginning nor an end. As the terms ‘perpetuitas’ and ‘sempiternitas’ could be used of both kinds of durations, it is not unusual to find them used of God, angels, souls, and heavenly bodies. The terms ‘aeviternitas’ and ‘aevum’ were often used in a similar way, and we have seen that there were occasions when these terms were used synonymously with ‘perpetuitas’ and ‘sempiternitas’. Nevertheless, there were serious disagreements amongst thirteenth-century thinkers about the nature of the aevum, in particular whether it was extended or not. During the course of this chapter we have seen that it is difficult to generate any ultimately coherent account of the aevum as both extensional and nonextensional models of it contained their own difficulties. It is possible to interpret this condemnation as aimed at radical Augustinians who were pressing Augustine’s sympathies for a psychological model of time, but it is equally possible that advocates of the condemned position were exploring mental models of time or aeviternity as a way of avoiding the clash between theology and philosophy which arose when angels were introduced to considerations of time.

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Advocates of extensional accounts of the aevum faced the difficulty of how they were to justify a distinction between an extensional aevum and an extended time, whilst advocates of a non-extensional aevum faced the opposite problem of explaining how it differed from a non-extensional eternity. In attempting to explain his extensional notion of the aevum, we saw that Bonaventure developed a notion of the aevum which bore some similarities to a Newtonian absolute time. How this notion was meant to cohere with the wider theory of relational durations which lay at the heart of medieval accounts of time, is not at all clear. Aquinas, on the other hand, sought to explain his nonextensional aevum by developing a separate discrete time. Unfortunately this committed him to a plurality of times, despite the fact that as we saw earlier he always argued strenuously against temporal plurality in his philosophical works. Apart from the philosophical difficulties entailed by the notion of an aevum, it also seemed to give rise to peculiarities and absurdities whereby certain particulars seemed to have to exist in multiple durations. The heavenly bodies were a particularly obvious example of this problem. While they were measured by the aevum in virtue of their metaphysical status, the Primum Mobile nevertheless was thought to rotate around the earth in a continuous motion generating the continuous time that measured everything occurring on the earth. We have already seen that ‘souls’ posed a problem and that Bonaventure had suggested that they should only be thought of as aeviternal after their separation from the human body. But further problems

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arose with the existence of factors such as the ‘fires of hell’, which Alexander, at least, thought must be measured by the aevum in virtue of their perpetuity, but measured by time in virtue of the change and mutability which burning fires must entail.42 Thirteenth-century reflection on the aevum resulted in what must arguably be one of the least satisfactory attempts to synthesize theology and Aristotelian philosophy. None of the principal figures of this period seem to have been able to present an account that was unambiguous and able to resolve all of the difficulties which they themselves identified as confronting the notion. Although it continued to be discussed and debated long after the thirteenth century, the philosophical problems surrounding the notion of an aevum meant that it was to become increasingly, less significant in mainstream intellectual thought. 42 Alexander, ‘Ad illud quod obiicitur de poenis inferni, dicendum quod quantum ad perpetuitatem mensurabuntur aevo, quantum vero ad variationem tempore’, Sum. Theol. 1. 1. 1. 2. 4. 3. 4. 2 (1, 108).

9 Eternity

This chapter will examine one of the most significant thirteenth-century atemporal terms, ‘aeternitas’. The English word typically used to translate this term is ‘eternity’, and it is used by contemporary philosophers in both an everlasting (extensional) and timeless (non-extensional) sense. One of the key questions in this chapter will be whether medieval accounts of ‘aeternitas’ should be thought of as instances of extensional everlastingness or whether they should be thought of as accounts of a non-extensional timelessness. By the beginning of the thirteenth century the term ‘aeternitas’ had had a long history of usage in both Christian and non-Christian philosophical contexts, and as a result of this it had come to be used in a wide variety of contexts. Some authors were happy to treat ‘aeternitas’ and ‘sempiternitas’ as equivalents, some viewed ‘perpetuitas’ and ‘aeternitas’ as synonyms, whilst others seem to have treated ‘aevum’ and ‘aeternitas’ as equivalent.1 1 Albert cites Cicero as a contributor to the tendency to equate ‘aeternitas’ and ‘sempiternitas’, Sum. de Creat. 2. 3. 4 (Borg. 34, 354) although Isidore’s influence should not be underestimated, Etym. 7. 1. Philip the Chancellor

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Although there is a degree of disagreement amongst medieval writers, we can nevertheless detect some common tendencies. One of those tendencies was to treat ‘aeternitas’ as if it were a long extension. Peter of Tarentaise, for example, took issue with such an approach and preferred to view ‘perpetuitas’ as equivalent to ‘sempiternitas’, and the word ‘aeternitas’ was then in his opinion to be contrasted with both terms, Sum. de Bono 1. 1. 4 (1, 49). Aquinas and Pecham seem to have accepted the equivalence of ‘perpetuitas’ and ‘aeternitas’. Aquinas, ‘duplex est perpetuitas vel perpetua durabilitas; una quidem per modum aeternitatis, alia vero per modum totius temporis’, Super Lib. de Causis 30. Pecham, ‘non eam [Deus] spatio praecurrens, sed manente perpetuitate praecedens’, de Aeternitate Mundi 1 ad 9; Albert, ‘loquitur [Dionysius] de aevo secundum illam acceptionem aevi, qua pro aeterno ponitur’, Sum. Theol. 5. 23. 2. 1 (34.1, 133, 73–4); Sum. de Creat. 2. 3. 3 (Borg. 34, 351–2); In Sent. 1. 30. B. 7 ad 2 (Borg. 25, 97); Aquinas, ‘Similiter aeternitas nominat durationem secundum illum modum quo est in principio suo; et ideo aliae durationes participatae non dicuntur nomine aeternitate.’ In Sent. 1. 19. 2. 1 ad 3; ‘dicendum quod quamvis actus qui mensuratur aevo, sit totus simul sine successione, hoc esse tamen est ab alio; et in hoc ab aeternitate aevum discernitur’, ibid. ad 5. For a similar position see also Bonaventure, In Sent 2. 2. 1. 1. Aquinas seems to have viewed the distinction between ‘aevum’ and ‘aeternitas’ as arising due to linguistic confusion, ‘Dicendum, quod ex ignorantia linguae graecae provenit quod communiter apud multos aevum ab aeternitate distingueretur, ac si distingueretur anthropos ab homine. Quod enim in graeco dicitur aevum, in latino aeternitas . . . .Sed quia nominibus utendum est ut plures; si utrumque distinguamus ab invicem, aevum nihil aliud erit quam aeternitatis participatio; ut scilicet essentialis aeternitas ipsi Deo attribuatur aevum autem quasi participata aeternitas substantiis spiritualibus, quae sunt supra tempus.’ Quaest. Quodlib. 5. 4. 1. For examples of patristic usage of ‘aeternitas’, Augustine, De Civ. Dei 11. 11 and 12. 16; John Damascene, de Fide Orthodoxa 2. 1. For more details, including references to Basil of Caesarea and Gregory of Nyssa, see F. H. Brabant, Time and Eternity in Christian Thought, chs. 1–3 and more generally G. Quispel ‘Time and History in Patristic Christianity’. For examples of classical usage, R. Sorabji, Time, Creation and the Continuum, ch. 8, and. A. J. Festugie`re, ‘Le temps et l’aˆme selon Aristote et le sens philosophique du mot aion’. As a source of medieval usage the significance of the Vulgate Bible should not be ignored. See Psalm 148; Ecclesiastes 1: 4; Titus 1: 2; Romans 16:25.

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uses ‘aeternitas’ interchangeably with ‘tempus’ and Alexander of Hales seems perfectly content to use the phrase ‘aeterna tempora’ (eternal times).2 Discussions of the ‘poena aeterna’ (eternal punishments) of the damned indicate an extensional usage of the word, as often does the phrase ‘de aeternitate mundi’ when used to refer to discussions about whether the world had a beginning and whether it would have an end.3 ‘Aeternitas’ was described as a ‘duratio’4 and was also said to be in a relation with time which was summed up with verbs such as ‘conplectens’ (encompassing),5 ‘excedit’ (exceeds),6 ‘comprehens’ (comprehends),7 ‘ambit’ (encircles),8 ‘includit’ (includes),9 ‘continet’ (contains).10 Furthermore, 2 Peter of Tarentaise, In Sent. 2. 2. 1; Alexander of Hales, Sum. Theol. 1. 1. 1. 2. 4. 1. 1. 2 (1, 86). 3 Aquinas, ‘dicendum quod peccato originali non debentur poena aeterna ratione suae gravitatis.’ Sum.Theol. 1–2. 87. 5 ad 2. See also Albert, Sum. de Creat. 2. 3. 4 (Borg. 34, 354). On the ‘eternity’ of the world, see Aquinas, Sum. Theol. 1. 10. 3 ad 2; In Sent. 1. 8. 2. 2 ad 4, where he seems to be following twelfth-century linguistic trends evidenced by, amongst others, Richard of St Victor, In Apoc. 3. 7 (PL 196, 790A) and Hugh of St Victor, In Eccles. 13 (PL 175, 207D). 4 Bonaventure, In Sent. 1. 8. 1 dub 7 and 1. 37. 1. 2. 2; Quaest. Disp. de Myst. Trin. 5. 1; ibid. ad 10; Aquinas, Sum. Theol. 1. 10. 1; Sum. Con. Gen. 2. 35; Quaest. Quodlib. 10. 2. 5 Bonaventure, In Sent. 1. 19. 1 dub 4. 6 Alexander, In Sent. 1. 8 [7] (1, 101, 14) and Sum. Theol. 1. 1. 1. 2. 4. 2. 3 (1, 92). Alexander thinks that eternity ‘exceeds’ time in the sense that a whole is often more than just the sum of its parts; although time he maintains is not a part of eternity, Sum. Theol. 1. 1. 1. 2. 4. 2. 1 ad 1 (1, 90). Bonaventure, Com. in Evang. Luc. 8 [51]. 7 Bonaventure, Com. in Evang. Ioan. 16. 4 ad 1; Aquinas, Quaest. Disp. de Ver. 12. 10. 8 Aquinas, Sum. Theol. 1. 14. 13. 9 Aquinas, Super Evan. Ioan. 16. 3; Quaest. Disp. de Ver. 3. 3 ad 1; Sum. Theol. 1. 10. 4. 10 Aquinas, Quaest. Disp. de Ver. 1. 5.

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‘aeternitas’ was said to be ‘immensum’ (immense),11 a ‘spatium’ (space),12 ‘indeficientia’ (unfailing),13 ‘continuum’ (continuous),14 ‘protensum’ (extension),15 ‘mora’ (period),16 and an ‘interminabilis immensitas’ (interminable immenseness)17 which was ‘comparabilis’ (comparable) to time.18 God and His duration of eternity are often said to be ‘infinitus’ defined as lacking a beginning and an end,19 and are said to be ‘simul’ (simultaneous) with time.20 Aquinas even goes so far as to compare time and ‘aeternitas’ in terms of the brevity of time which is ‘momentaneum’ (moment-like) when compared to ‘aeternitas’.21 It would be easy to conclude from texts and assertions such as these that Aquinas and his thirteenth-century colleagues thought that extension was an essential aspect of 11 Bonaventure, In Sent. 1. 37. 1. 2. 2; Quaest. Disp. de Myst. Trin. 5. 1; Albert, Sum. Theol. 5. 23. 1. 2. 1 (34.1, 129, 61 f.); In Sent. 1. 9. A. 2. 1 (Borg. 25, 272); Alexander, Sum. Theol. 1. 1. 1. 2. 4. 2. 1 (1, 90). It should be noted that Alexander entitles his discussion of God’s eternity as a discussion of the divine ‘immensitas’. 12 Aquinas, In de Caelo 1. 21 [215]. 13 Aquinas, Super Lib. de Causis 2. 14 Albert, Sum. Theol. 5. 22. 1 (34.1, 117, 24–45). 15 Albert, In Sent. 1. 9. A. 2 (Borg. 25, 273). 16 Albert, Sum. de Creat. 2. 3. 2 (Borg. 34, 348). Albert usually identifies the ‘mora’ with an extension in the mind of the person thinking about eternity. Sum. Theol. 5. 23. 1. 1. 2 (34.1, 125, 83–90) and 5. 22. 1 ad 3 (34.1, 117, 61–5). 17 Bonaventure, Quaest. Disput. de Myst. Trin. 5. 1 ad 13; Aquinas, ‘interminabili’, Super Lib. de Causis 2. 18 Albert, ‘dicimus aeternitatem esse indeficientem sine principio et sine fine durationem et ideo ad tempus comparabilem’, Phys. 8. 1. 13 (4.2, 575, 10–12). 19 Bonaventure, Quaest. Disput. de Myst. Trin. 5. 1. 20 Aquinas, ‘simul cum omni tempore’, In Sent. 1. 40. 3. 1 ad 5. 21 Aquinas, Super ad Hebraeos 10. 4. Super 2 ad Corinthios 4. 5.

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‘aeternitas’, but we have already seen in Chapter 1 that apparently extensional terms such as ‘duratio’ admitted of non-extensional senses which thirteenth-century thinkers were often intending in their usage. Furthermore, there is a widely attested tendency in medieval thought to use explicitly non-extensional terms when describing eternity. Not only is it explicitly asserted that eternity is not extended and non-successive,22 but it is also referred to as ‘simplex’ (simple),23 ‘totum simul’ (totally simultaneous),24 ‘impartibilitas’ (not consisting of parts),25 ‘invariabilis’ (unvarying),26 ‘indivisibilis’ (indivisible),27 and as a ‘discretum’ (discrete) element.28 It is said to have no ‘vicissitudo’ (change)29 and was considered neither as proportional to time nor as able to support tenses.30 The existence of extensional relations such as a ‘before and after’ 22 Aquinas, In Phys. 8. 2 [20]; Quaest. Disp. de Ver. 23. 2 ad 8; Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1 ad 6. 23 Bonaventure, In Sent. 1. 19. 1 dub. 4. He also draws attention to the fact that ‘simplex’ implies a lack of prior and posterior in a duration, Quaest. Disp. de Myst. Trin. 5. 1. Aquinas, Sum. Con. Gen. 2. 35; Albert, Sum. de Creat. 2. 4. 1 (Borg. 34, 358). Note also Ulrich’s insistence that God is ‘omnino simplex et necessarium necessitate immutabilitatis et nullo modo possibile’, de Summo Bono 4. 1. 1 (4, 7, 147–8). 24 Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1 ad 9; Aquinas, Sum. Theol. 1. 10. 1; 1. 14. 13; Quaest. Quodlib. 10. 2; Quaest. Disp. de Ver. 3. 3 ad 1 con.; ibid. 23. 2 ob. 8; Super Lib. de Causis 32; Alexander, In Sent. 1. 9 [12] (1, 120, 13–15). 25 Bonaventure, In Sent. 1. 19. 1 dub. 4. 26 Bonaventure, In Sent. 1. 5 dub. 8; 1. 8. 1 dub. 7. ‘Invariabilis’ is also attributed to angels by Ulrich, de Summo Bono 2. 4. 4 (2, 135, 83). 27 Albert, Sum. Theol. 5. 22. 1 (34.1, 116, 20–4); Aquinas, Opusc. de Rationibus Fidei 10; In Sent. 1. 19. 2. 2 ad 2; Sum. Theol. 1. 42. 2 ad 4. 28 Albert, Sum. Theol. 5. 22. 1 (34.1, 116, 65–74). 29 Bonaventure, In Sent. 1. 5 dub. 8. 30 Bonaventure, In Sent. 1. 8. 1 dub. 4.

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is denied31 and it is referred to as a ‘now’; a ‘now’ which medieval thinkers from Alexander of Hales to Albert seem to have been perfectly happy to gloss as an ‘instans’ (instant).32 We know from Albert’s comments that the existence of extensional and non-extensional language to describe eternity caused confusion,33 but it was confusion that medieval thinkers found it very difficult to avoid. The confusion arose only in part due to differences of thirteenth-century philosophical outlook; a more serious source of confusion was occasioned by the way the usage of authorities varied, sometimes forcing those in favour of a non-extensional 31 Aquinas, Super Lib. de Causis 2; Sum. Theol. 1. 10. 5; Sum. Con. Gen. 2. 35; In de Div. Nom. 10. 3; In Phys. 8. 2 [20]; Quaest. Disp. de Ver. 8. 4 ob 15; Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1; Alexander, In Sent. 2, Appendix (2, 422, 1–3). 32 Bonaventure, In Sent. 1. 5. 2. 2 dub. 8; 3. 8. 2. 1 ad 6; Quaest. Disp. de Myst. Trin. 5. 1 ad 13; Aquinas, In Sent. 1. 19. 2. 2; Sum. Theol. 1. 42. 2 ad 4; Albert, Lib. de Causis 2. 1. 8 (17.2, 70, 6–8); Alexander, In Sent. 1. 30 [2] (1, 289, 15–20). On at least one occasion Pecham gives an argument, the validity of which depends upon taking ‘instans’ and the now of eternity as synonyms, De Aeternitate Mundi (3). Aquinas is reluctant to explicitly use the word ‘instans’ of eternity, although his position sometimes implies that the term could be used, as when he talks of eternity measuring the act of a particular but an ‘instans’ measuring its ‘esse’, In Sent. 1. 19. 2. 2. There was clearly a hesitation in some authors to use the word ‘instans’ of eternity, and this may well have been because of concerns about its otherwise temporal pedigree. On this see Aquinas, In Sent. 4. 49. 1. 2 sol. 3; Bonaventure, In Sent. 2. 1. 1. 1. 2 ad 4. 33 ‘et haec difficultas accidit, quia non considerant aeternitatem nisi per modum cuiusdam durationis continuae sine principio et sine fine, et hoc per intellectum accipientem ex phantasmate, qui non accipit illam durationem nisi ut habentem partes protensas, quae non sunt simul in praeterito et futuro: hi enim imaginantur aeternitatem sicut tempus quoddam carens successione in partibus: et ideo non est mirum si decipiuntur’, Sum. de Creat. 2. 3. 2 (Borg. 34, 347).

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model to use extensional language which they then had to ‘reinterpret’.34 Perhaps most fundamentally of all, however, contemporary philosophers need to be aware that the medieval notion of eternity was not necessarily intended to be understood by its readers as offering a durational account of atemporality. As with the terms ‘sempiternitas’ and ‘perpetuitas’, which we looked at in the last chapter, some of the most important ideas that the usage of ‘aeternitas’ was intended to convey were about limits and limitlessness rather than about durations. It is revealing in this respect that Albert attempted to explain the word ‘aeternitas’ by tracing its etymology to ‘ex-terminus’, and we can see a more general focus on limitlessness when ‘aeternitas’ and ‘sempiternitas’ are used equivalently to denote existence which lacks an end. This can be seen when God’s existence is described as eternal precisely because He is doubly limitless, lacking both a beginning and an end: 34 Tarentaise cites Aristotle as a particularly important advocate of an extensional notion of eternity, In Sent. 1. 8. 3. 1; but patristic figures such as John Damascene clearly contributed too, with claims that ‘unum saeculum dei, quod est aeternitas, continet multa saecula, quae sunt spatia durationis singulorum, et ideo dicitur saeculum saeculorum’, de Fide Orthodoxa 2. 1. Amongst early medieval contributions was Isaac the Jew’s definition ‘aeternitas est spatium continuum non intersectum’ known to thirteenth-century thinkers as it is quoted by Albert at Sum. de Creat. 2. 3. 2 (Borg. 34, 340) and used also by Gilbert of Poitiers, In de Trinitate (327, 10–13). Confronted by Isaac’s definition Albert attempted to convert it into a non-extensional account by introducing a distinction between an extended spatial space and a non-extended temporal space, Sum. de Creat. 2. 3. 2 (Borg. 34, 342 and 34, 348) and In Sent. 1. 8. A. 8 (Borg. 25, 230). Aquinas too tried to distance himself from analogies which compared time to eternity on the basis of time being briefer than eternity, and he dismissed all such language as metaphorical, Contra Impugnantes 24 [1] (41, A159, 23–5).

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the measure of things which have a beginning and an end is called time, the measure of those things which have a beginning but lack an end is the aevum, and the measure of those things lacking a beginning and an end is called eternity.35

Although the primary focus of this definition was upon limits, it was possible to read it in a purely extensional sense so that it distinguished between durations in terms of durational limits. Albert’s comments about the confusion amongst his contemporaries indicates that some were reading the definition in this way and thinking of eternity as simply an infinitely long duration. Nevertheless, we can see that an alternative understanding of limits was developing in twelfth- and thirteenth-century thought so that the reception (or loss) of existence was also viewed as a limit. The implications of this were that even if something existed throughout a duration (and so had no beginning or end in that duration), it could still nevertheless be viewed as 35 Tarentaise, ‘mensura quippe rerum quae habent principium et finem vocatur tempus; earum quae carent quidem fine, sed habent princpium, vocatur aevuum, earum vero quae carent principio et fine vocatur aeternitas’, In Sent. 1. 8. 3. 1; Kilwardby, In Sent. 1. 31 (31, 5–23); Albert, ‘ ‘‘Aeternum’’ enim, sicut ipsum nomen monstrat, . . . id est, quod terminos esse non habet. Quod enim terminos habet, inter terminos est distensum et a termino usque ad terminum extensum, ut totum esse inter terminos sit comprehensum . . .’ Lib. de Causis 2. 1. 8 (17.2, 69, 64); also ‘Et hoc sonat nomen aeternitatis, quod componitur ab ‘‘ex’’ vel ‘‘extra’’ et ‘‘terminus’’ ’, Sum. Theol. 5. 23. 1. 1. 2 (34.1, 126, 11–13); and Phys. 4. 4. 1 (4.1, 293, 37 f., and 4.1, 294, 19–26); In Sent. 1. 8. A. 9 (Borg. 25, 233). Bonaventure, In Sent. 1. 9. 1. 3. 4; 1. 9. 1. 4 arg. 3; 1. 9. 1. 4 ad 4; 1. 19. 1 dub. 4; 1. 31. 2. 1. 3; 1. 44. 4 ad 1; 4. 3. 2. 3. 1 ad 1; Com. in Evang. Luc. 1 [33]; Alexander of Hales, In Sent. 1. 9 (1, 116, 10–13); Sum. Theol. 1. 1. 1. 2. 4. 1. 2 (1, 87); Aquinas, Sum. Con. Gen. 4. 97; In de Caelo 1. 21 [215]; 2. 11 [389]; In Meta. 5. 13 [941]; In Sent. 1. 8. 2. 2 ad 4. Theodoric of Freiberg, ‘aeternitas . . . [est] quod caret termino initiali et finali seu principio et fine secundum durationem . . .’, de Mensuris 2 (3, 216, 45–7).

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limited because it had been brought into existence. With this more nuanced notion of limits we can see a subtle transformation in what it means to talk of a double limitlessness of God, for such a notion would now amount to the claim that God was uncreated, with, in the fullest senses of the words, a ‘necessary’, ‘simple’, ‘immutable’, and ‘ex se’ existence.36 Once the double lack of limits was identified with properties such as simplicity and immutability, the notion of 36 Aquinas, ‘Oportet ergo quod illud cuius esse est aliud ab essentia sua, habeat esse causatum ab alio. Hoc autem non potest dici de Deo . . . Impossibile est ergo quod in Deo sit aliud esse, et aliud eius essentia.’ Sum. Theol. 1. 3. 4. Note also Aquinas’ account of the divine infinity (limitlessness), ‘Cum igitur esse divinum non sit esse receptum in aliquo, sed ipse sit suum esse subsistens, . . . manifestum est quod ipse Deus sit infinitus et perfectus.’ Sum. Theol. 1. 7. 1. Alexander, Sum. Theol. 1. 1. 1. 1. 1. 3. 3 (1, 53); 1. 1. 1. 2. 4. 2. 4 ad 1 (1, 96); ibid. ad 7 (1, 97). Albert, Sum. Theol. 4. 20. 3 (34.1, 105, 58–72). The twelfth-century origins of accounts of limitlessness that are beginning to stress simplicity and immutability can be seen in Hugh of St Victor, In Eccles. 13 (PL 175, 207D) and par excellence in Richard’s definition of ‘aeternitas’, as: ‘Quid est aeternitas, nisi diuturnitas sine initio et sine fine, carens omni mutabilitate.’ De Trin. 2. 4 (PL 196, 903). The significance of Richard’s definition for thirteenth-century thinkers should not be underestimated, as Albert’s discussion of it shows, Sum. Theol. 5. 23. 1. 1. 2 (34.1, 125, 34–6). Richard seems to be a little confused about eternity because he indicates an acceptance of an extensional account of it when comparing the brief length of time to eternity, In Apoc. 2. 8 (PL 196, 769A). Yet, as we saw above, he is still able to appeal to immutability as the defining difference between a limitless sempiternity and eternity. Gilbert of Poitiers evidences the transitional, and perhaps confused nature of twelfth-century thought particularly well with his definition, ‘aeternitas nomine intelligitur una singularis et individua simplex et solitaria mora, in qua neque collatio neque collectio est’, In de Trin. 1. 4 [69] (129, 8–12), where he is combining the extensional notion of a ‘mora’ with the ruling-out of the ‘collectio and collatio’ which, in the last chapter, we identified with extensionality. See also Albert, Sum. Theol. 5. 23. 1. 1. 2 (34.1, 125, 38–40) and for further analysis, R. C. Dales, ‘Time and Eternity in the Thirteenth Century’.

