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Studies in Aristotle’s Physics Morrissey, Christopher Stewart 1999

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STUDIES IN A R I S T O T L E ' S PHYSICS by C H R I S T O P H E R S T E W A R T M O R R I S S E Y FJ.Sc, The University of Manitoba, 1988 B .A., The University of British Columbia, 1995 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF CLASSICAL, NEAR EASTERN, AND RELIGIOUS STUDIES We accept this thesis as conforming to the required standard THE UNIVERSITY^ BRITISH COLUMBIA August 26, 1999 © Christopher Stewart Morrissey, 1999 UBC Special Collections - Thesis Authorisation Form Page 1 of 1 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the head of my department or by h i s or her r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada http://www.library.ubc.ca/spcoll/thesauth.html 26/Aug/99 Abstract The Aristotelian-Thomistic theory of the abstractive induction of immediate first principles and methodology of a priori demonstrations from immediate first principles is defended as found in actu signato in Aristotle's Posterior Analytics and in actu exercito in Aristotle's Physics. Aristotelian science is discussed in Chapter I as being certain knowledge through causes and effected by demonstration. Its certain character is derived from how it employs proper causes (neither remote causes nor effects) in the syllogism. Aristotelian science demonstrates through causes (not incidental principles or elements) as middle terms in the demonstrations, but only according to the order of causality among the four Aristotelian causes. This implies an order of distinct types of demonstration, the schema of which is discussed. Aristotelian science is demonstrative, i.e. it effects knowledge of what cannot be otherwise, because it reasons from premises more certain quoad nos (according to us) to conclusions more certain quoad se (according to nature). This fact is reflected in the schema of demonstration types set forth. In Chapter II, an attempt to clarify how the abstractive induction of universals is related to the per se nota principles of demonstration is made. Annotated translations of Aristotle on abstractive induction in Posterior Analytics 11.19, and the commentary of Themistius thereupon, are provided to support the argument. Once reasoning from immediate first principles is established as neither circular nor necessitating an infinite regress, the a priori demonstrations in the Physics about motion, place, and time are treated in Chapter III. Common misunderstandings about Aristotle's definitions of motion and place are refuted. A dialectical division and annotated translation of Aristotle's discussion of time is included. i i TABLE OF CONTENTS iii Abstract i List of Tables v PREFACE: Reason, Revelation, and the Esoteric Aristotle vi Acknowledgements xii CHAPTER I Methodology: Scientia 1.1 Science: Certain, Causal, Demonstrative 1 1.2 Certain: Of Proper Causes 5 1.3 Causal: Through Middle Terms 15 1.4 Demonstrative: By Order of the Causes 22 CHAPTER II Principles: Not a per se 2.1 Abstractive Induction 43 2.2. Annotated Translation (Aristotle and Themistius) 69 CHAPTER III Physics: Ens mobile 3.1 Motion (Phys. III. 1-3) 106 3.2 Place (Phys. IV. 1-5) 117 3.3 Time: Annotated Translation (Phys. IV.10-14) 135 CONCLUSION 174 (Continued on next page) TABLE OF CONTENTS (Continued) BIBLIOGRAPHY A. Primary Sources (Abbreviations) 177 A.l. Aristotle (Texts and Translations) 178 A.l. St. Thomas Aquinas (Texts and Translations) 180 B. Secondary Sources (Articles and Monographs) 181 Appendix I Aristotle's Perennial Physics 193 Appendix II Galileo's Early Notebooks 196 Appendix III Aquinas and the River Forest School 199 iV List of Tables Table 1: Certainty in Demonstrations (Order of Predication) 10 Table 2: Hierarchy of Middle Terms (Order of the Causes) 18 Table 3: Sub-Types of A Priori Demonstrations (From Middle Terms) 26 Table 4: Modes of Nota Per Se Predication 28 Table 5: Types of A Priori Demonstrations (From Predicates) 34 Table 6: Schema of A Priori Demonstrations (Types and Sub-Types) 37 Table 7: Examples of All Types of A Priori Demonstrations 38 Table 8: Types of A Posteriori Demonstrations 40 Table 9: Induction and Demonstration about the Universal "Hellebore" 51 Table 10: Divisio Textus of An. Post. 11.19 72 v P R E F A C E Reason, Revelation, and the Esoteric Aristotle "Aristotle writes about a rigorous method of scientific demonstration in his Posterior Analytics but it is extremely difficult to find that method actually employed in his other writings."1 This problem plagues every reading of Aristotle. No doubt it derives from the esoteric nature of the Aristotelian texts. Aristotle's exoteric works, almost all of which were written in dialogue format and published while he was a member of Plato's Academy, are not available to us, except in indirect fragments. That we today possess such a large body of his esoterica ~ his lecture notes ~ is a piece of good fortune not shared by most thinkers of the Hellenistic Age (from the death of Theophrastus to the first century BCE). The lecture notes, along with the rest of Aristotle's library, were inherited from Theophrastus by Neleus, who, upon falling out with Strata over the doctrinal direction of the School, transported them from Athens to Scepsis, a town of Troas. In the first half of the second century BCE, the heirs of Neleus hid the manuscripts of Aristotle in a cellar, away from the Attalid kings of Pergamum who were seeking to build a library to rival Alexandria. The wealthy bibliophile Apellicon of Teos, somewhere between the end of the second century BCE and the beginning of the first century BCE, bought the moldy and insect-ridden manuscripts and brought them back to Athens, where he attempted to edit and publish them, but produced faulty editions due to a lack of philosophical acumen. When Athens was conquered and sacked by Sulla in 86 BCE, Sulla seized the manuscripts and transported them to Rome. There the grammarian 1 Gerson (1999), second paragraph. vi Tyrannion, admirer of Aristotle, seduced Sulla's librarian (so says Strabo) and gained access to the texts, transcribing them and publishing further corrupt editions. Andronicus of Rhodes, obtaining his source material from Tyrannion, then produced the superior, monumental and authoritative edition that is the basis of the works of Aristotle that we possess and puzzle over today.2 Throughout the centuries, the task of the Aristotelian commentator has been to crack the obscurity of the esoterica. A great tradition has been preserved by commentaries on the works of Aristotle. How are we indebted to it, and how now shall we take a position in relation to it? On the one hand, even if Aristotle has not been properly understood in most of the tradition, the very fact that he was wrestled with by that tradition has been an inseparable part of the history and progress of science in the West. On the other hand, our best hope, perhaps, for coming to a proper understanding of Aristotle's texts, lies with that small part of the tradition that purports to grasp Aristotle at his most obscure: namely, in the Posterior Analytics and in the application of this methodology in his other writings. In this strand of the great tradition, the difficulty of the esoterica is attributed to the principle of economy that Aristotle employs, "wherein general methodological procedures are logically stated beforehand in actu signato, and then applied in each science in actu exercito."3 In other words, if the methodology of the Posterior Analytics is not adequately grasped, there can be no hope of an adequate grasp of the other works, because they presumably presuppose its methodology and are faithful to it. 2Reale(1990), 11-19. vii The Aristotelian-Thomistic tradition is that strand of the great Aristotelian tradition that offers, through the explication of the Aristotelian methodology, the promise of unlocking the secrets of the esoterica. In this study we propose to mine this strand of the tradition for insights that shed light where commentators, less familiar with the tradition of Thomas Aquinas's explication of Aristotle, come to grief. We proceed cautiously with this task, well aware of the fact that to grasp Aristotelian methodology is difficult for any commentator on Aristotle, even for the strand of the exegetical tradition from which we wish to draw our assistance.4 Aristotelian methodology is poorly understood by almost all readers, and not just in actu signato, in the Organon, but most especially in actu exercito, in the rest of his corpus. We can hardly accomplish singlehandedly a complete rehabilitation of the Aristotelian methodology, when it is so underestimated and underappreciated. Accordingly, we pursue only the modest project here of showing the integrity of the Aristotelian conception of science and demonstration as regards four specific problems (concerning first principles, motion, place, and time). But there are two objections that call our project into question at the outset. These two doubts stem from the fortunes of reason and revelation in the modern world. First, the Aristotelian-Thomistic tradition is in decline, and the Aristotelian method of demonstration that it propounds is preserved only in dogmatic theology, where it is even now widely held in disrepute. Thus, Aristotelian methodology, as explicated by Aquinas, seems to be of interest only to those wanting to understand the Thomist traditions that 3 Wallace (1957), 92 n.3 4 See Appendix III below for more on the River Forest school of Thomism from which we take our bearings. viii shaped Catholic theology. In fact, this is why Aristotelian methodology, as explicated within the Thomistic traditions, is so widely ignored today in Aristotelian studies: prior commitment to a revealed religion appears to be the only reason to grapple with it. Second, the advances of modern science hold • themselves up as the great achievement of reason in modernity. These advances, so the story goes, were gained by overcoming Aristotle and his methodology of demonstration. Here Galileo and his struggle with revealed religion is the paradigm case. Aristotelian methodology is obsolete, as is demonstrated by Galileo's breaking free of the religious tradition that clung to that methodology, and by his inaugurating the successes of modern science. Hence anyone wishing to go along with the greatest achievements of reason in the modern world allegedly has no choice but to repudiate Aristotelianism. In answer to the first objection, that Aristotelian methodology is an obsolete theological method, of interest only to those preoccupied with the dogmatic definitions of revealed religion, we answer that our studies here do not depend on the premises of revelation. While drawing upon the illumination Aquinas sheds on Aristotle, we set aside the controversy over what Thomas adds to Aristotle. For example, it has been argued that Aquinas imputes non-Aristotelian principles to Aristotle.5 We shall pass over the question of whether natural reason can know these "non-Aristotelian principles" without the aid of revelation. Instead, we shall focus on the recovery of the insights into Aristotelian methodology that the revelational tradition has preserved for us. Perhaps our study of the 5 Jaffa (1952), 187, lists some non-Aristotelian principles imputed to Aristotle by Aquinas as: "1. Belief in divine particular providence. 2. Belief that perfect happiness is impossible in this life. 3. Belief in the necessity of personal immortality to complete the happiness intended, evidently, by nature. 4. Belief in ix method of demonstration and definition in Aristotle will, by showing the permanent validity of the Aristotelian methodology for explicating the Aristotelian esoterica, result in one of the following: either in increased credibility for the Aristotelian-Thomistic tradition on matters of natural and revealed theology, simply by the association of this tradition with the most penetrating insights into the other problems posed for unaided reason by the Aristotelian esoterica; or in showing, on account of its permanent philosophical and scientific worth, the urgent need for recovering Aristotelian methodology from the grave of Thomistic theology where it is buried alive. In other words, rather than hold our study under suspicion for dogmatic allegiances, the reader may rest assured that it does not depend on them, and that its conclusions may be used either in the service of reason or of revelation, according to the disposition of the reader. In answer to the second objection, that Aristotelian methodology has nothing to do with modern science, we simply point to the body of scholarship that has unearthed the positive influence of the Aristotelian tradition upon Galileo6 and the development of physical science.7 The Aristotelian concept of science, as presented in the Posterior Analytics is of permanent scientific and philosophical interest, especially with regard to its promise of an architectonic unity among the speculative disciplines.8 Perhaps in this regard it holds great promise for the future self-understanding of modern science and all human knowledge. Yet, for our purposes here, it does not matter whether an interpretation of the history of science, whereby Aristotle's method is vindicated as being personal immortality. 5. Belief in the special creation of individual souls. 6. Belief in a divinely implanted 'natural' habit of the moral principles." 6 See Appendix II below ("Galileo's Early Notebooks") 7 In particular, Weisheipl (1959) and Weisheipl (1985). in essential continuity with science's progress, is accepted by the reader or not.9 For our project here is not to demonstrate Aristotelian methodology at work throughout the history of science. Our project is only to show it employed in its original context, in connection with four particular problems (concerning principles, motion, place, and time). In sum, Aristotelian methodology is underestimated and underappreciated. A proper understanding of the Posterior Analytics, especially as explicated by Thomas Aquinas and the Aristotelian-Thomistic tradition, renders much contemporary commentary on Aristotle otiose. There is an urgent philological need to apply Aristotle's own methodology to the exegesis of Aristotle. There has been a colossal "failure of contemporary thinkers to appreciate the way in which Aristotle's approach to the world of nature was truly scientific according to his own definition of science."10 We wish to illustrate this by means of a few notable examples (motion, place, and time) from the Physics. Therefore we must begin our study with an explication of Aristotle's definition of science and demonstration. 8 Wallace (1957), 90-91. 9 Although our own allegiances are made clear in Appendix I. 1 0 Wallace (1957), 91. xi Acknowledgements Thanks to Professor Robert B. Todd for enduring many drafts of my translations, and for teaching me how to do good translations for philosophical purposes. If my translations of Aristotle and Themistius are lucid and useful, and if my thoughts on Aristotelian scientia naturalis are now mature, then please attribute any such progress to arduous work under his patient pedagogy. Otherwise it is my own fault. I am also greatly indebted to Professor Todd for tracking down the manuscript of James Athanasius Weisheipl's commentary on the Posterior Analytics. The scholarship of J. A. Weisheipl, along with that of William A. Wallace and Vincent Edward Smith, has been the sine qua non of my studies here.11 Finally, we are all indebted to Aristotle, "the master of those who know".12 Parua Stagira decus tantum proferre sophorum, Implere & potuit Solis vtramque domum? Nemo acie ingenij, par verbis nulla facultas, Vt missum t err is numen honor e colo. Could little Stagira produce so great an honour among the wise, and could it fill both houses of the sun? [There was] no one with the keenness of his native talent, [There was] no ability with words equal [to his, and] so I honour and cherish [that] divine spirit sent earth.13 1 1 See Bibliography below 1 2 Wallace (1996), 426 1 3 From the cover illustration of Lang (1992). xii CHAPTER I Methodology: Scientia 1.1 Science: Certain, Causal, Demonstrative What is science? The modern meaning of "science" is either too loose or too obscure. "Science" can mean, quite broadly, organized knowledge of any kind, covering everything from physics to hotel management. Or it can mean, more narrowly, knowledge involving only measurement, correlation, and controlled experimentation. This latter meaning, however, is obscure, because its exaltation of metrical description cannot be accounted for by means of metrical description alone.14 In contrast, Aristotle defines science neither too broadly nor too narrowly, but precisely: Science is certain knowledge through causes and effected by demonstration.15 This definition may seem confusing, especially the phrase "certain knowledge" (because one might ask whether "uncertain knowledge" is still knowledge or whether it is belief). To make clear its content, let us restate it, giving the Greek to which it indirectly refers: Science ['ETUCXOCOGCU eKaoxov a7tA,eocJ is certain [6xt eKeivou aula eaxi] knowledge [yivcbaKeiv] through causes [xnv x' aixtav 8i' f|v XO vxpaypd eaxtv] and effected by demonstration [pf) ev8exeo9at xoux' aXXwc, e%etv]. And perhaps it is most helpful to restate it yet again, giving just one Greek term for each key English word: Science 1 4 Smith (1958), 2-3 1 5 This is the compressed formulation made by Wallace (1957), 91, of Aristotle's definition at An. Post. 71b 9-16; Cf. Weisheipl (1958), 2, and Smith (1958), 4 1 [e7tioxf|ii.T|] is certain [cciA-coq] knowledge [yvcbcucj through causes [crixicu] and effected by demonstration [a7to8eiKTiKf)]. Science is the species being defined, and its genus is knowledge. In other words, science is a special type of cognition, i.e. a special type of knowledge in general. (Sometimes people take the word knowledge to be synonymous with science, but that is not the meaning of knowledge here. Here, knowledge is the more general term, i.e. the genus of cognition in general, of which science is the species to be defined.) The other three terms (certain, causal, and demonstrative) correspond to the three differentia given by Aristotle16 to define the species science of the genus knowledge. Causal, i.e. through causes, represents the first difference given by Aristotle,17 XTJV T1 aixiav ... 8i' f|v TO 7tpay(j.d EOXIV: "the cause from which the fact results." Certain represents the second difference,18 oxi E K e i v o u cxixia saxi: "that it is the [proper] cause of the fact."19 Demonstrative, or effected through demonstration, represents the third difference, |rf) EVSEXEOGCU XOVJX' CXAACOC; E%EIV: "and that the fact cannot be otherwise." Demonstration is a scientific syllogism, i.e. a syllogism that allows us to know by the mere fact that we grasp it: CXTCOSEI^ IV 8E A i y c o rjt)A,X,oyirjir6v Erciaxriuovucov-e7cioxriiioviK6v 8e A i y c o KCC6' 6V xcp EXEIV arjxov £7tiaxd(ie9a.20 In other words, the form of the syllogism guarantees that, simply by the fact that it is executed, its conclusion cannot be otherwise. A flaw in the conclusion of a syllogism can only be due to a flaw in 16 An. Post. 71b 9-16 17 An. Post. 71b 11-12 18 An. Post. 71b 12 1 9 As Wallace (1962), 16, puts it: "we know that that cause is what makes the object to be what it is" 20 An. Post. 71b 17-19 2 its premises. But if its premises indicate proper causes of the fact, as Aristotle specifies with the first two differentiae (causal and certain), then the conclusion cannot be otherwise, provided that the syllogism is in the proper form. Its proper form is that which guarantees the results of science. In the demonstrative syllogism, i.e. in the scientific syllogism, we reason from premises more certain quoad nos to conclusions more certain quoad se.21 The rest of this study will clarify the Aristotelian understanding of science that we have summarized above. At this stage, it is most important simply to recognize that the three differentiae given to identify scientific knowledge (certain, causal, and demonstrative) are grounded in Aristotle's text. We shall proceed to argue that the Aristotelian demonstrations concerning motion, place, and time are not well understood by most commentators on the Physics. This widespread failure is due most of all to the prejudice that the modern conception of science is somehow superior to Aristotle's. By focusing on Aristotelian methodology, i.e. the careful structure of definition and demonstration in the texts, we shall argue that Aristotle's definition is "truly scientific"22 and superior to the self-understanding of modern science. Modern physics, in fact, occupies only one of the regions of knowledge already carefully defined by Aristotle: namely, scientia media. The proverbial obsolence of Aristotle's Physics is due to the alleged superiority of Galileo and Einstein's scientific knowledge of motion, place, and time. However, we shall claim that there is room for their brand of science within the architectonic of Aristotle's grander vision of science. 2 1 Wallace (1962), 21. We follow Wallace's preference for the pithy Latin terminology. 3 But first, in order to understand properly how Aristotle's demonstrations concerning motion, place, and time are neither obsolete nor in conflict with the progress of modern science, we must clarify what the principles of a demonstration are for Aristotle. This will clarify what physical science in the Aristotelian sense of science is. Before we can discuss some demonstrations in the Physics that are still unsurpassed (and, moreover, harmonious with modern science), we must clarify the causal and certain character of all demonstrative science, and of physical science in particular. Wallace (1957), 91 4 1.2 Certain: Through Proper Causes If physical science, in its demonstrations, is to be certain knowledge in terms of causes, as defined above,23 then "it needs principles to be causal knowledge and first principles to be certain knowledge."24 In other words, the scientific knowledge of physical science will be causal but these causes must be proper, i.e. they must be founded on certain knowledge of the causes. In Aristotle's own formulation, it is not just knowledge of "the cause from which the fact results" but also "that it is the cause of the fact"; i.e. not just causal, but also certain. And the certainty of what is predicated of the subject matter of a science depends on the subordination of that science within the architectonic of knowledge. If the reasoning within a particular science is properly founded both on first principles extrinsic to the science and through mediate principles intrinsic and proper to the subject matter within it, then it is scientific reasoning that is certain in Aristotle's sense, because it can be traced back in a chain of syllogisms right up to first principles which are self-evident and therefore absolutely certain. What this means is best expressed by showing the possible types of causal and certain demonstrations. There can be demonstrations of the fact (quia), and demonstrations of the cause (propter quid). The former (demonstratio quia) are more characteristic of science in its merely causal sense, i.e. as knowledge through causes?5 The latter (demonstratio propter quid) is, however, more characteristic of science in its In our parsing of the differentiae of the definition at An. Post. 71b 9-16 above in 1.1 Smith (1958), 11 Note that the most general difference of science's type of knowledge is knowledge through causes. 5 certain sense, i.e. as certain causal knowledge.26 The meaning of "certain" here is, not a synonym for "demonstrative" [d7to8eiKxiKfi], but instead indicates the dignity of the demonstration (and perhaps would be better put in English as "proper knowledge" ['Ercicj'cacjGat arcXcocJ than as "certain knowledge").27 The dignity of the demonstration, whether it is "better" (potior)2* than another demonstration or not, is based on the order of predication in the demonstration. Before we explain what this "order of predication" is, we should first be clear on the relation between science and demonstration. We have set forth the Aristotelian conception of science as certain, causal, demonstrative knowledge. We stated that Aristotle's definition of science contains three differentiae, one of which is the differentia demonstrative. However, looking at the text, apparently Aristotle defines demonstration separately from science. For Aristotle, science is certain knowledge of things in terms of proper causes or reasons or principles.29 Demonstration, however, is a syllogism producing such knowledge.30 But, in fact, these are not two separate definitions of two different things. The definition of demonstration simply follows the definition of science, in order to make clear what the third differentia means: i.e. science, most properly speaking, is demonstrative. 2 6 Note that the more specific difference of science's type of knowledge is certain knowledge through causes. 2 7 But we stick with the formulation of Wallace (1957), 91: "certain knowledge". For, in another way, this formulation is superior, because it also covers the other sense in Aristotle of the concept "certain," i.e. particular (eKaoTov djrAcoq). And this is appropriate for Aristotle, for whom "certainty" is not merely a formal, logical concept, but rather the demonstration appropriate for the particular subject matter: 'E7ciOTacj6ai E K a a t o v ankSx,. 2 8 Wallace (1962), 20 29 An. Post. 71b 9-16 30 An. Post. 71b 17-18 6 These two definitions of science and demonstration are two ways of expressing the same thing. The two definitions are related in the following way. The relation between science as certain knowledge through causes and science as effected by demonstration is a relation clarified only when we understand what the principle of a demonstration is. The middle term of a demonstrative syllogism represents the cause or reason or principle for connecting the major term with the minor in the conclusion.31 Demonstration is a syllogism in which the causal knowledge or middle term is certain, and therefore it yields certain knowledge in terms of causes, i.e. it yields science?1 Other types of syllogism, beside the demonstrative, are the dialectical, the rhetorical, and the literary.33 But what makes a middle term certain in itself? This is a very impotant question. It brings us back to the question of the order of predication in demonstrations. For the certainty of middle terms admits of gradation: i.e. considered with regard to the subject of the demonstration, some causes are more proper than others. For a demonstration to be certain, a middle term must be proper with regard to its subject. When perfected, science is knowledge through proper causes.34 In knowing proper and precise, as opposed to common and imprecise, causes, the mind knows better how one thing differs from another. This means knowing the subject matter of a science 3 1 Smith (1958), 4-6 3 2 Cf. Smith (1958), 5: "Demonstration is a syllogism in which the causal knowledge or middle term is certain. Put into other form, knowledge resulting from demonstration is always a certain knowledge in terms of causes, precisely what Aristotle called science." 33 Ibid. 34 An. Post. 71b 10-11 7 better. A middle term that represents a proper cause of a subject is a commensurate universal of that subject, i.e. appropriate to and coextensive with the subject.36 Let the subject of a demonstration be S. The form of demonstration is: "(All) M is P, but (all) S is M; therefore, (all) S is P."37 The middle term M has to be proper to S. (This means it is all or part of the real definition of S.)38 Discovering the proper M for a demonstration about S is not an exercise in logic, as if any observation could be plugged into a chain of dry reasoning. On the contrary, discovering the proper M that explains the predication of P to S is a genuine advance in knowledge, because it will clarify all other strands of scientific reasoning, showing how the principle M of this demonstration places the conclusion about S ("S is P") in relation to all other known principles, whether extrinsic or intrinsic to the matter under consideration. Otherwise, the demonstration utilizing M will simply be less certain, because it will be a demonstration not of the reasoned fact (propter quid), but merely of the fact (quia). For example, consider the negative demonstration that a wall does not breathe because it is not living.39 S is the wall, M is "not living" and P is "not breathing." M is not a proper cause and hence the demonstration, although still a priori (because M is a cause and not an effect of P), is only a demonstration of the fact (quia). M is a remote cause. "Many living things do not breathe, and yet the fact of the wall's not being alive is sufficient here to explain its not breathing."40 The proper cause of the wall's not breathing 3 5 Smith (1958), 5-6 36 Ibid. 3 7 Wallace (1957), 94 3 8 What a "real definition" is best discussed in Smith (1952), and in Wallace (1996), 286 ff. 39 An. Post. 78b 15-27 4 0 Wallace (1996), 295 8 is not having lungs. But if M were "not having lungs" instead of "not living" then the demonstration would be propter quid. Science in the Aristotelian sense, then, is produced by demonstration. Demonstration can be causal {propter quid) or factual (quia). The propter quid middle term is the real definition (at least in part) of the subject, and hence it provides the real cause or reason why the attribute belongs to the subject. The quia middle term usually represents the cause or reason why we know that the attribute belongs to the subject; it is not the proper cause in reality itself why this is so. In general, demonstratio propter quid goes from cause to effect (i.e. is a priori) and demonstratio quia goes from effect to cause (i.e. is a posteriori). But there are cases of quia demonstrations that are a priori; for example, when an a priori demonstration is made from a remote but not a proper cause, as in our example of the wall not breathing because it is not alive. Table 1 sums all this up schematically: 9 Table 1: Certainty in Demonstrations (Order of Predication)' Demonstration Order of Predication Example: "S is P because M . " (S = wall) propter quid a priori (reasoning from cause M to effect P) "The wall does not breathe because it does not have lungs." P = not breathing M (proper) = not having lungs quia a priori (negative proof through a remote cause in the order of predication is a priori but not propter quid) "The wall does not breathe because it is not alive." {demonstratio quia because many living things do not breathe) P = not breathing M (remote) = not living quia a posteriori (reasoning from effect M to cause P) "The wall does not have lungs because it does not breathe." P - not having lungs M (effect) = not breathing Note that when we speak of science as "certain" in the Aristotelian sense, we are referring to the order of predication involved in the demostration. In other words, we speak of the real relation of cause and effect with regard to the subject matter of the demonstration. In one sense (the usual English sense of "certain"), all demonstration is "certain" (cx7to5etKxiKfi) when in syllogistic form, because it "cannot be otherwise" (pf] ev8e%ec9cu TOUT' aXkoic, e%etv). But when we speak of Aristotelian science as "certain," this formal, logical sense of "certain" (coxoSeiKXiKTi) is not the meaning we should have 4 1 After Bennett (1943), 37 and Wallace (1996), 294-295 10 in mind. This is because that formal, logical sense (d7to8eiKTtKfi) is the sense indicated by the third differentia demonstrative (i.e. "cannot be otherwise") in Aristotle's definition of science, which is meant to express the character of the conclusions in a demonstration as more certain quoad se and the premises as more certain quoad nos. Rather, the sense here, of the first differentia, certain (aiik&q), indicates the real, factual relation between the terms of the propositions in the demonstration: OTI eKeivou a ix ia ecm, i.e. what in fact is cause and what in fact is effect with regard to the subject. In other words, a cause is more certain than an effect, and a proper cause is more certain than a remote cause. Therefore, a demonstration will be more certain (really speaking, and not simply logically) when the principle employed in the middle term M is a proper cause and neither a remote cause nor an effect. whether something is a cause or effect of a subject can, of course, only be observed from sense experience and made known through dialectic and induction.42 Concepts are then subordinated to one another in scientific demonstrations when they are cast in terms of the certainty of the order of predication, which is determined by whether the principle used in the demonstration is a cause or an effect. The common caricature of Aristotle is that his science is obsolete because he mostly reasoned a priori and not according to experimentation and sense data, and that Galileo initiated true scientific progress because he did the reverse, starting not from suspect "first principles" but from experimentation. But this is a gross misunderstanding of Aristotelian methodology. It is not our task here to show it, but in fact Galileo's innovations were made possible by the 4 2 An. Post. II. 19 (see Chapter II below) 11 Aristotelian tradition that reflected profoundly upon the Posterior Analytics? Galileo learned the "demonstrative regress" (regressus demonstrativus) from this tradition: the art of discovery by which an a posteriori demonstration quia is convertible to a propter quid demonstration. If an effect is not convertible with the cause, the a posteriori demonstration yields knowledge of the existence of the cause and some of its conditions. However, if the cause and effect are of commensurate universality, then a proper cause has been discovered and the terms M and P may be switched without circularity, i.e. the demonstration may be recast as a propter quid demonstration.44 For example, in Table 1, the cause is "not having lungs" and the effect is "not breathing" and therefore the demonstration is propter quid or quia depending on whether or not "not having lungs" is taken as the principle M of the demonstration or as the predicate P (i.e. propter quid if the former; quia if the latter). It is no mere logical game whether or not "not having lungs" is made the principle M or not. It is not a mere tautology to say, "Having lungs is not breathing," or to say, "Not breathing is not having lungs," although it appears that way to someone not acquainted with the subject matter of the science. Someone not familiar with the matter of the science will be mostly indifferent to the order of predication in the demonstration, and to what is or is not a principle, because they are not sufficiently familiar with all the observations and dialectical inductions made. They will think that demonstration is a mere game of transposing circular definitions. However, the scientist will know the difference between 4 3 See Wallace (1981a), Wallace (1981b), Wallace (1983), Wallace (1984), Wallace (1992a), Wallace (\992b), passim. See our Appendix II ("Galileo's Early Notebooks") for the conclusions we draw from our study of these works. 4 4 Wallace (1996), 295 12 cause and effect. The scientist will know by experience whether the principle of the demonstration should be "having lungs" or "having breath," because he will know the difference between cause and effect. In fact, it is the material presence of lungs in a body that causes breath, and therefore "having lungs" must be the principle of all respiratory science. If a wall without lungs is observed to breathe, then the principle will have to be reconsidered, i.e. a new principle will have to be found, since there can no longer be certain science founded on this principle. "Having lungs" will no longer be the proper cause for propter quid demonstrations about respiration. A proper cause must be the certain middle term of any scientific reasoning about cause and effect. Galileo mastered the art of the demonstrative regress, and was such an innovator because he was such a profound Aristotelian. The demonstrative regress is the conversion of a quia demonstration to a propter quid demonstration when the cause is observed, through careful and deliberate experimention and dialectical reasoning, to be convertible with its effect. The first stage of the procedure is the regress from effect to cause. The cause is materially suspected but not yet recognized formally as the cause. In the second stage, the intellect goes to work, testing to see if the cause is convertible with its effect, by eliminating other possibilities. In the third and final stage, the progression is made from the cause, recognized formally as the cause, to the proper effects.45 The examples and details of Galileo's applications of this Aristotelian methodology do not concern us here. But it does concern us to point out why Galileo and those who imitated him were so successful: i.e. they cultivated the skill of discovering proper causes of things. For while 4 5 Wallace (1996), 300-308 13 any demonstrative syllogism can be called "certain" simply by virtue of the form of its reasoning, it is truly certain when considered in terms of the real, factual description of the relation between cause and effect that it expresses. In other words, science and scientific demonstration are most truly scientific, i.e. certain in the proper sense, when proper causes are taken as the principles of propter quid demonstrations. Therefore, science is certain because it orders demonstrations according to the order of cause and effect. It does this by taking proper causes as the principles of demonstrations, thereby demonstrating propter quid, and not through a remote cause or through an effect. This order of predication is what is meant when Aristotelian science refers to its knowledge as being certain. It is certain because it is knowledge of proper causes. 14 1.3 Causal: Through Middle Terms We have made clear what is meant when Aristotelian science is called certain. However, we should now discuss what is meant when Aristotelian science is called causal. Because a question arises: What is the difference between a principle (dp%fD and a cause (aixia)? The middle term of a demonstrative syllogism represents a necessary and certain principle. This middle term represents a reality; it is not merely logical, as if it were a hypothetical possibility. To achieve certitude in demonstration, the true scientist must begin with not just any principles as middle terms, but with the first principles of his particular science. First principles are (1) the ultimate sources for everything in the order under consideration, and (2) themselves underived within that order. First principles assure certitude because they give the mind an absolute and unconditioned starting point. Since first principles govern the entire order of a particular science, any conclusions based on secondary principles may be upset when first principles are later discovered and applied to secondary ones.46 There are revolutions in science when new principles are discovered that are seen in fact to be more primary than the ones previously held to be primary. Not infrequently, new sciences are created as the new principles reveal new subject matters for further branches of science. We have indicated all this in our previous discussion47 about what makes a propter quid demonstration certain when we spoke of the architectonic of scientific knowledge (scire simpliciter). Smith (1958), 8-11 In 1.2 above. 