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‘aeternitas’ itself became more and more explicitly identified with immutability, and so divine immutability was often identified as the basis for predicating ‘eternity’.37 When the various different medieval understandings of limitlessness and immutability are appreciated, we can see that the word ‘aeternitas’ could be used to attribute any of the following properties to a particular: (i) double limitlessness in the extensional sense, existing throughout a duration (ii) double limitlessness in the extensional sense, including uncreatedness (iii) double limitlessness in the extensional sense, with the property of immutability (iv) double limitlessness in the non-extensional sense (v) double limitlessness in the non-extensional sense, including immutability (vi) double limitlessness in the non-extensional sense, including uncreated existence (vii) double limitlessness in the extensional sense, including uncreatedness and immutability (viii) singular limitlessness, i.e. existence with a beginning but without an end 37 It is no accident in this respect, that Aquinas organized his Summa Theologiae discussion of immutability (question 9) to be followed by the question 10 discussion of eternity. See also Alexander of Hales, Sum. Theol. 1. 1. 1. 5. 2. 1 [181] (1, 267), and Siger of Brabant’s discussion, Sup. Lib. de Causis 9 (58, 8–14); 11 (62, 12–17). Siger’s views on eternity were developing and changing during the second half of the thirteenth century, so particular care is required in interpreting them. For details, L. Bianchi, ‘L’evoluzione dell’eternalismo di Siger di brabante e la condonna del 1270’.

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(ix) singular limitlessness with the property of (participated) immutability (x) singular limitlessness, i.e. existence without a beginning.38 These usages represent a broad set of philosophical possibilities and it is not necessarily the case that any singular author would have used them all. The first sense was often used in discussions of the ‘eternity’ of the world where, on at least one level of the discussion, what was being examined was whether the world could exist at every instant of a duration. What this notion basically amounts to is the predication of ‘everlasting’ existence.39 38 Albert, In Sent. 1. 8. A. 9 (Borg. 25, 233); Sum. Theol. 5. 23. 1. 1. 2 ad 3 (34.1, 126, 43–5); Aquinas, In Meta. 5. 13 [941]; In Sent. 1. 8. 2. 2 ad 4. 39 The medieval disputes ‘de aeternitate mundi’ encapsulated a broad conspectus of issues, depending on whether the limitlessness ascribed to the world was understood to be everlastingness or uncreatedness. Aquinas, Sum. Theol. 1. 46. 2 ad 7; de Aeternitate Mundi (Leon. 87, 158 f.), understood the problem to be about whether the world could be everlasting and as such he had no problem in accepting that God could have created such a world, although he also believed that, as it happens, revelation shows that He did not choose to do so. Philip the Chancellor, however, had distinguished between the ‘perpetuitas’ of the world which Aristotle had demonstrated and the ‘eternity’ of the world which would have amounted to ascribing uncreatedness. See his Sum. de Bono, 1. 1. 3 (1, 49, 46–7). With this understanding of what predicating ‘eternity’ of the world amounted to, Alexander, Sum. Theol. 1. 1. 1. 2. 4. 2. 4 ad 1 (1, 96); Albert, Sum. de Creat. 2. 3. 1 (Borg. 34, 338); Bonaventure, In Sent. 2. 1; Pecham, de Aeternitate Mundi; and William of Baglione, Utrum Mundus habuerit suae durationis initium vel sit ponere mundum esse ab aeterno, had no hesitation in concluding that as a matter of faith the world could not be eternal. For further details of discussions ‘de aeternitate mundi’, see R. C. Dales, Medieval Discussions of the Eternity of the World, 27–129; and for a more generalized account, F. Van Steenberghen, La philosophie au XIIIe sie`cle, 363–9, 400–5. For an analysis of Aquinas’ interpretation and understanding of the dispute, J. B. M. Wissink (ed.), The Eternity of the World in the Thought of Thomas Aquinas and His Contemporaries, and (with a bibliography) J. F. Wippel, ‘Did Thomas

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The second and third usages of the word ‘aeternitas’ agree in predicating an extensional double limitlessness, but then differ in whether the properties of uncreatedness or immutability are additionally intended to be implied. These senses were evident in discussions about the nature of God’s existence, particularly whether He could be said to exist through (all) time. Immutability in its proper sense was believed to entail uncreatedness, for to be immutable included the idea of not receiving existence from another. As a result of this, medieval authors would generally not distinguish between the second and third usages unless a particular author was wanting to nuance or stress a particular aspect of a discussion. The fourth way in which ‘aeternitas’ could be used was simply to attribute a non-extensional duration. When used in this way, the word would be taken as attributing the absolute or relative timelessness which we examined at the beginning of the last chapter. In that chapter we saw that the aevum was characterized by many thirteenth-century thinkers as non-extensional, and we have already seen in this chapter that there was a tendency to use the words ‘aevum’ and ‘aeternitas’ interchangeably. The scope for interchangeability would have been particularly significant when ‘aeternitas’ was being used according to the fourth way identified above. The fifth, sixth, and seventh ways in which ‘aeternitas’ might be used agree in attributing a non-extensional dur-

Aquinas Defend the Possibility of an Eternally Created World (The De Aeternitate Mundi revisited)?’ 21–37. Ian Wilks, ‘Aquinas on the Past Possibility of the World’s Having Existed Forever’, 301.

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ation, but differ in whether they are meant to include further properties of uncreatedness, immutability, or both notions. The distinction between these usages is somewhat theoretical for, as we have already seen, most medieval thinkers would not have accepted that the properties of uncreatedness and immutability could be separated. Nevertheless, conceptually distinguishing between these usages is useful as it alerts us to the nuanced notions of limitlessness which gave rise to equally nuanced and potentially confusing ideas about eternity. The eighth and ninth ways in which the word ‘aeternitas’ can be used bring us again to instances where it was used to discuss aeviternal particulars. The eighth usage is one which simply picks out a particular that has a natural immortality, or unending existence. This might be attributed to angels, souls, the heavenly bodies, and even the fires of hell.40 The ninth usage is similar, but it draws upon a richer notion of limitlessness by including the further notion of participated immutability. Although immutability in its proper sense could only be attributed to God, medieval looseness of expression sometimes allowed the word ‘immutability’ to be used in a weaker sense denoting simply unchangeableness. As Proclus’ definition had proposed that unchangeableness was a defining characteristic of aeviternal beings, it was therefore possible for medieval thinkers to use the word ‘aeternitas’ in the ninth way identified.41 40 Aquinas, ‘dicendum quod ignis inferni dicitur aeternus propter interminabilitatem tantum. Est tamen in poenis eorum transmutatio’, Sum. Theol. 1. 10. 3 ad 2. 41 Aquinas, ‘oportet aliqua intelligere esse aeterna secundum certos modos, scilicet, inquantum existunt immutabiliter et sine tempore, sicut

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The tenth usage might initially seem peculiar as it is effectively referring to something that has no beginning but will have an end. We know that Aquinas, at least, felt that a particular could, theoretically, have an infinite past existence without thereby being uncaused, and it was precisely because of this that he differed from the Franciscan school and maintained that the world (considered apart from revelation) could indeed have had an infinite past existence even though it might then end at some point in the future. When Aquinas was using the word ‘aeternitas’ to describe the world in such a context, it was being used in the tenth sense. The ten possible ways in which ‘aeternitas’ can be used draw upon ten different conceptions of limitlessness to provide a wide range of senses and implications which provided obvious scope for significant confusion and misunderstanding in medieval thought. It was undoubtedly in an attempt to resolve these difficulties that thirteenthcentury thinkers began to distinguish between different senses of the word ‘aeternitas’. Tarentaise, for example, distinguished between ‘proprie’ (proper) and ‘large’ (broad) senses of the word, by insisting that ‘aeternitas’ is only used properly when it refers to the qualities of limitlessness and immutability, whilst it is used less properly when it picks out other types of limitlessness. Tarentaise’s distinction clearly had merits, as we can see sunt huiusmodi angelici spiritus . . . Sed illa quae sunt media inter existentia immobiliter et ea quae generantur et corrumpuntur, secundum aliquid participant tempore et secundum aliquid aeternitate, sicut corpora caelestia conveniunt quidem cum superioribus spiritibus, inquantum sunt incorruptibilia secundum substantiam et secundum hoc participant aeternitatem’, In de Div. Nom. 10. 3 [875].

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from the fact that it cut through the ten usages of ‘aeternitas’ which we have just examined, to distinguish the third, fifth, and seventh usages as ‘proper usages’, from the rest which were ‘broad’ senses of the word. Tarentaise’s distinction was able to differentiate between a proper predication of ‘aeternitas’ for God from what were effectively predications of ‘aeternitas’ of creatures, which he was now effectively treating as less proper, broad predications of the word.42 We find this same basic approach to distinguishing senses of ‘aeternitas’ throughout thirteenth-century writers, although there were widespread differences in precisely how they chose to state the distinction. Albert, in his early Summa de Creaturis, distinguished between ‘proper’ (proprie) and ‘less proper’ (minus proprie) senses of the word ‘aeternitas’, whilst by the time he comes to write his later Summa Theologiae he was distinguishing between a predication ‘per essentiam’ and a predication ‘per participationem’.43 Grosseteste preferred to state the distinction in terms 42 Tarentaise, ‘aeternus aliquando accipitur proprie et sic importat carentiam principii et finis et variabilitatis seu successionis in partibus et hoc modo soli deo convenit. Aliquando accipitur large secundum participatione conditionum aliquarum ipsius aeternitatis; aut ergo secundum carentiam principii et finis, sed non varietatis successivae; sic posuerunt aliqui philosophi mundum aeternum: aut finis et successione variabilitatis; sic dicitur vita aeterna aut finis tantum, sic dicitur mors aeterna’. In Sent. 1. 8. 3. 1. 43 Sum. de Creat. 2. 3. 4 (Borg. 34, 354), ‘Dicitur enim aeternum duobus modis, per essentiam scilicet et per participationem. Per essentiam solus deus aeternus est, et sibi proprium est esse aeternum, et incommunicabile est hoc nomen aliis. Participative autem dicitur aeternum omne quod aeterntiatis aliquam proprietatem participat’. Sum. Theol. 5. 23. 1. 2. 1 (34.1, 128, 8–26). Aquinas too uses this distinction, especially when commenting upon Dionysius, ‘dicit quod ea quae dicuntur in Scripturis aeterna, non oportet arbitrari esse simpliciter et aequaliter simul aeterna Deo, qui est ante aeternitatem participatam’, In de Div. Nom. 10. 3 [875]. In his Commentary on the

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of ‘first eternity’ and ‘second eternity’,44 whilst Aquinas distinguished between a ‘simpliciter’ predication and a ‘secundum quid’ predication.45 What all these approaches had in common was the recognition that the word ‘aeternitas’ could be used in a relatively broad set of ways, but there was a privileged set of proper uses in which it was predicated of God in order to stress the nature of divine limitlessness; a limitless which could include immutability and uncreatedness as well as non-successiveness.

Physics Albert introduces a further distinction between three ways in which particulars can participate in eternity, ‘Quaedam enim sunt aeterna et vere in aeternitate sicut prima substantia, quae est deus gloriosus et benedictus. Quaedam vero sunt aeterna et non vere in aeternitate sicut illa quae facta sunt immutabilia participatione incommutabilitatis, sicut dicit Plato de his quae licet sint natura commutabiles, tamen voluntate dei deorum et nobiliorum eius bonitatum participatione sunt manentes incommutabiles . . . Quaedam vero nec vere aeterna sunt nec vere in aeternitate, sed sunt similia secundum quid aeternis sicut temporaliter habentia successionem sine fine, sicut motus aeternus dicitur ab his qui ponunt mundum aeternum’. Phys. 4. 4. 3 (4.1, 297, 37–51). 44 In Phys. 4 (96). 45 Aquinas, ‘Uno quidem modo secundum quid, quod scilicet est aeternum vel saeculum alicuius rei: . . . Dicit ergo quod aeternum vel saeculum uniuscuiusque rei vocatur finis, idest mensura quaedam terminans, quae continet tempus vitae cuiuslibet rei . . . Alio modo dicitur aeternum simpliciter quod comprehendit et continet omnem durationem’ In de Caelo et 1. 21 [215]; In Sent. 2. 2. 1. 1. Note also Albert’s distinction between ‘aeternitas’ used ‘extenso nomine pro aeviternitate’ and a ‘potissime aeternum et simpliciter’, Sum. Theol. 5. 23. 1. 1. 1, (34.1, 124, 15–20); Sum. de Creat. 2. 3. 2 (Borg. 34, 350). Further idiosyncratic distinctions involving the word ‘aeternitas’ can be found in medieval literature. Bonaventure, for example, distinguished between using the word adjectivally or as a noun, In Sent. 1. 30. 1 ad 3, as he struggled to distinguish a use applicable to angels and a use worthy of God alone. See also Bonaventure, In Sent. 2. 2. 1. 1. 1 fund. 1; 3. 26 dub. 1.

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T H E NATUR E O F E T E R N I T Y We have seen that thirteenth-century thinkers typically made use of both extensional and non-extensional terms when discussing eternity. As a result of this there have been disagreements amongst contemporary philosophers about whether Aquinas and his thirteenth-century colleagues were committed to an extensional or a non-extensional model of eternity.46 Pseudo-Aquinas was clearly worried about using the Latin word ‘instans’ to describe eternity, nevertheless it seems to me that there are at least four factors that would encourage contemporary exegetes to interpret the medieval notion of eternity as that of an instant, or instant-like particular:47 46 C. Hughes, On a Complex Theory of a Simple God, 114–20, has suggested that we should view Aquinas’ notion of eternity as an instant. E. Stump and N. Kretzmann reject this and urge instead that it should be viewed as a non-successive but extended duration (‘Eternity’, 226; ‘Atemporal Duration’, 217). M. Sorley proposes that we should think of it as a specious present (Moral Values and the Idea of God, 465). On the issue of using both extensional and non-extensional language, see C. J. Peter (Participated Eternity in the Vision of God, 8) and B. Leftow (Time and Eternity, 118 n.–119 n.) who have suggested that there is a shift in Aquinas’ thought from a preference for extensional language in his earlier works to a preference for non-extensional terminology in his later works. Whilst there may indeed be a change of emphasis in contexts involving texts from specific authorities, a comparison of Aquinas’ analysis of Boethius’ definition of eternity in both the early Sentences and later Summa Theologiae indicates a surprisingly similar approach, stressing in each case the non-extensionality of eternity. See his In Sent. 1. 8. 2. 1 and Sum. Theol. 1. 10. 1. 47 Pseudo-Aquinas’ reasoning is not altogether clear but seems to be based on a rather narrow understanding of the role of an instant in time, an understanding which makes him hesitate to use the word ‘instans’ of angelic time and so a fortiori of eternity: ‘Si vero (angelus) intelligat per specias suas,

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The definition of eternity Analogies of eternity Discussions of the now of eternity Eternity and the aevum

The first factor which must encourage us to interpret thirteenth-century models of eternity as non-extensional arises from the way thirteenth-century figures such as Aquinas, Albert, Peter of Tarentaise, and Bonaventure accepted and interpreted Boethius’ definition of eternity as a ‘simultaneous whole and perfect possession of life without end’.48 With its reference to ‘life without end’ the definition clearly has its roots in the limitlessness tradition. But the introduction of the word ‘simultaneous’ (simul) at the beginning of the sentence subtly transforms the focus. We analysed the word ‘simul’ in Chapter 2 and saw that although it had a clear temporal sense, it also had a non-temporal sense where it could be used to affirm the (non-extensional) tunc actio sua, cum sit successiva, mensurabitur tempore quod non est idem cum nostro, . . . et huius temporis una particula cum multo tempore nostro esse potest nullo medio intercidente, quamvis in tempore nostro multa media cadant propter eius continuitatem. Cum vero intelligibilia sibi succedunt, erit ibi tempus perfectum ex multis particulis indivisibilibus in seipsis, et hae particulae non sunt instantia: quia nulla istarum est eadem in toto tali tempore, sicut est instans temporis in tempore. Nec aliqua istarum est continuatio temporis, sed quaelibet est pars sicut unitas numeri.’ De Instan. 4. 48 Boethius states his definition of eternity as ‘aeternitas est interminabilis vitae tota simul et perfecta possessio’, and this definition can be found echoed in Aquinas, Sum. Theol. 1. 10. 1; Albert, In Sent. 1. 8. A. 8 (Borg. 25, 229); Peter of Tarentaise, In Sent. 1. 8. 3. 1; Bonaventure, Com. in Evang. Luc. 18 [30]. On the background to this definition see J. D. Broussard, ‘Eternity in Greek and Scholastic Thought’, ch. 1; F. H. Brabant, Time and Eternity in Christian Thought, 63–6; and R. Amerio, ‘Probabile fonte della nozione boeziana di eternita`’.

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togetherness of particulars, so that when predicated of a single particular it could then be understood as negating the durational extension of that particular.49 Particularly revealing of medieval thought is the way that thirteenth-century thinkers always included objections and problems which their views had to be able to resolve. When dealing with Boethius’ definition, and the topic of eternity in general, these objections almost inevitably take as their point of departure a purported extensional implication of the definition, so that in resolving them the preferred model of non-extensionality is clearly demonstrated by thirteenthcentury thinkers.50 49 Aquinas, ‘aeternitas Dei, quae non habet extensionem aut prius et posterius, sicut tempus, sed est tota simul’, In Phys. 8. 2 [990]; ‘In hoc enim aeternitas a tempore differt, quod tempus in quadam successione habet esse, aeternitatis vero esse est totum simul.’ Sum. Con. Gen. 3. 61 [2359]. Albert, ‘aeternitas non habet partes . . . quia sine successione [est]’, Sum. de Creat. 2. 3. 4 ad 3 (Borg. 34, 355). Theodoric of Freiberg, Tr. de Mensuris 4 (3, 229, 39–44; 3, 230, 82–93). Philip the Chancellor explicitly identifies the role of ‘simul’ as excluding succession, ‘Unde cum dicitur ‘‘eternitas est interminabilis vitae tota simul ac perfecta possessio’’ quod dicitur ‘‘simul’’ removet successionem, quod dicitur ‘‘tota et perfecta’’ removet partium divisionem. Unde non est eternitatis pars eternitas sicut temporis tempus, et ita tres differentie eternitatis ad tempus.’ Sum. de Bono, 1. 4. 9 (1, 53, 51–61); ibid., de bono naturae intellectualis creaturae 9 (1, 295, 27–35). It should be noted that it is far from clear whether Boethius meant anything like this himself. Exegetes differ. R. Sorabji, Time, Creation and the Continuum, 119–20, affirms the medieval interpretation of Boethius whilst E. Stump and N. Kretzmann in ‘Eternity’, affirm an extensional interpretation of Boethius’ notion of eternity. It is clear that Boethius affirmed the immutability of God, but beyond that it is not impossible that even he himself was not altogether clear about what he was trying to affirm. 50 Aquinas, ‘Ad sextum dicendum, quod duratio dicit quamdam distensionem ex ratione nominis: et quia in divino esse non debet intelligi aliqua talis distensio, ideo Boetius non posuit durationem, sed possessionem,

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Equally revealing of how medieval thinkers viewed eternity is the second set of factors: the non-extensional analogies which they gave. The point of departure for most writers was Augustine’s comparison of eternity with a nonflowing present instant. Influenced by this approach, we find medieval thinkers comparing eternity to points, motion boundaries, instants, and even proposing geometrical models which compared eternity to time as the centre point of a circle to its circumference.51 Aquinas even went so far as to cite the distinction between a non-extensional ‘intellectus’ (understanding) and a discursive, extensional ‘ratio’ (discursive reasoning) as an analogy to illustrate the difference between a non-extensional eternity and an extensional time.52 The third factor which supports a non-extensional interpretation of eternity arises from the way thirteenth-century thinkers identified a ‘now’ (nunc) as existing in eternity.53 We have already seen that the medieval Latin word ‘nunc’ was generally treated as interchangeable with other nonmetaphorice loquens ad significandum quietem divini esse; illud enim dicimus possidere, quod quiete et plene habemus; et sic Deus possidere vitam suam dicitur, quia nulla inquietudine molestatur.’ In Sent. 1. 8. 2. 1 ad 6. 51 Augustine, Conf. 11. 14 (17); Albert, Sum. Theol. 5. 23. 1. 2. 2. B (34.1, 129, 76–82 and 34.1, 130, 41–5); Aquinas, In Phys. 4. 18 [586]; ‘Et sic aeternitas est tota simul, sicut et punctum partibus’, de Rationibus Fidei 10; Sum. Con. Gen. 1. 66; Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1 ad 7 and 8. Although Bonaventure used these analogies he seems to have been a little concerned that the analogy of eternity to a point could be pushed too far, in case talk of a ‘point’ was understood as implying the existence of a further extensional element to eternity that the point was bounding, Quaest. Disp. 5. 1 ad 14. 52 Sum. Theol. 1. 79. 8 ad 2. 53 ‘omnino stabilis in nunc aeternitatis’, Ulrich, de Summo Bono 2. 4. 2 (2, 121, 18).