15 But what is the difference between a principle and a cause? One might get the impression, from what we have just said, that "cause" refers to a reality, and "principle" merely to the logical function of this reality as the middle term M in a demonstrative syllogism. But this would be a misconception. And when we dispel this misconception we gain a more intimate access to what Aristotle means by science being knowledge through causes. Because one common controversy about "principles" in Aristotle is whether they refer to concepts or propositions. However, as Kahn has intimated, "there is no real dichotomy between a conceptual and a propositional view of the principles."48 This is because the "only propositions in question are essential definitions and assertions of existence."49 In other words, Aristotle's principles are not axioms of the Euclidean type.50 We can best dispel this misconception by seeing how principles are related to causes. We have seen above how propter quid demonstrations must employ proper causes in the order of predication, in order to achieve the highest degree of certainty.51 Now we must understand exactly what these proper causes are. Are they the same as or different from principles? In brief, proper causes in scientific demonstration can be elements, causes, or principles. One Thomist writer sums up the differences among the three in this way: "Every element is a cause and a principle. Every cause is a principle. But there are principles which are neither causes nor elements; and causes which are not elements."52 Principle is the loosest term; element is the strictest. This is the clarification Aquinas 4 8 Kahn (1981), 385 49Ibid., 395 5 0 / A i d ,393 5 1 See Table 1 16 brings to Aristotle's writings on the matter. Its consequence is that there is an order among the causes. Elements, causes, and principles stand in the aforementioned relation to one another. Therefore their use as proper causes in demonstrative syllogisms will stand in a similar hierarchy. We can best see this hierarchy by first understanding the relation between Aristotle's three principles of nature (matter, form, privation)53 and four causes (material, formal, efficient, final).54 In brief, the former three are principles of natural things, and the latter four are principles of natural science.55 Aquinas sorts out the relation by referring to Aristotle's texts, and we can sum up his exposition of Aristotle's texts56 in a table. (Note that privation is excluded from consideration because it is per accidens and the four causes are all per se.)51 5 2 Bobik (1998), 56, commenting on Aquinas, De Principiis Naturae, 3.20 "Phys. 1.7, 189b 30-191a22 54 Phys. II.3, 194b 16-195b 28 5 5 Aquinas makes this clear in his commentary: / Phys. ("de principiis rerum naturalium") and / / Phys. ("de principiis scientiae naturalis"). Cf. Spiazzi (1955), xi 5 6 From I Phys., lect. 1 n. 5, and De Prin. Nat. chapters 3-4 5 7 As Aquinas explains in De Prin. Nat., 3.17; Cf. Bobik (1998), 39-43 17 Table 2: Hierarchy of Middle Terms (Order of the Causes) Order of the Causes Phys. I Meta. V.3 Meta. XII.4 (1070b 22-27) Aquinas (I Phys. and De Prin. Nat.) final cause extrinsic cause ("principle") final cause (prior by way of perfection) efficient cause extrinsic cause (principle) efficient cause (principle: prior by way of generation) form principle "element" intrinsic cause ("element") formal cause (prior by way of perfection) matter principle element intrinsic cause (element) material cause (element: prior by way of generation) The inverted commas in Table 2 indicate how Aquinas reconciles the texts, and the columns from left to right show the movement of this reconciliation, as the terminology becomes more refined. Loosely speaking, the intrinsic principles of natural things (form and matter) are elements, as opposed to the extrinsic principles (efficient and final) of things; but all four are, strictly speaking, causes of natural science when they are the proper causes used in demonstrations of natural science. If they are not proper causes, then the looser terms can apply. For example, efficient causes are most frequently per accidens and therefore they are more likely to be called principles than causes. (Of 18 course, if they are per se, they are best called causes.) Accidental form can be called an "element", but substantial form is best called a "cause", since the material cause is more properly the element, i.e. the matter it informs. The material causes are strictly speaking the elements of natural things. In addition to the material cause, the formal cause is also the intrinsic principle of the natural thing. Form is ranked higher than matter because it is the act brought to the potency of matter. The efficient cause is extrinsic to the natural thing. Because extrinsic causes can be causes either per se or per accidens of the natural thing, it is proper to speak of the efficient cause as a principle rather than a cause. If it is per se, then it is a cause; if per accidens, then it is a principle. Hence, strictly speaking, the efficient cause is a principle, but when we consider it among the order of the four causes, we are treating it only in its per se sense (just as privation is omitted from the hierarchy). The final cause stands at the summit as causa causarum. The formal and final causes are prior by way of perfection, whereas the material and efficient causes are prior by way of generation. Hence the material and efficient causes are subordinated beneath the formal and final causes respectively. And thus the order of the causes is established from the way things in fact are. Perhaps it would be helpful to sum up the order among elements, causes, and principles, by returning to and explicating the Thomist writer's summary with which we began our discussion: First, "every element is a cause and a principle." In other words, the material cause is the primary element of natural things, and therefore it can be called, not just a cause, but properly speaking, the element. Second, "every cause is a principle." In other words, all four causes are also principles of natural things, besides their strict role 19 as per se principles of propter quid demonstrations in natural science. Third, "but there are principles which are neither causes nor elements." The efficient cause can be per accidens a cause. In that case it is no longer strictly speaking a cause, but simply a principle. (For example, when something is moved from blackness to whiteness, blackness is a principle of that movement, although not a cause, since blackness in itself is not a cause of the being of the whiteness coming into being.)58 Fourth, "and [there are] causes which are not elements." The final, formal, and efficient causes are all not elements; but the last two with qualifications: the efficient cause is a cause only when, as we said, it is not a per accidens cause; and the formal cause can be understood as an "element" insofar as it is an intrinsic principle of a natural thing. The formal cause, however, is rightly spoken of as a cause more than as an element, since it is substantial form that the scientist seeks out, and not accidental form. But let us end with a quote from Aquinas at length, for he himself best explains the difference among elements, causes, and principles, with the following gloss on these three terms that Aristotle uses at the very beginning of Physics 1.1: "Therefore, by principle [Aristotle] seems to mean moving causes and agents in which, more than in others, there is found an order of some progression. By causes he seems to mean formal and final causes upon which things most of all depend for their existence and their coming to be. By elements he means properly the first material causes. Moreover he uses these terms disjunctively and not copulatively to point out that not every science demonstrates through all the causes. For mathematics demonstrates only through the formal cause. Metaphysics demonstrates through the formal and final causes principally but also through the agent. Natural science, however, demonstrates through all the causes. ... For a man thinks he knows something when he knows all its causes from the Aquinas' example in De Prin. Nat. 3 20 first to the last. ... For matter is for the sake of form, and form is from the agent for the sake of an end, unless it itself is the end."59 In conclusion, a principle (dp%f|) is a source or starting point. It implies an orderly process. It is an originative source of order in the process. Principles can simply be beginnings. A cause (aixta), however, is a principle upon which a thing depends in being or becoming. Thus, every cause is a principle but not every principle is a cause.60 Aquinas sees well how the order among the causes implies an order of the demonstrations in which they are employed. Therefore, while the middle term of any demonstration is a principle, the middle terms or principles of scientific demonstrations will be causes. And natural science's demonstrations will use all four causes. To say that science is knowledge through causes is to understand how the causes it uses in its demonstrations as middle terms stand within a strict hierarchy of elements, causes, and principles. Science's causes are proper, per se causes of things, and not mere per accidens elements or principles. Therefore, to sum up all our considerations thus far, we can see that science is certain because its demonstrations use proper causes (neither remote causes nor effects) as its middle terms, and that science is causal because its demonstrations use proper causes (not incidental principles or elements) as its middle terms. The latter point necessitates that the order among elements, causes, and principles will also mean an order among demonstrations themselves. It is to an explicit outline of this order of the types of demonstration that we now turn. 591 Phys. lect. 1 n.5; English translation Blackwell-Spath-Thirlkell (1963), 5 6 0 Smith (1958), 7 21 1.4 Demonstrative: By Order of the Causes Science is effected by demonstration, i.e. it is demonstrative. It thereby determines that the conclusions about its subject matter cannot be otherwise. Contrary to Aristotle, the climate of opinion today believes that science can only be eternally hypothetical, and that its knowledge only extends as far as experiment, for further experiment can always overturn the current catalogue of results. But an Aristotelian can see that this opinion is in fact founded on an abuse of the term "science", where science has been redefined to mean a dialectical method, and not certain knowledge through causes and effected by demonstration. Because the proper causes of natural things are usually hidden from us, natural science most often reasons dialectically from effect to cause, and then uses experiment and dialectic to justify its tentative conclusions about cause and effect. Yet not everything in modern science is tentative, otherwise there would be no difference between science and playacting. Aristotelian-Thomistic science asserts that there must be firm demonstrations in natural science upon which all further investigations, however tentative, are built. As Aristotle recognizes, there must be first principles of all knowledge in general, and also first principles of each science. Perhaps Aristotelian methodology can help uncover the first principles that are assumed by the practice of dialectic in modern natural science. For as Wallace remarks in his tentative reconstruction of the Aristotelian methodology to be found in some demonstrations in the science of nature, ancient and modern: "In the things 22 regarded as true and certain by modern science, the original contributors were possibly more Aristotelian in their thinking than anyone hitherto has suspected."61 By clarifying the structure of the demonstrations of Aristotelian methodology, we will clarify how modern science can indeed have some certain knowledge about the physical world. "It is impossible that certain, mediate knowledge arises per se from dialectics; the dialectical process may well be the occasion for discovering such truth, but the certitude itself is attained by seeing the cause or reason why the reality comes to be as it is."62 In other words, real causes can be discovered by science, and such demonstrative knowledge is at least implicit in all successes of scientific research. The task is to render it explicit via Aristotelian methodology and thereby discern the difference between what science knows with certainty (scire simpliciter) and what is merely dialectical or hypothetical in its research. In his writings, Wallace has attempted a beginning of such a project. We wish to draw upon his classification of Aristotelian demonstrations, in order to apply them later on in our study and show how they illuminate Aristotle's arguments in the Physics. The two main types of demonstration are a priori and a posteriori demonstrations. The former reasons from cause to effect, and the latter from effect to cause. We have already noted this above, when we highlighted the certain character of science. Science is most certain, i.e. science is most truly science, when what it knows is effected by means of propter quid demonstrations a priori. However, in the normal order Wallace (1957), 116 Wallace (1957), 117 23 of knowing within the study of nature,63 an a priori demonstration usually comes after an a posteriori demonstration, as a product of experiment and dialectical reasoning that eventually confirms the convertibility of the effect with the cause. Nevertheless, while this is an instructive observation about the way human knowledge proceeds (i.e. struggling from sense observations to reason about hidden causes), and while this is an indispensable hermeneutic key for understanding the actual progress of science since the seventeenth century,64 for the purposes of our study here, we need only note the formal difference between a priori and a posteriori demonstrations, and do not need to explore their interrelation in the art of scientific discovery. As shown in Table 1 above, a priori demonstrations can be either propter quid or quia. Propter quid demonstrations contain a proper cause convertible with the effect. Quia demonstrations contain a common or remote cause not convertible with the effect.65 As suggested by Table 2 above, natural science uses elements, principles, and causes in its deliberations. But as we saw from our consideration of what these terms mean, natural science uses these explanatory factors strictly as causes when they function as a middle terms giving the propter quid demonstration of a conclusion. That is, if "S is P" is the conclusion, and if M is adduced as the proper reason why this is so, then it is a cause. And if it is a cause, it stands within the hierarchy of order among the causes, as indicated in Table 2 above, and as explained in the writings of Aristotle and Aquinas. Thus material, formal, efficient, and final causes are used as middle terms in the 63I An. Post., lect. 4, n. 16; Wallace (1957), 93 n.4 6 4 As Wallace has shown in his writings on the demonstrative regress. 6 5 Wallace (1957), 93 24 demonstrations of natural science, since natural science demonstrates through all four causes. This suggests that there are four types of a priori demonstrations, founded on the type of cause (of which there are four in number available to natural science) employed in the middle term. Following Wallace,66 we number them 1 to 4, from material cause to final cause, reflecting the order among the causes themselves.67 However, these four types of middle terms are really sub-types, since the type of the demonstration will derive from what is being demonstration with regard to the subject, i.e. its primary type will derive from the predicate being demonstrated about the subject, and not primarily from the explanatory cause given in the middle term. Before turning to these main types (derived from the predicate), however, let us summarize the four sub-types of explanatory causes (employed in middle terms). This is indicated in Table 3 below: Wallace (1957), 94-96 I An. Post., lect. 16, n. 5; Wallace (1957), 95, n.19 25 Table 3: Sub-Types of A Priori Demonstrations (From Middle Terms) Type of Middle Term Type of Cause M 4 final M 3 efficient M 2 formal M , material Next, before stating the main types of demonstration (based on the predicate) to which these sub-types (based on middle terms) apply, we must consider the difference between definition and demonstration, which is best seen in terms of the predicate. In definitions, the predicate P expresses the whole definition or an essential part of the definition of the subject S.68 However, a definition is per se nota of itself,69 and it cannot be demonstrated. There are four types of per se relations between subject S and predicate P.70 We can best understand what a demonstration is by seeing where these four types of per se propositions show up in demonstrations. The conditions required for a propter quid demonstration (i.e. a scientific demonstration) can be summed up by stating the types of per se propositions that must be present in the major premise (M is P), in the minor premise (S is M), and in the conclusion (S is P):71 The major premise (M is P) is in the fourth mode of speaking per se (where M is here the definitio continens principia passionis); the minor premise (S is M) is in the first mode of speaking per se (where M is 68IIAn. Post., lect. 9, n. 4; Wallace (1957), 94 6 9 Wallace (1957), 96 70 An. Post. 1.4, 73a34-b24; Cf. McKirahan (1992), 85-102 26 here the ipsa definitio); and the conclusion (S is P) is in the second mode of speaking per se (where the passio is predicated of the subiectum).12 We summarize the relation between propositions nota per se and scientific demonstration in Table 4.73 Table 4 states the Aristotelian conditions for a scientific demonstration, i.e. what per se nota judgements must constitute that demonstration, and also the conditions under which the demonstration itself can become a definition. This latter point — concerning the conditions under which the demonstration itself can become a definition -- is of the utmost importance for understanding Aristotelian methodology. It is the way an entire demonstration can become a definition by what Ross calls "regrouping its contents."74 An. Post. 1.6-12 Weisheipl(1958), 16 Based upon An. Post. 1.4, 73a34-b24; Weisheipl (1958), 14-16, 39; and Wallace (1957), 94-97 Quoted by Smith (1952), 356: Ross's Aristotle's Prior and Posterior Analytics (Oxford, 1949), 632 27 Table 4: Modes of Nota Per Se Predication Mode Judgment Expressed in the Proposition Occurrence in Demonstration Per se 1 M is the whole definition or part of the definition of S Minor premise of the demonstration (S is M) Per se 2 S is the material cause or the proper subject of the P attributed to it, i.e. P is a propria passio of S (S enters into the definition of P) Conclusion of the demonstration (S is P) Per se 3 signifies autonomous existence of subject S from accident P Per se 4 P is the proper effect of the causal action of M, i.e. produced by M formally as a proper cause, i.e. P is formally an effect and not part of the definition Major premise of the demonstration (M is P) Per se 4 S is both proper cause and proper subject when P is an accident i.e. same as per se 2 but S is also the proper cause because of M definitio est demonstratio positione differens (94a 12-13) Because this point (concerning "regrouping the contents") is so important, let us try and clarify this relation between definition and demonstration with an example. We will construct an example referring to the proper form of propter quid scientific Based on An. Post. 1.4, 73a34-b24; Weisheipl (1958), 14-16, 39; and Wallace (1957), 94-97 28 demonstration, the mode Barbara of the first figure, viz. "(All) M is P, but (all) S is M; therefore (all) S is P."76 First, in Table 4 we see that the minor premise ("S is M") of a demonstration is a formal definition, in the 1st mode dicendi per se. Accordingly, for our example, take the per se 1 minor premise, "Blood [S] is a fluid of limited quantity kept in constant motion in one direction [M]."77 This is a real definition, formally stating part of the definition of blood. This definition is an indemonstrable statement of essential nature.18 It becomes such an indemonstrable formal statement through induction, as intelligence (intellectus) raises the experiential observations of material components up from experience of a subject to the level of a formal statement of what is nota per se about its essence.79 Although M is a material principle (i.e. the material facts it describes could be considered as the origin of other material properties in the body), when M is taken as a predicate in this per se 1 judgement, it is being considered formally as part of the definition of S, and not as a cause. Second, in Table 4 we see that the major premise ("M is P") of a demonstration makes a formal statement about cause and effect, in the 4th mode dicendi per se. Accordingly, for our example, take the per se 4 major premise, "A fluid of limited quantity kept in constant motion in one direction [M] is moved circularly [P]."80 Here the predicate P, "moved circularly," is the proper effect of the causal action of M, "a fluid of limited quantity kept in constant motion in one direction." This is an important point: the 7 6 Wallace (1957), 94 7 7 Wallace (1957), 112; Cf. Wallace (1996), 350-355 78 An. Post. 94a 11-12; Weisheipl (1958), 42 79 An. Post. 11.19; Cf. Chapter II below. 29 fact that here P is subordinated to M as effect to cause. In other words, blood is "moved circularly" because it is a fluid of limited quantity flowing continuously in one direction, and not vice versa.81 The material property of circular movement is due to the material fact that blood is limited in quantity and kept moving in one direction. Therefore, the major premise "M is P" considers this material cause M formally, i.e. precisely as the cause of P. That is what speaking in the per se 4 mode means. Even though the fact that blood is "a fluid of limited quantity flowing continuously in one direction [M]" could be considered a material effect in one sense (e.g. as an effect of the efficient causality of the heart), with regard to the material property "moved circularly [P]," however, this M is a cause. Why? Because the material property P is consequent upon the material cause M. Hence the material cause M can be considered formally, in the major premise mode's of predication, i.e. in the 4th mode dicendi per se. And this is the major part of science's reasoning about cause and effect. The scientist observes the material phenomena (circular movement; limited quantity with constant flow) and formally subordinates some material properties (circular movement) to material causes (limited quantity with constant flow).82 The formal statement "M is P" can then be the scientist's major premise in a propter quid scientific demonstration, because it is his formal statement about subordination of cause and effect. Third, in Table 4 we see that the conclusion ("S is P") of a demonstration makes a formal statement about cause and effect, in the 2nd mode dicendi per se. Accordingly, for 8 0 Wallace (1957), 112 8 1 Galen thought blood in animals to be produced centrally and distributed to the extremities, gradually absorbed in the process; Harvey demonstrated otherwise: Wallace (1996), 350 8 2 Wallace (1996), 350-355 30 our example, take the per se 2 conclusion, demonstratively drawn from our two premises, which would be, "Blood [S] is moved circularly [P]."83 Here S is the subject of the proper passion P. We call P a "proper passion" because the circular movement [P] is a proper accident of the subject S [blood]. We call P a proper accident because blood can stop moving circularly (e.g. when the heart stops beating, or is ripped out of the chest in combat, etc.); it is not the whole essence of blood that it is always and everywhere in circular motion (e.g. it can be spilled out on the ground). Nevertheless, P is a proper accident of blood because it is a property that reveals something about the essential nature of blood; P expresses what blood, for the most part, does by its very nature. In fact, when P is predicated of S, this is special kind of scientific knowledge; because to say, "Blood [S] is moved circularly [P]," is more scientific than to say, "Blood is spilled on the shirt here." And the reason why "S is P" has acquired such a scientific status as a proposition here, is because it is the conclusion of a demonstration giving essential nature.*4 In other words, it is proposition of the 2nd mode of speaking per se.S5 In brief, blood in the body, moved circularly, is the proper subject of the science of blood, and not blood in the shirt; hence the circular movement is the proper accident indicating the proper subject, since it is properly absent from accidental subjects like shirts. When we speak of blood in the shirt, we are not speaking of blood per se; when we speak of blood per se (in the body) we must identify it by its proper accident "moved circularly." Wallace (1957), 112 Weisheipl (1958), 44 An. Post. 94a 13-14 31 Under these three conditions, i.e. with these three types of nota per se propositions (per se 4, 1, and 2: major, minor, conclusion)86 employed in the demonstration, the demonstration can be regrouped into a definition. We can see how this all comes together, if we realize that our example is of the most scientific type87 of demonstration, where we speak of the subject ("blood [S]") both in per se 1 and in per se 2. We speak in per se 1 in the minor premise, and in per se 2 in the conclusion, as we discussed above. Recall the 1st mode dicendi per se (minor premise): "Blood [S] is a fluid of limited quantity kept in constant motion in one direction [M]"). In speaking per se 1, we give the essential nature of S by stating the predicate M. Therefore, when we speak in per se 2 (as we do in the conclusion), "Blood [S] is moved circularly [P]", it is only per se 2 because P is the proper accident of S. And P is a proper accident of S precisely because of M. And this is because M is the material cause of the material effect P. In other words, the per se 2 conclusion is only possible because P is a property, the proper accident, of the subject S, and because M is the proper cause ofP being consequent upon the essential nature of S. Now, there are situations where P is not an accident (and we will state the types of demonstrations below),88 but in the situation here,89 S is not only the proper subject of the property P, it is also the proper cause of P, and therefore the conclusion "S is P" also speaks per se 4 as well as per se 2. In other words, we say that S is the proper cause of the property P because M is both the formal definition of S and the proper material cause of P. That is, when P was subordinated to M in the major premise 8 6 See Table 4 8 7 Type A in Table 5 8 8 Types B, C, D, in Table 5 8 9 Type A in Table 5 32 (by induction), we established the condition for S being the proper cause of the property P. Therefore, in this type of demonstration, given the per se propositions in the premises, a definition can be formed by "regrouping the contents" of the demonstration. We cannot reach definitions by demonstration (only by induction); but we can transpose the contents of a demonstration to lay bare a definition of a more perfect form. In our example, we can "regroup the contents" of the definition, and state a definition of blood, "Blood in the body [S] is moved circularly [P] because it a fluid of limited quantity that flows continuously in one direction [M]." Here, we see our definition has become more perfect than the purely formal one in the minor premise ("S is M"), because we have transposed a scientific demonstration, which consisted of three kinds of per se propositions, into a fuller statement of essential nature ("S is P because M"). We call this type of a priori demonstration Type A, and distinguish it from other types of a priori demonstrations in Table 5 below: 33 Table 5: Types of A Priori Demonstration (From Predicates) Type A a property demonstrated through a cause TypeB an efficient, formal, or material cause demonstrated through a final cause TypeC a formal or material cause demonstrated through an efficient cause Type D a material cause demonstrated through a formal cause Type E physico-mathematical demonstrations (scientia media): P is a property but M is a formal mathematical cause Type A a priori demonstrations are distinguished by their predicate P being a property. We have just seen that because P is a property, the demonstration can be transposed into a definition. We wish now to note that the middle term M can be any of the types of four causes.90 Therefore there are four types of Type A demonstrations, numbered after the four types of causes that can be used as middle terms to demonstrate the property P.91 In our example, we chose a material cause for M: "a fluid of limited quantity that flows continuously in one direction." Hence our example was of Type A,. 9 2 But we can easily see that it possible to demonstrate the proper accident P ("moved circularly") with other types of cause. For example, consider the heart as the efficient cause of the blood's circular movement. We can take "pumped by the heart"93 as the M and make a demonstration of Type A 3 and transpose it into a definition: "Blood [S] is moved circularly [P] because it is pumped by the heart [M3]." Notice, too, that we can 9 0 See Table 3 9 1 Wallace (1957), 94 9 2 See Table 6; Cf. Wallace (1957), 112 9 3 Cf. Wallace (1996), 353-354 34 combine a number of demonstrations of the causes of P together into an even more perfect definition of blood:94 "Blood in the body [S] is moved circularly [P] because it a fluid of limited quantity that flows continuously in one direction [MJ pumped by the heart [M3]." Scientific investigation "consists in finding the proper cause or explanation of a stated truth; and this is identical with finding the propter quid definition of the manifest properties or events." Therefore, by adducing the proper causes M„ M 3 , etc., in Type A demonstrations, we find the propter quid definition of the manifest property P. The other types of a priori demonstrations (Types B through D) occur when P, is not a property, but a cause. Because there is an order of the causes, whereby one cause may be considered to be an effect because of the exercise of a prior causality95 (i.e. prior because higher in the hierarchy)96, it is possible to have a cause as the predicate, as long as the cause in the middle term M is prior (quoad se) to the cause in the predicate P. Combining Table 3 with Table 5, we can set forth all the possible types and sub-types of demonstrations; and we do this in Table 6, which shows in schematic form how the demonstrated cause P is the effect of the middle term cause M as a prior causality (i.e. Types B through D), or how the demonstrated property P is the effect of the middle term M as cause (Types A and E). Note that Type E is a special case where "the middle term pertains to the genus of formal cause, but is in the order of quantity";97 this Type E is characteristic of scientia media that employs mathematical descriptions of natural things. The more causes, the more perfect the definition in natural science. Wallace (1957), 96 Cf. Table 2 and Table 3 Wallace (1957), 97 35 Because these considerations are so abstract, we have selected some examples to illustrate each type of demonstration in Table 6, and placed these examples in Table 7 below. The reader may wish to think over the examples to catch the gist of what the abstract schema in Table 6 describes. Of course, in all the demonstrations in Table 7, "no attempt is made to prove the premises or to indicate the dialectical reasoning that is the normal propadeutic to their acceptance by the reader."99 They are given merely to suggest, in conjunction with the example of blood discussed above, how definition and demonstration are related and how principles and middle terms are employed in them. Taken from Wallace (1957), 100-113 Wallace (1957), 100,n.51 36 Table 6: Schema of A Priori Demonstrations Demonstration Type S = Subject M = Cause in the Middle Term P = Predicated Property or Cause A, Subject Material Property A 2 Subject Formal Property A3- Subject Efficient Property A 4 Subject Final Property B, Subject Final Efficient B2 Subject Final Formal B3 Subject Final Material c, Subject Efficient Formal C 2 Subject Efficient Material D Subject (can be an accident) Formal Material E Subject Formal mathematical Property 37 Table 7: Examples of All Types of A Priori Demonstrations Demo Type S = Subject M = Cause in the Middle Term P = Predicated Property or Cause A , The first unmoved Mover (subject) An indivisible mover with unlimited power (material cause) Incorporeal i.e. outside the genus of quantified things (property) A 2 Whatever undergoes continuous (local) motion (subject) A thing that successively passes through the parts of a continuum (formal cause) Divisible i.e. a quantified body (property) A 3 A summer day (subject) A day that occurs when the pole of the earth is inclined towards the sun (efficient cause) Longer and warmer than a winter day (property) A 4 The direction taken by two opposing chemical reactions (subject) The direction that will bring all reagents in a system most quickly to equilibrium (final cause) The direction that offsets the normal effect of any strain on the system (property) B, Chemical change (subject) A fundamental change by which combining atoms tend to attain the most stable peripheral electronic structure (final cause) Effected by electron transfer [electrovalent bond] and/or by sharing of electrons [covalent bond] (efficient cause) B 2 Gravitational motion (subject) Regular local motion to rest at the center of gravity of the physical environment (final cause) A natural motion, or motion from an intrinsic principle (formal cause) B 3 A green plant (subject) An organism that prepares its own food [carbohydrates] by photosynthesis (final cause) An organism that contains a complex chemical substance [named "chlorophyll"] (material cause) c, Lightning (subject) A discharge of static electricity causing a violent disturbance of the air (efficient cause) Productive of a noise in the atmosphere [called "thunder"] (formal cause) C 2 Static electricity (subject) What is produced in a dielectric substance by mechanical friction (efficient cause) An accumulation of electrons or ions in a particular region of the substance (material cause) D An element (subject; but can be an accident) The first material part of a ponderable body that is capable of stable existence (formal cause) The smallest body that can per se undergo gravitational motion [or the proper subject of natural local motion] (material cause) E A circular wound (subject) A wound that presents the smallest healing surface for its area (formal cause: mathematical) One that heals more slowly than other wounds (property) 38 Finally, a brief summary of a posteriori demonstrations is appropriate to round out our treatment of the topic of the types of demonstration. Even though their schema will not be discussed in depth in our study (of motion, place, and time in the Physics), setting forth these types is of interest, if only because they are the usual procedure of the natural scientist. The demonstrations (about motion, place, and time in the Physics) that we shall discuss later on are all a priori demonstrations. But Aristotle's Physics is unusual natural science, and that is why it is so misunderstood. Its most puzzling demonstrations are a priori. Usually the natural scientist proceeds a posteriori, but this is not contrary to Aristotelian methodology; it is only a lesser part of it.100 The usual scientist demonstrates a posteriori, i.e. demonstrates causes from more-known effects. But, according to Aristotelian methodology, a posteriori demonstrations are quia, but nevertheless convert to propter quid if the effect is convertible with the cause. In other words, the scientist eventually comes across some certain knowledge, but he is unable to defend it as such in Aristotelian terms by recognizing the conditions under which his demonstration can be converted to an a priori demonstration. It is easy to be trained in a posteriori method. But Aristotle did not just think about the easy stuff. The problem most readers of the Physics have is that they are schooled in a posteriori thinking, and they are confused when confronted with an a priori demonstration. The a priori demonstration appears to them to demonstrate nothing, since their concept of demonstration or proof is restricted to the types of demonstration in Table 8, i.e. a posteriori demonstration: 1 0 0 Usually, a posteriori demonstrations manifest efficient causality (i.e. Type F in Table 8). S is usually distinct from the efficient cause demonstrated. M , as effect, is usually a nominal definition of the cause (because hidden causes are usually named by their effects). 39 Table 8: A Posteriori Demonstrations Demonstration Type S = Subject M = Effect as Middle Term P = Predicate (Property or Cause) F Subject Effect based on efficient causality First efficient cause G Subject Formal effect Formal cause and proper subject H Subject Formal mathematical effect Formal cause: physical quantity In conclusion, then, we wish to point out that Aristotelian methodology is quite aware of the conditions under which a demonstration is a posteriori and when it is a priori. We have seen that Aristotle considers science to be certain when it is most a priori. This occurs when the middle terms of demonstrations are proper causes (neither remote causes, nor effects, but proper causes). Aristotle considers science to be knowledge through proper causes, and we have seen that the principle of a propter quid demonstration is a cause as middle term (and not an incidental principle or element). In effect, this means that for Aristotle science is effected by demonstration, because the causal middle term M stands in a per se relation to the terms S and P: that is, M is part of the definition of S, and M exercises prior causality over P (whether P is a posterior cause or property). Because demonstrative knowledge requires these relations to be nota per se, the demonstration can be transposed into a definition that is self-evident and indemonstrable.102 1 0 1 Wallace (1957), 98-99 1 0 2 Cf. Weisheipl (1958), 42-44 40 Because Aristotle strictly adheres to his method of definition and demonstration in the Physics, it is possible to understand the most difficult parts of that text now that we are equipped with rudimentary insight into Aristotelian methodology. In brief, Aristotle's [1] certain, [2] causal, and [3] demonstrative science of nature can be seen as such, now that we know to be on the lookout for [1] a priori demonstrations reasoning from cause to predicated effect, that use [2] proper causes as middle terms prior in causality to what is predicated, and that effect [3] a real definition through proper causes of what cannot be otherwise, when this definition is a transposition of the contents of a demonstration founded on nota per se propositions about the principle M of the demonstration. But before we apply these insights to an exegesis of Aristotle's treatment of motion, place, and time in the Physics, we wish to dispel any scruples the reader may have about accepting any proposition as nota per se. And so we first turn to the classic text of An. Post. 11.19, where Aristotle discusses how a principle becomes the basis of propositions nota per se, in order that we may see this text in light of the Aristotelian methodology that we have sketched above. In this light, we will show that principles are universals potentially known by sensation in singulars, that principles are universals abstracted through induction in a process that progressively builds up the strength of the state of vouc, (i.e. the state of having principles), and that these principles afford actual learning when they are put to work in the nota per se propositions of a priori demonstrations. The commentary of Themistius on Aristotle is especially helpful to show this, and so we will translate both of their texts along with extensive annotation. We will show that definition and demonstration is not a vicious circle, by means of an example 41 ("hellebore") to which Type A, and Type D demonstrations apply.103 This will furnish the appropriate preparation for our subsequent treatment of motion, place, and time, because Aristotle's demonstrations about these three subjects are all Type A, or Type D. 1 0 4 1 0 3 Table 6 1 0 4 Wallace (1957), 101-102: demonstrations numbered 3, 5-10 42 CHAPTER II Principles: Nota per se 2.1 Abstractive Induction The purpose of this chapter is to dispel the most common doubts about the Aristotelian theory of scientific demonstration introduced above. Perhaps the reader's first impression is that the Aristotelian methodology we have outlined is an elaborate and confusing apparatus, irrelevant to the actual investigation of reality. It appears to be irrelevant, as if Aristotelian demonstration is an elaborate shell game, where the empty shells of the premises and conclusions are rotated round and round, and the mysterious peanut (allegedly self-evident) is the ever-elusive proper cause of the demonstrative swindle, the shell game's middle term that one can never quite pin down. Therefore it is entirely appropriate that we now discuss how principles, the causal middle terms, whose functions in demonstrations we have detailed above schematically, come to be known. In short, the common doubts about the Aristotelian methodology stem from the root concern whether principles necessitate an infinite regress or a vicious circle. To the contrary, Aristotle explicitly addresses these concerns,105 and affirms that there is neither an infinite regress nor a vicious circle because there are indeed principia immediata syllogismi.106 These principles are nota per se by abstractive induction.107 The best way to see how this occurs is to read closely our heavily annotated translation below of An. Post. mAn. Post, passim; but especially An. Post. 1.1-3, 19-23, and II.3-10, 13-19 1 0 6 Weisheipl (1958), \2-U;An. Post. 1.2-3 1 0 7 Wallace (1996), 421 ff.; An. Post. 11.19 43 11.19 and of the commentary by Themistius on this text.108 Before the reader does this, however, we should sum up our interpretation of this Aristotelian text, in light of the Aristotelian methodology that we have outlined above.109 We will do this by explaining how both demonstration and abstractive induction involve neither an infinite regress nor a vicious circle, and by giving an example ("hellebore")110 to which demonstrative science and abstractive induction apply, in order to illustrate the coherence of Aristotelian methodology. This will involve an account of the two types of nota per se principles: common and proper principles.111 The problem of the common principles (per se nota omnibus)112 of all demonstrations highlights the problem of the relation of intellect (vouc,) to science (eniaTfipn). Aristotle's classic text on this problem113 is best interpreted as explaining that principles are neither terms nor propositions, but the essential realities pointed to by these signs.114 Induction proceeds materially (i.e. through sensation)115 to abstract potential universals;116 and terms, propositions, and demonstrations only express universals formally, by means of signs.117 Terms, propositions, and demonstrations cannot be mapped in a one-to-one correspondence with universals, because they are all 1 0 8 See 2.2 below for details. 1 0 9 In sections 1.1-1.4. 1 1 0 Our example was inspired by the example of Themistius at 63.14-26: Wallies (1900), 63. We will apply the schema of Wallace (1957), 94-99 to the example (i.e. apply the same scheme of classification outlined for demonstrations in Tables 1-8 above). 1 1 1 Weisheipl (1958), 12-13, 17-19. m Ibid., 12 113 An. Post. 11.19; Cf. Weisheipl (1958), 19 1 , 4 Aquinas, IIAn. Post., lect. 20, and Kahn (1981), 385-386, 395. Cf. McKirahan (1992), 238 ff., and Byrne (1997), 170 ff. U5An. Post. 99b34ff. 1 1 6 Weisheipl (1958), 62 1 1 7 Smith (1952), 339 44 each, in a sense, universals;118 yet they are in fact universals expressed with a higher and higher degree of abstraction, i.e. expressing more and more the actual. However, universals cannot be grasped by an ascent from terms to propositions to demonstrations; for they already are somehow grasped,119 otherwise demonstration is impossible.120 Demonstration proceeds actually, from what is known to what is unknown, i.e. by argumentation;121 abstractive induction, however, proceeds from potency to act,122 which means that induction proceeds from what is known quoad nos to what is known quoad sem If a potential universal is known quoad nos in sense perception, then as experience is built up, this universal becomes more known as it actually is, i.e. known quoad se; and this greater actuality, obtained by greater degrees of abstraction, will articulate a principle, which expresses a kind of proportion between two relative levels of abstraction: i.e. the subject (higher level of abstraction) exercises a prior causality over the predicate (lower level of abstraction). Such propositions are nota per se.U4 The principle itself, however, should not be identified with this proposition, nor should it even be identified with a term or concept. (The latter identification would suggest itself since, because principles are the middle terms — the medium of demonstration ~ in a propter quid demonstration,125 they could be identified in concepts (i.e. terms) just as much as 1 1 8 Cf. McKirahan (1992), 239, on these three ways of conceiving universals mIIAn. Post. lect. 20, n. 14 1 2 0 Weisheipl (1992), 7-8 121 Ibid., 8 122 Ibid., 61 1 2 3 Cf. Phys. I and / Phys. lect. 1 nn. 6-7 1 2 4 See Table 4 1 2 5 Weisheipl (1958), 15-17 45 they could be identified in propositions.) Instead, the principle is the reality behind the idea that is abstracted. As rational animals, we abstract principles and express them in terms or propositions; but whether the principle is articulated in a term or a proposition, the important thing to note is that the principle is a reality, i.e. a real ordination of causality regarding what is abstracted. For example, "Hellebore," (here a term) is a principle, and "Hellebore is healing," (here a proposition) is a principle. The former principle ("Hellebore") is a cause, in the sense that it is a substance that will exercise causality over its proper accidents. Its effects are unstated in the term; but insofar as the term is a universal concept (i.e. already abstracted from the sensation of many singulars) it implies that it is something that will stand in at least some kind of causal relation. For that is what a principle is: a cause. The latter principle ("Hellebore is healing") also expresses causality, but in the sense that healing is a proper accident of hellebore (e.g. it yields alkaloids used in the treatment of heart disease), and in this way the substance hellebore is cause of its proper accidents. Because the proposition is articulated per se, it is a principle; i.e. it articulates essential causality. If this abstract proposition is fortified by enough experience, the principle can be articulated not only did per se (i.e. with the effect attributed essentially to the cause) but also did de omni (in every instance) and did ut universale (commensurately),126 and then the principle can be a principle of art or science:127 "All hellebore heals." Yet if hellebore is in fact not a real medicine, but only peddled by snake oil salesmen, then the proposition is not a principle, because it is not nota per se and no real causality is 1 2 6 Weisheipl (1958), 14-15 46 expressed; and this can be learned only from experience. However, if experience reaches a certain point of fortification, then this allows the articulation of what has been learned: "All hellebore heals." This principle, once it is known quoad se (i.e. nota per se) in the state of principles, can then be used by demonstration; because demonstration then reasons from what is known to us to what is unknown to us, i.e. from what is known quoad nos to what is unknown quoad nos (i.e. to what is known quoad se). As Aristotle teaches,128 the proper principles of a demonstration "must be prior and more known to us (quoad nos)."129 Wallace observes, "as Cajetan has stressed [in his commentary on An. Post.], demonstration is merely an instrument of our intellect by which we proceed from premises which are more certain quoad nos to conclusions which are certain quoad se. The certitude quoad nos permits of varying degrees depending on the simplicity of the matter which we are considering, but the certitude quoad se of the conclusion manifests a uniform type of necessity."130 Thus, when a principle becomes a principle of demonstration, this means that what is nota per se becomes utilized in demonstration, i.e. what is known by us to be known quoad se is adopted by us, from the state of principles, for demonstrative purposes, as actually known quoad nos (i.e. as known nota per se nobis) and therefore we can reason from what is known quoad nos to what is unknown quoad nos, i.e. to what is known quoad se. In other words, we learn something by experience, and then express it in demonstration. Yet demonstration also extends our knowledge scientifically over all experience, with necessity and certainty. 127 An. Post. 100a 3-9 128 An. Post. 1.4-5 47 If this sounds circular, in a sense it is, but due only to the way we have expressed it thus far (i.e. only in terms of "known quoad nos"' vs. "known quoad se"). For we have said, roughly, that induction proceeds from what is known quoad nos to what is known quoad se, and that demonstration also proceeds from what is known quoad nos to what is quoad se. Is there an infinite regress here (i.e. from quoad se back to quoad nos)? Or, if not, is there a vicious circle (i.e. back and forth among induction and demonstration, from quoad se to quoad nos, and vice versa)? No, there is not. For induction proceeds from the potentially universal to a more actual possession of this universal;131 but demonstration proceeds from the more actually universal to what is less actually universal.132 In other words, the movement, for induction, is from what is known quoad se (viz., the potentially universal) to what is known quoad nos (viz., to the state of principles); and for demonstration, from what is known quoad nos (viz., from whatever is actual in the state of principles) to what is known quoad se (viz. to what is not known quoad nos, not even in the state of principles, but which nevertheless is known quoad se to be more actual than the principles of the demonstration). Thus the conclusion of a demonstration is more actual than the premises because it is less universal than the principles of the demonstration.133 In this way, the principles of the demonstration propagate their ordination of causality by means of the subordination in the order of causality that is manifested in the conclusion.134 For a 1 2 9 Wallace (1962), 17 1 3 0 Wallace (1962), 21-22 m I Phys. lect. l , n . 7 m I Phys. lect. l , n . 6 133 Ibid. 1 3 4 As in all the types of a priori demonstrations outlined above in Tables 5-7. 48 demonstration to be a priori, in every proposition a lesser cause has to be subordinated to a greater cause (or at least an effect subordinated to a cause). Thus "science properly concerns universal natures, which beget necessary and universal characteristics."135 The common principles of human reason will thus be whatever is known to anyone with any experience whatsoever. They may be explicitly known to only a few (for example, to wise men who articulate propositions such as, "Affirmation and negation are not simultaneously true," or "The whole is greater than any of its parts.")136 Yet they are potentially known by anyone with any sensory experience, because sensation is not only of the singular but also of the universal (iced yap aicBccvexat pev TO KCCG' eicaaTov, f] 8' aioGnaic, tou KaGo^ou ecuv).137 This virtual knowledge is present in the very first act of sensation, no matter how confused or indistinct it is.138 Moreover, these dignitates or maximae propositiones (first principles of human reason) "are per se nota omnibus once the terms of the proposition are clearly understood."139 Proper principles (positiones) must be discovered in a science. They are either suppositiones or definitiones. Suppositiones are the proper axioms of the particular science. They are either per se nota sapientibus (i.e. to those deeply familiar with and experienced in the subject matter of the science) or accepted from another science in which they have been demonstrated. Definitiones constitute the proper medium of demonstration in a science.140 1 3 5 Weisheipl (1958), 33 1 3 6 Examples from ibid., 12 137 An. Post. 100a 14- 100b 1 usIPhys. lect. l ,nn. 7-8 1 3 9 Weisheipl (1958), 12 140 Ibid 49 Common or proper, the principles all express an ordination of causality with regard to that of which they are principles. It is more difficult to see this with common principles, since the discussion enters the realm of metaphysics;141 so, for a more vivid illustration, staying within the realm of physics (i.e. natural science), we return to the example of hellebore. Our illustration will show how induction and demonstration are neither circular nor necessitate an infinite regress in their operations that discern causes and effects. Let us begin with "All hellebore heals." This is a principle of science.142 It does not express scientific knowledge, i.e. a conclusion. Rather, it is a beginning of science because it is a principle expressing an ordination of causality. Therefore it could be a major or minor premise in a scientific demonstration, depending on what is actually nota per se in this principle.143 It could be among the suppositiones or definitiones of a science. So where in fact does it belong? What is the reality known by this principle known per se though abstractive induction?144 We can best explain this with reference to Table 9 below, an outline of induction and demonstration with regard to the principle, "All hellebore heals." Let us see what kind of scientific knowledge we can have about hellebore. 141 Ibid., 18 H2 Qf Themistius 63.14-26 translated and annotated below. 1 4 3 See Table 4 1 4 4 Assume that the principle has become known in abstractive induction exactly as Aristotle and Themistius describe (see my annotated translation below). What now does the principle offer science? (An. Post. 100a 3-9) 50 Table 9: Induction and Demonstration about the Universal "Hellebore" Principle Abstraction Induction Demonstration P proper accident most known quoad nos heals (i.e. yields alkaloids used in the treatment of heart disease) Type F M effect P efficient M, material cause more known quoad nos has a nitrogenous basic compound; has chlorophyll; has greenish flowers Type A, M material P property M 2 formal cause less known quoad nos any of various liliaceous plants of the northern temperate genus Veratrum, especially Veratrum album Type D M formal P material M 3 efficient cause less known quoad se nourished by carbon dioxide, water, and light energy Type C 2 M efficient P material M 4 final cause more known quoad se prepares its own food by photosynthesis and releases oxygen for the ecosystem Type B3 M final P material S subject most known quoad se hellebore universal (indemonstrable) Here we see that in the order of abstraction, the subject S, "hellebore," is the most universal subject of our science. This is because induction begins with the most universal potential in sensation and then subordinates all subsequent sense-images and memories to what is most universal.145 Abstrative induction does this with experiential judgements best characterized as of the form, "S is P," where S is a more universal term than P and, in the order of causality, S is prior to P. First, these judgements take the simple form, See 2.2 below: Aristotle 100a 14 - 100b 5, and Themistius 64.2-27 51 "[This singular] hellebore is [singularly] healing." Then, after more experience, they become, "Hellebore [universally] is healing [in particulars]." When enough experience is fortified, the pinnacle of abstractive induction is reached with the judgement, "Hellebore [universally] is healing [universally]." In other words, the judgement becomes articulated in what appears to be the familiar logical form, "All S is P", i.e. "All hellebore is healing." But note what is expressed in this proposition fortified by induction. It is not a subordination of a less universal S to a more universal predicate P, as in "All hellebore are plants," or "All men are animals." Those types of propositions are already cast into demonstrative form, i.e. where the less universal S is known from the more universal P. Instead, this proposition, "All hellebore is healing," is inductive, moving up from the less universal to the more universal. In other words, induction moves from the top of Table 9 to the bottom of Table 9; but demonstration moves from the bottom of Table 9 to the top. That is, induction sees the singular P and connects it with the singular S. But S is the more universal concept, and so the experiential judgement is "S is P." Hellebore [S] is the subject of investigation, because it is more universal in the sense that the less universal P is seen as an effect of S. But science begins when the question why is asked. Why is S P? Why is healing predicated universally of hellebore? Why is healing found in all hellebore? Why does all hellebore heal? In other words, science looks for a medium of demonstration, an explanatory middle term; in short, a more prior cause. The judgement, "All hellebore is healing," becomes a principle of science when we decide that healing [P] is an effect. The subject of our science is thus "hellebore". But there is no logical necessity in this, because we might have learned something different from experience. That is, it may have been the 52 case that we would learn from induction that, "All healing is hellebore." In other words, we may have learned in experience that hellebore is an effect of healing. For example, any time one goes to a doctor and gets healed, a hellebore plant springs up in the room. Or, when one gets over a cold or fever by taking medicine, a hellebore plant always starts to grow nearby. But this is manifestly not the case. In fact, it sounds absurd, because our experience is entirely contrary. Healing is not the cause and hellebore not the effect. Rather, from experience we know that hellebore is the cause and healing is the effect. And that is all that is expressed in the proposition articulated from abstractive induction that "All hellebore is healing." Namely, that hellebore is somehow the proper subject and that healing is the effect, because our experience is that hellebore is more universal in the causal relation to healing. Therefore this judgement can become a principle of science, where we ask why the effect is subordinated to the cause. The most frequent beginnings of scientific demonstration are not a priori but a posteriori. That is, they attempt explanations quia but not propter quid.Ub This is best illustrated by seeing that, once our hellebore principle becomes a principle of science, it is first cast in the form of a Type F demonstration.147 In fact, this Type F demonstration, because it is a posteriori and quia, mimics what has been learned in abstractive induction by moving from the less known and less universal to the more known and more universal. We can see this by casting our inductive proposition into the Type F form: "All healing [i.e. effects of efficient causality] is [due to] a first efficient cause, but all hellebore is healing; therefore, all hellebore is [due to] a first efficient cause [of healing]." 1 4 6 See Table 1 1 4 7 See Table 8 53 Notice that what we know from abstractive induction is cast as the minor premise. And the truth of what we know from experience is demonstrated when we see this Type F demonstration as consonant with experience. That is, we see hellebore as the cause and healing as the effect. We do not see hellebore sprouting up in doctor's offices as healing occurs. Thus the Type F demonstration is a kind of confirmation of our experience, because it articulates what we know to be true from induction by spelling out what our inductive experience means. That is, it demonstrates that what has been induced in the proposition, "All hellebore heals." For the question one may ask when hearing this proposition is, "Which is more universal, hellebore or healing?" If, in the order of causality, hellebore is known by experience to be the more universal, then the answer to the question is a demonstration of Type F. Of course, on the contrary, it could be that healing is more universal, and a hellebore plant always springs up nearby when healing occurs, and no one has undertaken a carefully observed study to document this. In that case, the inductive experience would be cast in a different demonstration, depending on what is observed. For example, imagine that a doctor must always clap his hands as a necessary condition for any healing to occur. Then the first efficient cause would no longer be seen to be due to hellebore itself as the hidden cause. Instead, our experience ("All healing [cause] is hellebore [effect]") would allow us to cast what we learn from induction in the following Type F demonstration: "All hellebore [i.e. effects of efficient causality] is [due to] a handclap, but all healing is hellebore; therefore, all healing is [due to] a handclap [as first efficient cause]." 54 However, what we experience affords no such inductions. And thus, "All hellebore is healing," is what becomes the principle of science. The Type F demonstration in which this principle is the minor premise is thus the appropriate model for our experience. But although the Type F demonstration is what most closely mimics our inductive experience, notice that the hidden cause in the predicate of the major premise (expressed above simply as "[due to] a first efficient cause") is still ambiguous. That is, the first efficient cause is still hidden. Is the first efficient cause the hellebore itself? Or is there something prior to hellebore (i.e. more universal in causality) that is the first efficient cause of the healing? In the first case, if the first efficient cause is to be found in the hellebore itself, then hellebore is that to which the property of healing belongs as a proper accident, i.e. intrinsically by the nature of hellebore. But in the second case, if something more universal than hellebore is the first efficient cause of healing, then healing is not an intrinsic property of hellebore, but rather just an extrinsic accident that occurs when the first efficient cause is exerted. However, we have already seen that we can rule out this second case. For we have already considered the doctor's handclap as an example. In the Type F demonstration for the handclap example, what we imagine to have occurred in abstractive induction is that the doctor is the first efficient cause of the healing, or more precisely, the doctor's handclap is the first efficient cause of the healing. That is what is expressed in the major premise of this Type F demonstration: "All healing is due to a doctor's handclap." Therefore, in the conclusion, "All hellebore [arising in the doctor's office] is due to [the first efficient causality of] a doctor's handclap," what we have demonstrated that we know is that hellebore is an extrinsic effect of the more intrinsic 55 activity of healing, the first efficient cause of which is the handclap. Therefore, let us go back to our real Type F demonstration, founded on real and not imaginary experience: "All healing is [the effect of] a prior efficient cause; but all hellebore heals; therefore hellebore [itself] is the prior efficient cause". Experience allows us to convert this Type F demonstration from an a posteriori demonstration to an a priori demonstration once we can discover the proper hidden cause of the hellebore having the property of healing. That is, the "demonstrative regress"148 can occur, whereby a quia demonstration can be recast as an a priori demonstration. For the predicate "healing" is known by abstrative induction to be a property [P] of the subject [S] hellebore, and this knowledge is certain, based on our two attempts to cast a Type F demonstration. That is, by confirming the actual order of causality in the Type F demonstration appropriate to experience, we have come to see that P is spoken of S in a per se manner. Healing is a proper accident of hellebore. Healing is an intrinsic property of hellebore. In other words, our principle "All hellebore heals" can be the principle of a propter quid scientific demonstration, if we can discover the fact or reason why healing belongs intrinsically to hellebore. In other words, we can demonstrate about our experience in an a priori demonstration of Type A: "All M [hidden cause of the effect] is [cause of] healing [P]; but all hellebore [S] is [intrinsically exercising the hidden causality] M; therefore all hellebore [S] is healing [P]." All we have to do is discover the hidden cause M. In Table 9, examples of such prior hidden causes are arranged in order of causality 1 4 8 Wallace (1996), 300-308 56 and abstraction. As we said, from the top to the bottom of the table, the order of absatraction becomes more universal. Hence material causes are most easily known quoad nos (because we learn everything beginning by abstraction from sensation), and then formal causes; these are.the intrinsic causes of a thing. Efficient causes express things more as they are known quoad se and hence are more abstract and universal, and final causes are the most abstract and powerful way of knowing something quoad se; they are extrinsic causes of being. In experience, we observe material and efficient causes as being prior in the way of generation, and hence they are the most easily recognized intrinsic and extrinsic principles (respectively) of a thing. And, in experience, formal and final causes are the more difficult causes to know, because they are more abstract and universal than the intrinsic and extrinsic causes to which they are respectively related. Formal and final causes are prior in the order of causality, although material and eficient causes are prior in the order of generation.149 Thus a Type A demonstration of Type A, is the first to be made about hellebore. That is, the proper accident "healing" [P] is to be shown to be due to a prior, hidden, material cause [M] that is intrinsic to "hellebore" [S]. Science asks the question, "Why does hellebore heal?" and looks for the propter quid principle M for the fact.150 Thus, by refined observations, one might realize in experience that certain material properties of hellebore are responsible for its having the property [P] of healing. For example, experience will eventually show that hellebore heals because it yields alkaloids in the treatment of heart disease, and so this property of yielding alkaloids and healing is due to 1 4 9 See Table 2 and Aristotle Phys. II and Aquinas De Prin. Nat. 57 a material cause in the intrinsic nature of hellebore. And this material cause would be the fact that hellebore has a nitrogenous basic compound [M,], and therefore it yields alkaloids used in the healing treatment of heart disease [P]. Therefore, from a fortified experience of careful abstractive induction, a demonstration of Type A, is made:151 "All that has a nitrogenous basic compound [cause M,] is yielding alkaloids used in the treatment of heart disease [property effected P]; but hellebore [S] is that which [intrinsically has] has a nitrogenous basic compound; therefore hellebore [S] is yielding alkaloids used in the treatment of heart disease [P, i.e. has the property of healing]." And this demonstration has the highest level of scientific certitude because its principles are articulated per se in the requisite manner.152 Scientific knowledge about hellebore will be perfected the more the subject S is known by means of causes of a higher order. Thus the science proper will not be just about hellebore, but about whatever subjects S afford demonstrations by the same higher cause. Science will go from being "the science of hellebore" (which is what we have so far with our Type A, demonstration above) to being a "science of plants" if we can know the formal causes M 2 , more abstract that the material causes M,. Once we observe all the intrinsic material causes M, ("has a nitrogenous basic compound; has chlorophyll; has greenish flowers") of which its proper accidents are the effects P ("yields alkaloids used in the treatment of heart disease"), we can move to a higher level of abstraction in order to define hellebore formally. In Table 9 we indicate the formal definition of hellebore M 2 1 5 0 Weisheipl (1958), 38-39 1 5 1 Table 6 1 5 2 Table 4 58 that is abstracted inductively from sensation: "any of various liliaceous plants of the northern temperate genus Veratrum, especially Veratrum album". And this definition has the same function as definitiones in Aristotelian methodology.153 That is, it can become the minor premise in an a priori demonstration (just like "S is M," was spoken in the Type A, demonstration's minor premise above). And the demonstration in which it becomes such a minor premise is the Type D demonstration typical of the philosophy of nature, where "matter is completed by form in the intrinsic composition of mobile being."154 The formal cause is prior to the material cause in the order of actuality, and thus the material cause is known per se from the formal cause in the Type D demonstration.155 That is, the formal cause becomes the medium of demonstration about the subject, because what hellebore's formal essence is is adduced as the real cause of its material constitution: "All of the various liliaceous plants of the northern temperate genus Veratrum [M2] are such that they have a nitrogenous basic compound [M,]; but hellebore [S] is a liliaceous plant of the northern temperate genus Veratrum [M2]; therefore hellebore [S] is such that is has a nitrogenous basic compound [M,]." This Type D demonstration moves us from having only a science of hellebore to having a science of plants, because the formal cause M 2 points the way to a more formal classification of all plants, which are composed by their own particular material causes and peculiar components. The more sophisticated experience becomes, the more abstract Weisheipl (1958), 12 Smith (1952), 345; Cf. Phys. I Table 5; Cf. Wallace (1957), 95-97 59 causes can be known per se and employed in further demonstrations. We indicate these in Table 9 with the efficient and final causes M 3 and M 4 . Let us quickly indicate how this science of plants would proceed to develop, along the lines indicated in Table 9. Type C 2 would demonstrate the material cause through the efficient cause. That is, the nourishment by carbon dioxide, water, and light energy [M3] is the efficient cause that effects the essential growth of the material organism [MJ; but all hellebore [S] is what is nourished by carbon dioxide, water, and light energy [M3]; therefore all hellebore [S] is a material organism that grows [i.e. dependent upon the specific efficient causes]. Next, Type B3 would demonstrate the material cause through the final cause.156 That is, whatever produces its own food by photosynthesis [M4] is that which has chlorophyll in its material constitution [M,]; but all hellebore [S] is that which produces its own food by photosynthesis [M4]; therefore all hellebore [S] is that which has chlorophyll in its material consitution [M,]. Taken together, all these conclusions are understood to constitute the body of scientific knowledge about the subject matter hellebore. Moreover, the principles employed in the demonstration are at such a high level of abstraction that they are applicable to other plants, and thus a science of botany is developed as formal causes are known to classify plants [M2] according to their material constitution [M2] (Type D demonstrations), efficient causes [M3] are known as the conditions for growth of the plants (Type C demonstrations), and final causes [M4] are known to account for the material constitution of the plants (e.g. photosynthesis in Type B3 demonstrations). 1 5 6 See the example for B 3 in Table 7 60 The key point to note from all this is that, according to the Aristotelian methodology, the contents of a Type A demonstration can be transposed into a definion of the essence of S by regrouping the contents of the demonstration.157 Thus Type A,' for hellebore above can be transposed into the following definition of hellebore: "Hellebore [S] is that which heals, yielding alkaloids in the treatment of heart disease [P] from the nitrogenous basic compound of its intrinsic constitution [M,]." But somehow this definition seems incomplete. And it is, because S is a natural substance composed of form and matter, and therefore a consequence from the peculiar nature of Type D demonstrations has not yet been drawn for hellebore. This peculiar nature of Type D demonstrations158 is the fact that the predicate M, is a material phenomenon, just as the predicate P in Type A demonstrations is also material. "Yielding alkaloids for healing [P]" is a material fact just as much as "being a nitrogenous basic compound [M,]" is a material fact about hellebore. Even though the former [P] is the effect of the latter [M,], these are both material facts known to sensation. Therefore, Type D demonstrations are "obliquely the same"159 as Type A demonstrations, because they both know matter. Yet "form, because it presupposes a disposed matter, really can never be the definition of a thing without the oblique inclusion of matter."160 But Type A and Type D demonstrations both include matter. This abstraction at the level of matter is the characteristic of physics (in the Aristotelian-Thomistic sense).161 Therefore hellebore, a composite of matter and form, is only perfectly and essentially defined, when a 1 5 7 Smith (1952), 356; An. Post, 1.8 (75b 30); I An. Post, lect. 16 n. 139; I Phys., lect. 1 n. 5 1 5 8 Wallace (1957), 96 mIbid. 1 6 0 Smith (1952), 354 61 combination of the Type D and Type A, demonstrations is made. This combination is licit, because it follows the demonstrative order in the demonstrations along the lines of strict necessity per se: i.e. from S to M 2 to M, to P. In other words, the Type A, demonstration follows in the chain of reasoning; the Type D demonstration's conslusion becomes the minor premise in the Type A, demonstration. And this is licit because the formal cause in the Type D demonstration is not greater in the order of causality than S, but subordinate to S, because it is the commensurate definition of S.162 That is, the formal cause is the commensurate definition of "hellebore" and not some form at a greater level of universality, like "living thing"; it may be true that "hellebore is a living thing" but this formal cause is inadequate for the major premise in the Type D demonstration and for the minor premise in the Type A, demonstration, because it is not proportional to the subject matter's level of abstraction. "Hellebore [S]" is more properly defined formally as "a liliaceous plant of the northern temperate genus Veratrum [M2]" than as "a living thing [M]", because M 2 is the point at which abstrative induction reaches the best universal knowledge of the form.163 In other words, the perfect definition of hellebore, from the viewpoint of the methodology of Aristotelian physics, is derived from the Type A, and Type D demonstrations together. And this is no small insight at which to arrive; for it is precisely this insight that is required to make sense of Aristotle's demonstrations about motion, 1 6 1 Smith (1958), 11-50; the three levels of abstraction are physical, mathematical, and metaphysical 162 An. Post. II.3-18 1 6 3 In dialectical induction, the inadequacy of the formal definition "living thing" for hellebore can be quickly pointed out, by means of an a priori demonstration quia of the fact that Socrates is a living thing, but Socrates is not hellebore. (See Table 1 above.) Thus, dialectical induction sends the scientist back to work for more sense observations and more abstractive induction. 62 place, and time in the Physics, and to be convinced by them. Aristotle's demonstrations about motion, place, and time are all Type A, and Type D. 1 6 4 Therefore let us explicitly show how these demonstrations about hellebore reveal the essence of this physical phenomenon. Linking the demonstrations according to the order of causality, we can regroup the contents of the demonstrations to achieve a full, perfect, and satisfactory real definition of hellebore: "Hellebore is any of various liliaceous plants of the northern temperate genus Veratrum, especially Veratrum album [M2], having greenish flowers, chlorophyll, and a nitrogenous basic compound [MJ yielding alkaloids used in the treatment of heart disease [P]." Note that we do not define hellebore with reference to extrinsic causes (i.e. efficient and final), because these are more proper to plants in general than to hellebore itself. Instead, we might wish to establish a science of botany as that science concerned with all subjects determined by these two extrinsic causes M 3 and M 4 , and then proceed to demonstrate the intrinsic causes from which they are derived (e.g. specifically, "chlorophyll" and "being a plant": from M[ and M 2 , respectively).165 Let us reiterate that Aristotle's solution to the problem of how learning occurs is indeed coherent, and neither an infinite regress nor a vicious circle. For the reader may still have the impression that the example above is unconvincing. The example of the search for the proper causes of hellebore may still have the scent of arbitrariness about it. For it is only by comprehension of how common first principles absolutely do not either necessitate a vicious circle or infinite regress that the reader can be convinced of the 1 6 4 Wallace (1958), 101-102 63 analogy to the relative case of a "science of hellebore" or a "science of plants". "Science in general" has to be seen as possible only through immediate first principles. If this philosophical truth is not grasped, one will always be skeptical of the employment of proper principles in any science. This is due to the fact that Aristotelian science in general is architectonic, i.e. it orders all sciences according to their causes and levels of abstraction. Hence metaphysics is higher than mathematics and mathematics higher than physics, and each has its own peculiar method or medium of demonstration proportionate to its subject mater.166 If one does not accept the philosophical truth of such an ordering as appropriate to reality itself, i.e. if one does not even see the truth that there are common principles of human reason, then one will be forever skeptical about the employment of proper principles in any science; for example, as we did with regard to hellebore. Therefore we reiterate that there is no better solution to the problem of how we learn than that of Aristotle. There are immediate first principles, and upon the fact of principia immediata syllogismi is founded the edifice of Aristotle's Physics. The demonstrations therein about motion, place, and time, can only be properly understood in this light. If one does not accept Aristotle's account of principles in the Posterior Analytics, and one rejects Aristotelian methodology, then there is little point in quibbling about Aristotle's physics. For the demonstrations will not be grasped by someone whose methodology is limited and skeptical. The best antidote to such skepticism is Aristotle himself. If a better solution to 1 6 5 See Table 9 64 how we learn is available, then it will have to show the flaws in Aristotle's account. Our own opinion is that all such attempts have created more problems than those they allege to solve, and that they end up making the philosophical mistake of attempting to demonstrate the indemonstrable. Therefore we offer Aristotle's classic text in translation below, with the commentary of Themistius and our annotations. The objection to Aristotle's methodology of demonstration is twofold. First, demonstration seems to be impossible because it requires first principles; therefore it is argued that the first principles would have to be demonstrated through prior principles, which is an infinite regress.167 Yet Aristotle argues that not all truths are demonstrated,168 and he explains how this occurs.169 Second, demonstration seems to be always possible because it is meaningless; everything can be demonstrated because all demonstration is circular, amounting in the end to saying nothing more than "if a thing exists, then it does exist."170 Yet Aristotle argues that there is a distinction between induction and syllogistic reasoning; some things are better known quoad nos (i.e. beginning potentially in induction) and some things are better known quoad naturam (i.e. in actual demonstration).171 Experience itself shows us that we learn things, so unless we are greatly deceived, there is more to learning than tautology. And therefore Aristotle solves the problem of how knowledge first begins, the problem being that, because further knowledge is learned through pre-existent knowledge, somehow pre-existent knowledge 1 6 6 Weisheipl (1958), 45-60 1 6 7 This argument is attributed to Heraclitus by St. Albert: Weisheipl (1958), 13 168 An. Post. 1.3 (72b 18-19); this argument is attributed to Empedocles by St. Albert: Weisheipl (1958), 13 1 6 9 The answer [A2] replies to the question prompted by the Heraclitean objection, i.e. to [Q2]; see below. 170 An. Post. 1.3 (72b 34); Weisheipl (1958), 13 65 must be in us. The difficulty lies in the false dilemma that this first pre-existent knowledge is either actually in us or not actually in us, i.e. non-existent. Aristotle disposes of the dilemma, by arguing that all knowledge is pre-existent potentially in sensation, and is slowing built up by induction into a state of first principles known as intellect (vouc,). When this state has sufficiently actual principles, it offers them to demonstration, which can reason from them with certitude. Of course, the problem seems to be what "sufficiently" actual means. We argue that it means that a universal proposition, e.g. "All hellebore heals," is nota per se and can then be employed in an appropriate demonstration for its subject matter. However, we leave it to the reader to decide the strength, both of our example above how this works, and of our exegesis of the text below. Either intellect (vouc,) operates as Aristotle describes, or we still have yet to understand how we really learn, and what intellect might really be. Intellect (vouc,), argues Aristotle, is the state of first principles known by abstractive induction, built up by the soul by a continuous "leading-up" from the less universal to the more universal in its rational operations. In this "leading-up" it moves from the less abstract to the more abstract, the less universal to the more universal. This is a movement from potential universals to actual universals, from potential abstractions to actual abstractions. If a universal abstraction becomes articulated, it can serve as a principle of a demonstration. Demonstration then uses it to reason from the more universal to the less universal. However, demonstration does this with absolute certainty, whereas induction is only as certain as the amount of sensation it as experienced. Intellect 1 7 1 The answer [Al] replies to the question prompted by the Empedoclean objection, i.e. to [QI]; see 66 stands between induction and demonstration, as the state of immediate principles forged from experiential judgements. It is like a reversal in battle, where the soul withstands the assault of sense experience, until intellect is able to turn the tide against the senses and triumphantly conquer them by means of demonstrations that have the greater force of certainty (i.e. more certain than anything the senses can offer intellect). Intellect is the brave army upon which all our cognitive fortunes turn. Its soldiers are the singular abstractions made, and their larger formations and divisions the state of intelligence.172 In conclusion, then, we see that vouc, is neither a magic power that pulls principles out of recollection, like actual rabbits out of an actual hat; nor a shell game swindle, in which the principle jumps around in a vicious circle among the three empty shells of a demonstration, as if the peanut allegedly "self-evident" to sense perception is really wherever the swindling logician happens to place it. Instead, it is a state built up by experience and sharpened by the exercise of abstract thought in scientific demonstrations. This intellectual activity is extrinsically characterized by the solertiam reached in maturity or in the precocious natural genius. But intrinsically it consists of a state of immediate first principles, the indispensable starting point for all subsequent real science. Burckhardt and Goethe, two gifted men who wrote mature works, understood well how Anschauung (the German word for Aristotle's vovq) is the real beginning of any real scienctific learning, as Erich Heller describes in his essay on "Burckhardt and Nietzsche": "It may be, [Burckhardt] says, 'that there is still hidden in Thucydides a fact of capital importance which somebody will note in a hundred years time.' For the below. mCf.An. Post. 100a 10-14 1 7 3 Cf. Weisheipl (1958), 37-38 67 present, Burckhardt maintains, 'a single source, happily chosen, can, as it were, do duty for a whole multitude of possible other sources, since he who is really determined to learn, that is, to become rich in spirit, can, by a simple function of his mind, discern and feel the general in the particular.' This is an echo from Goethe's world. For Goethe knew the difference in quality between a writer who, starting with preconceived ideas, assembles his particulars to fit the needs of his generalities, and a poet who 'discerns and feels' the universal in the particular phenomenon. Like Stifter, with whom he has so much in common, Burckhardt felt himself to be one of 'Goethe's family.' As a young man he hoped he would become a poet - and he actually did publish a number of poems - and throughout his life history remained for him a poetic activity. 'As a historian,' he once wrote, T am lost where I cannot begin with Anschauung.'' It is a Goethean word and hardly translatable. Its connotations are visual, and it means the mental process by which we spontaneously grasp, through observation aided by intuition, a thing in its wholeness."174 "Observation aided by intuition" is not a bad way of expressing "experience fortified by abstractive induction," because, in sum, it shows us that votJc, is not an intuition of principles, but a state of principles, built up over time. For we will always be surprised by what a gifted observer, strong in vouq, i.e. strong in the state of principles, can see in one thing; namely, what we overlook in that one thing, because our own powers of abtraction are insufficient to see what is more universally and more really there. 1 7 4 Heller (1988), 43-44. 