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extensional terms, such as ‘instans’. So the very fact that thirteenth-century thinkers continued to speak of a ‘nunc’ in eternity is a significant piece of evidence denoting how they conceived of eternity. One of the most interesting pieces of evidence indicating how the word ‘nunc’ was understood when it was predicated of eternity arises from consideration of what I shall refer to as the ‘simultaneity problem’. This problem arose for medieval thinkers because they referred to a ‘now’ in the durations of time, aeviternity, and eternity, and so naturally they asked whether the nows were simultaneous and, if so, were they the same now. As we know that the ‘now’ of time was an instant, this question could not have arisen and it would not have caused so many difficulties if the ‘now’ of eternity was not being construed, also, as an instant.54 54 Alexander of Hales, ‘quando deus est, angelus est et motus est; haec igitur tria sunt simul’, Sum. Theol. 1. 1. 1. 2. 4. 3; also Bonaventure, In Sent. 3. 8. 2. 1 ad 6. Sometimes the argument was stated in terms of sharing a ‘when’ (quando), Albert, Sum. de Creat. 2. 3. 3 (Borg. 34, 352); 2. 3. 5 ad quaest. (Borg. 34, 357); Lib. de Causis 2. 1. 10 (17.2, 72, 56–60). On the concept of the quando see Averroes, ‘Quando autem est id, quo aliquod tempus refertur ad aliquam rem quae in eo existit’, In Praedicamenta, Sermo de Praedicamenta Quando (49D–F). Aquinas in his earlier Commentary on the Sentences thought that there was a concomitance (concomitantia) between the nows of time, aeviternity, and eternity, suggesting thereby the relationship of togetherness which we have already seen medieval thinkers wanting to affirm. In Sent. 1. 19. 2. 2. Although he does not address the same question in his later Summa (Sum. Theol. 1. 10. 4 ad 2) the fact that he explicitly refrains from talking of a ‘concomitance’ suggests that the notion worried him and he was not entirely happy with his earlier answer. Albert seems to have agreed with talk of a ‘concomitance’ and distinguished between a substantival predication of ‘now’ which would imply identity of durations, and an adjectival predication which preserved their differences. Sum. Theol. 5. 22. 2. 2 (34.1, 120, 35–57; 34.1, 119, 32–40). For further discussions of this point see his In Sent. 1. 8. B. 13 ad 2 (Borg. 25, 240). Bonaventure extended

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A fourth set of considerations, which might support viewing the now of eternity as a non-extensional, instant-like particular, arise from Proclus’ reflections. We saw in the previous chapter that he believed that the nature of the now was related to the nature of the particulars which it measures. Thirteenth-century thinkers had little doubt that God was simple, uncompounded, unextended, and even identical with His eternity and its constitutive now. And so it made sense within the confines of thirteenth-century thought to also think of the now of eternity as non-extended and instant-like.55 There can be little doubt that medieval notions of eternity should be construed as modelling eternity as an instant or as an instant-like, non-extended, durational element. Albert seems to have also thought that, as a result of this ‘durational’ aspect of eternity, it was possible to go further and extend other durational properties to eternity, such as a topology. In earlier chapters we have seen that medieval thinkers seem to have believed that the now which constituted time was itself to be thought of as reducible to, the principle and identified adverbial and substantival uses of the word ‘aeternus’, In Sent. 1. 30. 1 ad 3. Peter of Tarentaise limps to the same conclusion, In Sent. 1. 8. 3. 1, as does Kilwardby, De Temp. 17 [107] (35, 11–13). 55 Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1. Strictly speaking nothing could be said to measure God, not even the now of eternity, but as the now of eternity was identified with God, talk of God’s being measured by a now was simply a way of saying that God was His own measure. See Aquinas, ‘aeternitas et nunc aeternitate non differunt re sed ratione tantum’, In Sent. 1. 19. 2. 2; Sum. Theol. 1. 10. 2; In Sent. 1. 14. 1. 1 ad 3; Alexander, In Sent. 2, Appendix (2, 422, 17–22); In Sent. 1. 9 [6] (1, 117, 24); Albert, Sum. Theol. 5. 23. 1. 1. 1 (34.1, 123, 34–41, and 34.1, 116, 20–4).

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in some sense, the Primum Mobile, the (moving) status of which gave rise to the now’s properties. Albert seems to have thought that this same model could be applied to eternity and so he spoke of a constitutive now of eternity which was reducible, in some sense, to God from whom it derived its properties and could only be distinguished conceptually.56 Although characterizing eternity as a duration implied a prima facie similarity between it and other durations, analogies ultimately broke down because of the uniqueness of God. Whilst the durations of time and the aevum could be thought of as accidents inhering in a durational subject, God’s immutability ruled out His having any accidents at all.57 Similar difficulties arose with the language of measurement. Influenced perhaps in part by their authorities, but also by Aristotle’s requirement that distinct kinds of esse needed their own measures, thirteenth-century thinkers 56 Albert, ‘sicut se habet nunc temporis ad temporis constitutionem, sic nunc aeternitatis ad constitutionem aeternitatis’, Sum. Theol. 5. 22. 1 (34.1, 115, 34–6); Aquinas, In Sent. 1. 19. 2. 2 ob. 4. Although Aquinas’ remark here is in an objection, his reply implicitly concedes the same point. See also Albert’s concession of the principle, ‘sicut nunc temporis est substantia temporis, et fluxus ipsius nunc est esse temporis: ita nunc aeternitatis est substantia aeternitatis, et duratio ipsius nunc est esse aeternitatis’, Sum. de Creat. 2. 3. 5 (Borg. 34, 356). Besides the references to motion and extension, eternity and time were also contrasted in virtue of the fact that whilst it was believed that it was possible to distinguish between the nature (substantia) and existence (esse) of time, the non-composite nature of eternity ruled out such a distinction. See Albert, Sum.Theol. 5. 22. 1 (34.1, 117, 15–17, and 34.1, 123, 33–4). 57 Bonaventure, In Sent. 1. 8. 2. 1; Aquinas, Sum. Theol. 1. 3. 6; 1. 14. 4; 1. 28. 2; In Sent. 1. 8. 4. 3; Sum. Con. Gen. 1. 23; Compend. Theol. 23.

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firmly accepted that eternity was a measure.58 We saw in Chapter 6 that there were two basic concepts of measurement, measure by position and measure by nature. Measure by position represented the metrical notion of measure. This involved using a measure which exceeded the thing to be measured, quantifying it according to a scale or metric. Besides the unacceptability of ascribing any superiority to a measure of God, a notion of measurement by position was totally inappropriate for a duration which had no extension. And so it would appear that where being-a-measure was attributed to the duration of eternity, it was not intended to be taken as claiming that eternity was a measure by position. Unfortunately, viewing eternity as a measure by nature was at least as problematic, for a measure by nature had to be ontologically more perfect than the particular which it was measuring, and nothing by definition could be more perfect than God.59 58 Albert, In Sent. 1. 8. A. 9 (Borg. 25, 233); 1. 8. A. 8 (Borg. 25, 229); Phys. 4. 4. 4 (4.1, 298, 33 f.); Aquinas, In Sent. 1. 8. 2. 2; 2. 2. 1. 1; Sum. Theol. 1. 10. 2 ob. 3; Bonaventure, In Sent. 3. 8. 3. 1 ad 6. Kilwardby, De Temp. 23 [144] (44, 2–3). Note Pseudo-Aquinas’ assumption that ‘being a measure’ is an essential property of eternity, De Temp. 4. Albert explores the same issue, Sum. Theol. 5. 22. 1 (34.1, 116, 10–20; 34.1, 119, 56–60). Concerns about predicating ‘measure’ of eternity arose because a measure was thought to be greater than that which it measured and so referring to eternity as a measure could be seen as implying that eternity was greater than God. On this see Bonaventure, Quaest. Disp. de Myst. Trin. 5. 1 ad 1; In Sent. 2. 2. 1. 3; Albert, Phys. 4. 4. 4 (4.4, 298, 83). Bonaventure’s discussion of the way Jesus’ birth was measured by the two measures of time and eternity is illustrative of the issues at stake for thirteenth-century thinkers, on which see, In Sent. 3. 8. 2. 2. See also 3. 8. 2. 1 ad 6, and Kilwardby, De Temp. 17 [107] (35, 21–2). 59 Sum. Theol. 5. 22 (34.1, 116, 16–20). For an extended discussion of this issue, see Capreolus, Defensiones 9 (2, 5).

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So, although thirteenth-century thinkers wanted to use the word ‘measure’ of eternity, it is clear that because of the uniqueness of God and eternity, neither of the medieval concepts of measurement could properly be applied to eternity. Despite the apparent implications of a common conceptual framework serving as the basis for predicating ‘measure’ of both time and eternity, the reality was that when it came to eternity the word ‘measure’ had to be stripped of precisely the content that warranted its predication of time, leaving its content when predicated of ‘eternity’ as, at best, unclear. As we draw to the end of this chapter it only remains to be asked whether medieval views about eternal existence should be thought of as accounts of everlasting existence or as accounts of timelessness. We have seen in this chapter that there were at least ten different ways in which the word ‘aeternitas’ could have been used and understood by medieval thinkers, some of those uses presupposing extensionality and some of those accounts implying notions of non-extensionality. Extensional and non-extensional accounts have much in common with (respectively) contemporary ideas of everlasting and timeless models of eternity but, as there is no one single medieval account of eternity, the question of whether it should be viewed as everlasting or timeless cannot arise. Nevertheless, we have seen that amongst the different usages of ‘aeternitas’, thirteenth-century thinkers did want to privilege some uses as ‘more proper’, and where this was the case it was inevitably the non-extensional instant model of eternity that they were referring to. If eternity is to be

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viewed as an instant then the question arises about how it should be understood in its relation to time. Thirteenthcentury thinkers do not explore this question in any clear kind of way, but in contemporary terminology one way of representing it would be to think of the instant of eternity as constituting a distinct durational stream, albeit a nonextensional one, a stream that could lie alongside time but not be reduced to it. In terms of the distinction introduced at the beginning of Chapter 7, between absolute and relative timelessness and everlastingness, this would mean that an eternal particular would be one that was everlasting with respect to its own duration and timeless with respect to time.60

C O N C LU S I O N As with the terminology and durations of earlier chapters, we have seen that medieval minds did not necessarily think of eternity in the durational way that contemporary philosophers do. Although durational aspects come to the fore in their discussions, they often preferred to construe eternity in terms of limitlessness and the different ways in which a particular could be limitless. As a result of this we have 60 A similar point has been made by G. Jantzen, God’s World, God’s Body, 36. The possibility of translating talk of language about timelessness into a discourse about alternative durational streams, of which God’s duration can be construed as just an instant, has also been noted by R. Swinburne, The Coherence of Theism, 223.

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seen that there were at least ten different ways in which thirteenth-century thinkers could use the word ‘aeternitas’ (eternity). In order to distinguish between uses of ‘aeternitas’ which were intended to convey notions of extensional or nonextensional existence, medieval thinkers distinguished between ‘less proper’ and ‘more proper’ uses of the word, reserving the more proper uses for non-extensional notions. It would be easy to equate a non-extensional notion of eternity with the contemporary notion of timelessness, but it would be misleading to do so. Timelessness involves existing at no instants at all but, when examining the nature of the medieval notion of eternity, we saw that there were four key reasons for thinking of it as an instant and so as, in effect, another duration to be contrasted with time and other durational streams. Whilst the duration of eternity shared some topological features in common with a duration such as time, ultimately analogies broke down because of the unique status of God. Nevertheless, the fact that eternity was being thought of as a separate duration ‘alongside’ time implies that exegetically the most accurate way of portraying the medieval notion of a non-extensional eternity would be as a separate duration consisting of just a single instant.

10 God and Time

This chapter will conclude the investigation by examining the particular question of how thirteenth-century thinkers viewed God’s relationship to time. In previous chapters we have seen that medieval thinkers were committed to a complex model of durations; a model which they inherited from Aristotle but had to adapt considerably in order to fit the needs of their Christian theology. As a simple example of this we saw in Chapter 2 that they were happy to accept Aristotle’s rejection of a plurality of times. Yet when it came to integrating angels into their world view we saw that many thirteenth-century thinkers were willing to posit an additional discrete or continuous time.1 All the figures which we have considered in this study accepted the broadly Aristotelian notion of a relational account of time, relating time and the flowing instant which generates time, to the Primum Mobile as the cause and subject of 1 Although Aquinas at times talks of the angelic time as discrete, at other times he is more ambiguous, ‘Sed istud tempus, sive sit tempus continuum sive non, non est idem cum tempore quod mensurat motum caeli, et quo mensurantur omnia corporalia, quae habent mutabilitatem ex motu caeli’, Sum. Theol. 1. 53. 3.

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time. But even whilst agreeing about these fundamental aspects of time, there were theological realities which impinged upon the Aristotelian framework. We saw in Chapter 6, for example, that there were occasions when medieval theologians needed to be able to talk of time before and after the existence of the Primum Mobile so that there would be a time to measure the sufferings of the damned and the actions of the blessed. These theological needs gave rise to a set of different concepts of time which we saw were distinguished from each other by the measure, or metric, of the durations. Whether these different concepts and notions of time should be thought of as constituting different times or not, is one of the crucial questions which thirteenth-century thinkers did not address. We have seen that Aquinas, at least, was willing to admit that a time with a different subject to the Primum Mobile would be a numerically different time, and so in his view time existing before or after the Primum Mobile would be a different time to the time which currently exists. To this set of times, or concepts of times, we saw that medieval thinkers wanted to add at least two further durations: that of the aevum (or aeviternity) and eternity. As a concept the aevum seems to have been mystifying and confusing, even to thirteenth-century thinkers, and we have seen that it was variously characterized as an extended absolute duration or as a non-extended measure. There was more agreement about the concept of eternity, which we saw in the last chapter was viewed as a non-extended ‘instant-like’ element. When it comes to trying to fit all these distinct elements together into a single coherent theory, I have suggested that the best approach seems

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to be to treat all the durations (and times) as akin to the durational (temporal) streams which we explored in Chapter 2. In the case of eternity this model would characterize nonextensional accounts of eternity as a durational stream consisting of simply one instant. When it comes to locating particulars within the durations, we have seen that medieval thinkers had a very clear sense of ontological propriety, a sense which determined the kinds of particulars which could be located in each of the durations. Under pressure to explain the interaction of different substances in different durations, they often found themselves needing to affirm notions of presence between the durations. This notion of presence was not particularly clear, even to thirteenth-century thinkers, and so it was that they introduced the terminology of particulars in one duration existing at or with some of the instants of other durations. Once again, precisely what it would mean for particulars in different durations, and for the wider philosophy of time, was left largely unexplored in thirteenth-century writings. When it comes to explicitly considering the question of God’s relationship to time, one of the clearest starting-points has to be the unambiguous affirmations that figures such as Aquinas, Albert, and Bonaventure make, insisting that God does not exist in time. Albert even seems to have believed that placing God within time entailed a version of the Arian heresy because in a temporal God the procession of the Son from the Father would be a temporal process giving rise to a time, or a ‘when’, as Arius had put it, when the Son did not exist.2 2 See Albert’s discussion, In Sent. 1. 9. B. 5 ob 5 sed con. (Borg. 25, 278–9).

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Despite the apparent clarity of medieval language, images, and arguments, the issue of God’s relationship to time is not as straightforward as it seems at first. Even the apparently clear reasoning provided by Albert is not without its ambiguities. In Albert’s argument it is clear, for example, that he has confused temporal existence with temporal causation and that what he is actually arguing against is not so much the placing of God in time as rather an application of the causal theory of time to the generation of the persons in the Trinity. Assuming a model of simultaneous causation, a model which we saw earlier that he and his contemporaries subscribed to, then it is difficult to see how a God existing in time could amount to a form of Arianism. If the Father begets the Son in an act of simultaneous causation then there need be no time prior to the existence of the Son. What Albert’s reasoning shows is the extent to which thirteenth-century thinkers were themselves confused about precisely what it meant to talk of God’s relationship to time. In this particular instance we can see that a claim is being made about God’s relationship to time, a claim which is taken to be a conclusion entailed by theological data. In reality, God’s atemporality is merely an assumption which Albert seems to have imported to the consideration at hand and then, mistakenly, taken as a firm conclusion entailed by theological orthodoxy.3 3 Aquinas’ strong defence of God’s atemporality, ‘Deus est omnino extra ordinem temporis’, de Interp. 1. 14 [194] (and also Sum. Theol. 1. 14. 13 ad 3) can also be viewed as an assumption intended to explain the relationship of free will to divine knowledge of future contingents. Aquinas’ argument cannot be taken at face value because the analogy he is using seems to imply that God

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Even where thirteenth-century language indicates that a statement is to be viewed as more than an assumption, as setting out a clear position, or conclusion, about God’s relationship to time, we have seen in previous chapters that language insisting on an absence from time can carry a variety of implications. We have seen that medieval figures, lacking the language to distinguish sharply between tensed and tenseless (A and B) theories of time, often confused the two and asserted the non-temporality of a particular when it seems that what they were actually trying to do was repudiate the predication of tenses. We have also seen that there is a variety of concepts of time, so an insistence that a particular is not within time does not necessarily rule out all associations with temporality. This is something that we have seen was the case with angels, who could be described as temporal or as non-temporal, depending upon the particular context. What should additionally make us cautious in jumping to conclusions about how thirteenth-century thinkers understood God’s relationship to time, is that there are three sets of considerations which, arguably, make more sense if we think of the medieval God as less than fully atemporal. These considerations include:

learns what happens in the world by seeing it from outside of time. If we take this analogy of seeing and learning too seriously, then it is difficult to reconcile its implications with his stress on divine immutability and in particular his claim that ‘Dicendum quod scientia Dei est causa rerum. Sic enim scientia Dei se habet ad omnes res creatas, sicut scientia artificis se habet ad artificiata.’ Sum Theol. 1. 14. 8. See also Albert’s explanation of ‘simul’ when predicated of God, Sum. Theol. 5.23. 1. 1 (34.1, 125, 77–9); In Sent. 1. 8. A. 8 (Borg. 25, 230); 1. 8. A. 12 (Borg. 25, 235).

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(1) The thirteenth-century language of ‘togetherness’ (2) The ‘analogy’ of duratio (3) The implications of the role of God as sustainer

T H E L A N G UAG E O F ‘ TO G E T H E R N E S S ’ At several points in previous chapters we have seen that thirteenth-century thinkers were struggling to find a language which would enable them to talk of a ‘togetherness’ between durations such as time and eternity. Lacking a specialist vocabulary, we have found that ‘simul’ (simultaneously) could be used in this respect, as could an affirmation of ‘praesens’ (present). In the previous chapter, we even saw figures discussing a common ‘quando’ (when) between eternity and time.4 4 Pecham, ‘aeternitas Dei est simul cum tempore’, Quodlibeta 2. 10 (99, 25–35). Although we saw in Chapter 2 that the word ‘simul’ has a clear Aristotelian pedigree, it should be noted that its application to God was something that was enshrined in both church decrees and scriptures, so occurrences of ‘simul’ cannot be taken as always carrying a philosophical import. The Fourth Lateran Council (1215), for example, had decreed of God, ‘qui sua omnipotenti virtute simul ab initio temporis, utramque de nihilo condidit creaturam spiritualem et corporalem . . .’ (N. Tanner, Decrees of the Ecumenical Councils, i. 230, 10–12) and the Vulgate claimed of God, ‘Qui vivit in aeternum creavit omnia simul’, Ecclus. 18:1. On the use of the term ‘quando’ note Albert, ‘quando motus est, deus est . . .’ Phys. 4. 4. 4 (4.1, 298, 34) and Sum. de Creat. 2. 3. 2 (Borg. 34, 349). One of Aquinas’ preferred modes of expression seems to be merely asserting God’s presence using the verb ‘adesse’ (to be present): ‘Deus videt omnia in sua aeternitate, quae, cum sit simplex, toti tempori adest, et ipsum concludit.’ Sum. Theol. 1. 57. 3; and ‘momentum eternitatis adest toti tempori, Quaesta Quodlib. 10. 2. 1 ad 1. Kilwardby went beyond the usual terminology to affirm a ‘relatio’ (relation)

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Two of the potentially most interesting terms to be used were the terms ‘concomitantia’ and ‘coexistere’. We examined these in Chapter 2 and saw that they were used in thirteenth-century thought as a way of affirming a ‘togetherness’ between particulars in different durations. Of these between the nows (or ‘whens’) of time and eternity, ‘Si tamen li ‘‘quando’’ sit temporale et li ‘‘tunc’’ spectet ad eternitatem, ut sit inter illa relatio simplex’, de Temp. 21 [141] (43, 13–15). Some commentators have cited Aquinas’ use of the word ‘semper’ as indicating potential temporal overtones (B. Davies, The Thought of Thomas Aquinas, 108). It is true that William of Auxerre seems to have analysed ‘Deus est semper’ with a temporal meaning, as when he writes, ‘Deus est dum presens est, fuit dum preterita fuerunt, erit dum futura erunt, et naturaliter precedit omnia opera et naturaliter subsequitur omnia tempora.’ Sum Aurea, Appendix 54 (1, 382, 22–4); and Alexander of Hales admitted a clearly temporal sense, ‘Si autem quaeritur quae sit intentio eius quod est ‘‘semper’’, cum dicitur, ‘‘Deus est semper’’, respondendum uno modo, secundum Augustinum quod ‘‘semper’’ supponit universum tempus. Unde sensus set ‘‘Deus est semper’’, id est ‘‘Deus est in omni praeterito, in omni praesenti, in omni futuro, nec deest alicui praeterito vel alicui praesenti vel alicui futuro.’’ ’ Sum. Theol. 1. 1. 1. 2. 4. 4 (1, 110). Kilwardby’s usage indicates more ambiguity, as it is subtly equating time to eternity, rather than implying any reduction to time, ‘diffinitio autem eius quod est esse semper est quia cum dicitur de Deo, potest dicere totum tempus in eternitate, ut sit sensus; ‘‘Deus est in omni tempore vel in toto,’’ vel ‘‘Deus est eternaliter.’’ ’ de Temp. 22 [143] (43, 21–5). This, and the clearly non-temporal implications of ‘semper’ and ‘sempiternity’ which we examined in Chapter 8, means that conclusions cannot be drawn either way from the mere occurrence of words such as ‘semper’. We have seen in the last two chapters that the language of ‘participation’ was sometimes used to describe relationships between durations and particulars, as for example Aquinas, ‘inquantum sunt incorruptibilia secundum substantiam et secundum hoc participant aeternitatem; inquantum autem transmutantur secundum locum . . . sic participant tempore’, In de Div. Nom. 10. 3 [875]. When medieval figures talk of a particular participating in another duration, the focus of the assertion is not so much to make a comment about existence in relation to that duration, but rather to ascribe qualities to the particular more usually identified with other particulars within the duration in question. The language of participation can therefore be ignored, as it has no implications for the question we are examining here.

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two terms it seems to be ‘concomitantia’ which was more frequently used. It was used of angels, and at other times it was used of God, but in both contexts it was used to claim a togetherness (concomitantia) between their own durations and time. It is difficult to be clear precisely what medieval figures were trying to affirm in their use of this term. Kilwardby, at least, was willing to talk of a ‘relation’ (relatio) between time and eternity and so it would seem that he was trying to develop a concept of a non-temporal relation of togetherness which could hold between the disunified instants. His contemporaries seem to have deliberately avoided using terms such as ‘relation’ and so their talk of a ‘concomitantia’ must be viewed as affirming a looser, vaguer notion of togetherness; one which they were probably not entirely clear about themselves. It is difficult to see how any such notion could have been fitted into their philosophical framework without utterly undermining the distinction between the durations which were so central to their philosophy of time.5 5 It is difficult to identify the origins of the term ‘concomitantia’, but Gilbert of Poitiers was using it in the twelfth century to affirm a ‘concomitantia’ between eternity and the parts of time, In de Trin. (295, 57–70). Typical of thirteenth-century usage is Albert, ‘Sed intelligendum est, quod aeternitas non dicit moram habentem partes et prius et posterius et praeteritum et futurum, sed in se indeficientem semper. Et cum talis sit in se, accidit ei, cum comparatur ad partes temporis, numquam defuisse in praeterito et numquam defuturam in futuro. Et hanc concomitantiam eius ad partes temporis ex indeficientia sua causatam dicunt verba praeteriti temporis et futuri, quando de rebus aeternis dicuntur.’ Phys. 4. 4. 2 (4.1, 295, 57–65); Kilwardby, ‘cum dicitur ‘‘quando est motus, est angelus’’ hoc est dictu, in quo nunc est motus, in illo est angelus et Deus, non ut in mensurante set ut in concomitante’, de Temp. 17 [109] (36, 7–10); also ibid. [108] and [110]. Bonaventure was happy to use the term but at times seemed worried in case

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We shall see below, in our investigation of the issue of God’s role sustaining the universe, that there were clear philosophical reasons why thirteenth-century thinkers would want to develop a notion of togetherness, but there were also strong scriptural reasons. The scriptures often use images of God that imply ancientness, longevity, or existence through thousands of years. Although some theologians interpreted such language as metaphorical, it was also possible to use the notion of durational togetherness (concomitantia) in order to justify attributing such apparently temporal terminology to God. If God’s duration existed together alongside time, then He could be said to exist ‘unfailingly’ and equivalent to the extent of time, although existing non-successively Himself in a non-extensional duration.6

T H E A NA LO G Y O F D U R AT I O A second consideration which might suggest that thirteenth-century thinkers were assuming a closer relationship between time and eternity than they are credited with, arises from their account of durations. talk of a ‘concomitantia’ undermined the idea of God’s existence prior to time, In Sent. 1. 1 dub. 7; 2. 2. 1. 2. 1. For further references see above in Chapter 2. On the use of the verb ‘coexistere’ note the (fourteenth-century) use of William of Ockham, ‘non solum Deus, sed omne quod est, est in tempore primo modo accipiendo esse in tempore, quia omne quod est, coexsistit tempori’, Quaest. in Lib. Phys. 54 (6, 542). 6 Albert, ‘sicut dicitur mille annis fuisse deus et quod anni sui non deficiunt, non quod sit suus dies et mensis et annus, sed quia non deficit in decursu temporis’, Phys. 4. 4. 4 (4.1, 298, 42–5).

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We have seen in previous chapters that the medieval notion of a duratio was applied to time, aeviternity, and eternity. Chapter 1 noted that the word ‘duratio’ did not necessarily imply any extension for thirteenth-century thinkers, as having a duratio was thought to be consequent upon possessing esse or existence. The type of duratio that a particular had was directly related to the type of existence or esse that it had. There were thought to be different types of esse or, more accurately, the word ‘esse’ was used in different types of ways. Nevertheless, Aquinas at least seems to have seen very clearly that it was essential to the validity of his proofs of God’s existence that the word ‘esse’ should be used analogously (and not equivocally) of God and creation. Given the relationship between esse and duratio, an analogous predication of esse must entail an analogous predication of duratio.7 Most models of timelessness posit a logical chasm between temporality and timelessness, a logical either–or that tends to draw much sharper distinctions than medieval 7 Bonaventure, ‘Sciendum, est igitur quod tria praedicta nomina ‘‘aeternitas’’ ‘‘tempus’’ et ‘‘aevum’’ significat durationem quamdam’, In Sent. 1. 10. 2. 1. Aquinas, ‘duratio autem magis respicit esse quam vitam . . .’ Sum. Theol. 1. 10. 1 ob. 2; ‘cum tamen nulla alia res sit sua duratio, quia non est summum esse’, ibid. 1. 10. 2; In Sent. 1. 8. 2. 1. On the predication of terms of God, Aquinas’ position was, ‘Sed nec etiam pure aequivoce . . . Quia secundum hoc ex creaturis nihil posset cognosci de Deo, nec demonstrari, sed semper incideret fallacia aequivocationis’, Sum. Theol. 1. 13. 5. The notion of analogous esse has sometimes been referred to as the doctrine of the ‘analogia entis’ (E. Przywara, Analogia Entis, chs. 1–3). It should be noted that Aquinas never talks of an ‘analogia entis’; merely ‘Ens quod analogice dicitur’, Sum. Theol. 1. 13. 10 ad 4, and as a result of this there have been serious misunderstandings of Aquinas’ views about the implications of talking of God as analogous to the creation. On this and Aquinas’ notion of analogy, R. McInerny, The Logic of Analogy: An Interpretation of St. Thomas, 32–7, 80–125.

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thinkers seem to have wanted to draw. Philip the Chancellor, for example, wanted to be able to talk of time and eternity as sharing a common genus, and Alexander of Hales wanted to be able to group all the different predications of ‘aeternitas’ as instances of analogy, in virtue of the common ‘diurnitas’ which eternal particulars had.8 It might be possible to account for the analogous use of the word ‘duratio’ by merely pointing to the shared topological structure which we have seen that thirteenth-century thinkers wanted to attribute to the different durations. So its use does not necessarily have any implications for God’s existence in or out of time. What an analogous predication of ‘duratio’ must query, however, is any attempt to stress the radical disjunction between the durations which an attempt to impose the distinction between timelessness and everlastingness would lead to.

T H E RO L E O F G O D AS ‘ S U S TA I N E R’ Arguably the most interesting set of factors to raise doubts about God’s separation from time arise when we examine 8 Philip the Chancellor seems to have viewed the analogous predication of duratio as entailing that time and eternity must share a common genus, ‘tempus et eternitas sunt eiusdem generis, quia utrumque duratio est’, Sum. de Bono, 1. 1. 4 (1, 52, 17–23). Few were willing to go quite this far and the preference seems to have been, as Alexander of Hales indicates, to think of an analogous class of eternal beings. ‘Dicendum ergo quod aeternitas, dicta de Deo, de angelo, de poena aeterna et de tempore, dicitur analogice . . . Et in hac ratione, secundum quod aeternitas dicitur diuturnitas non habens finem’. Sum. Theol. 1. 1. 1. 2. 4. 1. 1. 2 (1, 85).

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thirteenth-century accounts of God’s role in sustaining the creation. We have already seen that in the case of angels thirteenth-century thinkers believed that when they were acting on particulars in the world there could be occasions in which it made sense to say that they, or their acts, were measured by the Primum Mobile, and so they could be said to be existing, in effect, in time.9 When we bear in mind God’s role sustaining creation at every instant of its existence, the question arises as to whether He should not also be thought of as being, or acting, in time. Kilwardby seems to have been particularly taken with the logic of this argument and, appealing to Anselm’s authority, he argued that the contingency of creation required God to be present sustaining each and every instant of creation. Whilst stressing that such a presence certainly would not entail extension or mutability on behalf of God, Kilwardby nevertheless wanted to insist that such a presence continuously sustaining temporal elements must amount in some sense to a presence ‘in’ continuous time.10 9 Aquinas, ‘Si aliqua actio sit in tempore, hoc erit vel propter principium actionis, quod est in tempore, sicut actiones rerum naturalium sunt temporales: vel propter operationis terminum, sicut substantiarum spiritualium, quae sunt supra tempus, quas exercent in res tempori subditas.’ Sum. Con. Gen. 3. 61 [2361]. 10 Kilwardby, ‘Dico quod Deus est in omni tempore’, de Temp. 21 [133] (41, 18); and ‘Quod sit omni tempore probat Anselmus Monologion, capitulo 20 idem infra capitulo 22 versus finem, In omni loco vel tempore Deus est, quia nulli abest’, ibid. 20 [128] (40, 31 f.) Kilwardby’s reference to Anselm is not altogether accurate as Anselm actually claims, ‘convenientius dici videretur esse cum loco vel tempore quam in loco vel tempore. Plus enim significatur contineri aliquid cum dicitur esse in alio, quam cum dicitur esse cum alio. In nullo itaque loco vel tempore proprie dicitur esse, quia omnino a nullo alio continetur’. Monologium 22 (Schmitt 1, 41, 1–7); and also ibid. 20

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Whilst Kilwardby’s contemporaries would have accepted the importance of God’s (continuous) sustaining of creation, they were worried about associating God too closely with time. We have already seen that placing God in time had the unacceptable implication for thirteenth-century thinkers of implying mutability and imperfection in God. But even a merely loose association of God with time carried a metaphysical price, as it could undermine God’s omnipotence and infinity by suggesting that He could be measured, limited, or contained in some way. The challenge for thirteenthcentury thinkers was to safeguard the very fine line between maintaining God’s role as sustainer whilst ruling out all senses of limitation. Aquinas’ position is indicative of the stresses and tensions that this gave rise to. Like Kilwardby, he too was committed to God’s role as sustaining the world at every instant of its existence. God’s sustaining role was so essential in Aquinas’ view that the very concept of annihilation could be spelled out as simply God ceasing to sustain things in existence. Commenting upon God’s role in bringing about and main(Schmitt 1 35, 21 f.). Anselm’s position is therefore that God exists with time, rather than in time because existence in time would imply a limitation and metaphysical imperfection for God. Kilwardby’s reading of Anselm seems to be assuming that there is no effective difference between with and in time. If he is right then this would question traditional readings of Anselm which have ascribed timelessness to his God (as in J. Yates, The Timelessness of God, 36; N. Pike, God and Timelessness, 130) and it would instead favour the more nuanced interpretations of B. Leftow, Time and Eternity, 183–7. Kilwardby’s own argument states: ‘Quicquid [in ali]quo tempore est, et tunc adest; igitur Deus ei presens est, quare Deus est presens omni tempore, quia nec ipsum tempus esse posset nisi a Deo presente sustinetur in esse’, de Temp. 20 [128] (41, 3–6) and also de Temp. 21 [133] (41, 18–21), [137] (42, 14–17).

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taining virtues, Aquinas stresses the importance of God maintaining what he has caused: Those things which are caused by a divine infusion do not only need divine action at their beginning, in order to bring them into being; but they also need it during the totality of their duration, so that they might be conserved in being. Just as the illumination of the air needs the presence of the sun, not only at the beginning when the air first begins to be illuminated, but for as long as it remains illuminated . . . 11

To preserve God from being sullied by association with motion and time, Aquinas insisted that sustaining or maintaining was not a series of acts performed by God, but simply a continuation of His act of creation. Whilst this position avoided the problem of there needing to be a time in which a continuous series of divine sustaining actions took place, it didn’t really address the fact that, as Aquinas himself admitted, the terminus of the single act of sustaining has ‘continuity’ and so would count as an act in time, if he were to use the same criteria of God that he used of the angels.12 11 ‘Quae autem ex infusione divina causantur, non solum indigent actione divina in sui principio, ut esse incipiant, sed in tota sui duratione, ut conserventur in esse; sicut illuminatio aeris indiget praesentia solis, non solum cum primo aer illuminatur, sed quamdiu illuminatus manet.’ Quaest. Disp. de Caritate 2. 6. 12 Aquinas, ‘Dependet enim esse cuiuslibet creaturae a Deo ita quod nec ad momentum subsistere possent sed in nihilum redigerentur, nisi operatione divinae virtutis conservarentur in esse.’ Sum. Theol. 1. 104. 1. Aquinas insists that the causal act of sustaining a particular is not a series of acts but is the one act of creation extended continuously, ‘dicendum quod conservatio rerum a Deo non est per aliquam novam actionem sed per continuationem actionis qua dat esse, quae quidem actio est sine motu et tempore’, ibid. ad 4;

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We saw earlier that Aquinas and his colleagues were committed to a theory of causation which posited no temporal lapse between cause and effect. They characterized this as a ‘simul’ causation where the word ‘simul’ should be read as proposing a togetherness of some type, rather than as implying a necessarily temporal simultaneity. This togetherness was thought of as holding in all instances of causation, including the operation of sustaining, which was therefore only possible if God could be together with or in the temporal particulars which exist.13 The logic of Aquinas’ position seems to be leading inexorably in the same direction as Kilwardby’s, and certainly in his early Sentences he comes close to admitting that there is a sense in which God, or rather eternity, can be said to be in time: And that indivisible (eternity) is able to be in different times, indeed in all time, because the invariable now of eternity is present to all the parts of time.14 ‘dicendum quod si Deus rem aliquam redigeret in nihilum hoc non esset per aliquam actionem, sed per hoc quod ab agendo cessaret.’ ibid. 1. 104. 3 ad 3. He is also, of course, committed to God’s periodic intervention with miracles, on which, A. Van Hove, La Doctrine du Miracle Chez St. Thomas, 17–26, 117–25. It should be noted that Aquinas also accepted that the very instants constituting time possessed an ens (existence), ‘ipsum nunc est quoddam ens’, In Phys. 4. 18 [584], and so particularly in the case of the flowing now, the very existence of time itself would have depended on God’s continuous sustaining. 13 Aquinas, ‘movens enim et motus oportet esse simul, . . . Deus autem omnia movet ad suas operationes . . . Est igitur in omnibus rebus’, Sum. Con. Gen. 3. 68 [2423]; ‘Necesse est ut causa agens sit simul cum suo effectu proximo et immediato . . . oportet igitur simul Deum adesse in omnibus rebus; praesertim cum ea quae de non esse ad esse produxit, continuo et semper in esse conservet . . .’ ibid. [2427], and see also ibid. 3. 65. 14 ‘et tale indivisibile (aeternitatis) potest esse in diversis temporibus, immo in omni tempore, quia nunc aeternitatis invariatum adest omnibus

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In his later works Aquinas seems to have studiously avoided forms of expression which could imply any divine presence in time. Nevertheless, when commenting on God’s existence in things, when the question of time is not explicitly at issue, he is perfectly happy to maintain that God necessarily exists in all things causing and sustaining them in being. When commenting on God’s relationship to place (locus) he is also happy to accept that God is in place.15 If God can be said to exist in everything which exists in time, as the cause and sustaining principle, the question arises as to why there shouldn’t be some sense in which He can be said to exist in time itself. We have seen that Aquinas is prepared to concede precisely this point with the angels, where he allows that there is indeed a sense in which angels can be said to be in time, when they are bringing about effects in the world. So Aquinas’ decision to resist any similar concessions for God is not so much a consequence of his philosophical views about God or time, it is rather a pragmatic consequence of his concerns about allowing God’s perfection to be impugned by association with something as imperfect as time. He seems to feel that such an

partibus temporis’, In Sent. 1. 37. 2. 1 ad 4. Albert goes on to draw an additional conclusion from this that we can generate sentences of the form ‘God has existed for x amount of time’, Phys. 4. 4. 4 (4.1, 298, 42–6). 15 Bonaventure seems to have felt uncomfortable with allowing talk of God existing in place, and so he suggested that God should be thought of as having a relationship of super-excelling, ‘nec ex hoc sequitur quod separetur a loco sed ‘‘super-excedat omnem locum’’.’ In Sent. 1. 37. 2. 1. 3 ad 2 and 3. It is not at all clear what precisely super-excelling would amount to. For Aquinas’ position, Sum. Theol. 1. 8. 2.

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association could only undermine God’s perfection and limitlessness.16

GOD AND TIME: IS HE TIMELESS? Apart from Kilwardby’s clear affirmation that God could be thought of as ‘in time’, thirteenth-century thinkers were generally reluctant to associate God with time. The three 16 Aquinas, ‘Dicendum quod Deus est in omnibus rebus non quidem sicut pars essentiae vel sicut accidens sed sicut agens adest ei in quod agit . . . .Cum autem Deus sit ipsum esse per suam essentiam oportet quod esse creatum sit proprius effectus eius, . . . Hunc autem effectum causat Deus in rebus non solum quando primo esse incipiunt sed quamdiu in esse conservantur . . . Quamdiu igitur res habet esse tamdiu oportet quod Deus adsit ei secundum modum quo esse habet . . . Unde oportet quod Deus sit in omnibus rebus et intime.’ Sum. Theol 1. 8. 1. Aquinas’ position on this matter is typical of his contemporaries. Ulrich, for example, claims that, ‘inquantum ipse Deus in omnibus existens operatur immediate in principiis cuiuslibet naturae et cuiuslibet effectus ita.’ De Summo Bono 2. 3. 10 (2. 91, 24–6); Bonaventure, In Sent. 1. 37. 1. 1. 2. On the limitations and imperfection of existing in time, Albert, ‘in tempore esse est quadam parte temporis mensurari . . . Praeterea omne quod mensuratur a quadam suae mensurae, excellitur a mensura illa sicut . . . tempus excellit omne quod est in tempore’, Phys. 4. 4. 3 (4.1, 296, 77 f.). For further discussion about the coherence or otherwise of a timeless God’s sustaining a temporal creation, D. Lewis, ‘Timelessness and Divine Agency’, 159; N. Pike, God and Timelessness, 117. On God’s existence in place (in loco), Aquinas, ‘Utroque autem modo secundum aliquid Deus est in omni loco, quod est esse ubique’, Sum. Theol. 1. 8. 2. For evidence of Aquinas’ motivation in avoiding any talk of God as existing in time, it is worth noting that whenever he is forced by his sources to come close to using such language his immediate focus is upon insisting that God’s status and perfection is not impugned, e.g., ‘Dicit ergo primo quod cum dicimus Deum esse tempus vel aliquam partem temporis . . . .oportet hoc intelligere eo modo quo Deo convenit, non quidem ita quod Deus sit aliquid cuius esse sit aliquid successivum et divisibile’, In de Div. Nom. 10. 2 [862]; ‘Dicitur autem tempus,

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sets of factors above indicate tendencies in their thought which I have suggested might well imply far more nuance and ambiguity in their accounts than those who would attribute timelessness have traditionally allowed.17 I suggested in earlier chapters that when considering the existence of multiple durations it can be helpful to distinguish between relative and absolute notions of timelessness and everlastingness, so that we can investigate whether a particular such as God was viewed by medieval figures as timeless with respect to particular durations. In the last chapter we saw that eternity was construed as consisting of a single instant, at which God existed. With respect to eternity, therefore, God was viewed as existing such that there were no instants in eternity at which he did not exist, and this amounts to existing everlastingly with respect to eternity. With respect to time, God is clearly said not to exist at any of the instants of time and so the immediate temptation is to conclude that God is timeless with respect to time. But to conclude in this way ignores the factors we have explored in this chapter such as the existence of terminology used to assert a togetherness between God and time. We have seen that there were a variety of terms which medieval thinkers quod est numerus motus, ex hoc quod ipse Deus semper movetur . . . Non tamen sic movetur quod in motu Eius sit aliqua successio, qualis est in motu qui numeratur per tempus, sed Ipse Deus semper est permanens in Seipso.’ ibid. 17 The authors who affirm that Aquinas’ God is timeless are too numerous to begin to list. As a starting-point, Paul Helm, Eternal God: A Study of God Without Time, xi; R. Swinburne, The Coherence of Theism, 178, 223; B. Davies, ‘A Timeless God’; A. Padgett, God, Eternity and the Nature of Time, 50; W. Hasker: God, Time and Knowledge, 8.

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used to describe this togetherness. For the sake of simplicity I am simply going to refer to it as a relationship characterizing God as existing with time. Unfortunately, medieval thinkers tell us very little about this peculiar and vague notion, although they do seem to have thought of it as an asymmetrical relationship which can only hold between ontologically more perfect particulars and less perfect ones. Whilst more perfect particulars can be with less perfect ones, the less perfect particulars must be measured or ‘excelled’ by the more perfect particulars. Alexander of Hales illustrates the asymmetry particularly clearly in his discussion of how such terminology is applied to discussions of existence in time: when things are said to be in place or time, one understanding is [that they are] present in place and in time . . . another understanding is [that they are] contained by them. In the case of the supreme essence only one thing is understood, that He is present, not that He is contained. Thus when it comes to forms of expression it seems more convenient to say [that He is] with place and time rather than in place and in time.18 18 Alexander, ‘scilicet cum dicuntur res esse in loco vel tempore: unus intellectus est quia et praesentia sunt locis et temporibus, in quibus esse dicuntur; alius est quia continentur ab ipsis. In summa vero essentia unum tantum percipitur, scilicet quia praesens est, non quia continetur. Unde si usus loquendi admitteret, convenientius videretur esse cum loco et tempore quam in loco et tempore.’ Sum. Theol. 1. 1. 1. 2. 4. 2 (1, 91). For examples of the use of with (cum) see Peter of Tarentaise ‘Quidquid aeternum est simul, est cum toto tempore.’ In Sent. 1. 9. 4. 1 con. 3; and ‘tota cum qualibet parte temporis stando non fluendo, quia simplex est, patet ergo quod semper est in esse, numquam in fieri, quia sic non esset tota cum toto tempore’, ibid. ad 3. See also Aquinas, ‘prout aeternitas et aevum cum tempore simul sunt, nec sibi deficiunt’, In Sent. 1. 19. 2. 2. Kilwardby, as we saw earlier in this chapter, also builds his own model of God’s being in time, a model which he based on

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Once we take mid-thirteenth-century views about God’s existence with time seriously, it becomes much more difficult to justify claims that they thought God was timeless with respect to time. This is not to assert that God was thought of as everlasting with respect to time. As we have already seen, apart from Kilwardby they were adamant in opposing any presence of God in time because, on their model of what it meant to be in time, this would have implied serious metaphysical imperfection. If they had had a different understanding of what it meant to be in time, one that implied no imperfections, then it must be an open question as to whether they would have felt the need to insist so strongly on God’s not being in time. The fact remains, however, that medieval thinkers did insist that God was outside of time, so it would be inaccurate to interpret their views as postulating God existing his reading of Anselm’s claim that God is with time. On the asymmetry of the relationship note Aquinas, ‘Si significetur nunc temporis; tunc dicetur motus esse in illo, sicut in propria mensura; angelus autem et deus, non secundum rationem mensurationis, sed magis secundum concomitantiam quamdam, prout aeternitas et aevum cum tempore simul sunt, nec sibi deficiunt. Si autem significetur nunc aeternitatis; tunc dicitur deus esse in illo sicut in mensura propria et adaequata; angelus autem et mobile sicut in mensura excedenti. Si autem significetur nunc aevi, respondebit angelo sicut mensura adaequata, et deo secundum concomitantiam, et mobile sicut mensura excedens.’ In Sent. 1. 19. 2. 2 ad 1. Kilwardby, ‘set cum dicit, ‘‘Quando est Deus, est angelus et motus’’, hoc est dictu, in quo nunc est Deus ut in mensura propria, in eodem est angelus et motus ut in mensura communi non coequata set excedente. Similter cum dicitur ‘‘quando est angelus, est Deus et motus’’, sensus est, in quo nunc est angelus ut in mensura propria, in illo est Deus, non ut in mensura propria set ut in concomitante, et motus ut in mensura communi.’ De Temp. 17 [109] (36, 11–16). Different figures use different terminology, but the existence of an asymmetrical relationship seems to have been a widely shared assumption.

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everlastingly with respect to time. But, because they also wanted to affirm a notion of God’s existence with time, then it must be equally inaccurate to interpret their views as asserting that God existed timelessly with respect to time. It seems to me that mid-thirteenth-century accounts of God’s relationship to time are trying to affirm something that simply does not fall within the ambit of the concepts and thought patterns that contemporary philosophers use. Taking, as their point of departure, a universe populated and organized very differently from contemporary philosophical models, it should not altogether surprise us that their thought refuses to be categorized and confined by the parameters of contemporary distinctions, such as that between timelessness and everlastingness.