68 2.2 Annotated Translation (Aristotle and Themistius) Below we divide up Aristotle's text175 and translate it anew, in order to reveal the precise structure of its argument. We intersperse the close paraphrase of Themistius and our translation of his commentary,176 because his shrewd exegesis of abstractive induction supports and clarifies the interpretation we have given above.177 The texts and translations are placed in columns to facilitate comparison. The Aristotelian and Themistian texts are divided and subdivided according to the schema given below in Table 10. The divisio textus of Table 10 is, mostly, that of Thomas Aquinas. The explanatory Latin section headings and schematic arrangement are inspired by the Marietti edition178 of Aquinas's commentary In An. Post. The number in square brackets is the number given to the textual portion of the Latin Aristotle in the Marietti edition. We also refer to these numbered sections, not just with the square bracket Aristoteles Latinus numbers, but also with single-word Latin mneumonic names that we use to designate and sum up the content of the text. The (unnumbered) Themistian subdivisions also have mnemonic names that we have assigned. The subdivision and commentary performed by Themistius sheds light on the Aristotelian text. Themistius and Aquinas seem to be of one mind on the structure of the text. Themistius often comments at the same points Aquinas does. We also designate the three main questions considered- by Aristotle (and 175 An. Post. 11.19 1 7 6 C A G V : l Themistii In An. Post, ed. Wallies (1900), 62-66 1 7 7 Our interpretation has also been informed by C A G XIII:3 Anonymi In An. Post, and Philoponi In An., and by C A G XXI: 1 Eustratius In An. Post., although we do have space in this study to consider and discuss these commentaries. 1 7 8 Spiazzi (1955) 69 Themistius) in the text by [Ql], [Q2], and [Q3]; their answers are likewise identified, when they occur in the text, by [Al], [A2], and [A3] in square brackets; three key points made by Aristotle (in a passage difficult to unravel at 100b 5-14) are similarly designated as [PI], [P2], and [P3] (to aid the reader in unravelling); and the alternatives of the aporia (dubitatio) are marked [DI] and [D2]. The reader will note that it is this dubitatio that dialectically prepares the answer [A3] for question [Q3].179 The Greek text of Aristotle is from the Oxford Classical Text, and the Themistian Greek paraphrase and commentary on Aristotle is from the Commentaria in Aristotelem Graeca.m The Greek texts from the OCT and CAG editions were extracted from the TLG CD-ROM (version D) for use in this document. The textual portions are identified as either Aristotelian or Themistian by the use of either Bekker or CAG references, in brackets at their beginnings. Square brackets in the translation indicate what is implied in the Greek, but not literally there. This convention makes a side-by-side comparison of the English with the Greek even easier. Our interpretive glosses upon the text are usually given in the footnotes rather than also in square brackets. Again, at the beginning of each textual division, the square brackets containing numbers simply refer to the Aristoteles Latinus portions. (They hint at our enormous debt to St. Thomas Aquinas.) We are aware of Kahn's caveats regarding the "classical theory of abstraction," i.e. that "this theory is very largely Aristotelian in spirit, though not to be found in the 1 7 9 The close reader of the text will note also that the dubitatio is echoed yet again in the concluding passage at 100b 5-14, because [A2] finds the grain of truth in Platonic idealism [DI], and [P2] finds the grain of truth in Sophistic nominalism [D2]. 1 8 0 Wallies (1900), 62-66 70 letter of his text." Yet we are convinced that it is in fact in the letter of the text, and we attempt to show this below; for only this theory makes the best sense out of the letter of the text. Hence, in the following translations, we do not hesitate to translate Xoyoc, (ratio) consistently as "abstraction".182 Because, as Themistius observes,183 according to Aristotle184 man is the abstracting animal (£,£, dpxfjc, ecjxt (pt)aet A,oytKOv £6)ov 6 av9pa>7toc,) because his primary difference is vouq.185 This means he holds universals in abstract proportional relations to one another (i.e. in a ratio). 1 8 1 Kahn (1981), 409-10. Cf. Aquinas, Summa Theologica, Ia q.79. 1 8 2 Smith (1952), 339, translates ratio as "idea"; but this is too imprecise and, moreover, smells too Platonic for Aristotelian terminology. 1 8 3 Wallies (1900), 65, lines 10-15 184 An. Post. 11.19 1 8 5 In our annotations we will refrain from talking about active intellect and passive intellect except where strictly necessary. Psychological problems are outside the scope of our study. For our purposes we need only note the difference between agent intellect and intellect; the latter is the state of indemonstrable first principles. As Aquinas writes in his Quaestiones de Anima: "it is necessary that the agent intellect exist prior to the habit [i.e. state] of indemonstrable principles as its cause. For these principles are themselves related to the agent intellect as its instruments, because by means of these principles the agent intellect makes other things to be actually intelligible." English translation by Robb (1984), 88. 71 Table 10: Divisio Textus of An. Post. 11.19 Division Aristotle Themistius Aristoteles Aquinas Name Bekker CAG Latin us Paragraphs Reference Reference (Marietti (Marietti (page, edition) edition) lines) epilogat 99b 15-17 62.18-20 426 581 principia 99b 17-19 62.21-22 427 582 immediata 99b 20-22 62.23-28 428 583 tres questiones 99b 22-26 62.28-31 429 584 [Ql] [Q2] [Q3] latere [DI] 99b 26-27 62.31-33 430 585 de novo [D2] 99b 28-30 62.33-35 431 586 dubitatio 99b 30-32 432 587 solutio 99b 32-34 62.35-63.2 433 588 sens us [A3] 99b 34-36 434 589 memoria 99b 36-39 63.2-8 435 590 ratiocinatio 99b39-100a3 63.9-14 436 591 experimentum 100a 4-10 63.14-21 437 592 universalium 100a 4-10 63.21-26 437 592 anima 100a 10-14 63.26-29 437 593 pugna 100a 10-14 63.29-64.2 437 593 primus gradus 100a 14-b 1 64.2-9 438 594 inductio [Al] 100b 1-4 64.9-14 438 595 conceptiones 100b 1-4 64.14-18 438 595 tempus 100b 1-4 64.19-27 438 595 intellectus [A2] 100b 5-14 64.27-65.10 439 596 animal rationale 100b 5-14 65.10-15 439 596 propositio 100b 5-14 65.15-21 439 596 habitus 100b 5-14 65.21-24 439 596 corpus 100b 5-14 65.24-66.3 439 596 principiorum 100b 14-15 66.3-6 439 596 72 [426] Epilogat (99b 15-17) ITepi \iev ovv O"DA,A,OYIOI4,OV3 K a i aTtoSci^ ECuc;, xi TE eK&xepov erjTt Kai n&q yivETai, (pavEpov, aira 5E Kai 7t£pi £7r,io"TTpr|C, d7to8EiKTiKf|(;- TarjTov yap EOTIV. (62.18-20) TtEpi |X£V orjv dKo8Eic;EC0t; £ipT|Tai Ka i taq EOTI K a i n&c, yivETai -£ipr|Tai 8' <x\ia Kai 7t£pt dnoSEiKTiKfii; £7uo-Tfiur|c/ xamriq yap epyov anobei^ic,. (99b 15-17) So, as regards syllogism186 and demonstration, the definition of,187 and the conditions required to produce each of them,188 are now clear, and thereby [the conditions required to produce] demonstrative knowledge, since it is the same [as demonstration].189 (62.18-20) So, as regards demonstration, how [the definition] . is, and the conditions required to produce each of them, are stated, and thereby [the conditions required to produce] demonstrative knowledge are stated, because demonstration is the act of the 1 8 6 Cf. An. Pri. 1.1 1 8 7 literally, "what it is" 1 8 8 literally, "how they occur" 1 8 9 We adopt the English translation of Weisheipl (1958), 59 1 9 0 Aristotle says that science and demonstration are the same. Themistius notes why this is so: demonstration (the epyov) refers to the state (e^tq) of demonstrative science being enacted. 73 [427] Principia i i (99b 17-19) Tispi 8e xcov dp%rov, TTCUC, xe ytvovtai yvebpipoi Ka i xic, r\ yvcopi^orjoa eJjtq, EVTEUGEV eaxax i ! 8fjA,ov 7ipoa7iopr|aaCTi 7ip6oxov. (99b 17-19) Yet, as regards principles, both [QI] how they become cognized191 and [Q2] what the cognizing state is,192 will be manifest from hereon, with the difficulties being set forth first.193 (62.21-22) nepi 8e TCOV dpxrov tfjq i i cc7to8Ei^ eco(;, iz&q xe y i v o v x a i yv rop ipo i i Kai xiq r\ yvcopi^orjcja e^ iq, EVTEUGEV i EOTl 8flA,OV 7tpOCC7topf|0"aai IXpCOTOV. (62.21-22) Yet, as regards principles of demonstration,194 both [QI] how they become cognized and [Q2] what the cognizing habit is, will be manifest from hereon, with the difficulties being set forth first. 1 9 1 The answer to [Ql] will be [Al] , E7taYoyyf| ("induction"): 100a 14 ff. 1 9 2 The answer to [Q2] will be [A2], vovq ("intellect"): 100b 5 ff. 1 9 3 Cf. Smith (1958), 56-68, 73-77, 88-90 on this characteristic dialectical method ("the difficulties first") in Aristotle. We label the difficulties [DI] and [D2] below: 99b 26 ff. 1 9 4 Note that "of demonstration" is Themistius' gloss. It is the only word he adds to his repetition of the Aristotelian text. 74 [428] Immediata (99b 20-22) "Cm piv ouv OUK ev8e%eTat ercicTaaGai 8i d7to8eU;£eo<; pf) y i y v t b a K o v T i xdq npaxaq dpxdc , Tag dpeaouc,, ei'pnTat Jipoxepov. (62.23-28) a v d y K n yap fJTOt yivebaKeiv Tag Txpobxai; dp%dc, r[ pr| yivobcjKeiv ei 8e yivobcjKeiv, fJTca 8i' d7to8ei^ ecoq r\ aAAov xporajv, TJTOI 8i' emaxr]\xf\q r\ 8i' exepaq Suvduecoc/ noXXa ydp xcopiq drcoSei^ecoc, ejtiOTdueGa, KaGdrcep Sfi Kai xovc, opiapoug. OTI pev ouv dvayKatov yivobaKeiv xaq dp%dc, TO) peXA,ovTi yvcbceaGat Ta ei; eKeivcov, eipriTat KpoTepov, Ka i OTI ye pt) Si' a7to8ei^ ecoq otov T8 . (99b 20-22) So, that it is not possible to know scientifically by demonstration unless one cogitates immediate first principles, was stated previously.195 (62.23-28) Because it is necessary either to cogitate or not to cogitate the first principles. And if to cogitate, either [QI] through demonstration, or another way;196 either [Q2] through science or through a different power,197 because we scientifically know many things without demonstration (indeed, [we scientifically know] definitions just so).198 So, it was stated before that it is necessary for one to cogitate the principles if one intends to cogitate what follows from them, and that this is not in the least way possible through demonstration. 195 An. Post. 72a 8 - 72b 4. 1 9 6 The other way [Al] is ejiaycoyfi (induction). 1 9 7 The other power [A2] is \ovq (intellect). Note that 8\)vaui<; = here, because science is a state, and so is intellect. But we translate "power" to indicate a potency (Swoc|ii.q) in a state of partial actualization (e^iq), and to keep "state" for translating z\\c,. Themistius is alluding to the power of intellect; not as a power of the soul, but as a state of first principles. 1 9 8 Cf. An. Post. 72b 24. 75 [429] Tres questiones (99b 22-26) TCOV 8' duiccov TTVV yvcooiv, Kai rcoxepov f) avJTf| eoxiv fj ox>% f] arjiTj, Siarcopriaeiev dv TIC,, Kai rcoTepov £7ciOTfiur| EKaTepou [rj OV], fj TOVJ UEV 87llCTTfl|a,Tl TOVJ 8' ETEpOV TI yevoc,, Kai KOTepov OVJK evorjaai a i E^EIC, eyyivovTai r\ evorjaai A,eA,fi9aoiv. (99b 22-26) Yet one is likely greatly perplexed about the cogitation of immediates: i.e. [Ql] whether it is the same or not the same [for all learning],199 and [if not the same,] [Q2] whether [there is] science in both [states], or if, in the one case, science, and, in the other case, some different kind [of state],200 and [Q3] whether the states, [D2] although not being in [us at first], occur in [us later], or [DI] although being in [us already], they escape our notice. 1 9 9 Aristotle will deny the actual identity for all learning of first principles (see Weisheipl (1958), 61); instead, he will affirm that they are acquired differently, i.e. into a state and over time, by ejtaYroy-n, (induction), 100a 14ff. That is, here "the same" refers to actuality; "not the same" refers to a state. 2 0 0 The answer to [Q2] will be that [A2] voxx; is a different kind of state than e7tvatTi|iT|. 2 0 1 [Q3] asks for a solution to the aporia about the state of pre-existent knowledge: Is pre-existent knowledge [DI] completely potential, or [D2] completely actual? 76 [429] Tres questiones (62.28-31) A,ei7r.£Tcu xoivuv £7U0K£\)/CC09CU, 7t6x£pOV £7tlfJTfl)J.Tl XCDV aireacov ap%&\ eaxiv fj exepov TI yevog Suvairecflc,. ap r^i 5e xccuxrig xfjc; Gecopiag- Spa ec; dpxfjt; evorjaai 8iaA,eX,fi6aoiv Tinaq f) t>o"cepov TeA,eiot)p.£voi<; eyyivovxai; (62.28-31) Hence it remains to be examined [Q2] whether [cogitation of first principles] is science of immediate principles, or some different kind of [cogitative] power. And the beginning202 of this inquiry [is], [Q3] "Do [the cogitating states], [DI] although being in [us] from the beginning, totally escape our notice? Or do they [D2] later occur in those perfected [by them]?" 2 0 2 Themistius notes that Aristotle begins his inquiry into the cognition of first principles by starting with the third question posed in 99b 22-26. 77 [430] Latere (99b 26-27) ei u£v 8f| e%o|j.ev arjxdc;, dxoTiov aufiPaivei ydp aKpipeaxepai; exovxaq yvwaeic; dnoSeic^ ecoc; A,av0dveiv. (62.31-33) to T6 yap evofjaac, 8iaA,av0dveiv dSrJvctTov ovjSe yap draSSei^ iv e^ ovTac; A,av0dveiv SDVCCTOV, |iT|Ti ye 8r| yvcocuv dnoSei^ ecog dKpipeaTepav (99b 26-27) If [DI] indeed we have them [already], then that would be absurd; because it would follow that cogitations more certain203 than demonstration escape [our] notice.204 (62.31-33) Because, in the first case [DI], it is impossible for that being in [us] to escape [our] notice completely; because it is not possible that we would have a demonstration and not notice, at least if no cogitation is more certain than demonstration. 2 0 3 Lesher would translate "more exact," meaning "more in possession of first principles." Cf. Lesher (1973), 63 n. 51. But Aristotle means that the consequence of [DI] is that the conclusion of demonstration is more certain than the principles, which is absurd. The thesis of [DI] is that all knowledge is actual; principles and conclusions are actual, but for some crazy reason we are aware only of the actual conclusions, while the actual pre-existent principles are hidden from us. This is absurd, because demonstration requires principles to be better known than conclusions. Cf. Weisheipl (1958), 12 2 0 4 This is Platonic idealism: knowledge of pre-existent principles is actual and not acquired from sense experience; it is merely recollected. Cf. ibid, 7-8, 59-60 78 [431] De novo (99b 28-30) et 5e XapPavopxv pf) exovxec, rcpoxepov, n&c, av yvcopi^ otuev K a i pavOdvoipev CK pfj 7tpoi)7xapxo\)ari(; yvcbaemc/, a8\)vaxov yap, (BcjTTep K a i km. xfjc, a7io8ei^ eco<; eXeyopev. (62.33-35) TO xe XapPdveiv pf) exovxac, rcpoxepov OUK euStdOexov xdiq xtGepevoic, jxaaav 8i8aoKaX,iav K a i p&6r)aiv EK 7ipou7tapxo'UO"ri(; yiveaGai yvwaecoq- o\)8ev yap Kpoxepov xcov dp%cov. (99b 28-30) Yet, if [D2] we acquire [first principles] without having [any] beforehand,205 how do we cognize and learn, if not through pre-existing cogitation? Because [this]206 is impossible, just as we were also saying about demonstration.207 (62.33-35) In the second case [D2], to acquire [first principles] without having [any] beforehand, is not easily reconciled with those who posit all teaching and learning to occur from pre-existing cogitation (because nothing is before principles).208 2 0 5 This is Sophistic nominalism: knowledge of pre-existent principles is non-existent; learning is just the acquisition of new facts, and all "explanation" or "demonstration" is a vicious circle of already known facts. Cf. ibid 2 0 6 i.e. not having pre-existent knowledge, and yet still learning 207 An. Post. 71a 1 ff: there can be no demonstration without principles, i.e. (as Themistius puts it) "nothing is before principles." 2 0 8 The principles seem at first to be non-existent; and this is not easy to reconcile with the fact that we need to cogitate actual first principles in order to do demonstrations. How do they become actual if they are first non-actual? 79 [432] Dubitatio (99b 30-32) cpavepov xoivov oxi ox>% exeiv otov xe, cox' ayvoorjai Kai |xr|8eiiiav exovaiv ei;iv eyyiyvecBai. [433] Solutio (99b 32-34) dvdyKT] dpa z%zx\ laiv xiva 8rjvap.iv, irf) xoiarjxriv 8' e%eiv f| eaxai xorjxcov xiurooxepa Kax aKpi|j£iav. (99b 30-34) Wherefore it is evident that it is neither possible [DI] to have [first principles], while being ignorant [of them], nor [D2] for [first principles] to occur in [us], without having any [cognizing] state [beforehand]. Therefore, it is necessary [for us] to have some power,209 yet not to have the sort [of power] that will be of greater dignity according to certainty210 than these [actual first principles].211 2 0 9 Aristotle's solution to the difficulties is that pre-existent knowledge is neither [DI] actual principles, nor [D2] non-existent principles, but [A3] potential principles. That is, principles are first known in a state that is somewhere in between non-being and actual being (i.e. being full, complete, perfect). 2 1 0 "Greater dignity according to certainty" means "of greater actuality". 2 1 1 The first principles are fully actual when employed in a priori demonstration. 80 [ 4 3 2 - 4 3 3 ] Solutio (62.35-63.2) aXkmc, OVJV OVJK eoxi SiacpuyeTv xafjxac, xdc, arcc-piccc,, ei |IT| xic, efjpeGeiri 8fjvau.ii; xfjc, vox^ S KaG' fjv otov xe yivajciceiv p.r|5ev exepov Ttpoxepov ainfjc, yivroaKovxac/ xavjxri yap |x6vrj 7tpoaf|Koi dv fj Xfj\|/ic; xcov dpxcov. ( 6 2 . 3 5 - 6 3 . 2 ) So, there is no complete escape from these difficulties, unless some power of the soul can be found, according to which it is possible to cogitate nothing else before its [own type of] cogitating [occurs first]; because the acquisition of principles will belong212 to this [power] alone. 2 1 2 The optative with dv expresses a firm conclusion here. Cf. Goodwin, Moods and Tenses 238. 81 [434] Sensus (99b 34-39) (paivexat 8e xotno ye rcaatv x>%a.p%o\ xotg ^aoig. E%EI yap 8t>Vap.lV C'UpcpVJTOV KptTlKT|V, fiv KaA.oucjiv ataGnatv [435] Memoria evouaric, 8' aioGfiaecog tote, pev xrov a^pcov eyyiyvexai povf| tot) aiaGnuaxoc,, xotc, 8' O U K eyyiyvexai. OCTOK; pev ouv pr) eyytyvexai, f\ 6X(aq f\ nepi a pf| eyytyvexai, O U K eoxi TOUTOK; yvcocuc, e^ m tot) aioGdveoGai-(99b 34-39) But this [power], at least, is evident, existing in all animals. For they have a connate discriminatory power, which we call [A3] sensation. When sensation exists in animals, in some a persistence of the sense-image occurs; yet in others it does not occur. So, those in which [a sense-image] does not occur (either totally or as regards those [persistent sense-images] that do not occur [in their particular species])213 have no cogitation outside of sensation. 213 No sense-images occur for gnats, but some sense-images occur for birds. Yet, even though sense-images do occur in birds, they do not persist. Therefore, birds are pretty much equivalent to gnats, in whom there are no sense-images at all. That is, because both birds and gnats do not have any persistent sense-images. (We take this example from Themistius, who gives even more examples in his text below.) 82 [434-435] Sensus et memoria (63.2-8) cpaivexai 8e at>xr| ye raxcuv \)7tdpxeiv xoic, Copoic/ e x o - o a i Y«P Svjvauav arjiKp-uxov KpixiKfrv, fjv Ka^ or3|xev aicGriaiv. evofjonc, 8' aiaGriaecog xotc, ixev xcov £cba>v eyyivexai (lovfj xor) aioGfiiraxoc,, Ka i (prAdxxouaiv e7ti 7ioA,vj xorjxo oo riaGovxo, xotq 8e OVJK eyyivexai, xoic, irev otaoc,, racmep erjXaic, Kai irmaic, Kai 8U7UO-1, xotg 8' djiuSpcoc, Ka i 6A,iycov, otov opvecov xiai cpcovtov Ka i 68a>v tjKO^'uytOK;. oaoiq u iv OVJV \ir\ ep.ij.evei xd aioGfuraxa ev xfj K^"0XTi» xooxoic, OVJK ecm yvrooic; ec;a> xffiv aiaGriaecov. (63.2-8) But it is evident that this [power] exists, at least, in all animals. For they have a connate discriminatory power, which we call [A3] sensation. But when sensation exists in animals, in some the persistence of the sense-image occurs, and they keep, for a long time,214 that which they sensed; but in others [persistence] does not occur. For some of the latter, it does not occur at all (as in worms and flies and gnats), and for others, [it occurs only] indistinctly and in few cases (for example, in birds and roosters and beasts yoked for traveling). So, all animals for which sense-images do not persist in the soul have no cogitation outside of sensation. 2 1 4 Reading e7tt TloX\) as temporal, instead of as "for the most part". 83 [436] Ratiocinatio (99b 39 - 100a 3) ev otc, 5' eveoxiv <|iri> aioOopevou; e%eiv en ev tf i V°5Cfi- noMxov 5e totouxcov ytvopivcov fj5ri 8ux(popd TIC, yivexai, &cxe idle, pev yivecOcu Xoyov eic xfjq xrov TOIOUTOOV povfjc,, xoig 8e pf). (99b 39 - 100a 3) But [the animals] in which [there] is [persistence], when they are <not>215 sensing, still have [sense-images] in the soul. And when many such [memories]216 occur, then a difference occurs, such that in some [animals] an abstract thought occurs from the persistence of such [memories],217 but in others it does not. 2 1 5 A negative particle is inserted by Trendelenburg. Uberweg proposes reading a past participle ("after they have perceived") in place of the present participle ("while perceiving"). See Barnes (1993), 262-265, especially 263. Barnes follows Uberweg in his translation on 73. However, we argue that the sense of the passage is the same whether the negative partcle is inserted or not. For sense-images in memory persist both during and after sensation. Sensation does not have to stop in order for memory to operate; therefore there is no need to posit a negative particle in order to see memory at work, i.e. only after sensation. Memories persist both before and after sensation, and the text is still coherent even if it is talking about memory occuring during sensation (i.e. with no negative particle). 2 1 6 i.e. persistent sense-images 2 1 7 These animals are called "rational animals" (i.e. animals thinking abstractly) because their specific difference is ratiocinatio, i.e. abstraction. (An abstract thought is the ratio, "S is P," meaning that P is more universal than S.) 84 [436] Ratiocinatio (63.9-14) oooic, 8e Kai 8i%a xou aiaGnxoi) Suvaxov xo aiaGnpa e%eiv ev xfl x|/rjxti, otov Kai drceA.Govxoc, ZcoKpaxouc, xov xurcov Kai xfiv pop(pf|v, xouxotc, jtpoayivexai Kai exepa yvcSou;, f) uvfiun, Kai xotc, pev dxeXeaxepoic, ©ax e%etv xov XUTTOV povov eni noXv -xfjq npoXafiovc^c, aiaGfioecoc;, xotc, 8e oiaxe Kai xd opota cuvdrcxeiv 8uvaa6ai Kai ecpappo^ eiv Kai xauxa fj8r| xeA,etd xe Kai A,oyiKd, ev otc, f| xou opoiot) Gecopia xe Kai SiaKpiaiq. (63.9-14) But for those [animals] that have the power to hold the sense-image in the soul even apart from the [subject] sensed (for example, [if] the after-image218 and shape of Socrates [remains] even after he has gone away), a different cogitation219 also occurs in addition to these [sense-images]: memory. Some of these [animals] are too imperfect to hold the after-image (of the pre-acquired sensation) by itself [in memory] for a long time; yet, others have the power220 to conjoin and harmonize similar [memories]. And these latter [animals], in whom there is both contemplation and discrimination of the similar [among memories], are thereby perfect [animals], i.e. abstractive [animals]. 2 1 8 Literally, "imprint" 2 1 9 i.e. the second grade of the cogitation of principles 2 2 0 i.e. the power of the third grade of the cogitation of principles 85 [437] Experimentum (100a 3-9) >EK |iev orjv aiaGfiaecoi; yivexai uvfiur|, wcrcep X,8yo|xev, EK 8E HVT|UT|<; 7toA,A,ccKtc; xor} arjxor) yivo)j,£vr|c; EirttEipia- ai yap noXkax H-vfjum xcp dpiGpa) Eii7teipia i l ia Eaxiv. EK 8' £|A7t£ipia<; rj EK jtavxoc, fip£|a.TiCTavxoc; xorj KaGo^co EV xfj yoxfu xorj EV6<; racpd xd noXka, 6 dv EV ditacjiv v Evfi EKEivoiq xo afjxo, XE^vrjc; dpxii Ka i £Kirjxfi|j.r|(;, Edv |i£v Ttepi YEVECTIV, XE^vric;, Edv 8e Tcepi xo 6v, £7iifjxfi(a.r|(;. (100a 3-9) So, from sensation, memory occurs, as we said; yet, from a memory many times of the same [subject],221 experience occurs (because memories, [although] many in number, are a single experience). And the principle of art and science is from experience,222 or from the entire universal (the one apart from the many, which would be one in all, [i.e.] the same in these [many subjects]) being at rest [i.e. fully abstracted] in the soul.223 If it regards generation, it is [a principle] of art; yet, if it regards being, it is [a principle] of science.224 2 2 1 That is, the object of sensation as being both singular and universal. Byrne (1997), 174-175, says "the same" means "the same [object of experience itself]," i.e. the same universal connection (between singular and universal). 2 2 2 Experience is the progressive rational (i.e. abstractive) refinement of memories. Experience (eu7t£tpia) is the state of principles in the soul built up by abstraction of the universal over time; intellect (vovq) is the state offirst principles built up in experience. 2 2 3 We agree with McKirahan (1992), 243, that the "or" is progressive, rather than disjunctive or explicative. Abstractive induction perfects the abstraction of the universal over time, by much sense experience, until the universal as a first principle is reached. 2 2 4 We adopt and modify the English translation of McCarthy (1976), 78. r 86 [437] Experimentum (63.14-21) EK (j.ev orjv Tfjc, aiaBfiaecoi; eYYtvexai ^f | i ir | , cbcnep Xeyo\ie\, EK 8E |avfi(j,T|c; 7T.OA,A,&KIC, TOY) avjxorj Yivouivric, EurcEipia- a i yap noXXai u,vfjum T(p dpiGiiq) jxia eimeipia erjxiv. oxi iiev yap T 0 § e ecmv eXXkfiopoc, TO KaGfjpav, TJCGETO xai EUVTIUOVE'OO'EV aXXa Ka i OTI T68E EXAipopoc, TO naXiv KaGfjpav, TJCJGETO avjGtc; Ka i £pvTuj.6vEt>a£, Ka i atjGic, ye ETEpov Kai naXiv aXXo. noXX(bv 8E u.vri|iQ)v EK noXX&v aia0f|rj£©v YIVOUEVCOV EixKEipia dGpoii^ETai ixia Torj KaGaipsiv TOV eXAipopov (63.14-26) So, from sensation, memory occurs in [us], as we said; yet, from the same memory frequently occurring, experience [occurs] (because memories, many in number, are a single experience).225 One senses and remembers that this hellebore is one that heals. And that this hellebore is, on the next occasion, one that heals, one senses and remembers; and at least on a different occasion, and again at another. And when many memories occur from many sensations, one experience is amassed of the [potential universal]226 that hellebore heals. 2 2 5 Many memories become a single experience through abstraction, i.e. through the third grade of cogitation of principles. Themistius will now go on to explain how one abstraction from many memories occurs. 2 2 6 Weisheipl (1958), 61-62: "These experiential judgements are themselves potentially universal. They are reduced to actuality by the agent intellect. Therefore universal first principles are indeed acquired from preexistent knowledge, but from knowledge of a very different kind from what has been discussed above for scientific demonstration." That is, the knowledge is potential, and not actual. 87 [437] Universalium (63.21-26) fjc, aDvau^avopEvnc, TE Kai rcpoaA-apPavoucnc, ataGriatv opoiav Kai jivf|p.r|v 7ifiYvt)Tai fj8r] TO KaGoXoD Kai eu(iEvei TT} V^Xtl' OTI nac, kXXe^opoq KaGaipEi. Kai EOTI TO KaGoXorj TO ouoiov Kai Tatnov EV ToTg KaG' EKaoTov Kai TO EV Totg KoXXdiq, Kai TOVTO TEXvng apxfi Kai EitiCTTfiprig, T£%vnc, p i v , E ! JTEpi TCOV x>% at)Tfjc; yivopEvcov, ErciCTfiung 8E, E ! KEpl TCOV X>K6 (puaEcog. When this [experience] both is augmented and additionally acquires similar sensation and memory, the [potential]227 universal is thereby consolidated, and it persists in the soul that, "All hellebore heals." And the universal is the similar and the same in individual [subjects], and the one228 in many [singulars]. And this [potential universal] is the principle of art and science: [a principle] of art, if it regards the [subjects] it generates; but [a principle] of science, if it regards the [subjects] of nature. Cf. ibid. Reading ev instead of ev. 88 [437] Anima (100a 10-14) o u x e 8f) £vrj7rapxo,uavv acpcopiouivai ai e^ eiq, oux' an aAAcov E^ECOV yivovxai yvcoCTxiKcoxepcov, aXX anb aiaOfiaecoc,, o t o v e v p.a%n xporcfjc, yevopevnc, evoc, axdvxoc, exepoc, eaxn, etG' exepog, ecoc, eni apxfiv fjXOev. f) 8e \|/u%fi urcap%ei xoiauxri ouaa ota 8uvaa0at 7tdc%etv xouxo. (100a 10-14) Indeed, the states [cogitating invmediates] neither [DI] exist in [us] as determinate,229 nor [D2] occur from other states which are more cogitative,230 but [A3] [are abstracted] from sensation, as when in battle a reversal occurs: once one [soldier] mades a stand, another makes a stand, then another, until a fresh start is reached.231 And the soul exists being the sort of thing that has the power to be affected in this way.232 2 2 9 i.e. "determinate" = "already abstracted" (as in Platonic idealism) 2 3 0 As if science were to be the state of principles, i.e. as if the non-existent principles somehow were to become actual from the act of demonstration (as in Sophistic nominalism): i.e. "more cogitative" = "more actual" 2 3 1 Literally, "it [the battle] comes upon a principle," i.e. "principle" = "fresh start". When the tide turns in the battle, i.e. when there is a reversal of fortune, there is a new beginning. Barnes reads OCXKTIV for ap%T)v, a pun we would translate as "until [the battle-line] makes strength its principle." On either reading, Aristotle's point is the same: the strong reinforcement of memory is the required condition for a principle to be abstracted. 2 3 2 Kahn (1981), 403-404, observes that, "this is a promissory note, to be redeemed in the treatise on the psyche." Here, it is simply an analogy, indicating that the universal begins the same way a reversal in battle does: i.e. as the reinforcement of soldiers is to a reversal, so is the reinforcement of memory to an abstract principle. 89 [437] Anima (63.26-29) ouxe ouv zt, dpxfji; ev\)7idpxouCTiv ai dpxai (xeA,etot yap dv eyevopxGa), ouxe arc aXX^c, e^ eax; eyyivovxai yvcoaxiKcoxepac, wax' dvdyKnc, xi 7tpoei5evai, aXX drco aiaGfiaecoq xai n.vf|p,T|c, 5ieyeipovxai Kai dGpot^ovxat. (63.26 - 64.2) Therefore the principles neither [DI] exist in [us] from the outset (because we would have been perfect),233 nor [D2] do they occur in [us] from another state which is more cogitative234 (so that we must have some foreknowledge);235 rather, [A3] [the principles] are put together and amassed [in the soul] from sensation and memory. 2 3 3 i.e. the state of principles would have been entirely actual 2 3 4 i.e. science would be a more cogitative state than a state of having non-existent first principles 2 3 5 Demonstration requires some pre-existent knowledge for its principles. But this pre-existent knowledge can be neither [DI] already actual knowledge, nor [D2] non-existent until derived from already actual knowledge. Instead, the knowledge is [A3] potentially pre-existent in sensation and memory. 90 [437] Pugna (63.29-64.2) otov yap ev irdxTI xpo7tfj<; yevo|4.evr|<; etc; earn, Kai TtdXiv exepoc, eaxri, Ka i 7tdX.iv dXXoc, Ka i fj8r| xoaorjxot rooxe Tcapdxac^iv Ka i dp%r)v ar36i<; pd%rig yeveoGai, -ovjxco ueivavxoc, ev xi\ V°XTi xfjuorj orjvrip|i6a0T| Ka i dXXoc, Ka i arjOic, dXXoc,, Ka i xoaorjxov fj8r| XO 7r.Xfj0oc, dx; ia%rjp6v xo KaGoXou yeveaGai. r\ \\>v%r[ orjv a ix ia xoiarjxr|v e%orjaa cpfjoiv wfjxe xcov aioGrjxrov 7tapappe6vxcov e7tiXapPdveaGai xcov ojroicov ximcov Kai evarcoxiGeoGai xij Hvfipri, avjXXeyorjoav xo KaGoXorj xo ev xoiq KaG' eKaaxov ouoiov, orj Ka i arjxTi Ttcoc; fj aiaGrion; orjve(pd7txexai. Because, for example, in battle, when a reversal occurs, one [soldier] makes a stand, and again a different one makes a stand, then another, and thereby a battle-line and a fresh start to the fight occurs; so too, when an after-image remains in the soul, another and again another are fitted together, and then, when the number is so large that [the memory] is reinforced, the universal occurs. Therefore [A3] the soul is the cause, because it has the sort of nature that, when the sensations are flowing past, it makes acquisition of the similar after-images, and places them away in memory, gathering together the universal (the similar in individual [subjects]), with which even sensation itself is somehow involved.236 2 3 6 i.e. sensation potentially knows both the singular and the universal 91 [438] Primus gradus (100a 14 - 100b 1) 5 8' eAixGr] pev 7T.&A-CU, orj oacpcoi; 8e eXi^ On, 7cdA,iv 8i7tcou,ev. cxdvxoc, yap xwv d8ia(popcov kvoq, np&xov ixev ev xij yuxfj KaGoAotj ( K a i yap aiaGdvexai ixev xo KaG' eKaaxov, fj 8' ai'aGriatc; xorj KaGoAorj eaxiv, otov avGpamou, aXX orj KaAAaou avGpdmorj)-(100a 14 - 100b 1) What we have already said, but not said precisely, let us say again. When one of the undifferentiated [sense-images] has made a stand,237 the first [stage] of a [potential] universal238 is in the soul: i.e. because, on the one hand, the individual [subject] is sensed, but, on the other hand, sensation is [cogitation] of the universal (e.g. of "human," but not of "the human Callias.")239 2 3 7 i.e. when the sense-image persists in memory 2 3 8 We must presuppose that "a soul is capable of having universal knowledge and of actuating intelligibles by the abstraction of universals from singulars, which could not be possible if there were not in some way sense knowledge also of universals": McCarthy (1976), 32 (paraphrasing the argument of Aquinas at II An. Post., lect. 20, n. 11-14). McCarthy argues that the explanation of Aristotle and Aquinas does not fully resolve the issue; however, we find his invocation of "intellectual consciousness" (ibid.) to be even more problematic. We suspect he is trying to demonstrate the indemonstrable, by pushing the problem beyond Aristotle and Aquinas, who have already hit up the indemonstrable presupposition required. 2 3 9 On the one hand, sensation senses something singular; but, on the other hand, the subject of the first stage in sensation is always the most abstract, e.g. the more universal ("human") is sensed before the more particular and the less universal ("this human Callias"). 92 [438] Primus gradus (64.2-9) oxav ydp EcoKpdxouc, aia6dvr|xai, arjvavxiAai4.|jdvExai xai dvGpamou, xai oxav xou8i xorj AEDKOVJ, covaicGdvExar Kai AEUKOVJ-orj ydp (be, xarjxovj navxzX&q rjrjvairjGdvExai KaX,X.iovj XE Kai dvGpamorj- OYJKEXI ydp et7tev dv dvGpco7iov etepov ei ja.fi KaAAiav aXX' oxav opa ZcoKpdxr|v, TOTE opa EV arjxcp Kai TO %pbq xox>q aXXovc, ouoiov Kai KOIVOV. ©axE xportov xivd Kai aicGriaic, xorj KaGoAou, dAA' ox>% oijxooq aioxE arjxo %(£>piaai Kai dcpE^Eiv Kai KaG' Earjxo yva>vai, dAAd avjyKExrj(X£vov XE XO) KaG' EKaaxov Kai uaAAov E U ; EKEIVO d7COXEXpa|XLXEVOV. (64.2-9) Because, when "Socrates" is sensed, "human" is also apprehended conjointly, and when this [singular] white [subject is sensed], "white" [the universal] is also sensed with it. Because both "Callias" and "human" are not sensed conjointly as the same in all respects (otherwise one would no longer say "human" is different from "Callias"); instead, when one sees Socrates, one then sees in him also that which is similar and common in relation to others [e.g. human subjects]. As a result, sensation, in a way, is also [cogitation] of the universal (but not such that it separates and abstracts and cogitates [the universal] in itself;240 instead, [sensation] is both blended together with the individual and more oriented towards it [than ratiocinatio]). 2 4 0 Abstraction ( .^oyoq = ratiocinatio) does this, not sensation. 93 [438] Inductio (100b 1-5) nakw ev xouxotc, icxaxat, ecoc; dv xd dpepfj axfj Ka i xd Ka66A,orj, oiov xoiovSi £6)ov, emc, £6)ov, Kai ev xouxap aaamcoq. 8fjXov Sfj oxi fpTv xd rcpcoxa e7iaYC07fj yvcopi^ eiv dvayKatov Kai yap fj ataGncuc, OUXCQ xo Ka96A,ot> epnoiet. (100b 1-5) Next, a stand is made among these [sense-images],241 until the non-particular [memories] make a stand,242 i.e. the universals. For example, "this [particular] animal [e.g. a horse]" [stands in memory], until [the universal] "animal" [is abstracted]; and, in this [particular animal, e.g. a man], similarly [is the universal "animal" abstracted]. Indeed, it is clear that [Al] we must cognize first [principles] by a "leading-up" [to the most universal, i.e. by an induction],2*3 because this is how sensation produces the universal [i.e. the potentially universal is produced in the experiential judgements of the vis cogitativa].2™ 2 4 1 i.e. the second stage of the cogitation of principles: viz., memory 2 4 2 i.e. the third stage of the cogitation of principles: viz., abstraction 2 4 3 Sensation is the power that potentially knows the most universal content of the singular sensed subject. Abstraction returns to this most universal content of the singular, by induction, i.e. by leading back, from the comparisons and particularizations of memory to the universal. 2 4 4 Weisheipl (1958), 61-62, explains how experiential judgements are potentially universal 94 [438] Inductio (64.9-14) okX Exepa Suvauic, EOTIV, f| Tfjq aiaGfiaeax; rcepi TO Kaxd pepoq EVEpyoucnc, TO V E K rcoAAcov Ka i TO dSidcpopov E K Svacpopcov Kai TauTdv k.% ETEpcov auvdyet, otov TOV avBpamov E K KaXAaou Kai >ApioTcovo<; Ka i TO £G)OV i% dv8pa)7iot) Kai XEOVTOC, Ka i Tf|v ouoiav E K (pinou Kai r^oovj- dvEioi yap p-E^ptc, dv Etc, v Tza\xzX(aq Td noXka dvaydyr) TE Ka i at)v8fioriTai. (64.9-18) But there is a distinct power,45 which, after sensation is enacted with regard to the particular,246 brings together the one from many, and the undifferentiated from differentiated, and the same from different247 (e.g. "human" from "Callias" and "Ariston"; and "animal" from "human" and "lion"; and "substance" from "plant" and "animal"), because it rises up248 until it can both lead back the many to the one, and bind them together.249 2 4 5 i.e. intellect. However, Themistius is referring here to the agent intellect as a power of the soul, not to intellect as the habit of first principles. Aquinas remarks, in his Quaestiones de Anima, that "there are some men who hold that the agent intellect is nothing more than our habit of indemonstrable principles. But this cannot be true because we know even these indemonstrable principles by abstracting from singulars, as the Philosopher teaches near the end of the Posterior Analytics." (translation by Robb (1984), 88) Therefore agent intellect is not the state of first principles, but rather the soul's power of Xoyoc; {ratiocinatio) that abstracts from the memories (stored up in the passive intellect by sensation). 2 4 6 i.e. after the second stage of cogitation partitions sensation's universal knowledge of singulars into memory's particulars (cf. D.A. III.4-8 on the passive intellect) 2 4 7 i.e. the more universal is abstracted from the less universal 2 4 8 i.e. through abstraction to a higher genus 2 4 9 i.e. to make the Xoyoc, (abstract proposition), "All S is P," where P is more universal than S 95 [438] Communes animi conceptiones (64.14-18) ffloxe £7taya>yfi 6 xporcoc, eoiKe xfjc, avaxdaecoq xov KaGoXot) Kai Tfjcj yvwcscog, KaGo Aiyexai ercaymyfi naq 6 EK xa>v Kaxd pipoc, xo KaG6A,o\) KecpaX.aio'upevoq Xoyoc,. fj5r| 8e xov xoiouxorj Xoyov xd pev A/nppaxa Gfjaorjaiv a i aiaGfiaEtc/ dp%ai yap auxai Kai a ix ia i xa>v Kaxd pepoc, tmoXfixi/ecov- xriv 8e KaG6A.ox) emcpopdv 6 vovq Kovfiaexai-As a result, [Al] the manner of constituting and cogitating the universal is like a "leading-up," insofar as every abstraction that sums up the universal from [subjects] regarded partially is called a "leading-up" [i.e. an induction]. And, with such an abstraction,250 sensations will thereby establish [self-evident] concepts,251 because these are the [common] principles (i.e. causes) of particular [proper] suppositions;252 yet, intellect will effect the concentration upon the universal.253 2 5 0 "All S is P." 2 5 1 Self-evident concepts are universals expressed in nota per se abstractions of the form, "All S is P." These concepts will either be common principles or proper priciples; if proper principles, they can be either suppositiones or definitiones: as Weisheipl (1958), 12-19, clearly explains. 2 5 2 Weisheipl (1958), 18-19, on common principles: "The importance of these common principles should not be underestimated; for while they do not enter into a propter quid demonstration of a scientia particularism their truth makes scientific knowledge possible by illuminating and confirming every valid demonstration. . . . It is these that Aristotle will establish as the ultimate basis for the possibility of learning in Book II, chap. 19." See ibid, 12 ff. for proper principles (suppositiones, etc.). 2 5 3 Caveat: the mere form of an abstraction, "All S is P," does not guarantee a principle; intellect must experience it to be truly and necessarily so. 96 J [439] Tempus (64.19-27) xofjxou ydp epyov fi5ri xd TtoAAd evovjv Ka i xd a7tEipa, 07tep cpriai nAdxcov, 7r.epaxi orjv8f|aaa6ar Kai ydp SiaipexiKoc, Kai arjvGexiKoc, Kai iiexaPaxiKoq xe Ka i dAAcoc, 7toX,vjxp6n:a)(; etjKivrixoxaxoc,. eaxai 8e ox>X txp' v orj8' erjQvjc, ovj8' ev xpovra oAiyco f] xe xcov Anppdxcuv xfjc, e7taycoyfj<; xafjxric, aiaGnaic, Kai fi xorj KaGoAou E7ti(pd)vr|ai(;, dAAd TtAeiro Xpovov irexa^i) Ttapep7ii7txeiv ducpoxepcov dvdyKri. Ka i xd irev A,fip.uaxa erJGfjq f\ 7ipd)xr| fip.iv dp^apevri aioGr|ot<; xiGriai, rcoppco 8e fj8r| 7cpoeAGorjor|<; 6 vorjg e^ arjxcov xo KaGoAorj arjpTcepaivexat. 8id xi pevxoi 8id paKporj; erceiSfi 8id Xpovou arjvayeipeiv TtecprjKe xo KaGoAorj. (64.19-27) For [intellect's] activity is thus one of uniting the many (and, furthermore, to quote Plato, "to bind together the indeterminate things by a limit"),254 because intellect can divide and compound, and make transitions and otherwise variously alter with the utmost facility.255 And (T,) the sensation of the [self-evident] concepts of this "leading-up," and (T2) the articulation of the universal, will not be by a single [abstraction], nor right away,256 nor in a little time;257 rather, a lengthier time must intervene between (T,) and (T2).258 But sensation (the first beginning in us) establishes the [self-evident] concepts right away; yet since it proceeds from afar [i.e. with singulars], intellect joins in accomplishing the universal from them. But why does it take a long time? Because it is natural to assemble the universal over time. 254 Philebus 27d 9 2 5 5 Cf. Smith (1952), 341 2 5 6 multiple simultaneous abstractions 2 5 7 multiple abstractions in rapid succession 2 5 8 The articulation (at T 2 ) of the universal takes the form of the abstraction, "All S is P." But although this universal is potentially known to sensation immediately in the first sensation of the singular (at T,), it takes time for the soul to build itself up to a state where it can actually articulate (at T 2 ) this potential universal in the explicit 97 [439] Intellects (100b 5-14) >Ercei 8E TCOV 7t£pi TT|V Stdvotav e^ ecov ate, dA,n0£\)op.