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Subject Index Absolutism, 136–64, 147–8, 150 n. 19, 163, 280 A and B theory of time, see also temporal becoming: deWnition of, 177–8 Xowing time, 165, 182–6, 188, 262 omniscience and A and B theory accounts of time, 180, 189 relationship to angelic duration, 189 n. 24 aevum, see also time; now; Primum Mobile: as an instant, 91 n. 44 deWnition of, 252–3, 257–61, 264, 269 has a metric, 262–3 inheres in a subject, 262–3, 304 nature of the aevum, 253–4, 264–70, 279–80 now of the aevum, 262, 270 origins of the words aevum, 255–8, 264 n. 25 relationship to eternity, 237 n. 16 relationship to time, 232 topology of the aevum, 274–6 angels: actions are in continuous time, 321–3 angelic causation, 115–19 angelic (discrete) time, 88–9, 269, 273–8, 309 exist above time, 116 n. 22, 229 n. 7, 232 n. 12, 237 n. 16, 238 exist in discrete time, 87, 91 n. 44 relationship of angelic time to space, 142 relationship to past and future, 189 n. 24, 278 n. 40 relationship with eternity, 160 n. 31, 294

Arianism, 55, 57, 311–12 Atemporality: above (supra) time, 236–9 existence with (cum) time, 240–2 existence outside of time, 239, 312 chronons, see atomism co-existence, see concomitance: coexistence between durations, 315 concomitance, see also ET simultaneity: denotes metaphysical superiority, 91 n. 44 of God and angels, 91 n. 44, 241 n. 20, 302 n. 54, 315–16 of time with other durations, 91 n. 44, 126 continuous (continuum), 18–19, 20–2, 46, 183 causality (causation): backwards causation, 120–7 causal dependence, 99 n. 5 causal eYcacy of Christ’s passion, 122 causal necessity, 109–11 causal precedence, 99 n. 5 causal theory of time, 100–24 causal theory of time, thirteenth century attitudes to, 95 four types of Aristotelian causes, 101–3 heavenly bodies exercise a causal inXuence, 139 n. 9 non temporal causation, 124, 125–7 occasionalism, 110 n. 15 simultaneous causation, 107 n. 11–12 velocity of causal propagation, 112–13

360

Subject Index

change, see also Eucharist; rest: change is a broader description of ‘motion’, 138 n. 8 in an instant and in a period, 105 local motion takes time, 117 motion can be reduced to space, 135 time exists when motion is potential, 151 creation: activity before creation, 148 arguments against the possibility of creation, 156–61 createdness implies temporality, 233 creation before time, 156 n. 26 creation of time, 149 n. 18 Gods bringing about, 126 instant of creation, 105 n. 9 occurs simultaneously, 116 n. 22, 117 time before the creation of the Primum Mobile, 144, 216 discreteness: discrete time, 89 n. 41, 275 see also angelic time ordering, 18, 21–2 disuniWcation: Aristotle rejects multiple times, 93 durations, 310–11 matter, 74 multiple times required for theological purposes, 93 space, 74–5 time, 60–91, 93 see also eternity; time duration (duratio): analogy of duration, 317–19 caused by Primum Mobile, 77 n. 29 diVerent uses of ‘duration’, 35–7, 38–9 entitism, deWnition of, 173 eternity, see also now; Primum Mobile: as an instance of disuniWed time, 60 n. 14, 307, 311 deWnition of, 252, 299 n. 48

eternity is a duration, 303, 318–19 eternity of the world, 292–3 has a mental existence, 154–5 is a single instant, 298–307, 311, 326 is a measure, 304–6 is not an accident, 304 language about ‘eternity’, 282, 284–90, 292–7, 317–19 participation in eternity, 315 n. 4 relationship to time, 91 n. 44, 242 n. 21, 323 ET simultaneity: similar to concomitant existence, 92 n. 44 Eucharist, 76 n. 28, 105 n. 9 everlastingness, deWnition of, 244–5 faith and reason: conXicts, 63–4, 87, 88 n. 40–1, 94, 114–15, 156, 189, 276, 280, 309 role of authority, 13, 76 n. 28 Fourth Lateran council: on the simultaneity of God and time, 314 n. 4 free will: free will of angels, 116 n. 22, 117 has its own temporal measure, 86 n. 39 not inXuenced by the Primum Mobile, 86 n. 39, 139 n. 9 God: acts outside of time, 124 as sustainer, 319–25 cause of motion, 77 continuity of divine actions, 321–2 destruction of world, 81 does not exist in time, 311 existence and duration are predicated analogously of God, 318 existence ‘with’ time, 90 n. 43 exists at same time as angels and motion, 302 n. 54 exists everlastingly, 250 exists outside of time, 229, 238

Subject Index exists timelessly, 250, 312 exists with time, 241, 242 n. 21, 311 God’s activities before creation, 148 God exists with time, 327 God’s relation to time, 325–9 honoriWc notion of tenses and priority, 160 limitlessness of God, 249–50, 290 movement of the heavens inWnitely fast, 114 miracles and, 76 n. 28 necessary existence, 290 neither precedence by nature or time in God, 99 n. 5 nominales’ account of divine knowledge, 181 perpetuity, God can confer the property of, 256 n. 15 simultaneity/togetherness with other durations, 126–7 supreme measure, 196 temporal language and, 317 transcendence, 265 velocity of divine causal propagation, 113 illumination, 108–11, 117 imaginary time, 149 n. 18, 153–62 an eternity of imaginary time, 160 n. 31 time is a mental distension, 174 time is not a mental Wction, 82, 190 Immaculate Conception: depends on a temporally later cause, 122–3 immutability 52 denotes ontological superiority to time, 197 immutable beings exist before time, 160 n. 31 is related to eternity, 227 n. 3, 236 of God, 290, 293–4 inWnite velocity, 111–15 indivisibility of temporal boundaries, 15, 25

361

instant: contrast instants of time and nature, 24, 118, 128 distinction between instants and periods, 43 disuniWed instants, 60–2 existing at an instant, 248 Xowing instant, 182 n. 19 have substantival/absolute existence, 173 irreducibility of instants to periods, 45 mind joins instants to make time, 174 of angelic duration, 116 n. 22 of eternity, 90 n. 42, 298 of the aevum, 266 n. 27 present instant is the substance of time, 175 n. 11 instantaneous, 52 propagation of light, 109 Liber de causis, 32 Mass: eYcacy depends on Christ’s suVerings, 123–4 mathematics: geometrical models of reality, 47–8 mathematical modelling of reality, 48 n. 55 mathematical point, 45 mathematical set theory, 45 matter, 72 essence of matter, 73 unity of matter explains the unity of time, 86 measure, see Primum Mobile: concept of measure, 232 distinction: measure by nature and measure by position, 196–8, 205–6, 304–5 eternity as a measure, 304–6 improper use of the word, 195 inside and outside measures, 198 n. 6 intensive and extensive measures, 200 n. 9

362

Subject Index

measure, see Primum Mobile (Cont.) intrinsic and extrinsic measures, 198–201, 222 privileged measure, 201, 203–5, 208–14 token and type measures, 199 univocal and non univocal measures, distinction between, 207 metric of time: confusion about the unity of the metric, 84 constituted or evidence by the privileged clock, 213–19, 223 essential property of time?, 219–21, 224 is an instance of measure by position, 197 metric is mind dependent, 171 metric of angelic time, 274 n. 36 metrical criteria for identifying the subject of time, 82 n. 33 time before the existence of the Primum Mobile lacked a metric, 145 n. 14 time in the absence of the Primum Mobile has a diVerent metric, 218–19 views about the metric, 193–224 metaphysical perfection, 99 mind dependence: of time arises from deWnition of time, 167 full existence of time is mind dependent, 171 temporal becoming is mind dependent, 178 miracle, 76 n. 28 modality (modal): modal account of temporal experience, 168 modal relationship of fraternity, 150–1 temporal unity, 70 moment: indivisible motion boundary, 34, 138, 164 Xowing moment, 175 n. 11 of aevum, 33 of eternity, 32, 33 of time, 30–5

motion in a vacuum, see also change, 112–15 multiple times, see disuniWcation number: numbered number, 194 related to discrete quantities, 194 now (nunc), see also instant: of aevum, 91 n. 44, 270–3 of eternity, 270, 302 distinguished only conceptually from eternity, 303 existence in now of eternity, 91 n. 44, 301 identiWed with God, 303 the standing now, 28 n. 24, 183 n. 19, 323 of time, 27–30 analogy with geometrical point, 28 divisibility of temporal now, 28–30 indivisibility of temporal now, 27–8 proper & extended senses, 29 the Xowing now, 27 n. 24, 175 n. 11, 182–5 omnipotence, 114–15 and changing the past, 121 omniscience: omniscience and A and B theory accounts of time, 180, 189 omniscience as causing events in the world, 181 occasionalism, 110 n. 15 objectivism and conventionalist theories of measurement: distinction between, 202–3 medieval attitude to, 202–3, 222 period: can only exist in the present instant in a mind, 176 irreducibility of periods to instants, 45 of time, 30–1 origins of term, 30

Subject Index perpetuity: deWnition and uses, 247, 251–5 deWnition of, 252 sempiternity, equivalence to, 254–5 plurality: of worlds, 75 n. 27, 80 n. 32 of times, 87 priority: diVerent notions of priority, 96 n. 1 distinction between temporal priority and prior in nature, 97 of nature, 99 treated as a metrical rather than topological property, 98 present, see also instant: as a continuous part of time, 26–7 boundary between past and future, 25 logically indivisible, 25 prime matter, 69 n. 21, 72 limitlessness, 249–50 Primum Mobile: Averroan conception, 78–9 as cause of temporal becoming, 188, 191, 230 as the material cause of time, 137 as the Privileged Clock, 208–19 as the subject of time, 80 n. 32, 137, 262, 309 confused motion before the existence of the Primum Mobile, 145 created on the fourth day of creation, 144 destruction of, 81 eternal particulars are not causally inXuenced by Primum Mobile, 230 impossibility of multiple prima mobilia, 82–7 its nature and role in transmitting motion, 77–8, 212 Primum Mobile measures motion, 198, 207 relationship to time, 280 role in relation to temporal Xow, 182, 184 n. 20, 185, 262 scholastic interpretations of the Primum Mobile, 212 n. 27

363

time before and after the Primum Mobile, 216–17, 310 time is related to the Primum Mobile, 158, 176, 138, 185, 191, 215 n. 30, 217, 230 real time: as opposed to imaginary time, 82, 165–92, 188, 190 as opposed to time existing merely materially, 167 realism and anti realism: in relation to conventionalism and objectivism, 202 relations: accounts of relations do not cohere with philosophy of time, 163 background to medieval account of relations, 131 n. 1 distinction between mutual and non-mutual relations, 133–4 distinction of real relations and relations of reason, 133 medieval account of relations, 131–4 modal relations, 150–1 temporal relations are real relations, 140 reductionism, see relationism; questions about temporal topology reduced to Primum Mobile, 185 temporal reductionism, 43–9 relationism: instants reducible to periods, Ch. 1 modal relationism, 149–52 motion reducible to spatial topology, 135–7, 140 time reducible to motion, 135–64 rest: objects at rest, 151 relationship of objects at rest to time, 228 universal rest, 152

364

Subject Index

simultaneous (simul): acts & states of beatitude, 116 n. 23 Aristotle’s deWnition of temporal simultaneity, 59 contemporary misunderstandings of ‘simul’, 53 diVerent senses of ‘simul’, 51–3 physical changes cannot occur simultaneously, 117 simultaneity of equal and unequal times, 58–9, 82 simultaneity of God, humans and angels, 91 n. 44 simultaneity of God with creation, 126–7 simultaneity of instants and periods, 58 simultaneity of nature, 51, 53–7 simultaneity of space, 51 simultaneity of time, 51, 57–9 simultaneous causation leads to contradictory states, 118 simultaneous causes in the angelic fall, 115 time was created simultaneous with nature, 159 n. 29 specious present, 16–18 when the quando as a temporal element, 40 when the quando as a pan-durational element, 41 God, angels and motion in a quando, 41, 302 quando as the present, 42, 188 n. 24 souls, see angels: blessed souls exhibit variation, not change, 235 n. 15 body-soul relation to time, 261, 280 souls are non temporal, 234, 237 n. 16 time exists when a soul measures it, 167 supervenience, 45–8 sempiternity: deWnition and us, 247–51, 252 equivalence to perpetuity, 254–5 limitlessness of, 250–1

of angels, 249 n. 7 of God, 251 temporal senses of the word ‘semper’, 315 n. 4 substantialism, see absolutism temporal becoming, see also A and B theory of time: caused by Primum Mobile, 188, 191 reality of temporal becoming, 177–89 temporal unity, see also disuniWcation: arguments relating to temporal unity, 64–91 tensed theory of time, see A and B theory of time Time, see also other categories as relevant: argument against the existence of time, 172–6 arguments relating to temporal unity, 64–91 Aristotle rejects multiple times, 93 as a ‘space’, 31 n. 28 atomism of time, 15–16, 44 body-soul relation to time, 261, 280 causal theory of time, 100–24 causal theory of time, thirteenth century attitudes to, 95 concomitance of time with other durations, 91 n. 44, 126 criteria for existence in time, 226–36 deWnition of, 138 n. 8, 148, 193, 217 essence and esse of time, 184 n. 20 everlastingness, deWnition of, 244–5 existence with time, 91 n. 44, 250 n. 8 exists in reality, 65, 190, 278 n. 41 exists materially and formally, 167 experience of time, 165–6 freewill has its own temporal measure, 86 n. 39 geometric models of time, 14, 64, 159, 184 Immaculate Conception depends on a temporally later cause, 122–3

Subject Index indivisibility of temporal boundaries, 15, 25 language about time, 23–44 modal account of temporal experience, 168 multiple times required for theological purposes, 93 now of time, 27–30 of the blessed and the damned, 81, 87, 216–17, 281, 294, 230, 310 omnipotence and changing the past, 121 omniscience and A and B theory accounts of time, 180, 189 privileged clock, 212–19 relationship to motion, 83, 152 relationship to the Primum Mobile, 198, 217, 262, 280 simultaneity of time, 51, 57–9 successive (extensional) existence, 36–7, 49 ‘subject’ of time, 75–9, 81, 85, 137, 146–7, 262, 304 time before time, 155–6 time exists when a soul measures it, 167 time is a created entity, 149 n. 18 time is an accident, 12, 79, 83–4, 136, 146, 198, 262, 304 time is Wnite and bounded at both ends, 159 n. 29 temporal parts and boundaries, 14–15 temporal relations, see also simultaneous, 134–52

365

temporal relations as constitutive of time, 50 n. 1 temporality is identiWed with corruption and decay, 229 topology of time, 82 n. 33 unity of matter explains the unity of time, 86 uses of ‘time’ & its cognates, 159 n. 29, 214–19, 229, 234–5 togetherness, see also concomitance: common quando between durations, 314 non temporal, non simultaneous durational togetherness, 89–90 present as an expression of togetherness, 314 n. 4 use of ‘cum’, 89, 314 n. 4 use of ‘simul’, 89, 314 topology, see also aevum; eternity: confused with temporal metric, 66, 84–5, 86 n. 39, 89 n. 41, 94, 98, 135, 194, 224 derives from the Primum Mobile, 183 n. 19, 185, 219 exists independently of a mind, 171 of time, 82 n. 33 relationship with space, 140–3, 185 timelessness: deWnition of, 244–5 extrinsic timelessness, 60 n. 14 of God, 325–9 timeless knowledge, 180 Trinity, 55–7, 131 Truths: truths of reason and truths of fact, 203

Index of Ancient and Medieval Text References Bible: Gen. 1:1 Josh. 10:12 Wisd. 11:20 Ps. 148 Eccles. 1:4 18:1 Rom. 16:25 Titus 1:2 Apoc. (Rev.) 10:6 Albert: de Caelo 1. 2. 1 1. 2. 7 1. 2. 2 1. 3. 7 2. 2. 5 2. 2. 6

159 144 194 283 283 314 283 283

n. 29 n. 13 n. 3 n. 1 n. 1 n. 4 n. 1 n. 1

159 n. 29, 174 n. 36 16 n. 8, 46 n. 53 46 n. 53 32 n. 29 249 n. 7 209 n. 23 209 n. 22, 210 n. 24, 211 n. 26, 256 n. 15 46 n. 53, 48 n. 55

3. 1. 2 de Gen. et Cor. 1. 1. 11 16 n. 8 2. 3. 4 31 n. 28 2. 3. 5 30 n. 27 de Natura loci 1. 5 31 n. 28 de Prin. Mot. Proc. 1 14 n. 5 de Sacramentis 5. 4 76 n. 28 In Sent. 1. 8. A. 8. 36 n. 35 1. 8. A. 8 ad 5 40 n. 41 1. 8. A. 8 ad 9 52 n. 3 1. 8. A. 8 169 n. 6, 258 n. 17, 259 n. 18,

288 n. 34, 299 n. 148, 305 n. 58, 313 n. 3 1. 8. A. 8 ad 5 36 n. 35 1. 8. A. 8 ad 9 52 n. 3 1. 8. A. 8 ad 12 26 n. 23 1. 8. A. 9 197 n. 5, 289 n. 35, 292 n. 38, 305 n. 58 1. 8. A.12 26 n. 22, 31 n. 28, 110 n. 15, 138 n. 8, 169 n. 6, 226 n. 2, 229 n. 6, 232 n. 11, 233 n. 13, 257 n. 16, 276 n. 38, 278 n. 40, 313 n. 3 1. 8. B. 13 122 n. 26, 184 n. 20, 1. 8. B. 13 ad 2 263 n. 24, 302 n. 54 1. 8. B. 13. 2 201 n. 10, 206 n. 18, 207 n. 20, 278 n. 40 1. 9. 1. 2 18 n. 10 1. 9. A. 1 37 n. 36, 227 n. 3 1. 9. A. 2 285 n. 11, 285 n. 15 1. 9. A. 3 52 n. 3, 53 n. 4, 207 n. 20, 260 n. 19 1. 9. A. 3 sed con 1 52 n. 3 1. 9. A. 3. 2 204 n. 15 1. 9. A. 3 ad 1 263 n. 24 1. 9. A. 3 ad 4 227 n. 3, 272 n. 33 1. 9. A. 3. 2 268 n. 30 1. 9. A. 3. 2 ad 1 268 n. 30 1. 9. B. 5 54 n. 6, 56 n. 8, 126 n. 31, 183 n. 19 1. 9. B. 5 ob 5 55 n. 7, 311

Index of Ancient and Medieval Text References 1. 9. B. 5 sed con 1 1. 9. B. 5 sed con 2 1. 9. B. 5 sed con 3 1. 9. B. 5 sed con 4 1. 14. B. 10 1. 30. B. 4 1. 30. B. 4 ad 1 1. 30. B. 7 ad 2 1. 38. A. 1 2. 1. B. 10 2. 6. C. 3 4. 12. E. 16 Lib. de Causis 1. 1. 10 2. 1. 8 2. 1. 9 2. 1. 10 2. 3. 1 2. 4. 7 Lib de Praed. 3. 4 3. 9 3. 9 ad 2 4. 1 4. 2 4. 7 4. 10 Meta. 2. 9 5. 2. 11 5. 3. 1 5. 3. 2 5. 3. 7 8. 2. 1 9. 4. 1

56 n. 8 51 n. 2, 58 n. 11 96 n. 2 110 229 240 185

n. 15 n. 6, 234 n. 14, n. 19 n. 23

Phys. 3. 1. 1 3. 1. 7 3. 4 4. 2. 6 4. 2. 7 4. 3. 1 4. 3. 2 4. 3. 3

137 n. 7 283 n. 1 181 n. 17 214 n. 29 107 n. 11 76 n. 28

4. 3. 4 4. 3. 5 4. 3. 6 4. 3. 7

41 n. 42 155 n. 25–6, 287 n. 32, 289 n. 35 237 n. 16 302 n. 54 252 n. 9 183 n. 19 25 n. 19, 26 n. 22 25 n. 21, 28 n. 24 26 n. 23 136 n. 6 132 n. 2, 151 n. 21 54 n. 6, 55 n. 7, 134 n. 4 136 n. 6, 151 n. 21 110 n. 15 99 n. 4 14 n. 4, 137 n. 7, 141 n. 11, 186 n. 23 14 n. 5, 18 n. 10, 183 n. 19, 184 n. 20, 185 n. 22 132 n. 2, 134 n. 4, 150 n. 20, 110 n. 15 104 n. 8

4. 3. 8 4. 3. 9 4. 3. 10 4. 3. 11 4. 3. 13

4. 3. 16 4. 3. 17

4. 4. 1 4. 4. 2 4. 4. 3 4. 4. 4 5. 1. 3 5. 2. 1 5. 2. 3 5. 3. 3 6. 1 6. 1. 1

367

21 n. 14, 22 n. 15, 107 n. 12 18 n. 10 184 n. 21 59 n. 12, 109 n. 14, 112 n. 17, 113 n. 19 17 n. 9, 59 n. 12, 173 n. 8 63 n. 16, 83 n. 35, 83 n. 36 32 n. 29, 144 n. 13, 158 n. 28 139 n. 9, 158 n. 28, 137 n. 7, 141 n. 10–11, 143 n. 12, 186 n. 23 27 n. 24, 141 n. 11, 175 n. 11, 183 n. 19 183 n. 19, 183 n. 20, 186 n. 23 183 n. 20 66 n. 18, 167 n. 4, 195 n. 3, 204 n. 15 185 n. 23, 229 n. 6 228 n. 5 35 n. 34, 41 n. 42, 42 n. 44, 63 n. 15, 99 n. 4, 107 n. 12, 158 n. 28, 185 n. 23, 228 n. 5 90 n. 42, 168 n. 5, 231 n. 9 54 n. 6, 66 n. 18, 137 n. 7, 186 n. 23, 196 n. 4, 199 n. 8, 204 n. 16, 207 n. 19 232 n. 12, 289 n. 35 36 n. 35, 183 n. 19, 316 n. 5 297 n. 43, 325 n. 16 226 n. 2, 305 n. 58, 314 n. 4, 317 n. 6, 324 n. 14 107 n. 12 51 n. 2 20 n. 12, 20 n. 13 25 n. 19 18 n. 10 22 n. 15, 34 n. 33

368

Index of Ancient and Medieval Text References

Albert (cont.) 6. 1. 3 6. 2. 2 6. 2. 8 6. 2. 11 6. 3. 1 6. 3. 4 8. 1. 1 8. 1. 12 8. 1. 13 8. 3. 6

16 n. 8 186 n. 23 90 n. 42 228 n. 5 34 n. 33 186 n. 23 197 n. 5 110 n. 15, 118 n. 24 90 n. 42, 285 n. 18 15 n. 6, 28 n. 24, 105 n. 9 8. 3. 9 207 n. 20, 208 n. 22, 209 n. 23, 217 n. 31 Scientia libri de lineas Indivis. 1 34 n. 33 Sum. de Creat. 2. 2. 3 ad 1 36 n. 35 2. 2. 6 203 n. 13 2. 3. 1 240 n. 19, 292 n. 39 2. 3. 1 ad 2 259 n. 18 2. 3. 2 39 n. 40, 137 n. 7, 183 n. 20, 185 n. 23, 199 n. 8, 226 n. 2, 237 n. 16, 262 n. 23, 285 n. 16, 287 n. 33, 288 n. 34, 297 n. 45, 314 n. 4 2. 3. 2 ad 1 52 n. 3 2. 3. 2 ad 2 51 n. 2 2. 3. 3 283 n. 1, 302 n. 54 2. 3. 3 ad 6 98 n. 3, 160 n. 30, 237 n. 16, 238 n. 16, 242 n. 21 2. 3. 4 282 n. 1, 284 n. 3, 296 n. 43 2. 3. 4 ad 3 300 n. 49 2. 3. 5 42 n. 43, 302 n. 54, 304 n. 56 2. 4 256 n. 16 2. 4. 1 52 n. 3, 268 n. 29, 269 n. 30, 271 n. 32, 276 n. 38, 286 n. 23 2. 4. 1 ad 1 235 n. 15 2. 4. 2 79 n. 31 2. 5. 1 34 n. 33, 43 n. 49, 51 n. 2, 173 n. 8 2. 5. 2 216 n. 30

2. 5. 3 2. 5. 10 2. 5. 11 partic 3 Sum. Theol. 4. 20. 3 5. 1. 1. 1 5. 22 5. 22.1 5. 22. 1

5. 22. 1 ad 3 5. 22. 2. 1

5. 22. 2. 2

5. 23. 1. 1 5. 23. 1. 1. 1 5. 23. 1. 1. 1 ob 8 5. 23. 1. 1. 1 ad 8 5. 23. 1. 1. 1 ad.2 5. 23. 1. 1. 2 5. 23. 1. 1. 2 ad 3 5. 23. 1. 1. 2 ad 7 5. 23. 1. 2. 1 5. 23. 1. 2. 2 A 5. 23. 1. 2. 2. B 5. 23. 2. 1

27 n. 24 87 n. 39, 89 n. 41 188 n. 24 290 n. 36 14 n. 5 305 n. 59 196 n. 4 28 n. 24, 176 n. 12, 182 n. 19, 183 n. 20, 185 n. 23, 186 n. 23, 201 n. 11, 230 n. 7, 256 n. 15, 285 n. 14, 286 n. 27, 286 n. 28, 304 n. 56, 305 n. 58 40 n. 41, 285 n. 16 39 n. 40, 143 n. 12, 260 n. 19, 260 n. 20, 262 n. 22, 266 n. 27, 272 n. 34 182 n. 19, 183 n. 19, 183 n. 20, 196 n. 4, 204 n. 15, 206 n. 17, 302 n. 54 313 n. 3 36 n. 35, 229 n. 6, 248 n. 5, 297 n. 45, 303 n. 55 51 n. 2 52 n. 3 37 n. 36 227 n. 3, 252 n. 11, 40 n. 41, 285 n. 16, 289 n. 35, 290 n. 36 292 n. 38 249 n. 7, 253 n. 12 285 n. 11, 296 n. 43 159 n. 29, 195 n. 3 257 n. 16, 301 n. 51 258 n. 17, 259 n. 18, 260 n. 20,

Index of Ancient and Medieval Text References 5. 23. 2. 1 ad 7 5. 23. 2. 2. B 5. 23. 2. 2. 1 5. 23. 2. 2. 2 5. 23. 3. 1 5. 23. 3. 2 5. 23. 3. 3 5. 23. 3. 3. 1 5. 23. 3. 3. 2 9. 37 9. 38 9. 39. 1 9. 41. 2. 1 Super Diony. de Div. Nom. 4 [46] 10 [5] Alexander of Hales: In Sent. 1. 8 [7] 1. 9 [6] 1. 9 [12] 1. 30 [2] 2. 1 [13] 2. 1 [14] 2. 2 [7] 2. 3 [33] 2. Appendix