£v a i (j.ev del aA/nGeic, eiaiv, ai 8e emSexovTai TO \|/£u8og, o tov 86^a Kai X071.cm.6c,, dA,n0fj 8' dsi ETUOTfipn Kai vouc,, Kai OUSEV £7UCTTHJ.T|<; aKpiPeoTepov bXko yevoq fj vouc,, ai 8' dpxai TCOV d7to8£i^ecov yvcopipraTepai, ErciaTfpn 8' dracoa peTd Xoyou E C T I , TCOV dpxrov £7tlO"TTlp.r| p £ V 0 \)K dv £IT|,259 E71EI 8' ovbev dA-TjOEaTEpov £v8£X£Tai E i v a i EmCTTfipriq ri vouv, vovq dv eir\ T Q V dp%C0V, EK T£ TOVTCOV OK07toi)Ol Kai OTI d7to8£i^£coq dpxfi oi)K d7i68£i^ i<;, ©OT' OUS' £7IlCTTflpT|(; £7liaTf)p.T|. experiential judgement, "All S is P". Cf. Weisheipl (1958), 59-62 2 5 9 translated "will be" because the Greek is in the conclusive optative (100b 5-14) And [P3] since among the states that involve thought (by which we speak truth), some are always true, yet others (e.g. opinion and calculation) admit falsehood (but science and intellect are always true), and no other kind of science is more certain than intellect; and [PI] the principles of demonstration are more cognized [than the conclusions], and all science comes after an abstraction [of principles]: [P2] there will be no science of the principles;260 and since [P3] nothing can be more true than science, except intellect, [A2] intellect will be [the cogitation] of [first] principles.261 From these considerations [i.e. because P3 implies A2] and [from the fact PI] that the principle of demonstration is not demonstration, thus [P2] the [principle] of science cannot be science.262 2 6 0 P2 follows from PI. PI = "Theprinciples of intellect are more cognized (i.e. more actual) than the conclusions of science." Therefore, P2 = "There is no science of principles." 2 6 1 A2 follows from P3 and PI. P3 = "The state of intellect is more true and more certain than the state of science, because of what it possesses (and what it possesses is spelled out in PI, i.e. this state is more in possession of certain principles, i.e. abstractions more actual, than the state of science)." Therefore, A2 = "Intellect is the state cogitating principles." 2 6 2 Aristotle recapitulates the argument in order to emphasize P2 as a negative formulation of A2. 98 [439] Intellect™ (64.27-65.10) XavGdvei 8e ainoc, 6 Tporcoc, ETcaycoYfi xiq div, x a i rcapd xfj<; (pvjaeax; A,au,pdveiv aXX orj Ttap' eavjTorj So^eiev dv xdq evvoiac, zoic, drteipoTepon;. OTI 8e vovjc, eaxiv 6 vac, KaGoAovj Kai d)j,eaovj<; 7cpotdoei<; eYKaTacTKEVja^oixevog Kai ovjSeuia dX,X,r| 8vjvainc„ 8fjA,ov KdvTevjGev TCOV ydp Ttepi TT|V Sidvoiav e^ eoov xatg uev OVJK dei dA,r|9efjonev, xaiq 8e dei- OVJK dei (j.ev So^n Kai Xoyiairu), d|rcpotv (rev OVTCOV 7tepi TCOV ixXXoxe aXX(aq exovTcov, aXXa ir\q u.ev eic, avJTfrv TT|V Getopiav d7COTeA,evncbrjr|CJ KOXXOLKIC,, TOVJ 8e eic, Tcpd^iv drcoTeivouivovj TO OVJVOXOV ate, 8e dei Svjvdiieoiv dX,r]Gevjo|xev, eTciOTrmri ecui Ka i VOVJC/ Kai OVJK eoTiv emoTfiirri TCOV dpxcov 8i' aTtoSei^ecoc, ydp fj ye dKpiPcoc, e7tiaTf|ixr|- XeirceTai 8fjA,ov OTI VOVJV etvai TOV yvcopi^ovTa xaq d p x d q . (64.27-65.10) But the manner itself [of assembly] escapes notice, because [Al] it is a "leading-up",263 and it seems to take its notions for what is more indeterminate from nature and not from itself.264 But that it is intellect, and no other power, that supplies the universal and immediate premises, is clear from the following. For as regards the states of thought, with some we do not always speak truth, but with others, always: Not always with opinion and calculation (since both have reference to [subjects] being different at different times; yet, while [opinion] mostly terminates in inquiry, [calculation] is entirely directed towards action); yet the powers by which we always speak truth are science and intellect. And [P2] there is not science of principles, because [PI] science, at least, is certain by demonstration. Clearly, it remains that [A2] intellect is what cognizes [first] principles. 2 6 3 This is the grain of truth in [DI]: i.e. the pre-existent knowledge of principles escapes our notice insofar as it takes time to be assembled in abstractive induction, from potency to state. 2 6 4 Abstractive induction moves from what is known quoad nos to what is known quoad se (i.e. quoad naturam); as Aquinas says, "nos procedimus intelligendo depotentia in actum": I Phys. lect. 1 n. 7, Maggiolo (1965), 5; 99 [439] Animal rationale (65.10-15) Ka i ydp 5f| TtpoafJKei iiev dei xatc, ap%aiq dKpifieaxepov yivd)cjK8Cf8ai xcov pexd xdg dpxdc/ uovoc, , 8e vorjq dKpifJeaxepoc, £7n.oxf|pr|(;. vovq ovv 6 A/r)7r,xiK6<; xcov dpxcov, VOVJI; 8e 6 rcpcoxoc, Kai fj7td tfjc; (prjoecoi; eyKaxaoKerja^oirevoc, xa) AoyiKo) o^pco. 8rjvd|xei 8e OVJXOI; ©v eaxvv dKAovjaxaxoi; Ka i ©OTtep aAoyoc, xiq Ka i a K p i x o i ; xfjq v|/vj%fi(; 6\|n<;, KaG' f|v zt, dpxfjc, eoxt (pvjaei AoyiKov ^opov 6 avGpamoc,. (65.10-21) For indeed it is fitting that [PI] the principles always are cogitated with more certainty than the [conclusions] that come after the principles; yet [P3] intellect alone is more certain than science. So [A2] intellect is what can acquire the principles.265 And intellect is the primary [difference] supplied (i.e. by nature) in the abstracting animal. Yet this [state], when being [at first only] potential, is most simple, and is like some non-abstracting and non-discriminating "eye of the soul," according to which, from the beginning, by nature, man is an abstracting animal. Blackwell-Spath-Thirlkel (1963), 6: "we proceed in understanding from potency to act" 2 6 5 Note that Themistius unravels the structure of the argument exactly as we do in our annotations to 100b 5-14 above: PI and P3 imply A2. Likewise at 65.8-10 above, Themistius says, as we did on 100b 5-14, that PI implies P2. He then states A2 both proleptically (i.e. before his discussion of the fact that PI and P3 imply A2) and also because A2 is a positive reformulation ofP2. 100 [439] Propositio (65.15-21) OUTOC, 8e 6 vouc, Kai npo ouatv fipiv ODvarj^dveiai del Kai O"uv£7ti8i8cocu, TO U E V np&xov eic, xaq anXac,, darcep oporjc, ovopd^opev, Kai TCOV dovjv8eTcov Kai d7tA,orjo*TdTa>v xov Xoyov OTOixeicov Geaeic, Kai Tdc, dnXdc, avTiA,f|\|/eic/ dvGpamov yap f\ XBVKOV dpxeTai Kai Aiyetv 7tpa>Tov Td rcaiSia Kai voetv, erceiSdv eyKaTao"KeDd£nTo:i Xoyoc, a\)TOiq-rcpoPaivovToq 8e fj8r| Kai xov arjvTiGevai TanTa Td anXa Suvapiv 7tpoaXapPdvei Kai T ! dvGpco7t6<; E O T I V ri8r| 8iavoeiaGat. But this intellect also is always augmented as we develop, and grows along with us; at first, into the simple things [that are] established (which we call "terms,"266 i.e. the uncompounded and most simple elements of the abstraction) and [into] the simple acquired predications.267 For children first begin to say "human" or "white" (i.e. to think intellectually) when an abstraction is supplied to them.)268 But, when advancing, [intellect] also acquires in addition a power to compound these simple [terms],269 and, at that time, to think through what a human is.270 2 6 6 e.g. as Aristotle does in An. Pri.,passim. Terms are signs for universal concepts. Terms are not identical with universals; for example, propositions express more universal universals than terms. Cf. McKirahan (1992), 239, on the three conceptions of universals (viz. terms, propositional connections, and demonstrative principles), which he sees as problematic. We see them, however, merely as the three grades of the logical expression of one reality. Universals are real, as real as whatever is in act. Cf. Aquinas, / Phys. lect. 1, nn. 6-8 2 6 7 e.g. "This is P" 2 6 8 i.e. when we say, "This is P"; e.g. "This is a human," or "this is white"; or even when we just point and say "human" or "white" (which, although less articulate, is of the same level of abstraction, i.e. "This is P.") 2 6 9 i.e. "This S is P." 2 7 0 e.g. "This human is white." 101 [439] Habitus (65.21-24) erceiSdv 8E 7iX.£tova iaxuv A.dpri, Kai rcpoc, xr\v xov Ka66A.0D cuaxaaiv Kai vonatv 8\)vaxd)X£poi ytv6p.£8a, ECOC, dv xf|v A,oytKf)v E^IV, Ka8' fiv fjSTi XoyiKoi y£y6vap.£v, o\>aTTio6u.£0a na<j%ovor[cl xi Tfjq \|/t>Xf|g 7ipoa6p.oiov top aropaTv (65.21-66.3) And when [the state of intellect] acquires greater strength, we also become more powerful with regard to the constitution and [the application of] intelligence [to] the universal, until we are constituted by the abstracting state, according to which, at that time, we have become abstractors: since the soul is affected somewhat like the body is... 102 [439] Corpus (65.24-66.3) Kai yap xouxo dp%6p.evov pev xe^eiouoGat rcpaixov pev iaxtiv A,ap.pdvei npbc, auxf|v xrjv 8tavdo"xaatv Kai xrjv 81' eauxoi) %au66ev opGcocuv, etG' uaxepov Kai rcpoeiatv etc, xo rcpocGev erci piKpov, Kai oftxcoc, dei xeA,etot>pevov eiq rcepiraxxov xe Kai Spouov Kai xf|v rcpoi; xauxa pa>p,nv rcpoepxexai. ouxco 8f) Kai 6 vouc, xo pev rcpcoxov ovopd^eiv 8uvaxat uovov Kai xd x>nb xd ovouaxa voeiv rcpdypaxa, et^ fjc, 8e Kai auvxiGevai Kai SiavoetoGai, etxa xo xeXematov KaG6A,OD xtvd Kpipaxa PePatcocduevoc, ev auxa) a7toxiGexai. ... i.e. because this [body], when beginning to be perfected, first acquires strength with regard to standing up and standing erect from the ground on its own; and then next goes forward to the front to a slight degree; and thus, always being perfected, advances both to walking and to running, and their associated strength. In this way, indeed, intellect too is at first only able to apply predicates, i.e. to think intellectually the affairs [only] by means of the predicates.271 Yet, at the next stage, [intellect is able] both to compound and to think through [terms].272 Then, finally, when some discriminated things have become fortified, it treasures in itself the perfection of the universal.273 i.e "This is P." i.e. "S is P." i.e. "All S is P." 103 [439] Principiorum (100b 14-15) ei OVJV UT|8£V aXko map' e7ciaxfiiir|v yevoc, e%o|a.ev aXxfikq, VOYJC, dv ei'ri e7ciOTfmriq dp%f|. Ka i f) piv dpxfi Tfj<; dpxfjc, ei'ri dv, f| 8e Ttdaa ouoicoc, e%ei rcpoc, TO Tcdv 7tpdyu,a. (100b 14-15) Therefore, if [P3] beyond science, we have no other [always] true kind [of cognition], [A2] intellect will be the principle of science.274 And the principle [i.e. intellect] will be the [principle] of the [immediate] principle [employed in demonstration],275 yet every [immediate] principle [still] holds similarly [i.e. is still an indemonstrable immediate principle] in the direction of the whole domain [of scientific conclusions drawn from it] [ = Al]. 2 7 6 2 7 4 This is simply a reformulation of [A2] in light of the negative formulation of [P2], i.e. it is [P2] cast affirmatively in light of [A2]. 2 7 5 This is an anticipation of the possible "infinite regress" objection to the reformulation of [A2] just made. Cf. Weisheipl (1958), 13, 59-60. 2 7 6 The immediate principles of demonstration are no less immediate just because they arise through abstractive induction into the state of intellect. Hence it cannot be said that "intellect" is a half-baked solution, smuggling in an infinite regress under the guise of a deus ex machina solution. The proof of this is that the immediate first principles of demonstration are not suddenly replaced in demonstrations by the substitution of "intellect" as a more immediate principle taking their place. Rather, the first principles retain their immediate character, as Aristotle intimates, (despite the fact that this state of first principles has to derive from the potential universals in sensation), because first principles do not derive from intellect like conclusions derive from first 104 [439] Principiorum (66.3-6) vorjq orjv dp%T) emaxfiiiric,, Ka i f) (lev dpxf j xcov dp%cov yv&cic,, r\ 8e Ttaaa eTtiaxfmri xor) Ttavxoc, e7ciaxr|Torj- cog y d p f] apx t j 7tp6<; XTJV ap%r\v, OYJXCOC, f| rtaaa 7tp6<; 7tdv. (66.3-6) So, [A2] intellect is the principle of science. But the principle [i.e. intellect] is cogitation of the [first] principles;277 yet the entire science is still [cogitation] of the entire science [i.e. its conclusions].278 [Al] For just as the principle [i.e. intellect] is as regards the principle [in demonstration],279 so is the entire science as regards everthing [that it concludes].280 principles. Instead, they are derived by abstractive induction, not through demonstration. 2 7 7 This is an objection charging "infinite regress" 2 7 8 This is the answer to the objection. It is, in effect, an answer to [Ql] whether the cogitation of immediates is the same or not the same (99b 22 ff.) 2 7 9 i.e. they are different kinds of states of principles; science possesses the immediate principles actually in demonstration, whereas intellect has to abstract them from the potentially universal in sensation. 2 8 0 i.e. intellect is no more circular than demonstration is. Demonstration is founded on immediate first principles, and intellect is founded on abstractive induction of universals. Neither state is a vicious circle in itself; neither are these states an infinite regress in relation to each other. "Scientia est conclusionum, et intellectusprincipiorum": Aristotelian maxim quoted in Weisheipl (1958), 13 105 CHAPTER III Physics: Ens mobile 3.1 Motion (Phys. III.1-3) The order of abstraction opens up, through induction, the proper subject of natural science: mobile being.2" The difficulties that contemporary commentators282 have with Aristotle's definitions in the Physics are not well founded, we argue, because, once the types of demonstrations that Aristotle uses are properly understood, the alleged problems found by the commentators disappear. The demonstration about motion283 considers motion in its intrinsic character, and the demonstrations about place and time284 consider motion in its extrinsic character. Motion is the intrinsic property of ens mobile, and place and time are the extrinsic measures of motion. Place is the mensura entis mobile and time the mensura ipsius motus.285 Therefore any exegesis of Aristotle's Physics has to follow the first principles in that science. 2 8 1 Smith (1958), 14-33 2 8 2 e.g. Ackrill (1965), 121-141; Cf. Lang (1998) and Lang (1992): although attentive to the multiple misunderstandings of Aristotle's peculiar procedures in the Physics throughout history, Lang nonetheless suffers from historicism in her own method. Lang insufficiently grasps the trans-disciplinary character of Aristotle's methodology and explains its obsolescence in physics in terms of Aristotle's previous "commitments" in other realms (metaphysical, political, etc.). De Groot (1996) clearly and forcefully demonstrates the inadequacies of this approach to Aristotle. 2i2Phys. III. 1-3 2UPhys. IV.1-5, 10-14 2 8 5 IVPhys., lect. 1-8, 15-23 106 A science of ens mobile is possible only if there are physical principles in the physical world, a fact that Aristotle establishes.286 Through these principles (i.e. form and matter), demonstration is possible. The subject of physical science is whatever comes to be by nature (i.e. by these principles), and the middle terms used in demonstrations about whatever comes to be by nature are the final, efficient, formal, and material causes.287 Hence the types of a priori demonstration in the Physics will be exclusively Type D and Type A demonstrations, unless the demonstrations are not really proper to the science of ens mobile itself and are imported from another science (e.g. metaphysics); however, all the proper demonstrations about motion, place, and time are Type D. 2 8 8 And this stands to reason, since Type D demonstrates the material cause of the subject by means of the formal cause.289 Thus, we have, at the appropriate level of abstraction for physical science, the proper subject matter (ens mobile) and middle terms (formal, material, etc.) for demonstrations about that subject matter; yet one thing is missing, and that is what we may consider to be the most abstract predicate or property of this subject matter, namely, motion itself.290 Motion is the essential property of mobile being; it is involved in the very definition of nature and it is the most proper feature of any natural thing known to us in sensation.291 Our experience of mobile beings can be divided two ways; in one way, we experience them as either actual or potential, and in the other way, we experience them 2 8 6 Phys. I ™ Phys.U 2 8 8 Wallace (1958), 100-103 2 8 9 Table 5 2 9 0 Cf. Smith (1958), 255 2 9 1 Ibid. 107 divided into the ten categories. Through these two ways, we can see what motion roughly is: it is "an imperfect act and related to the category in which it occurs."293 (And thus it is correct to consider motion in terms of potency and act because any category to which the motion is reducible is divided by potency and act.)294 Yet it would be wrong, in trying make this observation from experience more precise, to define motion as the passage from potency to act; for that would be a circular definition, since "passage" is just another way of saying "movement".295 Nevertheless, because potency is a kind of capacity for actualization, and act is that state of fulfilled actualization, it seems that motion is somehow something somewhere between the two.296 In a way, it is partly one and partly the other, i.e. an imperfect, unfulfilled potency.297 Aristotle's demonstration about motion is an a priori demonstration of Type D. 2 9 8 It demonstrates the material cause through the formal cause.299 The subject S is "motion"; the middle term formal cause M 2 is "the actuation of a potential thing insofar as it is potential"; and the predicated material cause is "the act of a thing moved insofar as it is moved, not the act of the mover".300 (A more succint way of expressing the latter two causes is: M 2 = "the act of the potential precisely as potential" and M, = "the act of the mobile precisely as mobile";301 or, most succinctly, M 2 = "actus existentis in potentia Ibid, 256 Ibid., 270 III Phys., lect. 1, nn. 280, 284 Smith (1958), 257 Ibid., 257-258 Ibid., 258 Wallace (1958), 101 Table 5 Wallace (1958), 101 Smith (1958), 263 108 inquantum huiusmodi and M, = "actus mobilis inquantum est mobilis"303) Any criticisms of Aristotle's definition of motion miss the mark unless they consider the fact that his "definition" proper is what is established by the propter quid demonstration made up of these two definitions.304 The conclusion of the Type D demonstration perfectly establishes what the subject of motion S in fact really is: "motion is the act of the mobile precisely as mobile". Anyone who criticizes the formal minor premise, saying that Aristotle has not demonstrated it, has missed the point of the entire demonstration. The minor premise asserts that, "motion [S] is the act of the potential precisely as potential [M2]", i.e. motion is formally nota per se thusly. The only thing that can be demonstrated is the Type D demonstration itself, not this proposition. It can only be known through abstract induction, and Aristotle's dialectical arguments can help to clarify confused notions one may have about motion. But, in the end, there is no "demonstration" necessitating the acceptance of the minor premise "S is M 2" on the part of the Aristotle's interlocutor. For either this nota per se principle is comprehended by the interlocutor's intellect or it is not; such is the nature of first principles. Remember, per se nota as regards proper principles of a particular science, like scientia naturalis, does not mean per se nota omnibus; but rather per se nota sapientibus.305 Nevertheless, let us see if we too can become wise like Aristotle, now that we understand that the scope of his argument has a wider ambit, i.e. that his defense of a "definition" of motion is not something that he alleges to demonstrate, but rather only to 3 0 2 Maggiolo (1965), 143; IV Phys. lect. 2 3 0 3 Maggilo (1965), 151; IV Phys. lect. 4 3 0 4 Smith (1958), 263 3 0 5 Weisheipl (1958), 12 109 dialectically draw from what is abstracted inductively by our intellect, in order that he may make the demonstration proper about motion (the aforementioned Type D demonstration) with the first physical principles visible to intellect. As regards M 2 , "the act of the potential precisely as potential," there are three parts to this formal cause. The first is "the act" and the second is "of the potential" and the third is "the potential as such". Let us draw forth what we know in our intellect about these three by means of dialectical induction. In other words, we will supply an argument, and the reader can confirm the truth of it by universal experience. For physical counterexamples will be absolutely inconceivable, as long as the terms of the following argument are properly understood. Therefore, as regards the first of the three parts, "the act," observe that whatever is undergoing motion "was previously in a state of potency but, since it is in motion, is no longer in that previous state; it is therefore in the state of act or, put more simply, it is an act."306 For example, the reddening apple, the falling leaf, the house under construction, and the water being heated are all in imperfect act, i.e. in motion.307 As regards the second of the three parts, "of the potential," observe that whatever is in potency can be characterized by motion. In the physical world, the motion of a physical thing is over by however much the potency of the thing is fulfilled.308 For example, whatever is done in the apple, leaf, house or water in motion cannot be done any more; and yet what is not done still remains to be done. If the apple has fallen, it can 3 0 6 Smith (1958), 259 307 Ibid., 260 3 0 8 Ibid. 110 fall no more; yet it could still be picked up, etc. Potencies and acts abound in all their variations and gradations in the physical world around us. As regards the third of the three parts of the formal cause of motion, "the potential as such," observe that the act of the potential only insofar as it is still in potency to be whatever it is potentially is the motion we are trying to characterize.309 For example, consider a stone falling from a mountain, now halfway to the ground. Aquinas notes that, "motion is the act of that which exists in potency, such that its. ordination to its prior potency is designated by what is called 'act', and its ordination to further act is designated by what is called 'existing in potency'."310 Sachs argues that this is an "intelligent misinterpretation" of what motion is: "Thomas Aquinas ... took [motion] to mean that the special condition of a thing in motion is to be partly actual while partly potential, and directed to greater actuality of that same potentiality. But this account of motion would not distinguish motion from a state of balanced equilibrium, such as that of a rock caught in a hand, still straining downward but prevented from falling any farther."311 But Sachs has, we believe, overlooked the full point of Aquinas here. Aquinas is explicating the third of the three parts of the formal cause of motion: i.e. "potential precisely as such". Yet Sachs only picks up on the first clause of Aquinas that glosses this inquantum huiusmodi, viz., "its ordination to its prior potency is designated by what is called 'act'". That is, the rock still has an ordination to its prior potency when it is in motion. It is still potentially on the ground. Thus Sachs argues that when it is in the hand, in the act of being in the hand, it is still in ordination to its prior potency. The rock is still potentially on the ground when it is at rest in the hand, even as it was potentially on the 309 Ib id., 262 3 , 0 III Phys. lect. 2, n. 285; English translation from Blackwell-Spath-Thirlkel (1963), 137 111 ground when it was on the mountain. And Sachs is disturbed because, although the rock in the hand is still potentially on the ground, it is manifestly not in motion (because it is at rest in the hand) and that therefore Aquinas stipulated that the rock still has an inner potentiality or yearning to be on the ground and consequently we must conclude by Aquinas's understanding of inquantum huiusmodi that the rock in the hand is still in motion, which is absurd. (Yet it is really Sachs himself who mystically locates the inner yearning and inner straining as the third part of the formal cause of motion and he mistakenly attributes this mysticism to Aristotle.)312 But observe that Sachs has overlooked the second clause of Aquinas that glosses this inquantum huiusmodi, Viz., "its ordination to further act is designated by what is called 'existing in potency'". Therefore Aquinas indeed recognizes what Sachs overlooks. That is, Aquinas sees that the second component (to this third part of the formal cause, "inquantum huiusmodi") is the fact that the rock is no longer in ordination to further act when it is in equilibrium in the hand, because it is causation that supplies ordination. In other words, if the force of gravity is acting upon the rock, then it is acting such as to place the rock in ordination to further act. Thus the rock is in motion when it is in free-fall from the mountain to the ground. But if the rock is caught in the hand and placed in a state of balanced equilibrium, this means that it is no longer in ordination to further act, because the force of causation supplied by the hand, to counteract the causal force of gravity, balances both causes out to zero, and there is no more ordination to further act because there is no more ordination of causality. Hence it cannot be said that the rock is 3 1 1 Sachs (1995), 22 112 "existing in potency" and yearning to be on the ground (according to the sense that Aquinas intends in the second clause of his gloss on inquantum huiusmodi). To be sure, the rock is existing in potency (and in this sense only "yearns to be" on the ground) when it is in ordination to its prior potency (viz., being potentially on the ground) and this same ordination to prior potency is still there when the rock is in the hand (i.e. although now in the hand and no longer on the mountain, the rock is still being potentially on the ground). Yet this is only half the story. It is only the state of affairs described in the first clause of the gloss of Aquinas on inquantum huiusmodi. But Sachs wants to make this the whole story, and so he posits a mysterious inner yearning of the rock as his own private interpretation of what being in potency and being in act means. (He also invents a wacky mystical vocabulary that obfuscates Aristotle's texts in Heideggerian fashion: e.g. "being-at-work" and "being-at-work-staying-itself'.)313 Yet the other half of the story is the second clause of the gloss of Aquinas on inquantum huiusmodi: "its ordination to further act is designated by what is called 'existing in potency'". Therefore, because the rock in the hand is no longer in ordination to further act (because it is now in the hand and to this extent is no longer "existing in potency"), it cannot be said to be in motion. In sum, the rock in the hand fulfills only the conditions of the first clause, and not the conditions of the second clause. The rock (no longer on the mountain, or no longer rolling down the mountain, but now at rest in the hand) is still potentially on the ground (i.e. condition of first clause met); but the rock is no longer in ordination to the actuality of being on the ground (i.e. condition of second clause not met). In other words, when the rock is at 3 1 2 Cf. ibid, 22 ff. 113 equilibrium in the hand, the two Thomistic clauses cancel each other out, just like the two causal forces of hand and gravity cancel each other out; and so the rock (by definition) is not in motion because the inquantum huiusmodi no longer obtains (and the definition is thus adequate to the fact that the rock no longer rolls). But rolling merilly down the mountain, both clauses of the Thomistic gloss are still applicable, and indeed the rock is in motion according to the principle M 2: actus existentis in potentia inquantum huiusmodi. Once the truth of this formal cause as the principle of motion is grasped (and it must be grasped by the intellect, because it cannot be demonstrated or proved like a mathematical proof, i.e. from prior axioms), we are halfway to understanding Aristotle's demonstration about motion, because we have then grasped what M 2 means. The second half consists of understanding what M, is and why it can be predicated of M 2 . For once we grasp the major premise of the demonstration ("M2 is M,"), it is clear sailing to the conclusion (because we have just grasped the minor premise in our considerations above of the truth that "S is M2"). But we already know that the major premise is formally true, because of the order of causality.314 All that remains is for us to grasp materially what is expressed in the content of this principle M,. We have already stated that M, = "the act of a thing insofar as it is moved, not the act of a mover". To say that this is the material cause of motion invites a powerful objection, namely, that motion is in the mover, not in the moved. For example, the motion is not in the nail, but in the hammer moved by the hand; or so the objection goes, 3 1 3 Cf. i b i d , 244-245 114 reasoning that motion is what is imparted by the hammer to the nail. Also, "since the thing moved always reacts in some way upon the mover, it would look again as though the mover itself undergoes motion."315 In response to these objections, it can be said that the extent to which a hammer (a mover) moves, it is moved by something else (e.g. the hand); properly, it is not moved. And as regards the thing moved reacting upon on the agent mover, it can be said that in the reaction as such, the thing is no longer the thing as the thing moved, but the thing as an agent mover; and hence the agent mover, to the extent that it is moved by the reaction, is not the agent moved but what is moved by the reaction.316 Therefore, there is one motion, but two relations: action and passion. Nevertheless, motion is one; "as by (a quo) the agent, it is action; as in or out of (ex quo) the recipient, it is passion."317 Therefore, once we understand the terms S, M„ and M 2, and propostions; and once we understand what is articulated nota per se in them; we can make the Type 4 demonstration about motion: "The act of the potential precisely as potential [M2] is the act of the mobile precisely as mobile [M,], but motion [S] is the act of the potential precisely as potential [M2]; therefore motion [S] is the act of the mobile precisely as mobile [M,]."318 Thus motion exists in the ens mobile (the proper subject of physics) "because motion is the act of the potential or subjective precisely as potential or subjective."319 The upshot of this demonstration is that motion, observed by induction in mobile being, must 3 1 4 See Tables 2 and 3 and discussion 3 1 5 Smith (1958), 263 ™Ibid., 264-267 317 Ibid., 267 3 1 8 Ibid, 263 115 necessarily exist in the mobile being rather than in the mover. We now know the proper cause {propter quid) for what is in fact observed to exist (quia) in mobile being.320 In conclusion, we would remark that these claims are worthy of the most prolonged reflection. If they are inadequately grasped, any criticism of Aristotle will commit the mistakes of a beginner. For example, any attempt to understand the distinction between act and motion without any reference to the ordination of causality321 is doomed to flounder in unresolved aporias. 319 Ib id, 269 3 2 0 Ibid. Note that Smith says the Type D demonstration has "shown us the proper cause or reason why motion must (de jure) exist in the subject where it is (de facto) observed to exist." 3 2 1 e.g. Ackrill (1965), 138-141; Ackrill's "imperfect potentiality" is a useless tautology of a concept, e.g. just like "non-affirmative negative" is. If such a concept is to be attributed to Aristotle, it must be understood differently, as expressed against a background of the ordination of causality (operating on material potencies). Our refutation of Sachs above contains everything necessary to resolve the Ackrill case. Ackrill does not connect his formal dilemmas (over language) with material reality; and in missing the ordination between formal and material causality, he fails to consider the actual Aristotelian demonstration about motion. This is typical of all interpreters who read the Physics from the point of view of modern logic, rather than from the point of view of the Posterior Analytics and the order of the four causes. 116 3.2 Place (Phys. IV.1-5) The success of modern science is a dance on the grave of Aristotelian teleology. Such is the impiety of modern physics that it so mistreats the father of physics, Aristotle. His Physics is found in no physics classroom. To call a modern physicist "Aristotelian" would be an insult, not a compliment. But does the unparalleled improvement in man's estate, due to a wildly successful subjugation of nature, permit us to refuse ever to speak of final causes again? Apparently so, since Aristotle's cosmology, and the account of natural place within it, is the most quotidian illustration of Aristotle's absurdity.322 Nevertheless, to ridicule someone or to call him "useless" is not to refute him. We propose to consider the thesis that Aristotle's definition of place is simply true.323 And we do not mean true for his time, but for all times. Aristotle's Physics, we believe, contains permanent truths that will stand forever, no matter what the ephemeral achievements of modern physics.324 This thesis does not dispute the utility of modern science. Yet utility and truth are two entirely different things.325 Utility is easily discerned by anyone who uses an automobile, dishwasher, or personal computer. Truth, however, is not so readily discerned, and perhaps its competent judge is ultimately neither the scientist, nor the beneficiary of the scientist, but the philosopher. Accordingly we propose to clarify the fundamental relation between the concepts of place and space. The exaltation of the latter 3 2 2 Cf. Strauss (1953), 8. 3 2 3 Almost all non-Thomist Physics scholars conclude that Aristotle's definition of place in Physics IV is a false opinion in the history of the concept of space: e.g. White (1996), 183-198; Algra (1995), 121-260; Sorabji (1988), 186-201; Mendell (1987), 206-231. A notable exception is Bolotin (1998), 8, 77-113, who adopts the Straussian tack that historical difficulties with the doctrine are intentional consequences of philosophical esoterics. Cf. Strauss (1952), 22-37. 3 2 4 Cf. Coughlin (1994), 30-34. 3 2 5 Strauss (1953), 6. 117 as the useful mathematical entity of modern physics has obscured the truth about the former as the measure of mobile being.326 Nevertheless the judge of such truth can only be philosophy, which is open to the whole, and is therefore the only competent judge of the specific assumptions of natural science.327 As we set out to inquire into the truth of physics, and of the definition of place in particular, we ought to abandon any prejudice against Aristotle's definition of place. To be clear about the philosophical foundations of physics is no small task, and we would do well to measure our own worthiness before this task by recalling the words of Belloc: The conquests of physical science were due to minute and extensive observation conducted by vast numbers of men, and therefore, for the most part, by the unintelligent. Science attracted some few high men of culture and some even (much fewer) of strong reasoning power: but in themselves mere observation and comparison, the mere framing of hypotheses and the testing of them by experiment, need no intellectual qualities above the lowest and are therefore obvious occupation for those who despise or do not grasp the use of the reason.328 Perhaps Aristotle's reasoning about place has to this day only been understood by very Plato considers that it is said that "every being" (to on hapari) that "is [somejwhere" (einai pou) is said to be "in some place" (en tini topoi) and possesses "some space" (khoran tina):330 3 2 6 Cf. Smith (1950), 3-38. 3 2 7 In this vein, Maritain (1995), 182, appropriately approves of and admonishes a physics that liberates itself from Aristotelian final causes: "...let not this liberation from philosophy be taken as a new philosophy! There are two possible ways of interpreting the conceptions of the new physics philosophically. The one transports them literally, just as they are, on to the philosophical plane, and thereby throws the mind into a zone of metaphysical confusion. The other discerns their spirit and their noetic value, in an effort to determine their proper import." Our aim in this essay is to unravel the confusion about space and place in the latter fashion. 3 2 8 Belloc (1930), 19-20. 118 rcpoq 6 8fj Kai ovetporcoA.oup.ev fiXenovxEC, Kai cpapev dvayKatov etvai nox> xo ov arcav ev xivi xonco Ka i Kaxe%ov %cbpav Ttvd, TO 8e pfiT1 ev yfi pfite nov KCLX' oupavov o\)8ev etvai. xavxa Sf) rcdvTa Kai TOUTOOV aXXa dSeXcpd Kai rcepi tf|v dtmvov Kai aXnGroc, (puatv •braxpxoDoav vno xam^c; xf[q oveipw^ecog oi) bvvaxoi yiyvopeGa eyepGevxec, 8iopi£6pevoi xaXnGec, Xeyeiv 3 3 1 We are convinced that there is no more precise formulation of the problem of place than this proposition from Plato. Although formulated by Plato, the problem of place ~ defining what it is given what is said about it in this formulation ~ is solved only by Aristotle.3 3 2 We propose that all subsequent difficulties with the Aristotelian definition of place vanish once a threefold distinction about the being of place is properly understood: pou (where), topos (place), and khora (space).333 We take these three words from Plato's formulation as the vestigia parva334 by which Aristotle's definition of place can be made wholly intelligible: multaque praeterea tibi possum commemorando argumenta fidem dictis conradere nostris. verum animo satis haec vestigia parva sagaci 3 2 9 Cf. Bolotin, op. cit., 149-153, and Kramer (1990), 120-127. The latter does greater justice to the overlooked "unwritten doctrines." 330 Timaeus 52 b3-5. 3 3 1 Plato, Timaeus, 52 b3-c2: "We look at it indeed in a kind of dream and say that everything that exists must be somewhere and occupy some space and that what is nowhere in heaven and earth is nothing at all. And because of this dream state we are not awake to the distinctions we have drawn and to others akin to them, and fail to state the truth about the true and unsleeping reality." Lee (1987), 71-72. A more accurate translation of the proposition we emphasize in bold type would be: "Every being must 'be where' in some place and possess some space." 3 3 2 Cf. Physics 209 b\6-l7. 3 3 3 We consider the scholarship (e.g. White, Algra, Sorabji, Mendell, etc., op. cit.) historiographically erudite but philosophically unenlightening, and so we start from scratch (Plato's bare formulation) in order to distinguish these three terms, not in historical and philological detail (impossible here), but in a genuinely philosophical manner to demonstrate therewith the truth of Aristotle's definition. 3 3 4 Lucretius, De rerum natura, 1.402. 119 sunt, per quae possis cognoscere cetera tute. What place is must take into account these three ways of being: being somewhere, being in a place, and being in space. First, the concept pou (where) belongs to metaphysics. Metaphysics is the science of being as being, and in this science pou (where) is recognized as a requisite category for any speech about mobile being. Pou is one of the highest genera about which nothing more can be said.336 Second, the formal definition of topos (place) occurs as the minor premise of two a priori Type D demonstrations about place in natural science.337 Natural science investigates being as mobile being, and in this science topos is recognized as the measure of mobile being.338 Third, khora (space), in contrast to place, is the internal extension of a body (in Plato's word, what the body "possesses").339 With the concept of space, mathematical physics investigates mobile being as quantified with Type E demonstrations.340 Space mathematically refines our metrical knowledge about what we know to be in place.341 Note that a Type E demonstration differs from a Type D demonstration.342 On the one hand, the scientia media of mathematical physics presupposes place, but the investigation of place properly belongs to the Type D demonstrations more commensurate to the level of abstraction of physics, the science of ens mobile. On the other hand, the empirical 335 Ibid. 400-403: "Many another proof besides I can mention to scrape together credit for my doctrines. But for a keen-scented mind, these little tracks are enough to enable you to recognize the others for yourself." Rouse (1924), 35. 3 3 6 Cf. Brentano (1975), 112-118. 3 3 7 Wallace (1957), 101; Cf. Tables 5 and 6 above 3 3 8 Smith (1958), 26-51, 289-308. ™ Ibid,291. 3 4 0 Wallace (1957), 97-98; Cf. Tables 5 and 6 above 3 4 1 Smith (1958), 297-298. Cf. Maritain (1951), 73-156. 3 4 2 Wallace (1957), 95-98; Cf. Tables 5 and 6 above 120 investigations of mathematical physics are most properly refined by mathematics.343 In sum, the three concepts (pou, topos, and khora) belong to three distinct sciences: the science of being, the science of mobile being, and mathematical physics (scientia media). (The first two "sciences" are parts of what is today simply called "philosophy".) The cogency of this threefold distinction is evidenced in its application to Aristotle's definition of place as the "the innermost immobile surface of a surrounding body."344 We argue that this definition of topos, constructed as part of the Type D physical demonstration of place, is properly understood only when parsed out into the categories into which it is metaphysically reducible: "Surrounding body" (tou periekhontos) is the genus and "innermost immobile surface" (to peras akineton proton) is the specific difference. We propose to show how such a parsing solves the contact and immobility aporia associated with Aristotle's definition.345 Metaphysical considerations at a higher level of abstraction will dialectically convince skeptics about the self-evidence of Aristotle's definition; for an appeal to empirical experience and aporias will only result in increased skepticism and marked disdain for Aristotle, and unfortunately too many commentators now take the latter approach. Thus, a few metaphysical, and dialectical words about this categorial parsing are first in order. 3 4 3 Smith, op. cit., 166-167, 289-298. 