Sum. Theol. 1. 1. 1. 1. 1. 3. 3 1. 1. 2. 1. 4. 1 1. 1. 1. 2. 4. 1. 1. 1 1. 1. 1. 2. 4

270 n. 31, 272 n. 33, 283 n. 1

1. 1. 1. 2. 4. 1. 1. 2

269 n. 30 139 n. 9, 159 n. 29 256 n. 15, 263 n. 24, 264 n. 25, 268 n. 30 231 n. 9, 262 n. 23, 263 n. 24 216 n. 30, 276 n. 38 63 n. 16, 87 n. 39, 89 n. 41 79 n. 30 196 n. 4 91 n. 44, 214 n. 28 132 n. 2 131 n. 1 133 n. 3, 151 n. 21 56 n. 8

1. 1. 1. 2. 4. 1. 1. 2 ad 15 1. 1. 1. 2. 4. 1. 2 1. 1. 1. 2. 4. 1. 3 1. 1. 1 2. 4. 2 1. 1. 1. 2. 4. 2. 1 1. 1. 1. 2. 4. 2. 1 ad 1 1. 1. 1. 2. 4. 2. 1 ad 2 1. 1. 1. 2. 4. 2. 3 1. 1. 1. 2. 4. 2. 4 ad 1 1. 1. 1. 2. 4. 2. 4 ad 7 1. 1. 1. 2. 4. 2. 4 ad 15 1. 1. 1. 2. 4. 3 1. 1. 1. 2. 4. 3. 1 1. 1. 1. 2. 4. 3. 1 ad 2 1. 1. 1. 2. 4. 3. 1 ad 4 1. 1. 1. 2. 4. 3. 2 1. 1. 1. 2. 4. 3. 2 ob 3 1. 1. 1. 2. 4. 3. 3 ad 2 1. 1. 1. 2. 4. 3. 3 ad 3 1. 1. 1. 2. 4. 3. 4. 1

25 n. 21 34 n. 33 284 n. 6 303 n. 55 286 n. 24, 289 n. 35 287 n. 32 57 n. 9 251 n. 8 159 n. 30 107 n. 12 139 n. 8, 141 n. 10, 188 n. 24, 229 n. 6, 235 n. 15, 237 n. 16, 240 n. 19, 255 n. 15, 266 n. 27, 287 n. 31, 303 n. 55 290 n. 36 50 n. 1 247 n. 4 217 n. 31

1. 1. 1. 2. 4. 3. 4. 2 1. 1. 1. 2. 4. 3. 4. 2 ad 2–3 1. 1. 1. 2. 4. 3. 4. 2 ad 5 1. 1. 1. 2. 4. 4. 1

369

259 n. 19, 284 n. 2, 319 n. 8 217 n. 31 252 n. 9, 289 n. 35 269 n. 30 327 n. 18 285 n. 11 284 n. 6 237 n. 16, 239 n. 18 284 n. 6 290 n. 36, 292 n. 39 290 n. 36 217 n. 31 302 n. 54 257 n. 16, 271 n. 33 247 n. 4 262 n. 23 257 n. 16, 260 n. 20 263 n. 24 263 n. 24, 274 n. 36 274 n. 36 144 n. 13, 215 n. 30 274 n. 36, 281 n. 42 260 n. 19 252 n. 9 247 n. 4

370

Index of Ancient and Medieval Text References

Alexander of Hales (cont.) 1. 1. 1. 2. 4. 1. 1. 1 27 n. 24 1. 1. 1. 2. 4. 2. 4 36 n. 35 1. 1. 1. 2. 4. 3. 2 67 n. 19, 70 n. 21, 79 n. 30, 80 n. 32, 83 n. 36, 209 n. 22 1. 1. 1. 2. 4. 1. 3 52 n. 3 1. 1. 1. 2. 4. 1. 3 ad.4 52 n. 3 1. 1. 1. 2. 4. 3. 3 ad 3 88 n. 40 1. 1. 1. 2. 4. 3. 4. 1 183 n. 19 1. 1. 2. 1. 4. 2 57 n. 9, 97 n. 3 1. 1. 2. 1. 4. 2 ad 2 57 n. 9 1. 1. 1. 5. 2. 1 291 n. 37 2. 1. 2. 2. 4. 1. 1 ad 6 91 n. 44 2. 1. 1. 1. 2. 2. 5 90 n. 42 2. 2. 1. 2. 2. 4. 1. 1 ad 5 247 n. 4 2. 4. 2. 2. 2. 2 52 n. 3 Algazel: Metaphysics 96 n. 1 Anselm: Cur Deus Homo 2. 16 122 n. 27 de Veritate 13 63 n. 16 Monologium 22 320 n. 10 Aristotle: Cat. 1 20 n. 12, 22 n. 15 6 173 n. 8 7 133 n. 3 12 96 n. 1 13 51 n. 2, 54 n. 5, 57 n. 10, 59 n. 12, 59 n. 13 de Caelo 1. 8 82 n. 35

2. 6 de Int. 1. 13 Gen. et Cor. 2. 10 Phys. 3. 7 4 4. 1 4. 10–12 4. 10

4. 11

208 n. 22, 210 n. 24 229 n. 6 30 n. 27 141 n. 10 199 n. 8 143 n. 12 183 n. 19 27 n. 24, 59 n. 12, 82 n. 35, 96 n. 1, 135 n. 5, 173 n. 8 11 n. 2, 27 n. 24, 28 n. 24, 141 n. 10, 166 n. 1, 193 n. 1, 261 n. 21 228 n. 5 27 n. 24 169 n. 6 20 n. 12 14 n. 5 17 n. 9, 21 n. 14 141 n. 11

4. 12 4.13 4. 14 5.3 6.1 6.2 6. 4 Post. Anal. 2. 12 110 n. 15 Meta. 5. 11 96 n. 1, 98 n. 3 5. 15 131 n. 1 7. 7 228 n. 5 9. 8 96 n. 1 10 201 n. 11 Aquinas, Thomas: Com. in Isaiah. Prol. 2 30 n. 27 Compend. Theol. 23 304 n. 57 Con. Err. Graec. 1. 2 57 n. 9 Contra Impugnantes 24 [1] 288 n. 34 de Aetern. Mun. [7] 159 n. 29, 292 n. 39 de Gen. et Cor. 1.3 [20] 16 n. 8 1.3 [23] 16 n. 8 de Sen. et Sen. 18 [270–7] 17 n. 9

Index of Ancient and Medieval Text References de Interpretatione 1. 5 [12] 1. 14 239 n. 19 1. 14 [194] 312 n. 3 de Sub. Sep. 9 256 n. 15, 269 n. 30 19 261 n. 21 In de Caelo 1. 4 [41] 217 n. 31 1. 4 [45] 210 n. 24 1. 4 [49] 210 n. 24 1. 12 [122] 15 n. 6, 18 n. 10 1. 21 [215] 249 n. 7, 285 n. 12, 289 n. 35, 297 n. 45 2. 6 [356] 206 n. 17, 208 n. 22 2. 8–9 209 n. 22 2. 8 [368] 203 n. 13 2. 8 [372] 209 n. 23, 256 n. 15, 2. 8 [373] 211 n. 26 2. 9 [374] 211 n. 26 2. 9 [379] 208 n. 22 2. 11 [389] 289 n. 35 In de Div. Nom. 4. 3 196 n. 4 4. 5 [1] 196 n. 4 5. 1 197 n. 5, 203 n. 14 10. 2 [862] 325 n. 16, 326 n. 16 10. 3 [875] 239 n. 18, 287 n. 31, 295 n. 41, 296 n. 43, 315 n. 4 In de Trin. 5. 3 ad 5 186 n. 23 In Eth. Nic. 1. 6 136 n. 6 In lib. de Anima. 3.11 [756] 24 n. 18 In lib. de Sensu et Sensato 1. 16 [245] 109 n. 14 In lib. Peri. 1.5 [12] 25 n. 21 In lib. Post. Anal. 1. 36. [318] 203 n. 15, 201 n. 10 2. 10 [505] 52 n. 3 2. 11 [519] 34 n. 33

371

In Meta. 3.13 [507] 18 n. 10 5. 8 [872] 212 n. 27 5. 13 [936–40] 99 n. 4 5. 13 [937] 141 n. 10 5. 13 [941] 289 n. 35, 292 n. 38 5.15 [977] 14 n. 4, 173 n. 8 5.19 [1044–5] 18 n. 10 9. 7 [1848] 104 n. 8 10. 2 [1938] 195 n. 3 10. 2 [1939–40] 195 n. 3 10. 2 [1945] 212 n. 27 10. 2 [1950] 195 n. 3 In Phys. 1. 3 [22] 22 n. 16 2. 6 [195] 126 n. 32 3. 1 [277] 21 n. 14 3. 1 [280] 132 n. 2 3. 2 [285] 138 n. 8 3. 2 [294] 148 n. 17 3. 5 [322] 198 n. 6 3. 12 [393–5] 21 n. 14 4. 1 [406] 186 n. 23 4. 12 [529] 112 n. 17 4. 12 [534–6] 113 n. 19 4. 12 [539] 113 n. 18 4. 15 59 n. 12 4. 15 [559] 173 n. 8 4. 15 [560] 173 n. 8 4. 15 [562] 64 n. 16 4. 16 [566] 83 n. 35 4. 16 [567] 225 n. 1 4. 16 [568] 135 n. 5 4. 16 [569] 135 n. 5 4. 16 [570] 170 n. 7 4. 17 65 n. 17 4. 17 [574] 139 n. 9, 208 n. 21 4. 17 [575] 141 n. 10 4. 17 [576] 137 n. 7 4. 17 [580] 141 n. 11, 143 n. 12 4. 17 [581] 195 n. 3 4. 18 [583] 184 n. 20 4. 18 [584] 323 n. 12 4. 18 [585] 184 n. 20 4. 18 [586] 301 n. 51 4. 18 [590] 141 n. 11 4. 20 229 n. 6 4. 20 [602] 232 n. 11, 249 n. 7 4. 20 [611] 232 n. 12

372

Index of Ancient and Medieval Text References

Aquinas, Thomas (cont.) 4. 21 [615–17] 28 n. 24 4. 23 88 n. 41 4. 23 [626] 152 n. 22, 176 n. 11 4. 23 [629] 169 n. 6, 170 n. 7 4. 23 [630–37] 79 n. 31 4. 23 [631–3] 146 n. 15 4. 23 [631] 229 n. 6 4. 23 [633] 64 n. 16, 65 n. 18, 83 n. 35 4. 23 [633–6] 85 n. 38 4. 23 [635] 208 n. 21, 208 n. 22 5. 5 [691] 20 n. 12 6. 1 [755] 14 n. 5 6. 1 [757] 21 n. 14 6. 2 59 n. 12 6. 2 [758–65] 16 n. 8 6. 2 [762] 138 n. 8 6. 2, [765] 14 n. 5 6. 3, [769] 15 n. 6 6. 5 [788] 29 n. 26 6. 5 [789] 18 n. 10 6. 5 [792] 29 n. 26 8. 2 [976–8] 152 n. 23 8. 2 [979] 148 n. 17 8. 2 [983] 159 n. 30 8. 2 [988–9] 149 n. 18 8. 2. [990] 34 n. 33, 155 n. 26, 300 n. 49 8. 2 [992] 286 n. 22, 287 n. 31 8. 17 [1122] 43 n. 49, 105 n. 9 8. 21 [1146] 113 n. 19 8. 21 [1146–9] 114 n. 20 In Sent. 1. 8. 2. 1 37 n. 37, 318 n. 7 1. 8. 2. 1 ad 6 36 n. 35, 301 n. 50 1. 8. 2. 2 305 n. 58 1. 8. 2. 2 ad 4 284 n. 3, 289 n. 35, 292 n. 38 1. 8. 3 ad 3 231 n. 9 1. 8. 4. 2 ad 3 195 n. 3, 196 n. 4, 198 n. 6, 203 n. 15 1. 8. 4. 3 304 n. 57 1. 14. 1. 1 ob 3 33 n. 32 1. 14. 1. 1 ad 3 303 n. 55 1. 19. 2. 1. 36 n. 35, 37 n. 36, 137 n. 7, 138 n. 8, 167 n. 4 1. 19. 2. 1 ad 3 260 n. 19, 283 n. 1 1. 19. 2. 1 ad 5 272 n. 34, 283 n. 1

1. 19. 2. 2 1. 19. 2. 2 ob 4 1. 19. 2. 2 ad 1 1. 19. 2. 2 ad 2 1. 20. 1. 3 1. 24. 1. 1 1. 24. 1. 2 ob 4 1. 26. 2. 1 1. 27. 1. 1 ad 2 1. 33. 1. 1 ad 1 1. 35. 1. 4 ad 2 1. 37. 2. 1 ad 4 1. 37. 4. 3 1. 37. 4. 3 ob 2 1. 37. 4. 3

1. 37. 4. 3 ad 7 1. 40. 3. 1 ad 5 1. 44. 1. 4 2. 2. 1. 1 2. 2. 1. 1 ad 3 2. 2. 1. 1 ad 4 2. 2. 1. 1 ad 5 2. 2. 1. 1 ad 6 2. 2. 1. 2

2. 2. 1. 2 ad 1 2. 2. 1. 2 ad 2 2. 2. 1. 2 ad 4 2. 2. 1. 2 ad 3 2. 2. 2. 2. 1 2. 5. 2. 2 ad 1 2. 6. 1. 2 2. 9. 1. 1 ad 2 2. 19. 1. 4 3. 3. 5. 2 ad 4 3. 5. 1. 1 3. 18. 1. 3 3. 18. 1. 3 ob 1 3. 18. 1. 3 ad 1 3. 18. 1. 3 ad 3 3. 18. 1. 3 ad 4

196 n. 4, 287 n. 32, 302 n. 54, 303 n. 55, 327 n. 18 304 n. 56 91 n. 44, 328 n. 18 286 n. 27 56 n. 8 203 n. 15 196 n. 4 134 n. 4 136 n. 6 132 n. 2 201 n. 10 324 n. 14 25 n. 21 34 n. 33 50 n. 1, 82 n. 33, 105 n. 9, 137 n. 7, 138 n. 8, 139 n. 9, 184 n. 21 186 n. 23 285 n. 20 121 n. 26 26 n. 35, 201 n. 11, 297 n. 45, 305 n. 58 196 n. 4 260 n. 19, 275 n. 37 269 n. 30 21 n. 14 65 n. 18, 71 n. 21, 72 n. 24, 74 n. 26, 79 n. 31, 137 n. 7, 138 n. 8, 155 n. 26 198 n. 6 260 n. 19, 260 n. 20 81 n. 33 203 n. 15 126 n. 32 54 n. 5 107 n. 11, 116 n. 21 229 n. 6 30 n. 27 25 n. 21 131 n. 1 116 n. 22, 117 n. 23 97 n. 2 97 n. 3, 118 n. 24 99 n. 5 114 n. 20

Index of Ancient and Medieval Text References 3. 22. 3. 2b ob 1 3. 23. 1. 1 3. 37. 1. 4 sed con 2 4. 11. 1. 3 4. 11. 1. 3b 4. 43. 1. 3b ob 1 4. 44. 2. 3 4. 44. 2. 3 ad 5 4. 44. 2. 3c ob 2 4. 44. 2. 3c ad 3 4. 46. 1. 3 4. 48. 2. 2 ob 9 4. 49. 1. 2 ad 3 4. 49. 1. 2. 3

109 n. 14 196 n. 4 203 n. 15 137 n. 7, 138 n. 8 112 n. 17 30 n. 27 17 n. 9 217 n. 31 112 n. 17 112 n. 17 32 n. 29 24 n. 18 272 n. 34 237 n. 16, 260 n. 19, 287 n. 32

4. 50. 2. 2. 1 ad 3 229 n. 6 Opusc. de Rationibus Fidei 10 286 n. 27, 301 n. 51 Quaest. Disp. de Caritate 2. 6 322 n. 11 Quaest. Disp. de Pot. 1. 4 ob 2 203 n. 14 3. 10 ad 8 261 n. 21 3. 14 ob 2 37 n. 37 3. 14 ob 6 114 n. 20 3.17 ad 15 24 n. 18, 34 n. 33 3. 17 ad 20 37 n. 37, 155 n. 26 3. 19 ob 5 273 n. 35 4. 2 ad 19 260 n. 19 5. 5 ad 10 228 n. 5 7. 7 ad 1 201 n. 10 7. 8 ad 1 55 n. 7 7. 10 196 n. 4 7. 11 134 n. 4 8. 1 131 n. 1 8. 2 ad 10 24 n. 18 9. 5 ob 12 196 n. 4 9. 7 sed con 7 22 n. 15 Quaest. Disp. de Ver. 1. 5 198 n. 6, 284 n. 10 1. 5 ad 16 134 n. 4 2. 12 240 n. 19 3. 3 ad 1 284 n. 9, 286 n. 24

373

5. 3 203 n. 15 8. 4 ob 15 287 n. 31 8. 14 ad 12 269 n. 30 12. 10 284 n. 7 21. 1 ob 9 132 n. 2 23. 2 ob 8 286 n. 24 23. 2 ad 8 286 n. 22 23. 7 196 n. 4 24. 12 107 n. 12 28.2 ad 10 24 n. 18 29. 8 107 n. 11 29. 8 ob 6 25 n. 21, 183 n. 19 29. 8 sed con 8 109 n. 14 29. 8 ad 4 117 n. 23, 253 n. 12 Quaest. Disp. de Malo. 4. 6 ob 13 32 n. 30 4. 6 ad 13 105 n. 9 5. 5 ad 6 31 n. 28 16. 2 ob 7 25 n. 21 16. 4 141 n. 10, 159 n. 29, 228 n. 5, 275 n. 37, 278 n. 40 16. 7 ob 16 139 n. 9 16. 7 ad 3 238 n. 17 16. 9 ob 7 139 n. 9 16. 10 ob 5 139 n. 9 Quaest. Disp. de Spir. Creat. 9 ad 11 199 n. 7 Quaest. Disp. De Virt. in Com. 11 ad 10 200 n. 9 Quaest. Quodlib. 2. 3. 5 203 n. 15 5. 3. 2 203 n. 15 5. 4. 1 257 n. 16, 260 n. 19, 263 n. 24, 283 n. 1 5. 4. 7 229 n. 7, 231 n. 9,260 n. 19 7. 4. 2 24 n. 18, 25 n. 21, 106 n. 9 7. 4. 2 ob 2 201 n. 11 7. 4. 2 ob 4 105 n. 9 7. 4. 2 ad 3 107 n. 11 7. 4. 2 ad 4 105 n. 9 7. 10. 2 ad 3 201 n. 11 9. 4. 3, 24 n. 18 9. 4. 4 25 n. 21 9. 4. 4 ob 3 112 n. 17 9. 5. 1 sed con 3 114 n. 20 10. 2 284 n. 4, 286 n. 24

374

Index of Ancient and Medieval Text References

Aquinas, Thomas (cont.) 10. 2. 1 ad 1 314 n. 4 11. 4. 1 ob 1 109 n. 14 12. 1 132 n. 2 Resp. ad Lect. Venet. de 30 Art. 8 32 n. 30 Resp. ad Lect. Venet. de 36 Art. 10 31 n. 28 Sent Lib. Eth. 10. 5 32 n. 30 10.5 [2] 32 n. 30 Sum. Con. Gen. 1. 23 304 n. 57 1. 28 196 n. 4 1. 66 301 n. 51 2. 16 [942] 122 n. 26 2. 19 [960] 109 n. 14 2. 33 25 n. 21 2. 35 284 n. 4, 286 n. 23, 287 n. 31 2. 55 [1299] 256 n. 15 2. 55 [1308] 229 n. 7, 237 n. 16 2. 96 231 n. 9 3. 60 237 n. 16, 260 n. 19 3. 61 201 n. 11, 238 n. 17 3. 61 [2359] 300 n. 49 3. 61 [2361] 320 n. 9 3. 65 323 n. 13 3. 68 [2423] 323 n. 13 3. 68 [2427] 323 n. 13 3. 85 [2614] 32 n. 30 4. 14 131 n. 1 4. 63 [4000] 106 n. 10 4. 97 289 n. 35 Sum. Theol. 1. 3. 4 290 n. 36 1. 3. 6 304 n. 57 1. 7. 1 290 n. 36 1. 7. 3 ad.1 21 n. 14 1. 8 1 325 n. 16 1. 8. 2 324 n. 15, 325 n. 16 1. 9 291 n. 37 1. 10 291 n. 37 1. 10. 1 183 n. 19, 193 n. 1, 284 n. 4, 286 n. 24, 299 n. 48 1. 10. 1 ob 2 37 n. 37, 318 n. 7 1. 10. 1 ad 5 52 n. 3

1. 10. 2 1. 10. 2 ob 3 1. 10. 2. ad 2 1. 10. 3 1. 10. 3 ad 2 1. 10. 4 1. 10. 4 ad 2 1. 10. 4 ad 3 1. 10. 5

1. 10. 5 ad 1 1. 10. 5 ad 5 1. 10. 6

1. 10. 6 ad 1 1. 10. 6 ad 2 1. 11.2 ad 4 1. 11. 3 1. 13. 5 1. 13. 5 ob 3 1. 13. 7 1. 13. 7 ad 6 1. 13. 10 ad 4 1. 14. 4 1. 14. 8 1. 14. 13 1. 14. 13 ad 3 1. 14. 15 ad 3 1. 16. 7 ad 2 1. 25. 2 ob 3 1. 25. 2 ad 3 1. 25. 4 1. 28. 2 1. 33. 1 ad 1 1. 42. 1 ad 1 1. 42. 2 1. 42. 2 ad 4 1. 42. 3 1. 42. 3 ad 2 1. 45. 1

303 n. 55, 318 n. 7 305 n. 58 31 n. 28 227 n. 3, 260 n. 19 284 n. 3, 294 n. 40 284 n. 9 302 n. 54 196 n. 4 201 n. 11, 254 n. 13, 260 n. 20, 267 n. 28, 269 n. 30, 272 n. 34, 287 n. 31 263 n. 24 237 n. 16, 260 n. 19 65 n. 17, 65 n. 18, 67 n. 19, 69 n. 21, 73 n. 25, 85 n. 38, 137 n. 7, 138 n. 8, 263 n. 24 31 n. 28 278 n. 40 14 n. 5 64 n. 16 318 n. 7 196 n. 4 134 n. 4 55 n. 7 318 n. 7 304 n. 57 181 n. 17, 313 n. 3 181 n. 17, 284 n. 8, 286 n. 24 239 n. 18, 312 n. 3 182 n. 18 248 n. 6 114 n. 20 113 n. 19 121 n. 26 304 n. 57 56 n. 8 200 n. 9 90 n. 42 43 n. 49, 250 n. 8, 286 n. 27, 287 n. 32 56 n. 8 57 n. 9 149 n. 18

Index of Ancient and Medieval Text References 1. 45. 4 1. 46–7 1. 46. 1 ob 8 1. 46. 1 ad 6

149 n. 18 158 n. 28 160 n. 31 149 n. 18, 155 n. 26 1. 46. 1 ad 7 34 n. 33 1. 46. 1 ad 8 155 n. 26, 160 n. 31 1. 46. 2 ad 7 292 n. 39 1. 47. 1 ad 3 160 n. 30 1. 50. 1 ad 2 232 n. 12, 249 n. 7 1. 52. 1 278 n. 40 1. 53. 3 227 n. 3, 228 n. 5, 309 n. 1 1. 53. 3 ad 3 275 n. 37 1. 54. 1 ad 1 91 n. 44 1. 55. 3 ad 1 97 n. 3, 99 n. 5 1. 57. 2 237 n. 16 1. 57. 3 314 n. 4 1. 57. 3 ad 2 278 n. 40 1. 58. 2 52 n. 3 1. 61. 2 159 n. 29, 160 n. 31 1. 61. 2 ob 2 232 n. 12, 238 n. 17, 249 n. 7 1. 61. 2 ad 2 238 n. 17 1. 62. 5 ad 2 116 n. 22 1. 63. 5 107 n. 11, 109 n. 14, 116 n. 22, 117 n. 23 1. 63. 5 ad 3 116 n. 22 1. 63. 6 ob 4 39 n. 40 1. 63. 7 ad 3 273 n. 35 1. 63. 7 ad 4 89 n. 41, 266 n. 27, 275 n. 37 1. 63. 8 ad 1 52 n. 3, 116 n. 21 1. 66. 4 ad 3 219 n. 32 1. 79. 8 ad 2 301 n. 52 1. 104. 1 322 n. 12 1. 104. 1 ad 4 322 n. 12 1. 104. 3 ad 3 323 n. 12 1. 105. 2 ob 3 114 n. 20 1. 113. 1 231 n. 9 1. 115. 3 139 n. 9, 231 n. 9 1. 115. 4 139 n. 9 1–2. 5. 4 256 n. 15 1–2. 19. 4 ob 3 203 n. 15 1–2. 19. 4 ad 2 207 n. 19 1–2. 19. 9 203 n. 14

1–2. 31. 2 1–2. 34. 4 ad 2 1–2. 87. 3 ad 1 1–2. 87. 5 ad 2 1–2. 90. 1 1–2. 91. 3 ob 3 1–2. 91. 3 ad 3

375

256 n. 15 208 n. 22 32 n. 29 284 n. 3 203 n. 14 203 n. 15 208 n. 22, 212 n. 27 1–2. 96. 1 ad 3 203 n. 15 1–2. 96. 2 201 n. 11 1–2. 97. 1 208 n. 22 3. 2. 8 ob 1 132 n. 2 3. 8. 7 ad 2 116 n. 21 3. 22. 3 ad 1 124 n. 29 3. 22. 3 ad 2 124 n. 29 3. 22. 6 ad 2 124 n. 29 3. 61. 3 ob 1 121 n. 26 3. 61. 3 ad 1 121 n. 26 3. 62. 6 122 n. 26 3. 77. 1 76 n. 28 3. 77. 2 ad 1 136 n. 6 3. 81 124 n. 29 Super ad Hebraeos 10. 4 285 n. 21 Super ad Rom. 1. 3 197 n. 5 Super ad 1 Thess 4. 2. [101] 32 n. 29 Super Epist. ad Titum 2.3 [70] 31 n. 28 Super Evang. Ioan. 8. 6 116 n. 21 16. 3 284 n. 9 Super Lib. de Causis 2 285 n. 13, 285 n. 17, 287 n. 31 16 203 n. 14 30 255 n. 15 31 33 n. 31 32 286 n. 24 Super 1 ad Corinthios 15. 1 240 n. 19 15. 8 [1007] 32 n. 30 15.8 [1006] 32 n. 29 Super 2 ad Corinthios 4. 5 285 n. 21 Augustine: Conf 4. 16 (28) 174 n. 10 11. 13 (15) 149 n. 18

376

Index of Ancient and Medieval Text References

Aquinas, Thomas (cont.) 11. 14 (17) 149 n. 18, 174 n. 10, 301 n. 51 11. 23 (29) 80 n. 32, 144 n. 13 11. 23 (30) 144 n. 13 12. 29 (40) 96 n. 1 de Civ. Dei. 11. 11 283 n. 1 12. 16 247 n. 4, 283 n. 1 de Gennesi ad Litt. 8. 20. 39 274 n. 36 de Lib. Arb. 2. 8 [21] 247 n. 4 de Vera Religione 10 [18] 274 n. 36 Epistles 18. 2 274 n. 36 In 83 Quaest. 72 256 n. 16 Averroes: In Phys. 4 [71] 112 n. 17, 113 n. 19 4 [92] 59 n. 12 4 [93] 63 n. 16, 83 n. 35 4 [105–7] 24 n. 18, 51 n. 2 4 [106] 152 n. 23, 154 n. 24 4 [117] 229 n. 6, 232 n. 11 4 [118] 152 n. 23 4 [120–21] 28 n. 24 4 [120] 249 n. 7 4 [125] 154 n. 24 4 [126] 42 n. 44 4 [127] 41 n. 42 4 [130] 166 n. 1 4 [131] 167 n. 4 4 [132] 138 n. 8 4 [134] 66 n. 18 5 [22] 50 n. 2 5 [29] 48 n. 55 6 [2] 47 n. 53 6 [22] 17 n. 9 In Praedicamenta 49D-F 302 n. 54 58C-F 95 n. 1, 99 n. 4 Avicenna: Sufficentia 2. 8 112 n. 17, 113 n. 19 2.10 24 n. 18, 28 n. 24, 34 n. 33, 50 n. 1,

51 n. 2, 58 n. 11, 63 n. 16, 79 n. 30, 90 n. 42, 174 n. 10, 253 n. 12 184 n. 21

2. 12 Bacon, Roger Opus Maius 4. 4. 14 265 n. 26 Boethius de Cons. Phil. 2.6 [15] 32 n. 29 de Trin. 1. 4 249 n. 7, 256 n. 15 4 247 n. 4 4. 4 183 n. 19 In Cat. Aristotelis 2 25 n. 20 In Porphyrum 1 25 n. 20 Post. Anal. Aristot. Interp. 2.12 28 n. 24 Bede: de Temporibus 1 32 n. 29 Bonaventure: Com. in Evang. Ioan. 16. 4 ad 1 284 n. 7 Com. in Evang. Luc. 1 [33] 289 n. 35 8 [51] 284 n. 6 18 [30] 299 n. 48 Hex 3 [5] 18 n. 10 22 [3] 116 n. 21 In Sent. 1. 1 dub 7 317 n. 5 1. 3. 2. 2 195 n. 3 1. 5 dub 8 286 n. 26, 286 n. 29 1. 5. 2. 2 dub 8 287 n. 32 1. 8 dub 5 189 n. 24 1. 8. 1 dub 4 286 n. 30 1. 8. 1 dub 7 126 n. 31, 284 n. 4, 286 n. 26 1. 8. 1. 5 265 n. 27 1. 8. 2. 1 304 n. 57 1. 8. 2. 1. 2 arg 2 14 n. 5 1. 9. 1. 2 ad 4 133 n. 3 1. 9. 1. 3. ad 2 36 n. 35 1. 9. 1. 3. 4 289 n. 35

Index of Ancient and Medieval Text References 1. 9. 1. 4 arg 3 1. 9. 1. 4 ad 4 1. 10. 2. 1 1. 12. 1. 1 1. 14. 1. 1 ad 5 1. 17. 2. 1. 2 arg 2 1. 19. 1 dub 4 1. 20. 2. 1 1. 27. 1. 1. 2 fund 2 1. 30 dub 2 1. 30. 1 ad 3 1. 30. 1. 1 1. 31. 2. 1. 3 1. 37. 1. 1 1. 37. 1. 1. 2 1. 37. 1. 1. 2 fund 4 1. 37. 1. 2. 2 1. 37. 2 dub 3 1. 37. 2. 1. 1 con 2 1. 37. 2. 1. 3 ad 2 1. 37. 2. 1. 3 ad 3 1. 37. 2. 2. 3 fund 1 1. 40. 1. 1 ad 3 1. 42. 1. 3 1. 44. 4 ad 4 2. 1 2. 1. 1 dub 4 2. 1. 1. 1. 2 2. 1. 1. 1. 2. ad 3 2. 1. 1. 1. 2, ad 4 2. 1. 1. 2 2. 1. 1. 2 sed con 4 2. 1. 1. 3. 1 2. 1. 1. 3. 2 ob 3 2. 2. 1. 1 2. 2. 1. 1 fund 4

289 n. 35 289 n. 35 318 n. 7 56 n. 8, 96 n. 2 234 n. 14 14 n. 5 284 n. 5, 286 n. 23, 286 n. 25, 289 n. 35 96 n. 2 96 n. 2 241 n. 20 297 n. 45, 303 n. 54 226 n. 2 289 n. 35 181 n. 17 325 n. 16 51 n. 2 284 n. 4, 285 n. 11 215 n. 30, 274 n. 36 232 n. 11 240 n. 19, 324 n. 15 240 n. 19, 324 n. 15 43 n. 49 96 n. 2, 118 n. 24 122 n. 26 289 n. 35 292 n. 39 144 n. 13, 215 n. 30 159 n. 30, 260 n. 19

2. 2. 1. 1. 1 2. 2. 1. 1. 1 ad 2 2. 2. 1. 1. 1 fund 1 2. 2. 1. 1. 1 fund 3 2. 2. 1. 1. 1 fund 6 2. 2. 1. 1. 2

2. 2. 1. 1. 2 ad 4 2. 2. 1. 1. 3 2. 2. 1. 2. 1 2. 2. 1. 2. 2 ob 1 2. 2. 1. 3 2. 2. 2. 1 2. 2. 2. 1. 1. 2 2. 2. 2. 1. 2 sed con 4 2. 3. 2. 1. 2 ad 3 2. 5. 2. 2 ad 2 2. 7. 2. 1. 2 2. 7. 2. 1. 2 ad 3–4

105 n. 9 201 n. 11, 283 n. 1

2. 7. 2. 1. 3 ad 4 2. 12. 1. 1. 3 2. 12. 2. 2 2. 17. 1. 3 2. 18. 2. 2 fund 4 2. 24. 1 dub 1 2. 30. 1. 1 fund 4 2. 37. 1. 2. fund 2 3. 3. 2. 3. 2 ad 4 3. 8. 2. 1 ad 6

232 n. 12

3. 8. 2. 2

25 n. 21, 183 n. 19 25 n. 19, 28 n. 24, 184 n. 20, 287 n. 32 82 n. 34, 157 n. 27 59 n. 12 107 n. 11, 237 n. 16

377

27 n. 24, 33 n. 32, 232 n. 11, 257 n. 16 297 n. 45 257 n. 16, 265 n. 26 257 n. 16, 265 n. 26 65 n. 17, 69 n. 21, 80 n. 32, 86 n. 39, 214 n. 28, 263 n. 24 91 n. 44 52 n. 3, 268 n. 29 141 n. 10, 186 n. 23, 317 n. 5 33 n. 32 256 n. 15, 305 n. 58 215 n. 30 144 n. 13 237 n. 16 109 n. 14 58 n. 11 229 n. 6 225 n. 1, 238 n. 17 122 n. 26 265 n. 26 98 n. 3 261 n. 21 99 n. 5 39 n. 40 234 n. 14 37 n. 37 98 n. 3 287 n. 32, 302 n. 54, 305 n. 58 305 n. 58

378

Index of Ancient and Medieval Text References

Bonaventure (cont. ) 3. 8. 3. 1 ad 6 305 n. 58 3. 18. 1. 1 25 n. 19 3. 18. 1. 1 sed con 1 97 n. 2 3. 18. 1. 1 ad 1 97 n. 3 3. 26 dub 1 297 n. 45 3. 29. 1. 2.ad 5 14 n. 5 3. 34. 1. 2. 2 96 n. 2 4. 1. 1. 1. 2 ad 2 99 n. 4 4. 3. 2. 3. 1 ad 1 289 n. 35 4. 11. 1. 1. 5 25 n. 21, 30 n. 27 4. 17. 1. 2. 1 sed con 6 54 n. 5 4. 17. 2. 2. 2 fund 2 28 n. 24 4. 43. 1. 4 36 n. 35 4. 44. 2. 2. 14. 1 ad 1 230 n. 8 4. 49. 2. 3. 1 ad 4 198 n. 6 4. 50. 1. 2. 3 217 n. 31, 230 n. 8 Quaest. Disp. de Myst. Trin. 5. 1 170 n. 7, 284 n. 4, 285 n. 11, 285 n. 19, 286 n. 23, 287 n. 31, 303 n. 55 5. 1 ob 2 57 n. 9 5. 1 ad 1 305 n. 58 5. 1 ad 6 286 n. 22 5. 1 ad 7 301 n. 51 5. 1 ad 8 301 n. 51 5. 1 ad 9 286 n. 24 5. 1 ad 10 284 n. 4 5. 1 ad 11 52 n. 3 5. 1 ad 13 37 n. 36, 285 n. 17, 287 n. 32 5. 1 ad 14 301 n. 51 5. 2 ob.6 37 n. 36 5. 2 sed con 2 54 n. 5 5. 2 ad 2 57 n. 9 5. 2 ad 6 126 n. 31 Burleigh, Walter: Sup. Octo. Lib. Phys. 4. 3. 2 216 n. 30 Cajetan, Thomas de Vio: In Prim. Par. Sum. Theol. 10. 5 267 n. 28

Capreolus, John: Defensiones 2. 2. 2 64 n. 16, 73 n. 25 9 305 n. 59 Chalcidius: Timaeus a Calcidio Translatus (30) 256 n. 16 Damascene, John: de Fide Orthodoxa 2. 1 283 n. 1, 288 n. 34 Dionysius: de Div. Nom. 10 [3] 258 n. 17 Ferrariensis, Sylvester: Com. In Sum. Con. Gen. 1. 15 170 n. 7 Grosseteste: de Luce 1 47 n. 54 Hexaemeron 5. 12 214 n. 28 In Phys. 4 (87) 50 n. 1, 141 n. 11 4 (88) 214 n. 28 4 (88–9) 206 n. 17 4 (90) 195 n. 3 4 (95) 174 n. 10 4 (96) 52 n. 3, 59 n. 13, 252 n. 11, 297 n. 44 4 (97) 146 n. 15 4 (99) 25 n. 21, 28 n. 24 4 (100) 59 n. 12 4 (103) 24 n. 18 4 (104) 168 n. 5 4 (105) 186 n. 23 6 (116–18) 16 n. 8 6 (117) 21 n. 14 Gilbert of Poitiers: In de Trin. 1 252 n. 10, 288 n. 34, 316 n. 5 1. 4 [69] 290 n. 36 1. 4 [71] 247 n. 4 1. 4 [83] 196 n. 4 Giles of Rome: Quaest. de Mens. Angelorum 1 195 n. 3 Henry of Ghent:

Index of Ancient and Medieval Text References Lect. Ord. 1

Hugh of St Victor: de Sacramentis 1. 2. 10 1. 3. 16 In Ecclesiasten Hom 13

37 n. 36, 57 n. 9, 98 n. 3, 109 n. 14, 145 n. 14, 156 n. 26, 158 n. 28 247 n. 4 274 n. 36 227 n. 3, 247 n. 4, 284 n. 3, 290 n. 36

In Epist. ad Tim. 3 240 n. 19, 274 n. 36 Isidore of Seville: Etym. 2. 18 30 n. 27 5. 29 13 n. 3, 256 n. 16, 257 n. 16 5. 38 [4] 256 n. 16, 257 n. 16 7. 1 282 n. 1 10. 1 188 n. 24 De Differentiis 2. 11 [30] 156 n. 26 John of St. Thomas: In Sum. Theol. D. Thomae 2. 10. 10 274 n. 36 Kilwardby: de Temp. 1 [2] 26 n. 22 1 [3] 148 n. 17 1 [4] 174 n. 10 1 [9] 176 n. 12 2 141 n. 11 2 [11] 138 n. 8 3 141 n. 10 4 141 n. 11, 146 n. 16 5 [20] 195 n. 3 5 [24] 199 n. 8 5 [25] 214 n. 28 6 [26] 195 n. 3 6 [27] 32 n. 29, 199 n. 8 6 [28] 199 n. 8 6 [29] 43 n. 48, 43 n. 49 7 [34] 43 n. 49 8 [35] 146 n. 15 10 [39] 137 n. 7 10 [40] 146 n. 15 11 [44] 63 n. 15 11 [45] 79 n. 31 11 [49] 32 n. 29

11 [51] 13 [57] 13 [60] 13 [59] 13 [66] 13 [67] 13 [68] 13 [71] 14 [77] 15 [83] 15 [84] 16 [94] 16 [95] 16 [99] 17 [101] 17 [106] 17 [107] 17 [108] 17 [109] 17 [110] 20 [128] 20 [130] 21 [133] 21 [137] 21 [141] 22 [143] 23 [144] In Sent. 1. 31 2. 1 2. 3 2. 4 2. 10 2. 11 2. 12 Knapwell, Richard: Cor. Cor. Quare 1. 23

379

79 n. 30, 86 n. 39 69 n. 21, 89 n. 41 188 n. 24 84 n. 37 71 n. 21, 86 n. 39 67 n. 19 68 n. 20 89 n. 41 166 n. 3 25 n. 19 159 n. 30 226 n. 2 227 n. 4 41 n. 42, 42 n. 43 52 n. 3 28 n. 24, 266 n. 27 303 n. 54, 305 n. 58 316 n. 5 91 n. 44, 316 n. 5, 328 n. 18 316 n. 5 320 n. 10, 321 n. 10 228 n. 5 320 n. 10, 321 n. 10 321 n. 10 315 n. 4 315 n. 4 305 n. 58 289 n. 35 97 n. 3, 99 n. 5, 110 n. 15 25 n. 19 25 n. 19, 90 n. 42, 97 n. 2, 132 n. 2 237 n. 16, 256 n. 15, 256 n. 16, 257 n. 16 33 n. 32 257 n. 16 86 n. 40, 242 n. 21, 274 n. 36

Lombard, Peter: Sententiae 1. 8 251 n. 8 Macclesfield, William: Cor. Cor. Quaestione 23 88 n. 40, 261 n. 21, 274 n. 36

380

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Mainmonides, Moses: Guide of the perplexed 2. 13 154 n. 24 Marbes, John: Quaest. Sup. Octo. Lib. Phys. 2 216 n. 30 Marston, Roger: Quodlibeta 3. 2 265 n. 26 Middleton, Richard: In Sent. 2. 2 195 n. 3 Oresme, Nicholas: Le Liver du Ciel 2. 14 214 n. 29 Orford, Robert: Cor. Cor. Sciendum 1. 23 50 n. 1, 106 n. 9, 261 n. 21, 266 n. 27, 269 n. 30, 275 n. 37 Pecham, John: de Aeternitate Mundi (3) 238 n. 16, 287 n. 32 (13) 241 n. 20 (15) 283 n. 1 (31) 238 n. 16 Quodlibeta 2. 10 265 n. 26, 269 n. 30, 277 n. 39, 314 n. 4 4. 20 278 n. 40 Peter of Tarentaise: In Sent. 1. 8. 3. 1 37 n. 36, 42 n. 43, 288 n. 34, 289 n. 35, 296 n. 42, 299 n. 48, 303 n. 54 1. 8. 3. 1 ad 3 90 n. 43 1. 9. 2. 1 56 n. 8 1. 9. 4. 1 con 3 242 n. 21, 327 n. 18 1. 9. 4. 1 ad 3 327 n. 18 1.14.1. 1 ob 7 33 n. 32 1. 30. 1. 5 91 n. 44, 241 n. 20 1. 30. 1. 5 ad 3 91 n. 44 1. 38. 1. 1–2 181 n. 17 2. 1. 1. 2 153 n. 23

2. 1. 2. 2 237 n. 16, 2. 1. 2. 3 ob 4 97 n. 3 2. 1. 2. 3 con 9 37 n. 36 2. 1. 2. 3 ad 4 160 n. 31 2. 2. 1 284 n. 2 2. 2. 2. 1 ad 5 263 n. 24 2. 2. 2. 1 ad 6 28 n. 25 2. 2. 2. 2 79 n. 30, 79 n. 31 2. 2. 2. 3 159 n. 29 2. 2. 12. 2 215 n. 30 2. 6. 2. 1 116 n. 21 2. 6. 2. 1 ad 1 109 n. 14 Philip the Chancellor: Summa de Bono 1. 1. 3 254 n. 14, 292 n. 39, 271 n. 33 1. 1. 4 37 n. 36, 139 n. 8, 232 n. 11, 269 n. 30, 283 n. 1, 319 n. 8 1. 2. 1 239 n. 18, 259 n. 19 1. 2. 2 37 n. 36, 261 n. 20 1. 2. 11 106 n. 10, 107 n. 12, 112 n. 17, 113 n. 18 1. 3. 1 53 n. 5 1. 3. 3 97 n. 3 1. 3. 5 144 n. 13 1. 3. 6 144 n. 13, 159 n. 29, 160 n. 30, 215 n. 30, 216 n. 30 1. 3. 7 195 n. 3 1. 4. 9 32 n. 29, 88 n. 40, 230 n. 7, 254 n. 14, 257 n. 16, 300 n. 49 Proclus: Liber de Causis 31 259 n. 18 Pseudo Aquinas: de Inst. 1 137 n. 7, 138 n. 8, 170 n. 7 2 184 n. 21, 195 n. 4 3 175 n. 11 4 91 n. 44, 186 n. 23 5 197 n. 5 de Temp. 3 229 n. 6 4 305 n. 58

Index of Ancient and Medieval Text References Richard of St Victor: de Trin. 2. 2 2. 4 In Apoc. 2. 8 3. 7

Tr. de Mensuris 2 247 n. 4, 256 n. 15 290 n. 36 290 n. 36 217 n. 31, 284 n. 3

In Epist. ad Tim. 3 265 n. 26 Robert of Paris: Summa Breve Sit 1 251 n. 8 Siger of Brabant / Pseudo Siger: Phys. 7. 30 75 n. 27 8. 6 [201] 159 n. 30 8. 9 96 n. 2, 97 n. 3 8. 10 158 n. 28 8. 10 [207] 159 n. 30 Sup. Lib. de Causis 9 227 n. 3, 291 n. 37 11 137 n. 7, 184 n. 20, 186 n. 23, 227 n. 3, 291 n. 37 12 231 n. 9 Quidort, John: Cor. Cor. Circa 1 26 n. 22, 89 n. 41, 274 n. 36 Roger Bacon: Opus Maius Pers 1. 3 107 n. 12, 111 n. 16 4. 4. 14 79 n. 30 Mult Spec 5. 3 111 n. 16 Scotus: In Sent 2. 2. 2. 1. 3 263 n. 24 2. 9. 2 173 n. 9 4.14.2 24 n. 18 Theodoric of Freiberg: Tr. de Nat. et Prop. Contin. 1 14 n. 5, 18 n. 10, 21 n. 14, 2 18 n. 10, 25 n. 19 3 183 n. 19 4 138 n. 8 6 25 n. 21

3 4

381

232 n. 11, 254 n. 14, 257 n. 16, 269 n. 30, 289 n. 35 261 n. 21, 269 n. 30 260 n. 20, 269 n. 30, 274 n. 36, 300 n. 49 260 n. 19

7 Ulrich of Strasbourg: de Summo Bono 2. 3. 10 325 n. 16 2. 4. 2 228 n. 4, 248 n. 5, 301 n. 53 2. 4. 3 256 n. 15, 260 n. 19 2. 4. 4 286 n. 26 4. 1. 1 286 n. 23 4. 1. 2 250 n. 8 4. 1. 8 77 n. 29, 158 n. 29, 160 n. 31, 241 n. 20, 242 n. 21, 249 n. 7, 250 n. 8, 264 n. 25 William de la Mare: In Sent 2. 2. 1 257 n. 16 William of Auvergne: De Trin 1. 8 98 n. 3 William of Auxerre: Sum Aurea 1. 14. 4 91 n. 44 2. 8. 2. 1. 1 36 n. 35, 107 n. 12 2. 8. 2. 1. 5 50 n. 1 Appendix 315 n. 4 William of Baglione: de Aeternitate Mundi b and c 98 n. 3 11 252 n. 9 William of Ockham: In Sent. 2. 11 278 n. 41 Quaest. In Lib. Phys. 54 317 n. 5 Quodlib 4. 30 76 n. 28 William of Conches: Glossae Super Platonem 32 251 n. 8

Index of Ancient Medieval and Pre Modern Authors Albert the Great: God knows events by causing them, 181 n. 17 Immutable beings exist before (ante) time, 160 n. 31 On angelic time, 276 n. 38 On angels relationship to eternity, 160 n. 31 On arguments against the existence of time, 173 n. 8 On arguments against the possibility of creation, 158 n. 28 On Arianism, 311–12 On causation, 104 n. 8, 107 n. 12, 110 n. 15, 116 On confusion about topological properties, 84 On diVerent uses of the words time’ and ‘temporal’, 216 n. 30, 229 n. 6 On eternity, 282–97, 299–305, 309–11 On existence in time, 226–34 On existence above and outside of time, 236–40 On future contingents and backwards causation, 122 n. 26 On God’s relationship to time, 324 n. 14 On illumination, 109–10 On imaginary time and the mind dependence of time, 154–5, 174–6 On measurement, 196–9, 201–7 On movement in a vacuum, 112–13 On modal relations, 150–1 On multiple times and temporal unity, 70 n. 21, 83–4 On non temporal causal sequences, 126 n. 31 On relations, 131–4, 169 n. 6