3 4 4 Physics 212 a20-21. Our English translation comes from Smith, op. cit, 294. We prefer to be consistent with the tradition so admirably served by Smith; however we acknowledge that "the unmoved and primary limit of the container," while less intelligible English, is a more accurate philological rendering of the Greek suitable for non-Thomist specialists. 3 4 5 Sorabji, op. cit., 187-192. Briefly stated, the aporia is: The surface in primary contact with the contained can be mobile; therefore one must introduce fixed distances from fixed points and thereby render both contact and immobility irrelevant. 121 Topos is by specific definition the measure of mobile being. First, the highest genus of being under consideration in the definition is not substance but "being where" (einai pou). That is, the "surrounding body" that contains something is considered in the definition not as a substance (ousia) but as an accident, namely, as being-a-container for something else; this is what the genus pou denotes. Second, inasmuch as topos is a measure, poson (quantity) must come into the definition; hence "innermost surface" denotes the proper place of the surrounding body. Third, inasmuch as topos measures mobile (i.e. material) being, keisthai (posture) must come into the definition: The internal parts of a place arranged within their whole denote the common place of the container; although the parts are accidentally mobile in relation (pros ti) to one another, the whole is essentially "immobile" with respect to what is contained. Hence the "immobility" of place qua posture is an essential mark, and a necessary part of the definition. (More will be said later to elucidate these differentiae when we treat St. Thomas Aquinas's remarks on "proper" and "common" place.) Thus the physical concept of topos is not equivalent to the metaphysical category, pou. If it were, no differentiae would be required when stating what topos is. In fact, one could not even define what topos is, since it would be simply one of the highest genera and therefore unrefinable by further analysis. Instead, topos is a fundamental physical concept that is constructed with the categorial "being [some]where" (einai pou, i.e. to be contained by a surrounding body) conjoined with predicates reducible to other categories that are pertinent to the measurement of material being: namely, poson (quantity) and keisthai (posture). In brief, this abstraction articulates the measure of mobile being. 122 We maintain that when "innermost surface" is parsed out as the differentiating poson (quantity), and "immobile" as the constitution of that surface with regard to keisthai (posture), then topos (place) is defined as what it truly is. By the "innermost" differentia, a physical entity is situated in the proper material place of its generic categorial "where". By the "immobile" differentia, a physical entity is formally situated in the common place of its categorial "where". Specific physical place is therefore a definite concept composed of genus and differentiae, defining topos as the measure of mobile being. In short, Aristotle's definition is neither metaphysics nor mathematical physics. It belongs to the science of nature, which is the philosophical bridge between the two. Material being is the subject of natural science. The fundamental concepts of this science, when expressed as propositions with terms and concepts, will be dialectically reducible to the highest genera of metaphysics. Space is another concept susceptible to dialectical analysis; it operates at such a level of abstraction that it is not a concept commensurate with those of natural science, but nevertheless, because it is still definable, it is not a concept (i.e. category) of the highest level of abstraction. Therefore, like place, it too is not a metaphysical concept.346 This bare presentation of our thesis will appear somewhat schematic until we show how it dissolves the difficulties conventionally associated with the Aristotelian 3 4 6 Hence space is not a pure intuition as Kant would have it (Critique of Pure Reason, I. Transcendental Doctrine of Elements, First Part: Transcendental Aesthetic, Section One: Of Space), but rather a fundamental physical concept. We note that the predicates in every concept are analytically reducible to the categories (Aristotle's categories, not Kant's), and that the concept of space (by which Kant really means place, i.e. what he should be talking about philosophically, instead of Newtonian space) is more "pure" 123 definition of place. Before we do that, a few more words are required in order to justify two things: first, our distinction between pou and topos, and second, our use of the categories when parsing the definition of topos. Both follow from Aristotle's doctrine of being as properly understood by St. Thomas Aquinas. First, we simply differentiate pou from topos as does Yves Simon: "I beg you by the way not to identify, as a few great thinkers did, without any further ado what is called topos in the Physics and what is called pou in the Categories. Topos is place. In the Categories what is called pou means properly "where." ... The category where is not place; it is the accident which results in a substance from its being in a place. Take the predicates of the propositions: 'He is in the bedroom,' 'He is in the market place.' Those predicates belong to the category of where. They do not designate a place; they designate that which results in a subject, for instance, a man, from the fact that he is in such a place or in a different place. You will find histories of philosophy (sometimes done by competent people, which should lead you to take competence with a grain of salt) in which these two categories where and when are cold-bloodedly translated as place and time. That is definitely wrong."347 Accordingly we regard "of the surrounding body" in the definition of place as referring to the category when. Second, it is perhaps bizarre that we invoke other categories as differentiae of the genus when in order to parse the definition of place. Yet we emphatically do not deny the analogy of being and the multiplicity of the categories: The categories, the highest genera, cannot be reduced to one another by making them into differentiae of each other. In short, we do not rewrite Aristotle's metaphysics. What we are arguing, rather, is that any concept of the science of nature, like topos, can be dialectically parsed predicate-by-predicate into the higher genera. When we perform this exercise with topos, we equip than other concepts simply because the science of nature proposes it at the highest level of abstraction possible for the physical consideration of material being. 124 ourselves with the tools necessary to understand correctly Aristotle's definition in the face of difficulties (i.e. the notorious difficulties posed by those people who are obsessed with dialectical scruples over Aristotle's well-established a priori demonstrations): The "innermost surface" measures the poson (quantity) of the containing body; the "immobility" of the surface refers to the immobile keisthai (posture) of this surface as a whole, and not to any possible mobile arrangement of its parts. How this dissolves the contact and immobility aporia will be shown straightaway. We note beforehand, however, that we are adopting the reasoned analysis of the classification of the categories as it is found in St. Thomas Aquinas.348 By this classification we know that quantity (Greek poson, Latin quantitas) is that which is not the essence but inheres in the essence as consequent on matter, and that place (Greek topos, Latin locus) is an extrinsic denomination of the subject common to all, either as a measure of simply where (Greek pou, Latin ubi) or of the order of parts in position (Greek keisthai, Latin situs) in the where?49 Even Thomists highly sympathetic to Aristotle have concluded, "we can say his definition is successful when the container is motionless, but uncertain when the container is in motion."350 For the upshot of the contact and immobility aporia (viz., that the surface in primary contact with the contained can be mobile) is that one is apparently 3 4 7 Simon (1970), 114. The list of the categories on this page should end with "posture and habitus": "posture and situs" (114) is either a typographical error or a slip of the pen in Simon's manuscript. 3 4 8 III Phys., lect. 5, Leonine para. 15: Maggiolo (1954), 159; Blackwell-Spath-Thirkel (1963), 150-151. St. Thomas also treats the classification of the categories in V Meta., lect. 9, para. 891-892: Rowan (1995), 321-322. Cf. Scheu (1944), 46-63. 3 4 9 Cf. Scheu, op. cit., 56-57: a diagrammatic treatment of St. Thomas's classification. Cf. Brentano, op. cit., 115-117, attempting a classification from Aristotle's own testimony. 3 5 0 Simon, op. cit, 126. 125 required to introduce fixed distances from fixed points and thereby render both contact and immobility irrelevant.351 The infamous example is Aristotle's own, the boat in the river: How can the innermost moving surface of the river be the immobile place of a moored boat? Aristotle answers that the river as a whole is the place.352 The history of the problem saw the scholastics introduce a distinction between formal and material place (i.e. the material parts of the water are in motion but the formal whole of the river is immobile) in order to save Aristotle's definition.353 The distinction between formal and material place was eventually abandoned by mathematical physics as otiose metaphysics simply detracting from a properly mathematical representation of space.354 Thomists today may wish to revive the distinction in order to vindicate St. Thomas's interpretation of Aristotle,355 but in our view this is not a completely faithful exegesis of the words that St. Thomist himself uses when solving the difficulty of the moving river: "... it is better to say that the whole river is the place of the ship, for the whole river is immobile. Thus, therefore, the whole river, insofar as it is immobile, is a common place. However since proper place is part of common place, it is necessary to assign the proper place of the ship in the water of the river, insofar as it has an order to the whole river as immobile. Therefore the place of the ship is determined in the flowing water, not in respect to this water which flows, but in respect to the order or site [secundum ordinem vel situm] which this flowing water has to the whole river."356 Notice that St. Thomas remarks that place must be distinguished with respect to the site (situs). Apparently both Thomist and non-Thomist commentators on this problem have 3 5 1 Cf. Sorabji, op. cit., 190. We deny that St. Thomas, as Sorabji puts it, "goes beyond Aristotle," because we think St. Thomas's grasp of the categories is the authentic Aristotelian means for interpreting Aristotle's definition. Cf. Coughlin, op. cit., 22-30. 352 Physics 212 &19-21. 3 5 3 Sorabji, op. cit., 187-192. Cf. Grant (1976), 136-167. 3 5 4 Sorabji, op. cit., 190-201. 3 5 5 Cf. Coughlin, op. cit., 20-29. 126 overlooked the fact that situs is one of the categories.357 If they have not, then they certainly have failed to supply an adequate account of the function of the categories in the definition of place and the role of situs in that definition. We aim to remedy that lack. When we first stated our thesis, we said that the genus pou is the genus in the formal definition of topos. Topos is something that can be defined formally because it is not equivalent to pou, one of the highest genera (and nothing further can be predicated of these highest predicates). In our problem, one can ask, "Where is the boat?" and the answer, which contains the predicate of the type where, "The boat is in the river," says nothing about the substance of either the boat or the river, but instead says that the river is the container and the boat is the contained. In the formal definition of physical topos, the obvious place to start is with this metaphysical genus pou, the "being where" of any subject body that acts accidentally as a surrounding container. But in our problem, one can ask further, "Exactly where in the river water is the boat?" At this point, the category of situs becomes involved as a differentia. That is, the more precise answer to this more precise question will speak (as St. Thomas recognizes) secundum situm. "Is the water part of the river?" Yes, the water is essentially part of the river; the water is not part of the boat (if there is water on board the boat, it is accidentally so). The order of the parts in the river can be mobile; in fact they are especially so, which is why 3 5 6 IVPhys., lect. 6, para. 468: Maggiolo (1954), 227; Blackwell-Spath-Thirkel (1963), 212. 3 5 7 Sorabji, op. cit., 190, seizes upon the first word, ordo, but neglects theepexegetical second word, situs. As a result he interprets ordo to mean for St. Thomas "spatial relation." Coughlin, op. cit., 23-25, rightly protests that such a relational view of place cannot be pinned on St. Thomas. However Coughlin fails to resolve the controversy because he neglects what we maintain is the essential problem: i.e. the function of the categories in abstract concepts of the science of nature. In short, an exegesis of situs is required to vindicate both Aristotle and St. Thomas. A dialectical metaphysical argument is needed to convince the skeptics who believe in nothing but positivism and mathematical physics. 127 the "boat in the river" problem is such a vivid problem. Nevertheless, Aristotle maintains that the mobility of the parts does not contradict the immobility of the whole. The river as a whole is immobile. And this is so not because the material of the river (the water molecules) is mobile and the form (the geographic entity) is immobile. Rather, it is so because the posture of the water molecules is one of parts predicated of a whole, and not because the posture of the water molecules is predicated of some imaginary mathematical spatial entity (as if such an entity were one of the highest metaphysical presuppositions). The mathematical description of posture should not be confused with its metaphysical sense (i.e. the situs of parts in a whole). Metaphysically speaking, it is appropriate to speak of water molecules as mobile parts of the immobile whole river, not because we can imagine an immobile spatial form containing the mobile material parts of a river,358 but because the very nature of a whole and its parts is such that the parts of any whole must ultimately fall under the highest predicate, situs. "Exactly where in the river is the boat?" Moored to the dock as the river rushes past; or, plying its way between the banks; or, passing a boat going the opposite way down the river; or, floating still in the stopped tide:359 All these answers to the question have not discovered new places for the boat other than the river (e.g. alleged respectively: the dock; the distance relative to a bank; the distance relative to another boat; immobile water surfaces as opposed to immobile banks). They do not constitute objections to the 3 5 8 Hence the distinction between formal and material place is not as fundamental as the distinction between pou, topos, and khora. Only the latter distinction can satisfactorily resolve the controversy about Aristotle's formal definition, because it dialectically brings to light the formal definitions of the science of nature as the bridge between the metaphysics of the categories and the nonteleological natural science of mathematical and metrical physics. Dialectical induction is what people who are confused about what is per se nota sapientibus need most, because their intellects are too weak for the task on their own. 128 Aristotelian formal definition of place [M2]. In fact, when the definition is properly understood as belonging to the Type D demonstrations about place, they merely illustrate how well founded it is. For they show that the immobile surface of the definition refers not to parts of the surface, but to the whole surface. When Aristotle says "the river as a whole," he means "the river as a whole." To take another example: "... the movement of the various parts within a thing that is one, e.g. the movement of the molecules in a living organism, is not a movement in place. Such movements are in the order of posture or situs. A thing possessing such movements would be said to be undergoing local motion but only in some accidental way. Thus a sleeping dog could be said to be essentially at rest but accidentally and by reason of its parts to be in motion."361 The same can be said of the river as a whole. That is, as a whole geographical entity, it is essentially at rest. For example, we do not expect the Thames to relocate and swap places with the Nile. Only by reason of its parts (i.e. the water molecules) do we say it is in motion. Therefore when we ask about the place of the boat, we answer correctly that it is in the river. This river is the place of the boat, because to the question where the answer the river" is appropriately given even when the differentiae of this where are considered further: The common place of the boat is the river as a whole because the immobile surface as a whole that touches the boat is the river as a whole. Within this common place, the position of the boat can be located more precisely by reckoning its proper place with regard to the order of particular moving parts of the river. That is, the proper place of the boat can be described relative to the innermost surface of any mobile part of the immobile whole river. Nevertheless this proper place is not a topos within a 3 5 9 Cf. Sorabji, op. cit., 188. 129 topos, but rather the same place (the river) considered solely according to one of its differentia, i.e. according to the category of posture (secundum situm). Topos itself, however, is pou constituted by both differentiae. In conclusion, then, to answer the question, "Exactly where in the river is the boat?" with the reply, "One hundred metres 45 degrees south-east from the midpoint of the mouth of the river," does not force a philosopher to conclude that the place of the boat is no longer the river but rather a position in the mathematical entity known as space. As we have shown, such a precise description answering the question, which is characteristic of the answers of mathematical physics, should not be understood as naming a new place for the boat. The boat is in the same place that it always was: the river. Aristotle's definition of place should not be thought to entail absurdities when a boat is in a river simply because the parts of that river are in motion. The innermost surface of the river in the Aristotelian sense is neither the water molecules that are touching the hull at an instant in time, nor the imaginary order of distances marking the internal extension of the river. The innermost surface of the river in the Aristotelian sense is the immobile surface of the river itself as a whole. The parts of the whole may be in motion, but according to Aristotle's doctrine of the categories, which St. Thomas saw as especially germane to this case, motion according to situs and quantitative location in pou are two distinct modes of being that are fully compatible with the fundamental concept of topos. In fact, they are 3 6 0 i.e. M 2 = "the first immobile surface of the surrounding physical environment"; Wallace (1958), 101 and Table 6 3 6 1 Smith, op. cit., 296. 130 the very differentiae used in the abstraction of this fundamental physical concept, as our dialectical considerations here have revealed. The significance of this point cannot be overstated. The place of the boat is the river, and this truth belongs to the science of nature, since it follows from Aristotle's formal definition of place, precisely formulated on a highly abstract level to classify philosophically what we know (by abstractive induction from mobile being) being-in-place is. The formal definition appropriately embraces the observations about the various modes of being-in-place that are expressed so well in Plato's formulation, because each mode of being is not considered outside its appropriate realm of abstraction. The position of the boat within the river may be more precisely formulated with mathematical descriptions naming parts of the whole through which the boat is moving. Indeed, the place of the river is subject to differentiation: the river's innermost surface may be numbered (e.g. each water molecule counted and uniquely named within the river) and the river's immobile surface may be positioned (e.g. each of the water molecules postured within the whole of the internal extension - i.e. the space - of the river). But Aristotle takes this all into account when he makes innermost immobile surface the differentiae of the genus pou in order to define topos. That is precisely why he makes them the differentiae. The mistake of mathematical physics is to take its extraordinary competence at describing material being mathematically as an excuse for tossing out the significance of the metaphysical genus pou and its real differentiae (as applied to the proper extrinsic measure of mobile being, i.e. to place). For this is precisely what mathematical physics does if it considers the Aristotelian conception of place to be otiose metaphysics. 131 When the science of nature defines place so that the place of the boat is in the river, it is not preventing mathematical physics from precisely measuring the innermost immobile surface of the river with ever more refined predicates of quantity and posture. Only an arrogant positivism would think that it must replace the place river with an abstract spatial entity in the metaphysical realm in order to be licensed to measure quantity and posture in the physical realm. But this is precisely the philosophical aftermath of a rejection of the Aristotelian definition of topos. This has led to the odd situation where mathematical physics is alienated from metaphysics and natural science, and teleology has no philosophical foundation as it did in Aristotle. We hope we have made it clear that to affirm the truth that the place of the boat is in the river does not invalidate the claim that the boat is at position (x, y, z) in a matrix of molecules. This affirmation of non-spatial place, rather, points to deeper truths; e.g. boats are built to sail down rivers and rivers are good for transporting boats. These teleological propositions have no place in the highly mathematical enterprise of modern physics, but nonetheless philosophy demands a place for them somewhere. Everyday teleological presuppositions constitute an indispensable background to all natural science (not to mention all experience), and a science of nature must lay out the philosophical justification of any real teleology in nature. The Aristotelian formal definition of place leaves room for such teleology when it precisely defines place, for it says nothing about such final causality in its use in the two Type D a priori demonstrations made by Aristotle;362 rather, it leaves that to the experiential observations of those who build on the 3 6 2 Cf. Wallace (1958), 101 132 firm foundation of Aristotle's own fundamental demonstrations. Only a science of nature philosophically conscious of the ordination of causality adequately accounts for teleology within the whole of nature.363 Accordingly, Aristotle never formally defined place in order to erect a barrier to the utility of describing a boat's mathematical posture in the river, no matter how much the innovators in such utility have protested against Aristotle's formal definition. We are content to observe that the utility of the descriptions of nonteleological natural science has yet to refute the truth of Aristotle's doctrine of being and the science of nature - the Physics - founded upon it. In attempting to drive out final causes, a hubristic mathematical physics has forgotten that such causes are grounded not in mathematical physics but in the wiser science of nature, the Physics. Yet, "naturam expellas furca, tamen usque recurret."364 And so Aristotle's conception of place remains the hidden presupposition, ever present, behind all talk of space. Few are they who become conscious of this fact. For those readers now inspired to join the happy few, we conclude with an exhibition of the principles of Arisotle's two Type D demonstrations about place, and extend an invitation to the reader to return to the text itself.365 And following thereafter, we append our own translation of Aristotle's treatise on time from the Physics, along with a division of its dialectical argument and an exhibition of the principles of the two Type D and two Type A, demonstrations that it contains, in order that one may be inspired 3 6 3 Cf. Wallace (1996), 15-31. 3 6 4 Horace, Epistles I, x, 24: "You may drive out nature with a pitchfork, yet it will always return." 3 6 5 No attempt is made to argue for the premises of the Type D demonstrations in which these principles are to be employed, or to indicate the dialectical reasoning constitutes the normal propadeutic of such an argument; however, references are briefly given to point the reader in the right direction for self-study. 133 further to grapple with the matchless thought that the Physics contains, in the hope of storing up its demonstrative treasures in one's own soul. TypeD 3 6 6 Mx (material cause) = "proper to each body externally contained" M 2 (formal cause) = "the first immobile surface of the surrounding physical environment" S (subject) = "place" Type D M, (material cause) = "proper to a body that has natural local motion and rest in the universe" M 2 (formal cause) = "the first immobile surface of the surrounding physical environment' S (subject) = "place" Cf. IVPhys., lect. 1, n. 2 Cf. IVPhys., lect. 8, nn. 6-7 134 3.3 Time: Annotated Translation (Phys. IV.10-14) Below we provide a division of the argument of Aristotle's treatise on time and furnish a new translation. The Latin commentary is adopted from the Marietti edition of Aquinas.368 The Greek text is that of Ross (1950), extracted from the TLG D CD-ROM for our use here. The Type D and Type A, demonstrations (discussed above)369 about time consist of the principles:370 Type D 3 7 1 Mj (material cause) = "the per se measure of the existence of all things that are generable and corruptible" M 2 (formal cause) = "the measure of motion according to before and after" S (subject) = "time" Type A, 3 7 2 P (property) = "in time" M j (material cause) = "that which is measurable according to before and after" S (subject) = "every continuous, or successive, or sensible motion" Type A, 3 7 3 P (property) = "everywhere" M i (material cause) = "the measure of the locally movable" S (subject) = "time" Type D 3 7 4 M i (material cause) = "found in the first, most regular and continuous motion in the universe" M 2 (formal cause) = "the measure of all other times and motions" S (subject) = "universal time" The reader is now invited to discover them at work in the text itself: 3 6 8 IV Phys. ed. Maggiolo (1965) 3 6 9 In our first chapter and in Table 6 3 7 0 Wallace (1957), 101-102 371 Cf. IVPhys., \ect. 20, n. 12 372 Cf. IVPhys., lect. 22, n. 5 373 Cf. IVPhys., lect. 23, n. 2 374 Cf. ibid. 135 [ Chapter 10 (Time's Problems): An tempus sit et quid tempus sit ] Section One: Disputatur an tempus sit, et utrum sit idem nunc in toto tempore. Introduction: Impasse (217b 29 - 32) Dicit de quo est intentio et quo or dine procedendum. 'Exopevov 8e xcov eipnuivcov ecmv eneXQeiv nepi xpovov Kp&xov 8e KaX&q exei 8ia7topfjo-ai Kepi auxou x a i 8id TCOV e^coxepiKcov Xoycov, rcoxepov xcov ovxcov eoxtv 11 XCOV u.f| ovxcov, eixa xtc, r\ yvoic, auxou. Time is to be tackled while holding [in mind] the things said [above about place and the void]. First, it is best to become immersed in time's problems, especially through the commonplace arguments [about it]: whether it is among beings or is not among beings, then, about what its nature is. First Argument Against Time's Existence: Composition (217b 32 - 218a 3) Totum tempus componitur ex his quae non sunt, nempe praeterito et futuro: ergo est nihil. 6xi pev ouv r\ 6Xaq O U K ecmv f\ yioXiq Kai duuSpcoc,, eK xrov5e xtq dv uTtOTtxeuaeiev. xo pev yap anxon yeyove Kai O U K ecmv, xo 8e iiiXXzi Kai ou7tco ecmv. eK 8e xo<)xcov Kai 6 arceipoc, Kai 6 del XapPavopevoc, xpovoq ouyKetxat. xo 8' eK u.f| ovxcov avyKeipevov dSuvaxov dv etvai So^eie pexexeiv ouaiaq. One might suspect that time either totally is not or is only scarcely and in an obscure way from the following: On one side, part of time has been and is not, and, on the other, part of time will be and is not yet. Time is composed of these: both infinite time and the time always apprehended [by us]. But that which is composed out of non-beings would seem to be incapable of sharing in beingness. Second Argument Against Time's Existence: Division (218a 3 - 8) Quia temporis partes non sunt in actu, tempus non est. Ipsum nunc, quod actu est, nec mensurat, neque componit tempus. %pbq 8e xotnoic, 7tavx6<; pepioxou, dvnep fj, dvdyKTi, oxe eoxiv, fjxoi rcdvxa xd pepn etvai r\ evia-xou 8e xpovorj xd pev yeyove xd 8e \ieXXei, eoxi 8' ouSev, ovxoq pepiaxou 136 TO 8e vr)v orj uipoc/ peTpei T E yap TO pepog, K a i arjyKEioGai 8ET TO 6A,OV E K TCOV pepcov 6 8E xpovoc, orj 8 O K E I o-oyKEiaGat E K TCOV VVJV. Furthermore, everything divisible, if it really is, must, when it is, either be all or some of its parts. But part of time has been, and the other part will be, yet none of it is, even i f it is divisible. Because the Now is not a part. For a part is [by definition] commensurable375 [with the whole], and the whole must be composed of its parts. But time does not seem to be composed of [divisible and commensurable] Nows. The Now's Problem: Identity (218a 8 - 11) Inquirit de nunc, utrum sit idem in toto tempore. ETt 8E TO VVJV, 6 cpaivETai Siopic^Eiv TO 7tap£A,G6v Kai TO jreXXov, KOTEpov v Kai TafjTov CCEI 8 i a u£V£ i fj aXko Ka i aXko, orj pd8iov 15EIV. Further still, it is not easy to see whether the Now (which obviously divides the past and the future) always persists as one and the same or is other and other. Major Premise of the Argument For One Now: Non-Simultaneity (218a 11 - 14) Duo nunc simul esse nequeunt, cum unum, utpote indivisibile, aliud continere non possit. E I (0.EV ydp a iE i ETEpov Kai ETepov, P T | 8 E V 8' EOTi TCOV E V TCO xpovco aXko K a i aXko \izpoq ayva (6 jarf 7cepi£%£i, TO 8E TCEpiE^ETai, cbarcep 6 EA/JCTTCOV xpovoc, fj7t6 TOV) 7tX,£iovoa), For if [the Now is] always another and another [Now], then no part among [the parts] in time is other and other simultaneously, which means that [each Now] does not encompass [another Now], but [each Now] is encompassed [only by time], just like a shorter time [is encompassed] by a greater [time]. Minor Premise of the Argument for One Now: Annihilation (218a 14 - 19) Si ergo sint duo, prius corrumpi necesse est; non autem in ipso priori nunc, nihil enim corrumpitur dum est. TO 8E vvjv ufi 6v TtpoTEpov 8E 6v dvdyKri EcpGdpGai 7IOTE, 3 7 5 "To measure something, as Aristotle uses that word, means to be a proper fraction of it, to fit into it an exact number of times. The diagonal of a square is in-com-mensurable with its side because there is nothing that can measure them both." Sachs (1995), 132 137 Kai xd VVJV ajra (lev aXXr\koiq OVJK eaxai, ecpGdpGai 8e dvdyKri dei TO 7tp6xepov. ev avjxcp uiv OVJV ecpGdpGai 06% oTov xe 8id xo etvai xoxe, ev aXX® 8e vvjv ecpGdpGai xo npoxepov VVJV OVJK ev8e%exai. eaxco ydp dSfjvaxov e%6iieva etvai aXXi\X(£>v xd VVJV, cboTtep axiyixfiv axiyiifjc,. And the Now which is not but once was must be annihilated at some [prior] time; but Nows will not be simultaneously to one another, and the prior [Now] must always be annihilated. Therefore, in itself, on the one hand, [the prior Now] is not able to be annihilated because of its being then [when it was]; but, on the other hand, the prior Now cannot be received into another Now [where it later perishes]. (For let it be impossible that [different] Nows are holding each other, just like a point [cannot be] inside a[nother indivisible] point.) Conclusion (Reductio Ad Absurdum): Infinite Regression (218a 19-21) Nec etiam in posteriori, sic enim simul esset cum infinitis nunc intermediis. Non sunt plura, aliud et aliud, quia unum nunc cum sit indivisibile non continet alterum. eutep OVJV ev xcp ecpe^ fjc, OVJK ecpGapxai aXX' ev aXXq, ev xotc, pexa^vj [xoia] VVJV aTteipoic, OVJCJIV dpa dv evn-XOVJXO 8e d8vjvaxov. Therefore i f [the prior Now] is not annihilated in the subsequent [Now] but in another [Now], it would be [annihilated] at the same time as an infinity of Nows existing between those [prior and subsequent] Nows. But this is impossible. First Argument for Many Nows: Limits (218a 21 - 25) Quia nullius divisibilis finiti, quale est tempus, potest esse unus terminus tantum. aXXa irf|v OVJ8' a ie i xo arjxo 8iauiveiv Svjvaxov ovjSevoc, ydp Siaipexov) TreTtepaauevovj v Ttepaq eaxiv, ovjxe dv ecp' v fj rjvjvexec, ovjxe dv e%i 7tA,eico-xo 8e VVJV 7iepa<; eaxiv, Kai xpovov eaxi XaPetv Ttercepaaiievov. But truly it is not possible [for the Now] to always remain the same. Because there is nothing among the class of the divisible and the limited where the limit is one; a line segment could not exist with one [limit only], nor could [something] with more [dimensions, like a body, exist with one limit only]. But the Now is a limit, and [any finite] time is to be taken [as] limited. Second Argument for Many Nows: Order (218a 25 - 30) 138 Si in toto tempore sit idem nunc, sequitur simul esse quae fuerunt ante mille annos et quae sunt hodie. e x i ei TO d p a e t v a i KCXTCC %povov Kai pnTe rcpoxepov pf|Te uaTepov TO ev TO) auTcp e t v a i Ka i e v i [TCO] vtJv e c m v , ei TCX Te rcpoTepov K a i Td ftcnepov ev TCO vt>v TCO8I ecmv, apa d v eir i T a CTOC, yevopeva p u p i o c T o v Toiq y e v o p e v o i q Ttipepov, K a i ouTe TtpoTepov OUTB iknepov ou8ev aXko aXkox). Further still, if the Now is to be simultaneous throughout time and to be in one and the same [Now], neither prior nor subsequent, and if the prior and the subsequent are in this here Now [today], the things that happen ten thousand years ago would be simultaneous with the things that happen today, and "prior" and "subsequent" [would be] no different from one another. Epilogue: Existence (218a 30-31) Concludit tot opposita esse de ipsis nunc, quae sunt in tempore. max pev ouv TCOV tmapxovTcov auTCp ToaauT eoTco 8in7Topnpeva-Let this, therefore, be the mass of perplexities about what exists in t ime. Section Two: Quid sit tempus, et quomodo se habeat ad motum, disputative inquiritur. What Time Is: Conjectures (218a 31 - b 1) Quid sit tempus non constat ex traditis ab antiquis. T ! 8' e c m v 6 xpovoc, Ka i Tig a u T o u f| (puaig, ouoicoc, eK Te TCOV 7tapa8e8ouevcov d8nA,6v e c m v , Kai nep i cov r o y x d v o p e v 8ieA/nA,D96Tec, rcpoTepov. o i pev y a p Tfjv Tot) oXou Kivnaiv e t v a i (paaiv, o i 8e Trjv ocpaipav auTfjv. And what t ime is, that is, what its nature is, is s i m i l a r l y unclear from the tradi t ional [accounts], but about w h i c h we first happen to relate: Some say t ime is the m o t i o n of the universe, but others say it is the sphere itself. First Argument Against Time as Universal Motion: Parts (218b 1 - 3) Quia pars circulationis non est circulato. K a i T o i xfjc; rcepicpopag K a i TO pepog xpovoq Tic, e c m , 139 7C£picpopd 8e ye orj-uipoc, ydp Ttepicpopdq to X,r|cp0ev, dAX orj 7tepi(popd. Although the part is some time and [a part] of the circuit, yet [it is] certainly not the [whole] circuit [itself]. Fo3r part of the circuit is circumscribed, but not the [whole] circuit. Second Argument Against T ime as Universal Motion: Plurality (218b 3 - 5) Quia essent plura tempora cum sint plures circulationes pro pluralitate caelorum. CTI 8' ei TtXeicoc, fjaav oi ovjpavoi, ouoicoc, dv fjv 6 xpovoc, r\ OTOUOOV avJTCov Kivnoiq, COOTE noXXoi xpovoi apa. And, further, if there were many heavenly bodies, time would similarly be the motion of any given one of them, so that many times would be simultaneously. Argument Against T ime as the Universe: Legitimacy (218b 5 - 9) Quia non eodum modo aliquid dicitur in loco et in tempore et quia illegitime argumentantur ex duabus affirmitavis in secunda figura. fj 8e TOY) OAOYJ acpcapa eSo^ e IXEV TOIC, Ei7corjaiv Eivca 6 xpovoq, OTI EV TE TCO xpovcp 7tdvT(x EOTIV xai EV TTJ Tovj 6A,ovj acpaipcc EOTIV 8' £VJr|0lKCbTEpOV TO £ipTUJ.£VOV fj cboTE 7cepi avJTorj Ta dSrjvaTa ETtiOKOTCEiv. And it seems the sphere of the universe (at least for those who say it is time) is [time] because all things are in time and [likewise all things are] in the sphere of the universe. But the declaration is [even] more simple-minded than [the fact that] it yields questionable impossibilities [e.g. if all of the universe is in the present then all of time must be in the present,] [because, as a syllogism of the second figure, it is simply logically invalid]. First Argument Against the Identity of T ime and Motion: Presence (218b 9 -13) Dum tempus est ubique et apud omnia, motus est in transmutato, vel in loco transmutati et transmutantis. excel 8E SOKEI pdXioTa Kivnoi<; Eivai Kai peTaPoAjj TIC, 6 xpovoq, TOVJT' dv etTj OKe7tTeov. f| irev ovjv eKarjTovj p.eTaPoXf| Kai Kivnaic, ev avjTcp TCO neTapdAAovTi uovov eaTiv, 140 ti ox) dv T U X T I 6v auTO T O Kivovpevov Kai peTaPdAAov 6 8e xpovoq opoicoc, Kai rcavTaxoi) Kai rcapd naaiv. But since time seems very much to be a sort of motion or change, this needs to be investigated. On the one hand, then, the change or motion of each [being] is solely in the changing [being] itself, or where it itself happens to be the being that is moved or changing; but time [is] similarly both everywhere and available to all [as a measure]. Second Argument Against the Identity of Time and Motion: Velocity (218b 13- b 20) Tempus non est, ut motus, velox vel tardus; non enim tempus a tempore determinatur. ETt 8e peTaPoXfi pev ecm GCCTTCOV Kai PpaSwepa, Xpovoc, 8' O U K ecmv TO yap PpaSi) Kai Taxi) XP0V(P cbpiGTai, Taxi) pev TO ev oMycp 7toX,i) Kivoupevov, PpaSi) 8e TO ev noXk& 6/Ayov 6 8e xpovoq ox>x copiaTai XP0VCP> ouTe TCO 7toa6<; TIC, etvai OUTC TO) %oioq. OTI uev Toivuv O U K ecmv Kivnaii;, cpavepov pn8ev 8e 8ia<pepeT<o Aiyeiv f|uTv ev TCO rcapovTi Kivnaiv f\ peTaPoA,f|v. And further, while change is of the faster and the slower, time is not. For the slow and the fast is marked by time: fast [being] what is moved much in little [time], slow [being] what is moved little in much [time]. But time is not marked by time, neither by that which is some quantity nor by that which is some quality. Wherefore it is obvious that [time] is not motion. (And let there be no difference for us presently in speaking of motion or change.)376 [ Chapter 11 (Time's Definition): Numerus motus secundumprius etposterius ] Introduction: Paradox (218b 21 - 219a 2) Ostendit tempus non esse sine motu, quia tunc percipimus fieri tempus, quando sentimus motum. >AAA.d u\f|v ot)8' dvet) ye peTaPoA/fjc/ OTav yap pnSev auToi ueTaPdAAcopev Trjv Sidvoiav fi XdGcopev peTapdXX,ovTeq, oi) 8oKei fipiv yeyovevai xpovoc,, KaOaTxep ou8e Toiq ev ZapSot uuGoXoyovjpevon; KaGeuSeiv raxpd xoiq fipcoaiv, OTav eyepGcoar oi)vd7CTOi)CTi yap TCO npoTepov vuv TO vcjTepov vt>v Kai v noiouaiv, Aristotle goes on to distinguish the two in Book V. 141 e^aipovjvTec, 8id Trjv dvaio6r|oiav TO iiexa^v. cbonep OVJV el ixfj fjv eTepov TO VVJV dXXd TCXYJTO K a i ev, OVJK dv fjv xpovoc,, OYJTCOC, K a i eTcei taxvGdvei eTepov 6v, ovj 8 o K e t etvai TO peTa^vj xpovoc,. Yet truly neither [is time] in the least without motion. For whenever we ourselves do not change our thought, or are unaware of its changing, time does not seem to us to have been: just it did not for the mythological men in Sardis when they awoke from the sleep they began in the time of the heroes, because they joined the subsequent Now with the former Now and made [them into] one [Now], removing the [time] inbetween because it was not perceived. In this manner, then, if the Now would be, not different, but [always] one and the same [Now], time could not be. And, in the same manner, when [we are] unaware [of two Nows'] being different, the time inbetween does not seem to be.377 ei Sf] TO |if| oieoGai etvai xpovov TOT£ cro|j.paiv£i fjirtv, OTav |xf| opiacoiiev irr|8euiav peTaPoXfjv, aXX ev evi Kai d8iaipeTcp cpaivnTai f) \\ix>%r\ (xeveiv, OTav 8' aiaGcbireGa Kai opiacopev, TOTe cpapev yeyovevai %povov, (pavepov OTI OVJK eaTiv ctvevj Kivfiaecoc, Kai ireTaPoA/fjc, xpovoq. OTI |xev OVJV ovJTe Kivriaig OVJT' dvevj Kivfiaecoc, 6 xpovoc, eaTi, cpavepov Indeed, if time is not known precisely when we happen not to mark any change, but [known only] when the soul appears to remain in one undifferentiated [state], and if, when we perceive and mark [change], then we say time has been, it is clear that time is not without motion or change. It is obvious, therefore, that time is neither motion nor without motion. Section Three: Temporis definitio traditur et explicatur. First Part ("of Motion"): General Perception of Motion (219a 2 - 10) Tempus est aliquid motus: quia perceptio motus infert perceptionem temporis, et e contra A/r|7tTeov 8e, ercei ^nTovjirev Ti eaTiv 6 xpovoq, evTev)Gev dp%o|revoic„ TI Tfjc, Kivfioecbc, eoTiv. dira ydp Kivfjaecoc, aiaGavoiaeGa Kai xpovovj-3 7 7 Aristotle refers back to the impasse of 218a 8 - 30, namely, whether the Now exists as the same or different, as one or many. This existential impasse is resolved from the perspective of the soul's essence: Time's essence in the soul is its existence ecstatically numbering motion. As such it can appear from the perspective of existence to be either the same or different, either one or many. The distinction between essence and existence arises from investigating the human soul and its nature, an investigation that articulates these two modes of being. 