On ‘sempiternity’ and ‘perpetuity’, 249, 252, 253 n. 12, 256 n. 15 On supervenience, 46 n. 53 On temporal parts and boundaries, 15, 26, 30, 47 On the A theory of time, 188 n. 24 On the aevum, 263 n. 24, 266 n. 27, 268–72, 278 n. 40 On the creation of time, 159 n. 29 On the deWnition of time, 138 n. 8, 149 n. 17, 214 n. 28 On the distinction between order of time and of nature, 54, 118 n. 24 On the Xowing moment, 175 n. 11 On the Xowing now of time, 182–6, On the now of eternity, 28 n. 24, 183 n. 19 On the Primum Mobile and its role, 83–5, 86 n. 39, 137, 185 n. 23, 208–15, 217 On the reducibility of time to space, 141 n. 10–11, 143 On the relationship between God, angels & our time, 88–91, 302 n. 54, 314 n. 4, 316 n. 5, 325 On the relationship of rest and change to time, 227 n. 3, 228 On the relation of time to the blessed and damned, 235 n. 15 On the terms ‘aevum’ and ‘eternity’, 256 n. 16, 259–60, 262 n. 22, 264 n. 25 On time as an accident, 136 n. 6, 139 On truths of fact and truths of appearance, 203 n. 13 On types of priority, 96 n. 2, 98 n. 3, 99 n. 4 Time exists even when not experienced, 167 n. 4, 168

Index of Ancient Medieval and Pre Modern Authors 383 Alexander of Hales: A plurality of prima mobilia would have a single time, 83 n. 36 On aeviternal beings, 259–61, 265 n. 27, 269 n. 30 On ageing, 188 n. 24 On analogous predication of ‘eternity’, 319 n. 8 On angelic time, 88 n. 40, 274 n. 36 On criteria for temporality, 229 On diVerent uses of the word ‘time’, 215 n. 30 On eternity, 284 n. 2, 284 n. 6, 285 n. 11, 290 n. 36, 291 n. 37, 303 n. 55 On existence which is above & outside time, 237 n. 16, 239 n. 18, 240 n. 19 On existence ‘with’ time, 327 On God, angels and motion existing at the same time, 302 n. 54 On God is ‘semper’ (always), 315 n. 4 On non temporal durational togetherness, 90 n. 42 On participation in eternity, 315 n. 4 On sempiternity and perpetuity, 247–51, 255 On temporal unity, 64, 80 n. 32, 83 n. 36 On the ‘aevum’, 256 n. 16, 262 n. 23, 264 n. 24, 271 n. 33 On the distinction between ‘subito’ and ‘repente’, 107 n. 12 On the Xowing now, 183 n. 19 On the relation of the blessed and damned to time, 217 n. 31, 235 n. 15, 281 On the role of the Primum Mobile, 138 n. 8, 209 n. 22 On the ‘saeculum’ (age), 273 n. 36 On types of priority, 97 n. 3 Temporal topology arises from the topology of space, 140 n. 10 Time began in an instant, 159 n. 30 Algazel: On temporal priority, 96 n. 1 Andrew of Newcastle: On the immaculate conception, 123 n. 28

Anselm: Forgiveness of Old Testament patriarchs depends on Christ’s later suVerings, 122 On God’s relation to time, 320 n. 10, 321 n. 10 On temporal unity, 63 n. 16, On the use of the word ‘always’ (semper), 247 n. 4 Aquinas, Thomas: Critique of Bonaventure’s argument for temporal unity, 70–5 On accidents as concreated, 149 n. 18 On angelic duration, 269 n. 30, 278 On angelic time, 88 n. 40, 186 n. 23, 273–8 On angelic free will, 116–17 On Angels relationship to time, 232 n. 12, 237 n. 16, 238 n. 17 On arguments against the existence of time, 172–4 On causation, 104 n. 8, 106 n. 10, 126 n. 32, 116 On concomitant existence, 91 n. 44, 302 n. 54, 327 On creation, 105 n. 9, 116 n. 22, 117 On durational togetherness, 90 On eternity, 283–305, 309–14 On existence above & outside time, 236–40 On God’s causal knowledge, 181 n. 17 On God’s existence in the now of eternity, 91 n. 44 On God’s existence prior to creation, 160 n. 31 On God’s relationship to space, 324 n. 15 On God’s relationship to time, 309, 311–12, 314 n. 4, 316–29 On God’s sustaining role, 321–4 On illumination, 109 n. 14, 117 On imaginary time, 149 n. 18, 154–62 On inWnite divisibility, 21 n. 14 On language about existence ‘in’ time, 225 On measurement, 195–207 On movement in a vacuum, 112–13 On omnipotence, 114, 121 n. 26

384 Index of Ancient Medieval and Pre Modern Authors Aquinas, Thomas: (cont.) On order of nature and order of time, 54, 118 On relations, 131–4 On sempiternity and perpetuity, 254–5 On simultaneous causation, 105 n. 9,107 n. 11, 117 On temporal atoms, 15 n. 6 On temporal relations, 136 On temporal unity, 75–9 On the aevum, 263 n. 24, 267 n. 28, 272 On the deWnition of time, 148 n. 17, 193 n. 1 On the distinction between ‘subito’ and ‘repente’, 107 n. 12 On the Xowing now, 182–6 On the heavenly bodies, 139 n. 9 On the Immaculate Conception, 123 On the Mass, 124 n. 29 On the metric of time, 218–22 On the mind dependence of time, 167–72, 174–6 On the nominales, 181–2 On the now of eternity, 323 n. 14 On the Passion and Sacraments, 121 n. 26 On the Primum Mobile, 137, 138 n. 8, 139 n. 9, 145, 146 n. 13, 208–13, 309 On the reducibility of time to motion and space, 135, 140, 143, 151–2 On the rejection of the plurality of times, 83 n. 35 On the relation of the souls in heaven to time, 217 n. 31 On the relationship of time to change, 227 n. 3 On the ‘subject’ for time, 81, 85 On the word ‘collatio’, 253 n. 12 On the word ‘semper’, 248–50 On truths of fact and truths of appearance, 203 n. 13 On types of priority, 96 n. 2, 97 n. 3, 99 n. 4–5 Time exists from the Wrst instant, not in it, 159 n. 30 Time is bounded at both ends, 159 n. 29 Aristotle: DeWnition of time, 11, 70–1, 193

Development of Aristotle’s thought, 89 InXuence of Aristotle, 10–11 The Categories view of time, 12, 75–6, 198 On arguments against the existence of time, 173–5 On causal necessity, 110 n. 15 On concepts of priority, 96 n. 1, 98 n. 3 On criteria for a measure to be privileged, 203–5 On criteria for temporality, 229 n. 7, 249, 250 n. 8 On discrete elements, 21–2 On equal and unequal times, 58–9 On eternity, 288 n. 34, 292 n. 39 On measurement, 199 n. 8, 201 n. 11, 263 n. 24 On objects at rest, 228 n. 5 On relations, 131 n. 1, 133 n. 3 On Simultaneity of nature, 53–4 On the deWnition of temporal simultaneity, 59 On the distinction between ‘numbering’ and ‘measuring’, 195 On the experience of time, 165–6 On the Xowing now, 183 n. 19 On the four types of causes, 101 On the Primum Mobile, 210 n. 24 On the reducibility of time to motion, 135 On the reducibility of time to space, 141 n. 10–11 Augustine: InXuence of, 10 On angels’ relationship to time, 274 n. 36 On causal priority and causal orderings, 56 On notions of priority, 96 n. 1 On sempiternity, 247 n. 4 On temporal unity, 80 n. 32 On the aevum and eternal times, 256 n. 16 On the creation of time, 149 n. 18 On the mind dependence of time, 174–5 On the relationship of the movement of the heavens to time, 144 n. 13

Index of Ancient Medieval and Pre Modern Authors 385 Averroes: On contiguity, 46 n. 53, 47 On criteria for temporality, 249 n. 7 On eternity and eternal particulars, 229 n. 6, 283 n. 1 On existence in time, 232 n. 11 On geometrical models of time, 48 n. 55 On imaginary time, 153–4 On instants, 24, 28 n. 24 On measurement, 197 On movement in a vacuum, 112 n. 17, 113 n. 19 On senses of priority, 95 n. 1 On temporal atoms, 16–17 On temporal terms, 42 n. 44, 51 n. 2 On temporal unity, 63 n. 16, 75–91 On the beginningnessless of time, 157–8, 186 On the experience of time, 166 n. 1, 167, 171 On the impossibility of creation, 157–8 On the plurality of times, 83 n. 35 On the quando, 302 n. 54 On the relationship of time to the Primum Mobile, 138 n. 8 On universal rest, 152 n. 23 The velocity argument, 16–18 Avicenna: On geometrical analogies of time, 184 n. 21 On movement in a vacuum, 112 n. 17, 113 n. 19 On temporal elements, 253 n. 12 On temporal unity, 63 n. 16, 79 n. 30 On the mind dependence of time, 174 n. 10 On the substantiality of time, 137 n. 6 On the word ‘moment,’ 32 n. 29, 34 n. 33, 50 n. 1 On the word ‘now’, 28 n. 24 On the word ‘simultaneous’ 51 n. 2, 58 n. 11 Bacon, Roger: On illumination, 111 On simultaneous causation, 107 n. 12 On temporal unity, 79 n. 30

On the aevum, 265 n. 26 Baconthorpe, John: On the immaculate conception, 123 n. 28 Bede, St, / Pseudo Bede: On cataloguing the parts of time, 13 On temporal terminology, 173 On time atoms, 15 n. Boethius: On eternity, 299–300 On sempiternity, 247 n. 4, 249 n. 7 On the Xowing now, 183 n. 19 On the word ‘moment’, 32 n. 29 On the word ‘now’, 28 n. 24 Bonaventure: On aeviternal beings, 260 n. 19 On analogical language about God, 318 n. 7 On angelic duration, 189 n. 24, 274 n. 36 On angels relation to time, 238 n. 17 On causal dependence (exigentia), 99 n. 5 On creation, 105 n. 9, 157 On diVerent types of priority, 96 n. 2, 97 n. 3 On durational togetherness, 90, 91 n. 44 On Eternity, 283–92, 297 n. 45, 299, 303 n. 55, 305 n. 58, 317–18 On existence ‘above’ time, 237 n. 16 On existence in time, 225, 226 n. 2, 228–32, 234 On existence ‘with’ time, 241 n. 20 On free will as an issue for temporal unity, 80 n. 32 On future contingents and backwards causation, 122 n. 26 On God, angels and people existing concomitantly, 91 n. 44, 302 n. 54, 316 n. 5 On God’s relation to time, 311, 325 n. 16 On God’s relation to space, 324 n. 15 On illumination, 108–9 On perpetuity, 256 n. 15 On simultaneous (instantaneous) causation, 107 n. 11 On souls’ relationship to time, 261, 280

386 Index of Ancient Medieval and Pre Modern Authors Bonaventure: (cont.) On temporal unity, 70–5, 80 On the boundedness of time, 159 n. 30 On the deWnition of time, 14 n. 28 On diVerent uses of the word ‘time’, 215 n. 30, 221, 257 n. 16 On the aevum, 265 n. 26, 267 On the distinction between principium originale and principium initiale, 126 n. 31 On the distinction between relations secundum esse and secundum dici, 133 n. 3 On the distinction between the essence and esse of time, 184 n. 20 On the fall of the angels, 116 n. 21 On the Xowing now, 183 n. 19, 186 n. 23 On the Immacultae Conception, 123 On the measurement of time, 198 n. 6, 201 n. 11 On the order of nature and order of time, 118 n. 24 On the plurality of aeva, 263 n. 24 On the Primum Mobile, 81–2, 143–4 On the reducibility of time to space, 141 On the relation between Gods knowledge and events in the world, 181 n. 17 On time as a mental phenomenon, 82 n. 34, 170 n. 7 On time for the damned, 81, 217, 230 Bradwardine, Thomas: On backwards causation, 122 n. 26 Burleigh, Walter: On diVerent uses of the word ‘time’, 216 n. 30 Cajetan: On the aevum, 263 n. 24, 267 n. 28 Candia, Peter: On the Immaculate Conception, 123 n. 28 Capreolus, John: On eternity, 305 n. 59 On temporal unity, 64 n. 16, 73 n. 25 Chalcidius: On the use of the words ‘aevum’ and ‘aeviternity’, 256 n. 16

Cicero: On the use of the words ‘eternity’ and ‘sempiternity’, 282 n. 1 Clarke, Samuel: On the substantiality of time, 137 n. 6 Cowton, Robert: On the immaculate Conception, 123 n. 28 Damascene, John: On Eternity, 283 n. 1, 288 n. 34 Damien, Peter: On backwards causation, 122 n. 26 Democritus: On atomism, 16 Dionysius: On the deWnition of the aevum, 258 Euclid: On geometrical models of time, 14 n. 5 Ferrariensis, Sylvester: On Aquinas and experiencing time, 170 n. 7 Gilbert of Poitiers: On backwards causation, 122 n. 26 On concomitance between time and eternity, 316 n. 5 On Eternity, 288 n. 34, 290 n. 36 On measurement, 196 n. 4 On the distinction between ‘sempiternity’ ‘perpetuity’ and ‘eternity’, 252–5 On the notion of the mora (period), 40 n. 41 On the use of the word ‘always’ (semper), 247 n. 4 Giles of Rome: On measurement, 195 n. 3 Gregory the great: On the word ‘simultaneous’, 52 n. 3 Gregory of Rimini: On backwards causation, 122 n. 26 Grosseteste, Robert: On eternity, 296–7

Index of Ancient Medieval and Pre Modern Authors 387 On light as an example of supervenience, 47 On measuring and numbering, 195 n. 3, 206 n. 17 On ‘number’ in the deWnition of time, 168 n. 5 On temporal relations, 50 n. 1 On the deWnition of time, 214 n. 28 On the mind dependence of time, 174 On the now of time, 186 n. 23 On the reducibility of time to space, 141 n. 11 On the ‘subject’ of time, 146 On the word ‘collatio,’ 252 n. 11 On the word ‘now’, 28 n. 24 On the word ‘simultaneous’, 52 n. 3, 59 n. 12, 59 n. 13, 62 Henry of Ghent: On arguments against creation, 158 n. 28 On before the Primum Mobile, 145 n. 14 On illumination, 109 n. 14 On simultaneity, 57 n. 9 On the word ‘duratio’, 37 n. 36 On the word ‘instant’, 24 On time before time, 155 n. 26 On types of priority, 98 n. 3 Hugh of St Victor: On angelic time, 274 n. 36 On eternity, 283 n. 3, 290 n. 36 On existence which is outside of time, 240 n. 19 On the Relationship of change to time, 227 n. 3 On the use of the word ‘always’ (semper), 247 n. 4 Isidore of Seville: On the Etymology of ‘present’, 188 n. 24 On the parts of time, 13 n. 3, On the use of the words ‘aevum’ and ‘eternity’, 256 n. 16, 282 n. 1 On the word ‘period’, 30 n. 27 On what God made before time, 156 n. 26

Jerome, St: On God’s power over the past, 121 John of St Thomas: On angelic time, 274 n. 36 Kilwardby, Robert: On causal necessity, 110 n. 15 On diVering senses of ‘quando’, 40–1 On durational togetherness, 90 On existence in time, 226 n. 2, 228 n. 5 On existence outside of time, 237 n. 16 On God existing when the angel and motion exist, 316 n. 5 On God’s relation to time, 320 n. 10, 327 n. 18, 328 n. 18 On measuring and numbering, 195 n. 3, 199 n. 8 On relations, 132 n. 2 On sempiternity and perpetuity, 256 n. 15 On temporal unity, 63, 67, 67 n. 19, 69 n. 21, 71, 79, 85–6 On time as an ‘accident’, 84 n. 37 On the aevum and eternity, 256 n. 16, 266 n. 27, 305 n. 58 On the boundedness of time, 159 n. 30 On the deWnition of time, 138 n. 8, 148 n. 17, 214 n. 28 On the experience of time, 166 On the mind dependence of time, 174, 176 n. 12 On the present, 188 n. 24 On the reducibility of time to space, 141 n. 10–11, 143 n. 12 On the relationship between change to time, 227 n. 3 On the relationship between time and eternity, 315 On the ‘subject’ of time, 137 n. 7, 146 On the unity of the metric, 86 On the use of the word ‘instant’, 24 On the use of the word ‘moment’, 32 n. 29 On the use of the word ‘now’, 28 n. 24 On the use of the word ‘present’, 26 n. 22 On the use of the word ‘simultaneous’, 52 n. 3 On the use of the word ‘when’(quando), 40–2 On types of priority, 99 n. 5

388 Index of Ancient Medieval and Pre Modern Authors Knapwell, Richard: On angelic time, 274 n. 36 On the existence of a discrete and a continuous time, 87 n. 40 On time measuring our souls, 241 n. 21 Leibniz, Gottfried Wilhelm: On time as a relational entity, 137 n. 6 Leucippus: On atomism, 16 Locke, John: On the use of the word ‘duration’, 36 n. 35 Lombard, Peter: On predicating tenses of God, 251 n. 8 On temporal unity, 62 MacclesWeld, William: On angelic time, 274 n. 36 On multiple times, 88 n. 40 On the soul’s existence ‘above’ time, 261 Maimonides, Moses: On creatio ex nihilo, 153 On imaginary time, 154 On temporal atomism, 15 n. 6 On the impossibility of creation, 156 Marbes, John (Joannes Canonicus): On diVerent uses of the word ‘time’, 216 n. 30 Marston, Roger: On arguments for the extensionality of the aevum, 265 n. 26 Middleton, Richard: On measurement, 195 n. 3 Newton, Isaac: On the substantiality of time, 137 n. 6 On absolute time, 258 Orford, R.: On angelic time, 274 n. 36, 275 n. 37 On temporal relations, 50 n. 1 On the extensionality of the aevum, 266 n. 27, 269 n. 30 On the soul’s existence ‘above’ time, 261 n. 21 Oresme, Nicholas: On changes in the rate at which time passes, 214 n. 29

Pecham, John: On angelic duration, 269 n. 30, 276–8 On argument for the extensionality of the aevum, 265 n. 26 On Eternity, 287 n. 32, 292 n. 39 On God’s existence before or outside time, 238 n. 16, 241 n. 20 Philip the Chancellor: On aeviternal beings, 259 n. 19, 261 n. 20, 269 n. 30 On angelic time, 88 n. 40 On causation, 106 n. 10 On diVerent notions of priority, 97 n. 3 On diVerent uses of the word ‘time’ 215 n. 30 On Eternity, 292 n. 39, 300 n. 49, 314 n. 4, 319 n. 8 On existence ‘above’ time, 239 n. 18 On existence in time, 230 n. 7, 232 n. 11 On movement in a vacuum, 112 n. 17, 113 n. 18 On the creation of time, 159 n. 29, 160 n. 30, 215 n. 30 On the now of the aevum, 271 n. 33 On the temporal metric, 194 n. 3 On the use of the word ‘moment’, 32 n. 29 On the use of the word ‘duration’, 37 n. 36 On use of the words ‘sempiternity’ and ‘perpetuity’, 254 On the use of the word ‘simultaneous’, 53 n. 5 On time’s relation to the Primum Mobile, 144 n. 13, 215 n. 30 Plato: InXuence of, 13, 68 On the concept of measure, 195–6, 221 Platonism and Aristotelianism, 197 n. 5 Priscian: On the use of the word ‘present,’ 26 On time as measuring mutable things, 229 n. 7 Proclus: On the deWnition of the aevum, 258–61

Index of Ancient Medieval and Pre Modern Authors 389 On the relationship of time, aeviternity and eternity, 33 n. 32 Pseudo Aquinas: On criteria for being in time, 229 n. 7 On eternity, 298 n. 46, 299 n. 46, 305 n. 58 On measurement, 197 On non temporal durational togetherness, 90 On temporal unity, 63 On the Primum Mobile, 137 n. 7, 138 n. 8 On the relationship between the aevum and time, 91 n. 44 On the role of experience in constituting time, 170 n. 7 On the substance of time, 175 n. 11 On the now, 184 n. 21, 186 n. 23 Quiddort, John: On angelic time, 274 n. 36 On philosophy as contrary to scripture, 88–9 On the use of the word ‘present’, 26 n. 22 Richard of St Victor: On eternity, 284 n. 3, 290 n. 36 On sempiternity and perpetuity, 256 n. 15 On the aevum, 265 n. 26 On the relation of the blessed to time, 217 n. 31 On the use of the word ‘always’ (semper), 247 n. 4 Robert of Paris: On existence outside of time, 251 n. 8 Rossy, Thomas de: On the Immaculate Conception, 123 n. 28 Simplicius: On Aristotle’s notion of time, 195 n. 3 Siger/Pseudo Siger of Brabant: On diVerent types of priority, 96 n. 2, 97 n. 3 On eternity, 291 n. 37 On the boundedness of time, 159 n. 30

On the now, 184 n. 20, 186 n. 23 On the subject of time, 137 n. 7 Sutton, Thoma: On the Immaculate Conception, 123 n. 28 Siger of Brabant: On arguments against creation, 158 n. 28 On temporal unity, 75 n. 27 On the relationship between time and eternity, 227 n. 3 Scotus: On entitism, 173 n. 9 On instants, 24 On the aevum, 263 n. 24 Tarentaise, Peter of: On causal sequences in the angelic fall, 115–16 On comparing the aevum to time, 263 n. 24 On creation, 153 n. 23 On diVerent uses of the word ‘time’, 215 n. 30 On eternity, 284 n. 2, 288 n. 34, 295–6, 299 On existence ‘before’ time, 159 n. 29, 160 n. 31 On existence ‘with’ time, 327 On Gods existence ‘with’ time, 91 n. 44 On Gods relation to time, 90 n. 43 On illumination and instantaneous changes, 109 n. 14 On non temporal Durational togetherness, 90 On prior in time and prior in nature, 97 n. 3 On temporal unity, 79 On the now, 28 On the relation of God’s knowledge to events, 181 n. 17 On the use of the word ‘duration’, 37 n. 36 On the use of the word ‘moment’, 33 n. 32 On the use of the word, ‘now’, 28 Tempier, Stephen: Proposition 25 of the 219 condemned propositions, 256 n. 15

390 Index of Ancient Medieval and Pre Modern Authors Theodoric of Freiberg: On aeviternal beings, 260–1, 269 n. 30 On eternity, 289 n. 35, 300 n. 49 On existence in time, 232 n. 11 On the aevum, 274 n. 36 On the Xowing now, 183 n. 19 On the role of the Primum Mobile, 138 n. 8 On sempiternity and perpetuity, 254 n. 14 Themestius: On the relationship between time and space, 142 Ulrich of Strasbourg: On aeviternal beings, 260 n. 19 On eternity, 286 n. 23–6, 301 n. 53, 325 n. 16 On existence prior to creation, 160 n. 31 On sempiternity and perpetuity, 256 n. 15 On the extensionality of the aevum, 264 n. 25 On the relationship of time and change, 227 n. 3 On the word ‘always’ (semper), 248–50 On the world as existing ‘with’ time, 241 n. 20

On time as concreated with the heavens, 158 n. 29 William de la Mare: On eternal times, 257 n. 16 William of Auvergne: On types of priority, 98 n. 3 William of Auxerre: On backwards causation, 122 n. 26 On durational togetherness, 90 On eternity’s relation to time, 91 n. 44 On God as existing ‘always’, 315 n. 4 On the use of the words ‘subito’ and ‘repente’, 107 n. 12 William of Baglione: On the notion of perpetuity, 252 n. 9, 292 n. 39 On types of priority, 98 n. 3 William of Conches: On the use of ‘always’ (semper), 251 n. 8 William of Ockham: On the aevum, 278 On the use of the word ‘coexist’, 317 n. 5