142 Kai ydp edv fj OKOXOC, Ka i |j,r|8ev 8id xof) acb|j.axoc, 7cda%coiiev, Kivriaic, 8e TIC, ev xfj yuxfj evfj, efjGfjc, aira 8oKeT xic, yeyovevai Kai xpovoq. aXXa ]xr\v Ka i oxav ye xpovoc, 8OKTJ yeyovevai xic,, dua K a i Kivnaic, xic, SOKBI yeyovevai. cbaxe fjxoi Kivriaic, fj xfjc, Kivfiaecoc, xi eaxiv 6 %povoc,. creel OVJV orj Kivnaig, dvdyKri xfjc, Kivfiaecoc, xt etvai arjxov. And since we seek what time is, we must take up from the origins what it is [within the genus]378 of motion. For we perceive motion and time simultaneously. For even if it should be dark and we undergo nothing via the body, but some motion is interior in the soul, directly, then, does some time seem to have happened simultaneously [with the interior motion]. And indeed also when at least some time seems to have happened, simultaneously also does some motion seem to have happened. Consequently, time is either motion or something [ruling over the general sphere] of motion. Since therefore [we already concluded that it is]379 not motion, it is necessary for it to be something of motion.380 Second Part ("Along Prior and Subsequent"): Continuity of the "Along" (219a 10 -14) Continuitas est in tempore ex motu et magnitudine. E7tei 8e xo Kivofjuevov Kivetxai eK xivoc, e'ic, xi K a i Ttdv uiyeGoc, arjve%ec,, dKoXouGet xcp ueyeGei fj Kivriaic,-8id ydp xo xo ueyeGoc, e ivai auvexec, K a i fj Kivriaic, eaxiv aYjve%f|c„ 8id 8e xfjv Kivriaiv 6 xpovoc/ oan ydp f) Kivriaic;, xoaofjxoc, K a i 6 xpovoc, a ie i 8oKei yeyovevai. And since the being moved381 is moved from something to something, and the whole 3 7 8 The root meaning of the genitive case is that it is the case of the genus. This does not mean that motion is a genus and that time is a species of that genus. Aristotle simply means that the relation of time to motion in general needs to be investigated. Because the investigation is of motion in general, it must be taken up from the beginnings or sources or origins of any general account of motion. Aristotle thus treats time and motion as they are ruled in the soul, the principle of which is self-moving. 3 7 9 The inference from the two arguments of 218b 9 - 20. 3 8 0 That is, "something of motion" is objective genitive. An expanded translation: "It is necessary for it to be something [which in its being takes the general sphere] of motion [as its object of perception]." 3 8 1 The being moved is the "something of motion" read as subjective genitive, i.e. the being moved is the object of motion, i.e. motion is the subject which is the being in motion from potency to act. When "something of motion" is read as objective genitive, it means time, which takes the motion of the being itself as its object. "Being's motion" = subjective genitive; "time's motion" = objective genitive. Time numbers being in motion, i.e. being being actualized. 143 magnitude [traversed in the motion's path from something to something] is continuous, the motion accompanies the magnitude. Because through the [fact that being] continuous [is] "to be a magnitude", the motion is also continuous. And through the motion [being continuous], time [is continuous]. For as much as [it does follow] motion, so much also does time always seem to have happened. Second Part ("Along Prior and Subsequent"): Position of "Prior and Subsequent" (219a 14-19) Prius et posterius sunt per prius in magnitudine propter positionem, de cuius ratione sunt. xo Sf) rcpoxepov Kai ucxepov ev xorccp rcpcoxov ecmv. evxat>0a pev Sf) xfj Geaer ercei 8' ev xcp peyeGei ecm TO rcpoxepov Ka i uaxepov, dvdyKn Kai ev Kivfjoet etvai TO rcpoxepov Kai uaxepov, dvdXoyov xoic, eKei. aXXa pfiv Ka i ev %p6vcp ecmv xo rcpoxepov Ka i uaxepov 8id xo dKoXovjGeiv dei Gaxepcp Gdxepov aincov. Indeed, the prior and subsequent is first in place. To be sure, they are there by position.382 And since the prior and subsequent is in magnitude, it is necessary that the prior and subsequent also are in motion, in proportion to those [positions] there [in magnitude and place]. And truly, the prior and subsequent is also in time through its always following another with another. On the "Prior and Subsequent" in Motion: The Same "Being" in Subject, but Different "To Be" by Reason (219a 19 - 21) Prius et posterius sunt idem subiecto cum motu, sed differunt ratione. Motus enim ratio est quod sit actus existentis in potentia; sed quod in motu sit prius et posterius, contingit ei ex or dine partium magnitudinis. eoxi 8e xo rcpoxepov Kai fiaxepov ev xfj Kivfiaei 6 pev rcoxe 6v Kivnoiq [ecmv]-xo pevxoi etvai auxcp exepov Kai oi) Kivnau;. And it is the prior and subsequent in motion which is ever "being" motion [i.e. motion in respect to that which is].383 However the "to be" [i.e. the essence perceived by reason] for 3 8 2 Everyone translates this as "position" (Hope as "relative position") except Hussey ("by convention") who maintains "the phrase is too obscure to be of any real help" (147). 3 8 3 Urmson translates the troublesome phrase, "what (else) it has to be in order to be time" (122 n.177). But he renders the entire passage here, "The before and later in change is, as regards its subject, change, but its 144 it [i.e. the prior and subsequent] is different [from the "being"] and is not motion [because the "to be" of motion is the potency, known potentially in reason, of the act, which actually exists in motion]. On the "Prior and Subsequent" in Time: Perception of Motion "Being" (219a 22 - 25) Tempus sequitur motum ratione prioris et posterioris ex or dine partium magnitudinis, quia tempus accipimus cum accipimus prius et posterius in motu. aXka uf]v Kai xov xpovov ye yvcopi^ ouev 6xav opiacopev xf|v Kivncriv, xcp rcpoxepov Kai vaxepov opi^ ovxec/ Kai xoxe cpapev yeyovevai xpovov, oxav xou rcpoxepot) Kai uaxepou E V xfj Kivfjaei aiaOncriv Xdpcopev. And truly too, we do at least recognize time whenever we mark motion, marking with the prior and subsequent. And then we say time has happened whenever we take the perception of the prior and subsequent in motion. Third Part ("Number"): Being-marked by the Now (219a 25 - b 3) Tempus esse dicimus, cum accipimus in motu duo extrema alicuius medii, seu duo nunc, hoc prius et illudposterius, quasi numerando motum. opi^ opev 8e xcp akXo Kai aXko t>7toA,aPeiv auxd, Kai pexa^u xi aincov exepov oxav yap exepa x d a K p a IOV peoou vofjocopev, Kai 8uo eurn f| yuxT) x d vuv, xo uev rcpoxepov xo 8' ijaxepov, xoxe K a i xouxo cpapev e t v a i xpovov xo yap opt^ opevov xcp vx>v %po\oc, etvai 8 o K e r K a i u7toKeia0co. And we mark by taking the same [moving] things under the other and other [of prior and subsequent position], i.e. between them something [of magnitude] is different. For whenever we think the extremes of the middle [to be] different, and the soul says "two Nows", one the prior [Now], the other the subsequent [Now], then too we say this is time. For the being-marked by the Now seems to be time. And let this be the foundation. essence is different and not change." (120) This is better English than our translation, but we try to preserve the etymological link between "subject" and "essence" as given in Aristotle's Greek, which is grammatically a distinction between the participle "being" and the infinitive "to be". The philosophical distinction seems to be between the actual existence of a thing (the participle) and the rational comprehension of its potency (the infinitive). 145 oxav ixev ovjv cog v xo vvjv aiaGavcbpeGa, Kai |xf| fjxoi cog Ttpoxepov Kai vjaxepov ev xij Kivfjaei ij cog xo avjxo (xev upoxepou 8e Ka i vjaxepoi) xivog, orj SoKei xpovog yeyovevai ov)8eig, 6xi ovj8e Kivnaig. oxav 8e xo 7tp6xepov Kai rjoxepov, xoxe Xeyopev xpovov xovjxo ydp eaxiv 6 xpovog, dpiGpog Kivfjaecog Kaxd xo rcpoxepov Ka i vjaxepov. OVJK dpa Kivnaig 6 xpovog aXX,' fj dpiGudv e^ei f| Kivriaig. Therefore, on the one hand, whenever we perceive the Now as one, and neither as prior or subsequent in motion, nor as the same [Now] as some prior [Now] or even [the same as] some subsequent [Now], no time seems to have happened, because motion has not [happened]. On the other hand, whenever the prior and subsequent [is], then we say time [is]. For this is time: number of motion along the prior and subsequent. Thus time is not motion, but that by which motion has number. Evidence for the Definition: "Number of Motion" in Judgement (219b 3 - 5) Tempus est numerus motus, quia eo motum iudicamus maiorem vel minorem. aripeiov 8e-xo [xev ydp 7tA,etov Ka i eXaxxov Kpivouev dpiGpcp, Kivnaiv 8e TtXeico Kai eXdxxco xpovqr dpiGirog dpa xiq 6 xpovoq. And the evidence is this: We judge the greater and lesser by number; [we judge] motion great or small by time; therefore time is some number. Evidence for the Definition: How Time is Numbered "Along Prior and Subsequent" (219b 5-9) Tempus non est numerus quo numeramus, sed est numerus numeratus; sicque est quantitas continua. enei 8' dpiGuog eaxi 8ixcog (Kai ydp xo dpi6uorj|ievov Ka i xo dpiGirnxov dpiGirov Xeyopev, Kai cp dpiGp.ovju.ev), 6 8ij XP0V0S £0"riv xo dpiG(4.orj(j.evov Ka i ofjx cp dpiG(a.ofj|j.ev. eaxi 8' exepov cp dpiGu.ov3ij.ev Kai xo dpiGuovjpevov. And since number is twofold (because we say number is both (a) the being-numbered [in act] or the [potentially] numerable and (b) that by which we number), time certainly is the being-numbered [in act] and not that by which we number. And it is different from that 146 by which we number, i.e. the being-numbered [is different]. Section Four: Quomodo sit vel non sit idem nunc in toto tempore. Ratio eorum quae dicuntur de nunc. On the Now as Same and Different: Simultaneously and Non-Simultaneously (219b 9-12) Utrum sit idem nunc in toto tempore, vel aliud et aliud, quod supra in dubio positum est. Ponit quod nunc quodammodo est idem et quodammodo non est idem. Kai cbo7t£p f| Kivncuc, aiei aXXn Kai aXKy\, Kai 6 xpovoq (6 8' ana nac, xpovoc, 6 auxoc/ TO yap vuv to auto 6 rcox' fpv-xd 8' etvai auxcp exepov-to 8e vuv xov xpovov 6pi£ei, fj rcpoxepov Kai uoxepov). And just as [the parts of] motion [are] always other and other, so too time. But time simultaneous anywhere is the same,384 because the Now is the same which it once was.385 But the "to be" for the Now [i.e. its rational essence, i.e. what it always is] is [to be always] different [i.e. other and other]. For the Now marks time inasmuch as it is prior and subsequent [i.e. inasmuch as the Now is non-simultaneous]. On the Now as Same and Different: Restatement of the Argument (219b 12 - 15) Exponit quod dixerat: Nunc est idem subiecto, sed ratione aliud et aliud, et prius et posterius. xo 8e vuv eaxi pev cb<; xo at)xo, eaxt 8' ac, ov xo auxo-fj pev yap ev aAAcp Kai aAAcp, exepov (xouxo 8' rjv auxcp xo vuv etvai), 6 8e rcoxe 6v eaxi xo vuv, xo auxo. 3 8 4 Simplicius comments, "Having stated what is common to time and change, he reasonably adds their difference." (129) The parts of time and motion are always other and other, but a part of time, i.e. the Now, can be everywhere the same in the same Now when motions are not the same in the same Now. 3 8 5 Urmson translates, "The now is identical as substrate." (130) This is an accurate interpretation, but the literal meaning fleshes it out: The Now is the same whenever it is. Saying that it is the same Now which it once was avoids saying that the Now is always the same (i.e. its "to be" is always the same). The "was" preserves the temporal identity of the Now as it exists fleetingly in time (e.g. when different motions happen simultaneously in the same Now) whereas the "to be" states its atemporal essence. "Was" is preferable to "is" in the formulation here because "is" carries overtones of an answer to the question, "what is it?", i.e. "what is its atemporal essence?", but the sentence can be translated just as accurately using "is", as in this rendition, "The Now is the same [Now] which it is in its instance". The all-important qualifier is "in its instance" or "at some time", which is the opposite of the eternal "to be" of anything. 147 Thus the Now is in one way the same, and in another way it is not the same. Because, in one way, inasmuch as [it is] in other and other [time], [it is] different (since this was for it its "to be [a] Now"), but in another way, the Now is the same which it is "being" at some On the Now as Same and Different: Analogy to Motion (219b 15 - 28) Probat quod dixerat: Quod sit idem subiecto et aliud et aliud ratione. dKoXovjeet yap, cog £XE%QT\, TCO iikv IXEYEGEI fi Kivriaic,, TavjTri 8' 6 xpovog, cog cpapEV Kai ouoicog 8f| TTJ aTiyu.fi TO cp£p6|a.£vov, co TT|V Kivnaiv yvcopi^oiiEV Ka i TO npoTEpov E V avnij Kai TO vjaTEpov. TOVJTO 8E 6 11EV 7IOTE OV TO afjTO (fj aTiy|xf| ydp fj XiGog fj TI aXko TOIOYJTOV EOTI) , TCO A,6ycp 8E aXko, coaKEp oi aocpiaTai XanPdvouaiv ETepov TO KopiaKov EV AVJKEICO Eivai Ka i TO KopiaKov E V dyopd. Kai TOVJTO 8f| TCO aXKoQx Kai aXkoQx Eivai ETEpov For, as explained,387 motion accompanies magnitude, and time [accompanies] motion, as we maintain. And similarly indeed, that which is being carried [by motion] [accompanies] the point, by which we recognize motion and the prior and subsequent in motion. For this [point] is that which, on the one hand, "being" then, [is] the same (for [example], it is either a point or a stone, or any other sort of thing). But on the other hand, in [its] account, [the point is that which is] other, just like the sophists take "the [being of] Coriscus in the Lyceum" to be different from "the [being of] Coriscus in the agora". And indeed this [object, e.g. statue of Corsicus] is different in [its moving from] one place to another. TCO 8E cpEpouivcp dKoA,OVJ0£l TO VVJV, cba7t£p 6 xpovog Tfj KivfjaEi (TCO ydp cpEpouivco yvcopi£ou£v TO rcpoTEpov K a i viaTEpov EV KivfjaEi, fj 8' dpi0|j.r|Tdv TO TcpoTEpov Ka i vjaTEpov, TO VVJV EOTIV)-cbaTE Kai EV Tovnoig 6 U £ V 7T.OTE OV VVJV EOTl, TO afjTO (TO TtpoTEpov ydp Kai vjaTEpov E O T I TO EV KivfjaEi), TO 8' ElVai ETEpOV (fj dpiGpnTOV ydp TO TtpoTEpov Kai vjaTEpov, TO vvjv EOTIV) . 3 8 6 Urmson translates with an accurate interpretation, "As ever differently positioned, it is different, for that is what it is to be a now, but as substrate it is the same." (130) 3 8 7 219a 10-14. 148 And the Now accompanies that which is being moved, just like time [accompanies] motion. For we recognize in that which is being carried [by motion] the prior and subsequent in motion. And that by which the prior and subsequent is [potentially] numerable is the Now. So that also388 in these examples that which the Now is "being" at some time is the same (for the prior and subsequent is that which is in motion) but [its] "to be" [is] different (for that by which the prior and subsequent is [potentially] numerable is the Now). On the Now as Same and Different: Analogy to That Which is Being Carried (219b 28 - 33) Ipsum nunc est est id quod de tempore est maxime notum, sicut de motu vel loci mutatione maxime notum est mobile, quod est aliquidper se stans. Kai yvcbptpov 8e udAacna T O U T ' ecmv Kai yap f\ Kivncuc, 8id TO Kivoupevov Kai f] (popd 8id TO (pepopevov To8e yap T I TO (pepopevov, f| 8e Kivnaiq oi). eom pev ov>v cbc, TO auTO TO V U V aiei, ecm 8' cbc, ou TO auTO-Kai yap TO (pepopevov. And indeed this is especially [what is] recognizable: motion [is recognized] through that which is being moved, and locomotion389 [is recognized] through that which is being carried. For that which is being carried is this [particular] thing, but motion is not.390 Therefore, on the one hand, the now is always the same, but, on the other hand, it is not the same, i.e. because it is that which is being carried.391 On Time and the Now: Analogy to Locomotion and That Which is Being Carried (219b 33 -220a 4) Sicut tempus est numerus mutationis loci, ita nunc est unitas numeri. cpavepov 8e Ka i O T I e'tre xpovoc, pf| eir), TO vuv O U K dv ein, eiT£ TO vuv uf| eir|, Xpovoc, O U K av ei'ir 3 8 8 i.e. the analogy to the object in motion being both same and different holds 3 8 9 literally, "carrying", which is a special sense of motion, i.e. locomotion: change of place 3 9 0 This enthymeme bears Aristotle's hidden premise, "Individuals are more easily recognized than universals." 3 9 1 The thing being carried is the same inasmuch as it is a thing but different inasmuch as it is being carried. 149 d p a yap coorcep T O (pepopevov K a i f| (popd, O V T C O C , K a i 6 dpiGpoc, 6 T O U (pepouivorj K a i 6 xfjc; (popag. Xpovoc, p i v yap 6 xr\q (popaq dptGpoc,, T O vuv 8e cbc, T O cpepopevov, otov uovdc, dptGpou. And it is obvious also that should time not be, the Now would not be; that should the Now not be, time would not be.392 Because just as that which is being carried and the locomotion [of it] are [said to be]393 simultaneous/so too number is [simultaneously] the number of that which is being carried and the number of locomotion. Thus, on the one hand, time is the number of locomotion, but, on the other hand, the now is like that which is being carried, something like a unit of number. On the Now in Account: Marking Prior and Subsequent Motion (220a 4-9) Nunc dividit et continuat temporis partes: ex parte motus et mobilis K a i ouvexfiq Te 8fi 6 xpovoc, T O ) V U V , K a i SifipnTat KaTa T O V U V aKoA-ouGei ydp K a i T O U T O TTJ (popd K a i TCO cpepopevcp. K a i ydp f| Kivnoic, K a i f| (popd p i a TCO (pepopevcp, O T I ev (Kai oux 6 7toTe 6 v - K a i ydp dv 8taX,i7tot-dA,Xd TCO A,6ycp)-K a i 6pi£ei 8e T T | V rcpoTepov K a i ucTepov Kivnotv T O U T O . But [unlike number] time is indeed both a continuum by [means of] the Now, and divisible according to the Now. Because this too accompanies the locomotion and that which is being carried. For both motion and locomotion are one in that which is being carried, because it is one and not that which it is "being" [incidently] at some time (i.e. because it could pause [and thus be "that which is being-at-rest" instead of "that which is being-in-motion"]) but [the subject] in account [of which a predicate is said "to be"]. And this [rational] Now marks off the prior and subsequent motion. On the Now: Analogy to the Point (220a 9 - 18) Nunc dividit et continuat temporis partes: ex parte lineae et puncti 3 9 2 The Now is, in logical terms, both the necessary and the sufficient condition for time. 3 9 3 Talk about the "to be" (the rational essence) of a "being" (a thing) is always about the "to be" because it occurs in speech in indirect statement, the form of which (in Greek) uses the infinitive. Any assertion is a predication, an account in ratio, of the being which is experienced in intellectual or sensory perception, an assertion which takes the form of "I maintain x to be y " (more commonly in English, the form of the account or ratio is "I maintain x is y"). The beginnings of the self-reflexive understanding of the grammar of discourse and what it points to is the birth in Plato and Aristotle of their philosophical terminology. Grammar as a clue or guiding thread in philosophy (speculative grammar) is then given extended treatment by the tradition in the Middle Ages. 150 dKoXorjGei 8e Ka i TOVJTO TCCOC, TTJ axiyixfj-Kai ydp fi cmynfj Ka i avjve%ei TO irfJKOc, Ka i opi^er eoxi ydp TOVJ ixev dpxf) TOVJ 8e Te^evjTTj. aXX OTav (rev OVJTCO XapPavrj TIC, cbc, 8vjoi xpcb|xevo<; TTJ | i id , dvdyKT| lOTaaGai, ei eoTai dpxf| Ka i Te^evjTf) fj avjTfj aTiyixfj-TO 8e VVJV 8id TO KiveioGai xo cpepoirevov a ie i eTepov. cbaG' 6 xpovoc, dpiGuoc, OVJX cbc, Tfjc, ainfjc, aTiyu.fjc,, OTI dp%r| K a i TeA,evjTf|, aXX cbc, Ta eo%axa Tfjc, ypaiiixfjc; lidAAov-Kai ov% wq Ta u.epr|, 8id Te TO eipT|ii,evov (TTJ ydp neoTi aTiypfi aq Svjcri xpTjoeTai, cbaTe fipeixetv rjvj(j.pfiaeTai), And this too accompanies in a way from [drawing an analogy to] the point: that the point does also both hold together [i.e. make continuous] and mark off [i.e. divide] the length [of a line]. Because it is the beginning of one [part] and the end of the other. But, on the one hand, whenever one takes it in this way, using the one [point] as two [i.e. as an end-point and then as a starting-point], it is necessary to make it fixed,394 if the same point is to be beginning and end. Yet, on the other hand, the Now, through the being-moved of that which is being carried, is always different. As a result, time is number, not like [number] of the same point (because [the same point is both] beginning and end), but more like the ends of the line. But not like [number of] the parts [of the line], because of what has been said (for the middle point could be used as two, so that [time] would turn out to be at rest). On the Now: Both Limit and Number (220a 18-24) Nunc non est pars, sed terminus temporis. Kai eTi cpavepov OTI ovj8ev udpiov TO VVJV TOVJ %p6vov>, ov)8' fj 8iaiperjic, Tfjc, Kivfjaecoq, cbcmep ofj8' fj oTiypfj Tfjc, ypamifjc/ ai 8e ypapirai a i 8VJO Tfjc, urdc, uopia. ?fj u.ev OVJV 7tepac, TO VVJV, of) xpovoc,, dX.A,d cu|j,pePr|Kev fj 8' dpiGjxet, dpiGuoc, ?• Ta (rev ydp TtepaTa eKeivou udvov eaTiv of) eaTiv rcepaTa, 6 8' dpiGuoc, 6 Tcbv8e TCOV i7uicov, fl SeKdg, Ka i a^AoGi. 3 9 4 "One must pause" (Urmson), "there must be a pause" (Waterfield), "a pause is necessary" (Hardie and Gaye), "requires a stop" (Hope), "it is necessary to make a stop" (Sachs), "one must come to a halt" (Hussey). The idea is correct, but it is better to emphasize that a point is always a fixed point on a line (and therefore when one comes to a point one always "stops" at this point insofar as the point is by its nature fixed) whereas a Now is never fixed. 151 And yet it is clear that the Now is no part of time, nor is division [a part] of motion, just like the point is [not a part] of the line. For the two lines are the parts of the one [divided line]. Therefore, the Now, inasmuch as it is a limit, is not time, but a characteristic [of time]. Inasmuch as it numbers, it is a number [and thus time itself, i.e. number of motion]. For, on the one hand, the limits are only [limits] of that of which they are limits, but the number, on the other hand, is [the number] of these horses, e.g. ten, and [the number of other things] elsewhere. Section Five: Manifestantur quaedam quae de tempore dici solent. Time's Number: Minimum in Multitude, not in Magnitude (220a 24 - 32) Ostendit quomodo in tempore invenitur minimum et quomodo non. O T I \ie\ xoivuv 6 xpovoc, dpiGuoc, eax iv Kivfjaecoc, K a x d X O rcpoxepov K c d rjoxepov, Kai auvexTJc, (avvexofjc, ydp), tpavepov. [ Chapter 12 (To Be in Time): Quomodo motus et alia in tempore sint ] 'EXdxioxoc, 8e dpiGuoc, 6 pev drtAxbc, eoxiv fj Suae/ xic, dpiGuoc, eaxi iiev cbc, eaxiv, eaxi 5' cbc, O V J K eaxiv, oiov ypa|j,u.fjc, eX,dxiaxog TtXfjGei |iev eaxiv ai 8fjo fj fj ufa, peyeGei O V J K eaxiv eA,dxiaxoc/ dei ydp Siaipeixai rcdaa ypapiifj. cbaxe oiroicoc, K a i xpovoc/ eAxxxiaxoc, y d p K a x d uev dpiGuov eaxiv 6 etc, fj o i 8VJO, K a x d uiyeGoc, 8' O V J K eaxiv. That time, therefore, is number of motion along the prior and subsequent, and continuous (for it is [number] of [motion along] a continuum), is clear. But the smallest number which simply is is two. Some number is, on the one hand, because it is, and is, on the other hand, because it is not. For example, the smallest [number] of a line in multitude is either the two or the one, but is not in magnitude. For every line always is divisible. So similarly also is time. For the smallest along number is the one or the two, but along magnitude is not. Time's Number: Numbering Much or Little, Not Fast or Slow (220a 32 - b 5) Ostendit quomodo tempus dicitur multum et paucum, breve et longum, nori autem velox et tardum. 152 (pavepov 8e Kai oxi xax^ c, pev Kai PpaSix; ov Xeyexax, noXvc, be Kai 6A,iyo<; Kai uaKpoq Kai Ppaxuc,. fj pev ydp avve%i\c„ paKpoc, Ka i Ppaxug, fj 8e dpiGuoc,, 710A/UC, Ka i oAayoc,. xaxuc, 8e Kai PpaSix; O U K eaxiv ouSe yap dpiGpoc, fj dpiGuoupev xaxvq Kai Ppa8i)c, ot)8eic,. And obviously it is not said that [time is] fast or slow, but much or little, and long or short. Insofar as [time is] continuous, [it is] long or short; insofar as [time is] number, [it is] much or little. But it is not fast or slow. For the number by which we number anything is neither fast nor slow. Time's Number: The Numbering Now is the Same, the Numbered Prior and Subsequent is Different (220b 5-12) Ostendit quomodo tempus est idem et non idem simpliciter. Kai 6 auxoc, 8e rcavxaxou aua-rcpoxepov 8e Kai uaxepov ov% 6 auxoc,, O T I Kai f| p.exaPoA,f| f| pev raxpouaa pia, fi 8e Y£Y8vr|u.£vri Kai fj uiAAouoa exepa, 6 be xpovoc, dpiGuoc, eaxiv oux cp dpiGpoupev aXTC 6 dpiGpoupevog, ouxog 8e aupPaivei rcpoxepov Ka i uaxepov dei exepoc/ xd ydp vuv exepa. eaxi 8e 6 dpiGuot; etc, pev Ka i 6 auxoc, 6 xcov eKaxov ircrccov Kai 6 xcov eKaxov dvGpcb7tcov, cov 8' dpiGpoq, exepa, oi i7T7toi xcov dvOpdmcov. And [time is] also [said to be] everywhere simultaneously the same. But prior and subsequent is not the same. Because, for example, the present change is one, but the past [change] and the future [change] are different. And time is number, not by which we number, but that which is numbered. In this manner, prior and subsequent always happens [to be] different. For the Nows are different. But the number of a hundred horses and a hundred human beings, on the one hand, is one and the same, but on the other hand, the things of which the number is are different ([i.e.] horses [are different] from human beings). Time's Number of Motion: Seasonal Reiteration (220b 12 - 14) Ostendit quomodo tempus reiteratur idem secundum quid. 153 exi cbc, ev8e%exai Kivnoiv etvai xfiv ai)xf|v Kai \xiax naXiv Kai naXiv, ouxco Kai xpovov, otov eviauxov ri eap f\ pexorccopov. Furthermore, as motion admits of being one and the same again and again, so also time; for example, a year, or spring, or fall. Time's "Number of Motion" (Subjective and Objective Genitive) Double Genitive: Motion's Number, Number's Motion (220b 14-24) Ostendit quod sicut motum cognoscimus tempore, ita tempus cognoscimus motu: ex ratione numeri et numerati. ov povov 8e xrjv Kivnaiv xcp Xpovcp uexpoupev, aXXa Kai xfj Kivfjoei xov xpovov 8id xo 6pi£ea6ai viz aXXr(X(i)\-6 uev ydp xpovoq opi^ ei xrjv Kivnaiv dpiGpoc, cov auxfjc,, fi 8e Kivncuc, xov xpovov. Kai Aiyopev noXvv Kai o i^yov xpovov xfj Kivf|aei pexpouvxec,, KaOdrcep Kai xcp dpiOpnxcp xov dpiOpov, otov xcp evi iKTicp xov xcov i7t7icov dpiGpov. xcp pev ydp dpiOpcp xo xcov i7t7rcov KXf|9o<; yvcopic^ opev, 7tdA,iv 8e xcp evi ircrccp xov xcov ircrccov dpiGpov auxov. opoicoc, 8e Kai eni xov xpovou Kai xfjq Kivfiaecoc;-xcp pev ydp XP0VCP Kivnaiv, xfj 8e Kivfiaei xov xpovov pexpotJpev. But not only do we measure motion with time [as we do the seasons], but also time with motion, through their being-marked by one another. For time, on the one hand, marks motion, being its number. Motion, on the other hand, [marks] time, i.e. we say much or little time, measuring by the motion, just like [we] also [determine] the number by [means of] what is to be numbered. For example, the number of the horses by [means of] the one horse. For, on the one hand, we recognize the multitude of the horses by [means of] the number; on the other hand, conversely [we recognize] the number of the horses itself [as one and the same] by [means of] the one horse. And similarly [do we happen] both upon time and motion: for on the one hand we measure motion by time, but on the other hand we measure time by motion. Time's Number of Motion: The Mutual Determination Along Magnitude (220b 24 -32) Ostendit quod sicut motum cognoscimus tempore, ita tempus cognoscimus motu: 154 ex comparatione motus ad magnitudinem. K a i TOVJT ' efjA,6ycoc, CTVj(xPePriKev dKoA,ovj8et ydp TCO pev peyeGei f| Kivricnc,, TTJ 8e Kivfjaei 6 xpovoc,, TCO Kai Tcood Ka i auvexij Ka i 8iaipeTa etvai-8id ixev ydp TO TO uiyeGoc, eivai T O I O V J T O V fj KIVTIOIC, TafjTa 7ce7cov6ev, 8id 8e Tfjv Kivnaiv 6 xpovoc,. Kai (j.eTpov)ixev Kai TO ueyeOoc, TTJ. Kivfjoei Ka i TTJV KivT|aiv TCO ireyeGev TCOAATJV ydp etvai cpairev Tijv 686v, dv fi nopeia rcoAAfi, Kai TafJTriv 7toA,A.fjv, dv fj 686<; [fj] TCOA,A,TJ-Kai TOV xpovov, dv f) KIVTIOIC;, Kai TTIV Kivnciv, dv 6 xpovoq. And this [mutual determination] has happened reasonably. For the motion, on the one hand, accompanies the magnitude. But time, on the other hand, accompanies the motion, by which it [is] to be so much and continuous and divisible. On the one hand, through the "to be" of the magnitude as [being a subject for] these sorts [of predicates], motion undergoes [the predication of] these things. On the other hand, through the motion, time [suffers these predicates], i.e. we also measure the magnitude by it [i.e. motion]. [Time] also moves motion by magnitude. For we say the road to be long when the journey is long. And we say [the journey] to be long when the road is long. And [we say] time [to be long] when the motion is, and [we say] motion [to be long] when time is. Section Six: Quomodo motus et alia in tempore sint. Quae sint et quae non sint in tempore. Intratemporality: Time Compared to Motion (220b 32 - 221a 7) Tempus mensurat motum et motum et eius durationem, quia tempore determinatur aliqua pars motus, et per hanc mensuratur totus motus. e7tei 8' C O T I V 6 xpovoc, uiTpov Kivfjoecoc, Ka i TOVJ KiveiaQai, ireTpei 8' OVJTOC , Tf]v Kivncuv TCO opioai Tivd Kivnoiv fj KaTa|ieTpf|0"ei xr\\ 6A,r|v (cba7cep Ka i TO p ,fJKOc, 6 nf[%vq TCO opioai T I uiyeGoc, o dvaireTpfiaei TO 6AOV), Kai eaTiv TTJ K i v f j o e i TO ev XP0VCP etvai TO ireTpeiaGai TCO XP0VCP Kai afjTfjv Kai TO e ivai afjTfjc, 155 (cx|xa ydp xrjv K i v n a i v Ka i TO etvai Tfjc, K i v f i a e c o c , ireTpet, Kai TOVJT eaTiv ainfj TO ev xpovco etvai, TO peTpetaGai avJTfjc, TO etvai), And since time is [a] measure of motion and of being-moved, [so] also this [measure called time] measures motion by marking some motion which will measure out the whole (just as the cubit, by marking some magnitude, also measures off the whole length). But for motion to be in time is [for motion] to be measured by time in respect of both itself and its being (for it [i.e. time] simultaneously measures both the motion and the being of the motion); and this is [what it is] for it [i.e. motion] to be in time: the being measured of its being. Intratemporality: Time Compared to Things Other Than Motion (221a 7 - 26) Aliae res sint in tempore, non sicutparte autpassiones ipsius, sed sicut numerata sunt in numeris. 8fjA,ov OTI K a i TOIC, aXXoiq TOVJT' eoTi TO ev XP 0 V F P etvai, TO peTpetaGai avJTcbv TO etvai VJTCO TOV) xpovovj. TO ydp ev XP 0 V C P etvai 8v>oiv eaTiv GaTepov, v p.ev TO etvai TOTe OTe 6 %povoq eaTiv, v 8e cbarcep evia Xeyopev OTI ev dpiGircp eaTiv. TOVJTO 8e armaivei fJTOi cbc, irepoq dpiGuov) K a i ndQoq, K a i oXatq OTI TOV) dpiGuov) TI , fj OTI eoTiv avjTOV) dpiGuoc,. e7tei 8' dpiGp.6<; 6 xpovoc,, TO |rev VVJV Ka i TO npoTepov Ka i oaa ToiavjTa ovncoc, ev XP 0 V C P cbq ev dpiGpcp povdi; K a i TO 7cepiTT6v K a i dpTiov (Td pev ydp TOV) dpiGuov) TI , Ta 8e TOVJ xpovovj TI eoTiv)-Ta 8e TcpdyixaTa cbq ev dpiG)j,cp TCO XP 0 V C P eoTiv. ei 8e TOVJTO, itepiexeTai vmo xpovovj cborcep K a i Td ev dpiGpcp vj7c' dpiGuov) K a i Td ev TOTCCO VJTCO TOTCOVJ. cpavepov 8e K a i OTI OVJK COTIV TO ev XP 0 V T P etvai TO etvai O T e 6 xpovoq COTIV, cborcep ovj8e TO ev Kivfjoei etvai ovj8e TO ev TOTCCO OTB r\ K i v r i a i c ; K a i 6 TOTCOQ COTIV. ei ydp eoTai TO ev TIVI OVJTCO, rcdvTa Td Tcpdyp.aTa ev OTCOOVJV eoTai, Ka i 6 oupavoq ev TTJ Keyxpcp-OTe ydp f i Keyxpoc, eaTiv, eoTi K a i 6 ovjpavoc,. dX,X,d TOVJTO \iev ovjp.pePr|Kev, eKeivo 8' avdyKT) icapaKoAovjGeiv, Kai TCO OVTI ev XP O V 0 P etvai Tiva xpovov OTe KaKetvo eaTiv, Kai TCO ev Kivfjaei OVTI etvai TOTB Kivrjaiv. And it is clear that for other things too this is [what] "to be in time" [is]: the being measured of their being by time. For "to be in time" is one of two things: either to be whenever time is, or to be - as we say of some things, that they are - "in number". A n d this means either that they are a part of number or an attribute or something wholly belonging to number, or that there is a number belonging to them. But since time is 156 number, the now and the prior and any such things are in time in the same way as one and the odd and even are in number (for the latter are things belonging to number and the former are things belonging to time). And things are in time as [they are] in number, and, if this is so, they are encompassed by time, just as things in number [are encompassed] by number and things in place by place. But it is obvious that to be in time is not to be when time is, any more than to be in motion or in place is [to be] when motion or place is. For if this shall be what [to be] "in something" is, all things shall be in any thing whatsoever, and the sky in a millet seed (for when the millet seed is, the sky is too). But this [to be "in something" whenever something else is] is incidental, whereas it is necessary for the other [mode of being, i.e. to be "in number",] to accompany [both time and motion], both for the being in time to be at some time when that [time] is too [i.e. the being is "in that time then"], and for the being in motion to be then a motion [i.e. the being is "in that motion then"]. (221a 26-30) Quae sunt in tempore totaliter continentur et concluduntur sub tempore, ut locata sub propriis locis. ercei 8e eaxiv cbc, ev dpiGpa) xo ev XP0V(P> XncpGfjaexai xic, 7tA,eicov xpovoc, rcavxoc, xou ev XP0VCP ovxoc/ 816 cxv&YKn rcdvxa xd ev xpovcp ovxa rcepiexeaGai tm6 xpovou, cbarcep Kai xaXka oaa ev xivi eaxiv, otov xd ev x67xcp xrnb xou xorcou. And since "[to be] in time" is like "[to be] in number", a time may be taken greater than any being in time. Because of this it is necessary that all beings in time are encompassed by time, just like any other things are also [encompassed] in something, e.g. the things in place [are encompassed] by place. (221a 30-b 3) Quae sunt in tempore aliquidpatiuntur sub tempore; utpatet modo loquendi: tempus tabefacit, omnia senescunt, in oblivionem cadunt. Kai rcda%ei 8f) xi i)7i6 xou xpovou, KaGdrcep Kai Xeyeiv eicbGapev oxi Kaxaxf)Kei 6 xpovoc,, Kai ynpdaKei rcdvG' i)7to xou xpovou, Kai e7tiA,av0dvexai 8id xov xpovov, aXX ou pepdGnKev, ou8e veov yeyovev ou8e KaA,6v (pGopdq ydp aixioq KaG' eauxov pdX,Xov 6 xpovoc/ dpiGuoc, ydp Kivfjaecot;, f| 8e Kivnau; e^iaxnaiv xo tmdpxov And indeed something is acted upon by time, just as we are accustomed to say "time grinds things away" and "by time everything grows old" and "through time things forget" 157 but not "things have learnt" or "have become new" or "beautiful". For in itself time is more a cause of decay, because it is number of motion, and motion displaces the constituent. (221b 3-5) Concludit propositum ex primo proposito: quia sempiterna non continentur sub tempore, nec eorum duratio tempore mensuratur. coaxe (pavepov O T I TCX aiei O V T C X , fj oriei O V T O C , O U K E O T I V ev xpovcp-ou ydp rcepiexeTca tmo xpovou, ou8e peTpetxat T O etvai auxcov xrtib T O U xpovorr As a result, it is obvious that things which are always being, insofar as [they are] being always, are not in time, because they are not encompassed by time, nor is their being measured by time. (221b 5-7) Concludit propositum ex altero proposito: quia sempiterna nil patiuntur a tempore; non tabescunt, nec senescunt anpetov 8e T O U T O D O T I ou8e rcdaxet ot)8ev urco T O U xpovou cbc, O U K O V T C X ev XP°VCP-Evident from this is that they are not affected in any way by time, as if [they were] not being in time. (221b 7-9) Proponit quod intendit, scilicet tempus mensurare, etsiper accidens, quietem. ercei 8' ecmv 6 xpovoq peTpov Kivfioecoq, eoTCu Kai fipepiaq ueTpov [KaTa auuPePnKocJ-rcaaa ydp fipepia ev XP0VC9-And since time is [a] measure of motion, it shall also be [a] measure of rest, because every act of resting is in time. (221b 9 -12) Excludit quietem non mensurari tempore, quia et ipsa est in numero motus, in tempore, licet non sit motus. oi) ydp cborcep T O ev Kivfjrjei 6v dvdyKn KivetoGai, O U T C O Kai T O ev XP°VCP' 158 orj ydp Kivriaic, 6 xpovoc,, aXX' dpiGuoc, K i v f i a e c o c ; , ev dpiGiicp 8e Kivfjaecoc, evSexeTai eivai Ka i T O fipeuovjv. For although the being which is in motion must be being-moved, [this is] not so for the being in time. Because time is not motion, but [a] number of motion, and it is possible for the resting thing also to be in [a] number of motion. (221b 12 - 16) Probat propositum, idest quiescens esse in numero motus, quia est privatio motus, et esse quiescentis est in tempore, ab eo mensuratum. orj ydp rcav T O aKivnTOv fjpeiiei, aXka T O eaTepnuevov Kivfjaecoc, TcecpvjKdc, 8e KiveiaGai, KaGdrcep eipnrai ev T O I C ; icpoTepov. T O 8' etvai ev dpiGpco eaTiv T O e ivai Tiva dpiGpov Tofj TcpdyurxToc,, Kai (xeTpeTaGai T O eivai afJTorj TCO dpiGucp ev cp eaTiv, C O O T ' ei ev xpovcp, VJTCO %p6vov>. For not every motionless thing is at rest, but only the thing deprived of motion which naturally is being-moved (as was said beforehand). But [for a thing] to be in number is [for there] to be some number of a thing and [for] its being to be measured by the number in which it is, so that if [the thing is] in time, [then it is measured] by time. (221b 16-20) Tempus mensural quod movetur et quod quiescit, inquantum positive vel privative sub motu. u.eTpf|rjei 8' 6 xpovoc, T O Kivovjuevov Kai T O fjpepovjv, fj T O irev Kivovjirevov T O 8e f)peuovjv T T J V ydp Kivnaiv avjTCbv ireTpfiaei Ka i Tijv fjpeuaav, rcoari T IC; . cbaTe T O Kivovjp,evov oox dTcAxoc, eaTai iieTpriTOv VJTCO xpovovj, fj Tcoaov T I eaTiv, akX fj fj Kivriaic; avJTorj Tcoaf). But time will measure the thing being moved inasmuch as it is a thing being moved and the thing resting inasmuch as it is a thing being moved. Because it will measure the motion and the rest of the things: [as] a quantity. As a result, the thing being moved will not simply be measured by time inasmuch as it [i.e. the thing itself] is some quantity, but inasmuch its motion is [a] quantity. Corollary (221b 20-23) 159 Substantiae separatae nec moventur nec sunt in tempore. cbaxe oaa jafixe KiveTxai u.f|x' fjpejaei, O V J K eaxiv ev xpovcp-xo |aev ydp ev XP 0 V (P etvai xo |xexpeia6ai eaxi xpovcp, 6 8e xpovoc, Kivfiaecoc, Kai fjpeiuac, iiexpov. As a result, whatever is neither moved not at rest is not in time. Because, on the one hand, to be in time is to be measured by time, and, on the other hand, time is [a] measure of motion and rest. Not All Non-Beings Are in Time (221b 23 - 222a 9) Non omnia non entia sunt in tempore. Omnia impossibilia quia nec fuerunt, nec sunt, nec erunt, non mensurantur tempore. cpavepov O V J V O X I ovjSe xo uf] 6v eaxai rcdv ev XP0V(P> otov oaa \ir\ evSexexai dX,A,coq, coarcep xo xrjv 8idjiexpov etvai xfj rcXevjpa avjiiuexpov. oXcoc, yap, ei uexpov uiv eaxi Kivfiaecoc, 6 xpovoc, Ka9' avjxo, x©v 8' dAAcov Kaxd avj|i.pePr|K6c,, 8f]Aov oxi cov xo etvai pexpei, xovjxoiq drcaaiv eaxai xo etvai ev xcp fipeiretv fj KivetcGai. oaa (xev ovjv cpGapxd Kai yevrixd Kai 6A,coc, oxe iiev ovxa oxe 8e jj.f|, dvaYKTi ev XP 0 V CP etvai (eaxiv ydp xpovoc, xic, rcA,eicov, 6c, tmepe^ei xovj xe etvai avjxcbv Kai xovj |j.expov)vxoc, xrjv ovjaiav avjxcbv)-xcov 8e jj.fi ovxcov oaa jrev rcepiexei 6 xpovoc,, xd jrev fjv, otov "Ouripoc, rcoxe fjv, xd 8e eaxai, otov xcov peMovxcov xi, ecp' onoxepa rcepiexer Kai ei ere' diicpco, djicpoxepa [Kai fjv Ka i eaxai]-oaa 8e |xf| rcepiexei jiTiSajifi, ovjxe fjv ovjxe eaxiv ovjxe eaxai. eaxi 8e xd xoiavJxa xcov ja.fi ovxcov, oacov xavxiKeijieva aiei eaxiv, otov xo davj(j,(aexpov etvai xfjv Sidpexpov dei eaxi, Kai O V J K eaxai XOVJX' ev XP0V(P-ovj X O I V V J V ov)8e xo avjiijiexpov 816 aiei O V J K eaxiv, oxi evavxiov xcp aiei ovxi. oacov 8e xo evavxiov jifi aiei, xavjxa 8e 8vjvaxai Kai etvai Kai jifi, Kai eaxiv yeveaic, Kai cpBopd avjxcbv. 1 6 0 Consequently it is obvious that not every non-being will be in time; for example, things that do not admit of being otherwise, such as the [purely hypothetical] being of a diagonal [of a square] that is commensurable with the side [of the square]. For if, on the whole, time in itself, on the one hand, is a measure of motion, and, on the other hand, [is a measure] of other things [only] incidentally, it is clear that for all those things for which it measures being, their being will be in being-at-rest or in being-moved. Thus, on the one hand, for things that pass away and come into being (i.e. [for things which], on the whole, at one time [are] being and at another non-being), it is necessary [for them] to be in time, because there is a greater time which exceeds both their being and the [time] measuring their beingness; but, on the other hand, of the non-beings which time encompasses, some were (e.g. Homer once was), and others will be (e.g. something about to happen): [time] encompasses [them] on whichever end (and if [the non-beings] both [were and will be], [then time encompasses them] on both ends). But whatever things [time] does not encompass in any way, they neither were, nor are, nor will be. And such things are [in the generic sphere of] non-beings: whatever has opposites that always are (e.g. the diagonal's being-incommensurable always is), this will not be in time (hence the [diagonal's] commensurability will not [be in time], due to the fact that it always is not because its opposite is always in being). And whatever does not have the "always-opposite", these things are able both to be and not [to be]: both coming-to-be and passing-away is theirs. Section Seven: Comparat tempus ad ea quae sunt in nunc. Quid significent nunc, iam, modo, olim et repente. [ Chapter 13 (To Be in the Now): Quomodo corruptio attribuatur tempori. ] The Now's Primary and Proper Signification: Horizonal Stretching (222a 10 - 13) Nunc continuat prateritum futuro, ut terminus praeteriti et principium futuri. To 8e vuv eottv rjuvexeta xpovou, cbarcep eAixQrr ouvexet ydp T O V xpovov xov rcapeXnA/oOoTcx K a i eaouevov, Kai Ttepac, xpovou eoxiv eoxi ydp T O U pev dpxf), T O U 8e xzkz\)%r\. bXka T O U T oox tocrcep eni Tfjc, OTtypfjc, pevouonq cpavepov. And the Now is a continuity of time, as was said,395 because it holds together [i.e. makes continuous] time past and future. And it is a limit of time, because it is the beginning of one part and the end of another. But this is not obvious, as it is with the point which stands still [on a line]. At 220a 4. 161 The Now's Primary and Proper Signification: Unity in Act (222a 14 - 19) Nunc dividit et continuat seu copulat tempus; dividit ut multa in potentia, unit ut idem. 8iaipeT 8e Suvdpei. Kai fj pev xoiouxo, aiei exepov xo vuv, fj 8e cruv8ei, aiei xo ai)xo, cbcraep erci xcov paGnpaxiKcov ypappcov (ou ydp fj auxfi aiei axiyp.fi xfj vofjaer 8iaipouvxcov ydp a.Xkr\ Kai dA,A,iy fl 8e pia, f| auxfi 7tdvxr|) -ouxco Kai xo vuv xo pev xou %povou 8iaipeaic, Kaxd 8uvap.iv, xo 8e rcepaq dpcpotv Kai evoxnc/ And [the Now] potentially divides. And, on the one hand, inasmuch as it does this, the Now is always different; on the other hand, inasmuch as it binds together, it is always the same: just as with mathematical lines (for a point is not always the same in thought, because dividing it is other and other, but, inasmuch as it is one, it is the same in every respect) so also the Now is, on one hand, a division of time along potency, but, on the other, the limit and union for both [parts]. The Now's Primary and Proper Signification: Actually the Same in the Subject, but Potentially Different in Account (222a 19-21) Nunc dividens et copulans est idem subiecto, differt ratione. eaxi 8e xauxo Kai Kaxd xauxo fj Siaipeaic, Kai fj evcoaiq, xo 8' etvai ou xauxo. xo pev ouv ouxco Xeyexai xcov vuv, And the division and the unity are [both] the same [act] and [horizonally stretched] along the same [thing], but [their] "to be" is not the same. Consequently, in one respect, is it said thus of the Nows [that they were "to be" to mark a horizon]. The Now's Secondary Signification: Being Stretched to Nearby Time (222a 21 - 24) Nunc significat secundario tempus (sive praeteritum sive futurum) propinquum praesenti nunc. aXko 8' oxav 6 xpovoq 6 xouxou eyyuq fi. fi^ei vuv, 6xi xfipepov fi^ei-T I K C I vuv, 6xi fjA,0e xfipepov. xd 8' ev >IX,icp yeyovev ou vuv, ou8' 6 KaxaKA/ooudc, [yeyove] vuv Kaixoi ouve^Tig 6 xpovoc, etc, auxd, a%X oxi O U K eyyuc,. 162 But, [it is said of Nows that they were "to be"] in another respect, whenever [the time to be "now"] may be near the time of this [time to be Now]. "He will come now," because he will come today; "he has come now," because he came today. But the things in the Iliad have not happened "now", nor has the Flood; assuredly, the time to these things is continuous, but because they are not nearby [they are not "now" because the Now marks them in the horizon of the past]. The Indefinite "Sometime": Limited in Relation to the Now (222a 24 - 28) TO 8e TCOTE< xpovoc, cbpia|ievoc; repot; TO rcpoTepov vvjv, otov TCOTC eA/fjcp6r| Tpoia, Kai rcoTS ecTai KaTaK^vjauoc/ 8ET yap rcercepdvGai rcpoc; TO VVJV. eaTai dpa rcoaoc; TIC; drcd TovjSe xpovoc, eig E K E I V O , K a i fjv eig TO rcapeXGov. But the time "sometime" is marked in relation to the primary [signification of the] Now. For example, "Troy was captured sometime" or "there will be a flood sometime." For [the time "sometime"] must have been limited in relation to the [present] Now. Therefore "there will be" a quantity [of time] from this time to that time [of the flood], or "there was" [a quantity of time from this time] to the past [time of the Trojan War]. The Indefinite "Sometime": Unlimited in Relation to Beginning and Ending Motion (222a 28 - b 7) ei 8e |xr|8eig xP o v °c , oc; or) TCOTB, rcag dv ein xpovog rcercepaauivog. ap' OVJV vjrtoA,ei\|/ei; fj ovj, ei'rcep aiei ecm Kivriaic;; bXkoc, OVJV fj 6 avjTog rcoAAocKig; SfjXov OTI cog dv f) Kivriaig, OVJTCO Kai 6 xpovog-ei (rev ydp fj ainrj Kai ixia yiyveTai rcoTe, eaTai Ka i xpovog etg Kai 6 avJTog, ei 5e ja.fi, OVJK eaTai. ercei 8E TO VVJV TEXEVTII Kai dpxfj %pb\ov, akX OVJ TOVJ avjTov), aXko. TOVJ jiEv rcapfJKOvTog T£X,£VJTf|, dpxfj 8E TOVJ u.EA,A,ovTog, EXOi dv coarcEp 6 KVjKXog EV TCO avjTco rccog TO KVJPTOV Ka i TO KOIXOV, OVJTCOC; Kai 6 X P ° V 0 ^ a £ i e v "PXTJ K a i TEA.£VJTTJ. Kai 8id TOVJTO SOKET dsi ETEpoq-ovj ydp TOVJ avjTofj dpxf| Kai TE^EVJTII TO vvjv dpa ydp dv Ka i KaTd TO afjTO TdvavTia dv ein. 163 Kai oux U7toXei\|/ei 8fV aiei ydp ev apxfl. But if [there is] no time which is not [spoken of as] "sometime,"396 then every time would be limited.397 Surely [time] shall therefore come to an end?398 Or [will it] not [ever end], if there is always motion?399 Then [will time be always] different or the same on many occasions?400 It is clear that as the motion would be, so too the time [shall be]. For if, on the one hand, one and the same [motion] occurs [limitlessly] "sometime," then time too will be one and the same. But, on the other hand, if [motion is] not [limitlessly one and the same], then [time] will not be. And since the Now is an end and a beginning of time, but not of the same [time] (rather, an end of the part having come past and a beginning of the part about to be), it would be in a state401 just like the circle in the same [place] is convex and concave. So too is time always in a beginning and an end. And through this [state] it always seems different. For the Now is not beginning and end of the same [time].402 Because [if it were] it would be opposite things simultaneously and along the same [thing].403 And [time] will not come to an end indeed. For it is always in a beginning. To Be "Presently": Proximity to the Present Now (222b 7-12) xo 8' f|8n< T O eyyuc, eoTi T O U rcapovToc, vuv aTopou uepoc, T O U peA,A,ovToq xpovou (rcoTE Pa8i£eic/, TJ8T|, O T I eyyuc, 6 xpovoc, ev cp iieXXei), K a i T O U 7rapeA/r)Xu96Toc, xpovou T O pf| 7t6ppco T O U V U V (rcoTe PaSi^ etc,; fj5r| Pepd8iKa). T O 5e "IA,iov (pdvat fj8n eaXcoKevai ou A.eyopev, O T I A,iav 7toppco T O U V U V . "Presently" is the part of time about to be which is near the present, indivisible Now ("When are you walking?" "Presently," because the time is near in which [the walking] is about to be) and the part of time past which is not far from the Now ("When are you walking?" "Presently I have walked"). But to say that Troy was "presently" conquered [is something that] we do not say, because it is too far from the Now. 3 9 6 Which must be the case if the secondary, unlimited signification of "sometime" is spoken with reference to the primary, limited signification of the Now. 3 9 7 Sachs clarifies the meaning by translating "every time will be of a definite extent" (127). 3 9 8 The question expects the answer "yes" because the assumption is that every time is limited. 3 9 9 The difficulty to be explored passim is that this second assumption leads to the conclusion ("time never ends") opposite to the conclusion ("time will end") which follows from the first assumption. 4 0 0 That is, will never-ending time be cyclical? 4 0 1 Literally, "how it would hold would be." 4 0 2 As Aristotle just said, it is the end of the past and the beginning of the future. 4 0 3 Sachs translates, "at the same time and in the same respect," but doesn't the "in the same respect" parallel the phrase used at 222 al9? 164 To Be "Lately", "Once", or "Suddenly": Proximity to the Present Now (222b 12 -15) Kai TO dpTi< TO eyyix; T O U rcapovToc, vuv [TO] popiov T O U 7tapeX,66vToq. noxe fj^Geq; dpTi, edv fj 6 xpovoq eyyuc, T O U eveaTCOTOc; vuv. naXai< 8e TO rcoppco. TO 8' e^ai(pvna< TO ev dvataGriTcp %povcp 8id piKpoTTua E K O T C C V "Lately" is a part of the past which is near the present Now. "When did you come?" "Lately," if the time is near the Now at hand. But "once" if [the time is] far [from the Now at hand]. And the "sudden" is that which is displaced in an imperceptible time through [the time's being the] the smallest [possible time] [and hence is nearest to the present Now]. Section Eight: Quomodo corruptio attribuatur tempori. Omnis motus et mutatio est in tempore. Time the Displacer: Incidentally a Cause of Coming into Being (222b 16 - 22) Tempori magis tribuenda corruptio, quia numerus mutationis per se tendentis ad corruptionem, cum sit recessus a dispositione prius habita peTaPoXfj 8e jcaoa (puaei eKcrraTiKov. ev 8e TCO xpovcp rcdvTa yiyveTai Ka i cpGeipeTav 8to Ka i oi pev oocpcoTaTov eXeyov, 6 8e IIuGayopeioc, ndpcov dpaGeaTaTov, cm Kai eni?iavGdvovTai ev TOUTCO , Xeycov opGoTepov. 8fjA,ov ouv O T I (pGopdc, \iQXko\ eaTat KaG' auTov aixio? ij yeveoecoc;, KaGdrcep eXexGn Kai npoTepov (eKCTTaTtKov ydp f| peTaPoXfj KaG' auTTiv), yeveoecoQ 8e Ka i T O U etvai KaTd oupPePnKot;. Every change is by nature a displacer. And in time everything comes into being and passes away: wherefore some used to say [it is] "the wisest thing," but the Pythagorean Paros, speaking more rightly, [used to say it is] "the stupidest thing," because in it they404 are forgotten. Consequently it is clear that in itself it will be more of a cause of passing away than coming into being,405 just as was also said before (because in itself change is a displacer) and [only] incidentally [is change a cause] of coming into being and the "to i.e. all things Entropy increases with time. 165 be." Time the Displacer: Incidentally a Cause of Passing Away (222b 22 - 27) Tunc tempori tribuitur corruptio, cum non manifeste apparet quid moveat ad corruptionem. O I I U E I O V 8e I K C X V O V O X I yiyvExai |xev O V J S E V dvevj xovj KivetaGai Tccog avjxo Ka i TcpaxxEiv, cpGeipexav 8e Kai |XT |8EV K I V O V J I T E V O V . Kai xafjxr|v ii.dX.iaxa A&yEiv EicbGajiev VJTCO xovj xpovou cpGopdv. ovj u,rjv dAA' O V J S E xafjxriv 6 xpovog TCOIET, dAAd av»ij.|3aivEi E V XP0VCP yiyvEaGai Ka i xavjxr|v xfjv ii.ExaPoA.fjv. And sufficient evidence [for this] is that nothing comes into being without somehow itself being-moved and being-an-agent,406 but [something] passes away and in no way is that which is moved. And especially this [extrinsic degeneration is what] we are accustomed to say is the "passing away wrought by time." But, truly, time does not [as agent] make this [passing away]. Rather, this change too407 comes into being in time incidentally. Epilogue: Things Said about Time and the Now (222b 27 - 29) Epilogus dictorum. oxi p.£v ovjv E O X I V 6 xpovog Ka i xi, Kai rcoaaxcbg AiyExai xo vvjv, Kai xi xo T C O X E Ka i xo dpxi Ka i xo fj5r| Kai xo 7tdA.ai Ka i xo e^ aicpvng, Eiprixai. Therefore, that time, then, is [a being], and what it is, and how many ways the Now is spoken of, and what "sometime" and "lately" and "presently" and "once" and "suddenly" are, has been said. [ Chapter 14 (Time and Motion): Omnis motus et mutatio est in tempore. ] A l l Motion is in Time: The Prior Accompanies, As "Faster" Change Presupposes (222b 30 - 223a 4) Quia in omni mutatione invenitur velocius et tardius, quae determinantur tempore. Tovjxrov 8' fjiiiv ovjxco 8vcopio|xevcov cpavEpov oxi 4 0 6 A l l generation involves the movement and action o f what is generated. But passing away is only extrinsically kinetic, not intrinsically, as coming into being is. 4 0 7 T ime was shown above to be incidentally a cause o f coming into being; here too it is shown to be an incidental cause, but this time o f passing away. 166 Tcdca UETaPoX/n. Ka i arcav TO KIVOUIIEVOV E V xpovcp. TO ydp GaTTOV Kai (3pa8rjTepov KaTd Tcdadv ecmv ii.ETaPoX.fjv (EV rcaai ydp OTJTCO cpaivETai)-Xiyco 8e GdTTOV KivEiaGai TO rcpoTepov peTapdX,Xov EIC, TO vjTCOKei|i.£vov KaTd TO afjTO SidoTnua Kai ouaX/ijv Kivriaiv KivovjpEvov (OlOV ETCl TTJC, CpOpdq, fil dllCpCO KaTd TfjV TCEplCDEpfj KlVElTai fj diicpco KaTd Tfjv EVjGEiav ouoicoc, 8E Kai ETCI TCOV dX,X,cov). And with these things thus thoroughly marked off for us, it is obvious that every change and any thing at all which is moved is in time. For the faster and slower is [predicated] along every change (because in all [of them] it is obviously so). And I say "being-moved faster" [is] "the prior change into the phenomenon along the same interval," i.e. moved [prior] by a uniform motion (e.g. in locomotion, i f both things are moved along a circumference, or both along a straight path, and similarly too with other [types of motion]). A l l Motion is in Time: The Prior is in Time (223a 4 - 15) Quia ad omnem motum sequitur prius etposterius quae dicuntur per distantiam ab ipso nunc quodpertinet ad tempus: in eodem est nunc et distantia ipsius. dXX,d pfjV TO YE TCpOTEpOV EV XpOVCp EOTV rcpoTEpov ydp Ka i vjaTEpov X,£yo|X£v KaTd Tfjv rcpoq TO vfjv drcooTaoiv, TO 8E VVJV opoq TOVJ TCapfJKOVTOq Kai TOVJ uiXXovTOC/ © O T ETCEI T O VVJV E V xpovcp, Kai TO rcpoTEpov Kai vjaTEpov EV XP 0 V CP eoxav E V co ydp TO VVJV, Kai fj TOVJ VVJV dTcooTaoiq. (EvavTicoc, 8E X,EyETai TO rcpoTEpov KaTd TE TOV rcapEX/nX/oGoTa xpovov Ka i TOV \izXkovxa-EV p.£v ydp TO) Tcap£X.r|X,V)G6Ti TCpOTEpOV XEyopEV TO TCOppCOTEpOV TOVJ VVJV, vJOTEpov 8E TO EyyvjTepov, EV 8E TCO uiX,X.ovTi TCpOTEpOV (XEV TO EyyVJTEpOV, VjOTEpOV 8e TO TCOppCOTEpOV.) cbfJTE ETCEI TO (J.EV TCpOTEpOV EV XpOVCp, icdori 8' dKoX,ovjGEi Ktvfjoei TO npoTEpov, cpavepov OTI Ttdoa ii.ETaPoX.fi Ka i rcdoa Kivriaiq EV xpovcp EOT IV. But surely, at least, the prior is in time. For we say "prior" and "subsequent" along the extension related to the Now, and the Now is the mark of that which has-come-by and 167 that which is-about-to-be. As a result, since the Nows are in time, the prior and subsequent will also be in time. Because in that in which the Now is, the extension from the Now is also. ("Prior" is spoken of in opposite ways along both the time which has-gone-by and [the time] which is-about-to-be. Because, on the one hand, for that which has-gone-by, we say the farther from the Now is "prior" and the nearer "subsequent," but for that which is-about-to-be, the nearer is "prior" and the farther "subsequent.") As a result, since, on the one hand, the prior is in time, and [since], on the other hand, in all motion, the prior accompanies, it is obvious that all change and all motion is in time. Section Nine: Solvuntur dubitationes circa existentiam et unitatem temporis. Time's Constitution: The Soul and Everything (223a 16 - 18) oc^tov 8' £7UCTKev|/8coc, K a i rccoc, 7tox£ z%ei 6 xpovoc, rcpoc, Tf|v \|/uxfiv, K a i 8td T i ev 7tavTi S O K E I etvai 6 xpovoc,, K a i ev yfi K a i ev 6aA,aTTT| K a i ev oupavcp. And worthy of inquiry too is how time is constituted with regard to the soul, and [how] through time some [time] seems to be in everything: on the earth and in the sea and in the sky. Time's Constitution: Relation to Motion (223a 18 - 21) fi O T I Kivfiaecbq Tt 7td0oc, ri e^iq, d p i 8 p o q ye cov, xama 8e K i v n T d mxvTa (ev T07tcp y d p navta), 6 8e XP 0 V 0 C, K a i Tl Kivncic, d p a K a T d Te 8uvap.iv K a i K a T evepyeiav; [Is it] because [time is] some attribute or state of motion ([since] it is at least number [of motion]), and all of these things [i.e. earth, sea, sky] are movable (because all are in place), and time and motion are simultaneous along potency and act? [Yes.] Time's Existence: Relation to the Soul Still an Aporia (223a 21 - 22) rcoTepov 8e p.tj ovcnc, i|/uxf|c, ein d v 6 xpovoc, ii ou, d7topf|oeiev d v T IC, . But [still] one might be flummoxed about whether if the soul were not, time would be or not. Time's Existence: Counting, Number and the Soul (223a 22 - 26) 168 dSuvdTou ydp O V T O C , etvai xov dpi9pfjaovToc, advvaxov Ka i dpi9p.nT6v T I etvai, cboTE 8fjA,ov O T I ou8' dpiGuoc,. dpi9u\6c, ydp fj T O fjpi9p.r|uivov ii T O dpi9p.r|T6v. ei 8e (xr|8ev dA,A,o rcetpuKev dpi9u.etv fj i|/uxfl 9Kai yoxfjc, vovq, advvaxov etvai xpovov yuxfjc, pfj ouan<;, For if it is impossible for there to be a counter, then it is impossible for anything to be counted. It is clear that as a result neither [would there be] number. Because number is either that which has been counted or that which is to be counted. But if nothing else has the nature to count other than the soul and the soul's intellect, then it is impossible that time be if the soul is not. Time's Existence: Order, Motion and the Soul (223a 26 - 29) aXX' tj T O U T O 6 rane 6v ecmv 6 xpovoq, otov ei ev8exeTai Kivnaiv etvai dveu yuxfjc,-T O 8e rcpoTepov K a i uaTepov ev Kivtiaei eaTiv Xpovoc, 8e TauT ecmv fj dpi9ur|Td ecmv. Unless this [is the case]: time is that which it is "being" at some time. For example, if it is possible for motion to be without the soul. But the prior and subsequent are in motion, and, inasmuch as they things counted, they are time. Time's Number of Motion: Quality of Motion (223a 29 - 30) d7topfiaeie 8' dv T K ; K a i rcoiac, Kivfjaetoc, 6 xpovoc; dpiOpoc,. But [still] one might be flummoxed about what sort of motion time is number [of]. Time's Number of Motion: Quality is Continuous, not of a K i n d (223a 30 - 223b 1) ii orcoiacjouv; K a i ydp yiyveTai ev XP0VCP K ( x l <p9eipeTai K a i au^dveTai K a i dA,A,otouTai K a i (pepeTar fj ouv KivncFic, ecm, TauTn eoTiv eKdoTriq Kivfjaecoc, dpi9poc,. 816 Kivfjaecbi; eaTiv archaic, dpi9po<; cuvexouc,, aXX' ov Tivoq. Or [is time a number of] any kind [of motion] whatsoever? For in time a thing comes into being and passes away and grows and alters and changes place [i.e. these are the kinds of motion]. Therefore, inasmuch as [anything] is motion, by this much [time] is number of each motion. Wherefore it is simply number of continuous motion, not of some [kind of motion in particular]. 169 Simultaneous Motion: Simultaneous Times? (223b 1-3) aXX' EOTi VVJV KEKivfjcGca Kai aXXo-cov EKaTEpac, Tfjc, Kivfjaecoc, ei/n, dv dpiGpoi;. ETEpOQ OVJV %pOVOC, EOTIV, K a i aua 8vjo 1001 xpovoi dv E I E V But it is also [possible that] something additional is being-moved now, and of these two things [being moved] there would be number of each motion. Therefore, is there another time, and would two equal times be simultaneously? Simultaneous Motion: Simultaneous Numbers (223b 3-12) fj ovj; 6 avjToc, yap xpovoc, K a i Etc, 6 i'aoc, K a i dpa-ei8et 8E K a i oi uf| ajxa-EI ydp EIEV KVJVEC,, oi 8' ITCTCOI, EKaTEpoi 8' EicTd, 6 avjToc, dpiGixoc,. OVJTCO 8E Ka i TCOV KivfjaEcov TCOV dpa TCEpaivouivcov 6 afjToc, xpovoc,, 6.XX' fj U E V Taxeta IOCOC, fj 8' ovj, Kai fj [rev cpopd fj 8' dXAoicorjic/ 6 U.EVT01 xpovoq 6 avjTO<;, EI'TCEP K a i [6 dpiGpoa] looq K a i dira, Tfjc, T E dXAoicboEcoc, K a i Tfjq cpopaq. K a i 8id TOVJTO a i iiev KIVTJOEK; ETEpai K a i x^Pt^-6 8E xpovoq rcavTaxovj 6 avnoc,, OTI K a i 6 dpiGiroq EIC, K a i 6 avjxoq rcavTaxovj 6 TCOV iocov K a i dpa. Or not? Because equal and simultaneous time is one and the same. And even those [times] not simultaneous and in the same species. For if there were dogs and horses, and [there were] seven of each, the number would be the same. So also with motions limited simultaneously is time the same, even if perhaps one motion is faster and the other is not, or if one is locomotion and the other is alteration. Surely the time of both the alteration and the locomotion is the same, especially if it is equal and simultaneous. And on account of this, on the one hand, motions are distinct and separate, and on the other hand, time is everywhere the same, because the number is one and the same everywhere for the number of what is equal and simultaneous. Measuring Time and Motion: Mutual Determination of Quantity (223b 12 - 18) excel 8' E O T I cpopd Kai TavJTTic, fj KVJKXCO, dpiGuEttai 8' eKaoTOV evi TIVI cuyyeveT, uovdSec, uovdSi, ITCTCOI 8' ITCTCCO, OVJTCO 8e K a i 6 xpovoc, XP 0 V C 9 T l v t cbpiap,evcp, 170 (xexpetxai 8', cborcep eircopev, 6 xe xpovoc, Kivfjoei Ka i fj Kivfjaic, XP0VCP (xofjxo 8' eaxiv, oxi fjrco xfjc, cbpiaixevTn; Kivfiaecoc; XP0VC9 M-expetxai xfjc; xe Kivfjaecoi; xo rcoaov Ka i xof) xpovou)-And since there is locomotion, and, of this, motion in a circle, and each thing is numbered by some one thing of the same kind (units by units, horses by a horse), so too is time also marked off by some time, and, as we said, time is measured by motion and motion is measured by time. (This is because [it is] by the motion marked off in time [that] both the quantity of motion and the quantity of time is measured.) Measuring Time and Motion: Uniform Circular Locomotion (223b 18-21) ei OVJV xo rcpcbxov uixpov rcdvxcov xcov auyyevcbv, fj KDKAocpopia fj ouaXfjc; pexpov (idAaaxa, oxi 6 dpiGuoc; 6 xavjxric; yvcopurcbxaxoc,. dXAoicoaic, p.ev ofjv oi)8e afj^ riaic; ofj8e yeveaic; OVJK eiaiv 6|a.aX,ei<;, cpopd 8' eaxiv. If then the first measure [is a measure] of all things of the same kind, uniform circular motion is a measure most of all, because the number of it is most recognizable. On the one hand, neither alteration nor growth nor coming into being is uniform, but, on the other hand, locomotion is. Time's Circularity: Mutual Determination of Time and Motion (223b 21 - 23) 816 Kai SOKEI 6 xpovoc; eivai fj xfjc, acpaipac; Kivriaic;, oxi xafjxri (j.expov3vxai ai aXXai Kivfjaeic; Kai 6 XP 0 V 0? TOCVJTTI xf\ Kivfjaei. Wherefore time also seems to be the motion of the sphere [of the universe]; because by this [motion] the other motions are measured, and time too by this motion. Time's Circularity: Circuits and Measurement (223b 23 - 224a 2) 8id 8e xofjxo Kai xo eicoGoc; XeyeaGai aunfJaivev cpaaiv ydp KVJKXOV eivai xd dvGpcbrciva rcpdypaxa, Kai xcov aXXxov xcov Kivnaiv exovxcov cpuaiKijv Kai yeveaiv Ka i cpGopdv. xofjxo 8e, oxi xafjxa rcdvxa xcp XP0VCP Kpivexai, Kai Xau|3dvei xeA,ei)xfjv Ka i dpxfjv cbarcep dv ei Kaxd xiva rcepio8ov. 171 Kai ydp 6 xpovoc, auxoc, etvai S O K C I KUKAXX ; X I C / xouxo 8e 7idA,iv 8oKei, 816x1 xoiauxng eaxi cpopaq pexpov Kai pexpetxai auxoc, U7T6 xoiauxnc,. cbaxe xo Xeyeiv etvai xd yiyvopeva xcov rcpaypaxcov K U K X O V xo Xeyeiv eoxiv xou xpovou etvai xiva K U K ^ O V xouxo 8e, oxi uexpetxai xfj KUK^ocpopicr rcapd ydp xo pexpov ou8ev aXXo rcapepcpaivexai xcp pexpouuivco, aXX' TJ 7tX,eico pexpa xo 6Xo\. And from this comes the thing customarily said: They say that human affairs are a circle, as well as things having motion naturally, i.e. coming-into-being and passing-away. But this is because all these things are judged by time and reach an end and a beginning as if along some circuit. For time too seems to be itself a circle. And this in turn seems to be so because it is a measure of such locomotion and itself is measured by such [locomotion]. As a result, to say that the coming-into-being of [human and natural] affairs is a circle is to say that time is some circle. But this [is the case] because [time] is measured by circular motion. For, apart from the measure, nothing else shows itself alongside that which is being measured. But the whole [of time] is nothing other than a number of measures. Time's Number: Counting and Counted (224a 2-17) Xeyexai 8e opGcoc, Kai oxi dpiGpoc, pev 6 auxoc, 6 xcov 7tpo(3dxcov Kai xcov K U V C O V , ei iooc, eKdxepoc,, 8eKdc, 8e oux T\ auxfi ou8e 8eKa xd auxd, cbarcep ou8e xpiycova xd auxd xo iaorcXeupov Kai xo o~KaA,nve<;, Kaixoi CTxfjpd ye xauxo, oxi xpiycova dpcpco-xauxo ydp X,eyexai ou pr) Siacpepei Stacpopd, aXX' ouxi ou 8iacpepei, otov xpiycovov xpiycbvou xpiycbvou 8ia<popd 8ia(pepev xoiyapouv exepa xpiycova-axfpaxoc, 8e ou, aXX' ev xfj auxfj 8iatpeoei Kai pad. oxfJM-« ydp xo pev xotov8e K U K X O C , , X O 8e xoiovSe xpiycovov, xouxou 8e xo pev xoiov8e iCT07tX,eupov, xo 8e xoiovSe OKaA/nvec,. CTxfjpa pev ouv xo auxo, Kai xouxo xpiycovov, xpiycovov 8' ou xo auxo. Kai dptGpoc, 8fj 6 auxo<; (ou ydp 8iacpepei dpiGpou Siacpopa 6 dpiGpoc, auxcov), SeKdc, 8' oux f| auxfj-eq>' cov ydp Aiyexai, Siacpepev xd pev ydp K U V C C , , xd 8' 'innoi. Kai Ttepi uiv xpovou Kai auxou Kai xcov 7tepi auxov oiKeicov xfj aKe\|/ei eipnxai. It is also rightly said that the number is the same of sheep and of dogs if the two are equal, but not the same [counted number] ten nor the same ten things, just as the equilateral and the scalene are not the same triangle, though surely they are at least the 1 7 2 same figure, because both are triangles. For things are called the same with regard to how they do not differ by difference, not with regard to how they differ; for example, as one triangle differs from another triangle by the difference of a triangle: this is how triangles are distinct. But [they do] not [differ] by figure, but are in one and the same division [of figure]. For one kind of figure is a circle, another a triangle, but one kind of the latter is equilateral, another scalene. Therefore they are the same figure, i.e. this [figure of] triangle, but the sameness is not [predicated] of the triangles [but just of the figure]. And the number is the same (for the number of them does not differ by a difference of number) but is not the same [counted number] ten, because the things of which it is said differ (some are dogs, others are horses). The topic of time itself, and the things proper to the inquiry about it, has been addressed. 173 C O N C L U S I O N In this study, we have defended the Aristotelian-Thomistic theory of the abstractive induction of immediate first principles and of the methodology of a priori demonstrations from immediate first principles. We have attempted both to expound the Aristotelian methodology of demonstration from principles (as it is found in actu signato in Aristotle's Posterior Analytics), and to defend examples of it (as found in actu exercito in Aristotle's Physics). In Chapter I, we outlined the Aristotelian methodology of demonstration. We set forth (in 1.1) that Aristotelian science is certain knowledge through causes and effected by demonstration. We argued that Aristotelian science is a species of knowledge distinguished by three differentiae: certain, causal, and demonstrative. We explained (in 1.2) how the certain character of Aristotelian science is derived from how it employs proper causes in the syllogism. Proper causes are neither effects nor remote causes. An a posteriori demonstration uses an effect as its middle term (e.g. the effect "not breathing" can be used to explain why a wall does not have lungs); however, an a priori demonstration uses a cause as its middle term. But there are two types of a priori demonstration: quia and propter quid. A demonstration quia uses a remote cause as its middle term (e.g. the remote cause "not living" can be used to explain better why a wall does not breathe). But a demonstration propter quid uses a proper cause as its middle term (e.g. the proper cause "not having lungs" can be used to explain best why a wall does not breathe). The certainty of scientific demonstration is thus ordered according the order of its predication of cause and effect. The most certain scientific demonstrations are demonstrations propter quid. 174 We explained (in 1.3) how the middle terms of demonstrations can be principles, elements or causes. The middle term of a propter quid demonstration has to be a per se cause and not a per accidens principle or element. Aristotelian science, therefore, demonstrates through causes (not incidental principles or elements), i.e. it demonstrates through causal middle terms. We explained (in 1.4) how demonstration can occur according to the order of causality among the four Aristotelian causes. This implied a hierarchy of distinct types of demonstration, the schema of which we set forth.408 We discussed (using the example of a scientific discussion of the circulation of the blood) how the ordination of causality in a demonstration expresses what is nota per se. The real relation of subject and predicate to the causal middle term is thus known according to the order of causality. This observation clarified how Aristotelian science is demonstrative, i.e. effecting knowledge of what cannot be otherwise, because it reasons from premises more certain quoad nos to conclusions more certain quoad se. In Chapter II, an attempt was made to clarify how the abstractive induction of universals is related to the per se nota principles of demonstration. We argued (in 2.1) using the example of hellebore, in order to illustrate how the schema of demonstration is to be understood as regards this problem. We argued that reasoning from immediate first principles is neither circular nor necessitating an infinite regress. We translated and commented upon Aristotle's classic account of abstrative induction in the last chapter of the Posterior Analytics, and we mined the insights of Themistius on this chapter by also 4 0 8 See Table 6 175 translating his commentary (in 2.2). In Chapter III, the a priori demonstrations in the Physics about motion, place, and time were treated. Controversies about Aristotle's definitions of motion and place were engaged. We applied (in 3.1) the schema of demonstrations to an exegesis of Aristotle's demonstration about motion in the Physics. We defended the commentary of Aquinas on this text, arguing that Aquinas fathoms Aristotle's formal definition of motion, and best accounts for its references to potency and act. We explained (in 3.2) how metaphysics, physics, and mathematical physics are related to the problem of space. Strictly speaking, mathematical physics alone deals with the concept of space, and metaphysics is concerned only with the category "where"; physics, however, is concerned with place. We argued that Aristotle's Physics contains the proper formal definition of place, and we defended Aristotle from the charge that his definition employs "immobility" as an otiose requirement. We indicated (in 3.3), along with a fresh translation, how the structure of Aristotle's discussion of time is ordered and which types of demonstration it uses. We conclude, therefore, that Aristotle's Physics should be confused neither with mathematical physics, nor with metaphysics. A proper appreciation of Aristotelian methodology opens new vistas on the truly scientific rigour of this work. Aristotle's Physics stands, in the light of its own principles, as a Kifjua eq aiei.409 Thucydides, 1.22 176 Bibliography A. Primary Sources (Abbreviations) Aristotle and St. Thomas Aquinas are the primary sources. The following abbreviations are used in the footnotes to denote Aristotle's works, usually with Bekker references in addition, or with book and chapter. Cat. = Categoria De Int. = De Interpretatione An. Pr. = Analytica Prior a An. Post. = Analytica Pos teri or a Phys. = Physica D.A. = De Anima Meta. = Metaphysica N.E. = Nichomachean Ethics The same abbreviations are used for Aquinas' commentaries on Aristotle, but with a Roman numeral in front, indicating the number of the book upon which Aquinas is commenting, e.g. II Phys. = Commentary on the Second Book of Aristotle's Physics. (Also, for Aquinas, De Prin. Nat. = De Principiis Naturae.) Any references to particular editions of Aristotle or Aquinas that use the editor's or translator's surname, along with the date of the edition in brackets, are referring to those works listed below in A.l. and in A.2. Note that both these lists, as well as those in B. below, have two dates; the first, in parentheses, refers to the print or reprint date of the edition consulted (sometimes along with an alphabetical suffix, if the author or editor published more than one work in that year), and the second, not in parentheses, but at the end of the bibliographical information, indicates the year that the first edition was published. In the cases of multiple reprint editions, these dates are different from those in brackets. 177 A . l . Aristotle (Texts and Translations) Apostle, Hippocrates G. (tr.) (1980) Aristotle's Physics. Grinnell, Iowa: Peripatetic Press, 1969. Apostle, Hippocrates G. (tr.) (1981) Aristotle's Posterior Analytics. Grinnell, Iowa: Peripatetic Press, 1981. Barnes, Jonathan (tr.) (1975) Posterior Analytics. Oxford: Clarendon Press, 1975. Barnes, Jonathan (tr.) (1994) Posterior Analytics, Second Edition. Oxford: Clarendon Press, 1994. Charlton, W. (tr.) (1970) Aristotle's Physics, Books I and II. Oxford: Clarendon Press, 1970. Hardie, R.P. and R.K Gaye (trs.) (1930) Physics. Oxford, 1930. Hope, Richard (tr.) (1961) Aristotle's Physics. Lincoln, Nebraska: University of Nebraska Press, 1961. Hussey, Edward (tr.) (\983) Aristotle's Physics, Books III and IV. Oxford: Clarendon Press, 1983. Ross, William David (tr.) (1927) Posterior Analytics. In Aristotle - Selections. New York, 1927. Ross, William David (ed.) (1950) Aristotelis Physica. Oxford: Clarendon Press, 1950. Ross, William David (ed.) (1964) Aristotelis Analytica Priora et Posteriora. Oxford: Clarendon Press, 1964. Sachs, Joe (tr.) (1995) Physics. New Brunswick, New Jersey: Rutgers University Press, 1995. 178 Tredennick, Hugh (tr.) (1989) Posterior Analytics. Cambridge, Massachusetts: Harvard University Press, 1960. Warrington, John (tr.) (1967) Posterior Analytics. London: 1967 Waterfield, Robin (tr.) (1996) Aristotle Physics, With an Introduction and Notes by David Bostock. Oxford: Oxford University Press, 1996. 179 A.2. St. Thomas Aquinas (Texts and Translations) Anonymous (edd.) (1988) Summa Theologiae. Editio altera paululum emendata. Torino, Italy: Edizione Paoline, 1988. Blackwell, Richard J., Richard J. Spath, and W. Edmund Thirlkel (trs.) (1963) Commentary on Aristotle's Physics. New Haven: Yale University Press, 1963. Bobik, Joseph (tr.) (1998) Aquinas on Matter and Form and the Elements. A Translation and Interpretation of the De Principiis Naturae and the De Mixtione Elementorum of St. Thomas Aquinas. Notre Dame, Indiana: University of Notre Dame Press, 1998. Fathers of the English Dominican Province (trs.) (1920) Summa Theologica. Westminster, MD: Christian Classics, 1920. Larcher, F.R. (tr.) (1970) Commentary on the Posterior Analytics of Aristotle. Albany, New York: Magi Books, 1970. Maggiolo, P.M. (ed.) (1954) S. Thomae Aquinatis In Octos Libros Physicorum Aristotelis Expositio. Turin, Italy: Marietti, 1954. Oesterle, Jean T. (tr.) 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Weisheipl, James Athanasius, O.P. (ed.) (1980a) Albertus Magnus and the Sciences: Commemorative Essays 1980. Toronto: Pontifical Institute of Mediaeval Studies, 1980. 191 Weisheipl, James Athanasius, O.P. (1980b) Thomas d 'Aquino and Albert His Teacher. The Etienne Gilson series 2, 6 March 1980. Toronto: Pontifical Institute of Mediaeval Studies, 1980. Weisheipl, James Athanasius, O.P. (1982) "The Interpretation of Aristotle's Physics and the Science of Motion." In Kretzmann-Kenny-Pinborg (edd.) (1982), 521-536. Weisheipl, James Athanasius, O.P. (1985) Nature and Motion in the Middle Ages, Studies in Philosophy and the History of Philosophy 11. Washington, D.C: Catholic University of America Press, 1985. White, Michael J. (1996) "Concepts of Space in Greek Thought." [Review of Algra (1995)]. Apeiron 29 (1996), 183-198. 192 Appendix I: Aristotle's Perennial Physics Why study Aristotle's Physics? In the popular view, the successes of modern science render it obsolete. Today, no one interested in knowing natural phenomena begins with Aristotle. Moreover, in the popular view, Galileo, who fought against Aristotelians and the authority of Aristotle, is modern science's hero and martyr.410 He became the father of modern science because (so the story goes) he challenged not just the authority of the Church in Scriptural exegesis, which allegedly held back scientific progress, but also the authority of Aristotle in natural science, which allegedly did likewise. Among scholars, those approaching Aristotle's Physics do not treat it as a locus of permanent truths about natural science. In historical studies, the diverse forms of Aristotelianism that struggled with this obscure and difficult text are studied as sandcastles in the sands of time. In philosophical studies, these Aristotelian traditions are not mined to solve any difficulties in exegesis. Instead, Aristotle is measured primarily against the theories of the day. Scholars busy themselves with finding flawed arguments and cataloguing errors or difficulties in Aristotle's outdated Physics *n The popular prejudice that Arisotle is outdated is well received among scholars, whether philosophers or scientists. Philosophers, on the one hand, can read the Physics merely as a collection of stimulating errors, about which they publish studies for a very small audience. Scientists, on the other hand, need not bother with the Physics at all, because Galileo has freed them from antediluvian philosophical reasoning, and freed them for experiment and for the mathematization of nature, the technological benefits of 4 1 0 Machamer (1998), 388. 193 which are obvious to a wide audience. In short, modern scholars, philosophers or scientists, with professional hindsight, know that they know better than Aristotle — because the philosophers know, at least, when Aristotle is wrong; and scientists, no longer needing to contend that Aristotle is wrong, simply look to their own practice of science to know when they are right.412 Our intent in this study has been to stand opposed to these dominant views about Aristotle's Physics, and to offer now uncommon, but nevertheless traditional, interpretations of Aristotle that actually resolve four difficulties in his science of nature known to Aristotle scholars — principles, motion, place, and time. These uncommon interpretations were based on evidence now available from historical studies recently made by others in science and Aristotelianism.413 On the one hand, contrary to the common views, both popular and academic, we consider the Physics to contain permanent truths about nature, and therefore hold that it is not obsolete, but rather the permanent possession of science in any age.414 We orient ourselves in general within the Aristotelian-Thomistic tradition that preserves this view, 4 1 1 Cf. Charlton (1970), Hussey (1983), and Bostock in Waterfield (1996). 4 1 2 Cf. Einstein-Infeld (1966), 6-7: "The method of reasoning dictated by intuition was wrong and led to false ideas of motion which were held for centuries. Aristotle's great authority throughout Europe was perhaps the chief reason for the long belief in this intuitive idea.... The discovery and use of scientific reasoning by Galileo was one of the most important achievements in the history of human thought, and marks the real beginning of physics. This discovery taught us that intuitive conclusions based on immediate observation are not always to be trusted, for they sometimes lead to the wrong clews." 4 1 3 In particular, the studies by James A . Weisheipl and William A . Wallace. See our bibliography below. 4 1 4 Cf. Adler (1964), 15: "I get angry at the so-called orthodox Aristotelians who read Aristotle as if every word were true. In Aristotle, science, philosophy, and religion are confused. Since Aristotle doesn't know their distinctions, they are all inchoately mixed." We suggest "orthodox Aristotelianism" is a caricature invented by those who prefer their own dubious distinctions to Aristotelian methodolgy; e.g. Adler asserts, "The fundamental characteristic of any science [as opposed to philosophy] is that it investigates." Ibid, 8. We agree with Wallace (1957), 118, that any opposition between philosophy and science is a mistake. 194 and in particular we draw upon the recent River Forest school,415 which works within this tradition, that sheds light, through its emphasis on particular points made by Aquinas, on the four problems examined in this thesis.416 On the other hand, contrary to the dominant views, both popular and academic, we consider Galileo's innovations in mathematical physics not to have overturned Aristotle's natural science, but to be part of a tradition in fundamental continuity with it.417 This latter point assumes importance for our studies here, because the traditional interpretation of Aristotelian demonstration that in fact influenced Galileo lies behind all four of our studies in Aristotle's Physics. A full appreciation of the Aristotelian methodology of demonstration, and its history, disposes of the common opinion that Aristotle is irrelevant for the actual method and practice of modern science. Galileo, in other words, can no longer be seen as Aristotle's antithesis.418 The traditional understanding of Aristotelian methodology and its employment in natural science, which today is either forgotten or poorly understood, is capable of handling the most difficult objections to Aristotle's Physics. The permanent value of Aristotle's science can be affirmed, and this is what we have attempted, in a small way, in our study. 4 1 5 See Appendix III below. 4 1 6 Cf. Adler (1964), 2: "But unfortunately there are other positions taken by Catholics. I am thinking in particular of the work that is being done at the Albertus Magnus Lyceum in River Forest, Illinois, where the natural sciences are seen as continuous with the philosophy of nature. By various turns and tricks with Thomistic apparatus, the natural sciences are assimilated to philosophy and made continuous with it." In our four studies here we hope at least indirectly to show that Adler has misjudged River Forest. 4 1 7 See Appendix II below. ' 4 1 8 Cf. Einstein-Infeld (1966), 52: "Science connecting theory and experiment really began with the work of Galileo." 195 Appendix II: Galileo's Early Notebooks On September 14, 1640, Galileo, near the end of his life,419 wrote to his friend r Fortunio Liceti, "I consider (and I believe you do too) that to be truly a peripatetic - that is, an Aristotelian philosopher - consists principally in philosophizing according to Aristotelian teachings, proceeding from those methods and with those true supposizioni and principles on which scientific discourse is founded, supposing (supponendo) the kind of general knowledge from which one cannot deviate without the greatest defect. Among these supposizioni is everything that Aristotle teaches us in his logic, pertaining to care in avoiding fallacies in discourse, using reason well so as to syllogize properly and deduce from the conceded premises the necessary conclusion, and all this teaching relating to the form of arguing correctly. As to this part, I believe that I have learned sureness of demonstration from the innumerable advances made by pure mathematicians, never fallacious, for if not never, then at least very rarely, have I fallen into mistakes in my argumentation. In this matter, therefore, I am a peripatetic."420 On the one hand, these words can be interpreted as bitter and sarcastic. On the other hand, early manuscripts of Galileo have been discovered showing the substantial influence on his early period of the progressive Aristotelianism of the Collegio Romano, the Jesuit university in Rome.421 MS. Gal. 27 was written probably in 1589, when Galileo was teaching or preparing to teach at the University of Pisa, and it contains a treatise on demonstration, appropriated from a course on Aristotelian logic and methodology taught in 1588 by Paulus Vallius, S.J., at the Collegio Romano.422 Aristotelians at the University of Padua in the fifteenth and sixteenth centuries had developed a distinctive refinement of Aristotelian methodology, known as the demonstrative regress (regressus 4 1 9 Seven years after the tragic trial of 1633, and three years after he founded his new science of motion in the 1638 book, Due nuove scienze. Cf. Wallace (1983), passim. 420 Le Opere di Galileo Galilei, Antonio Favaro (ed.), 18:248, as translated in Wallace (1981), 75. 4 2 1 Wallace (1984), passim. 196 demonstrativus), which Galileo learned from the Jesuits and creatively applied throughout his career.423 There is evidence, then, that Galileo's nuovo scienza is in essential continuity with the ideal of scientia as set out in Aristotle's Posterior Analytics. And even if the topic will always be controversial,424 there is a textual basis that shows that this continuity thesis is not inconsistent with any polemics against Aristotelians in Galileo's writings. The sixteenth-century Aristotelians, emulating Aristotle, had searched for causes, but had brought upon themselves Galileo's wrath because they had stopped short in their inquiry for true causes, which Galileo was in fact unveiling in his proposed "new science."425 Galileo's logic of science and discovery, then, need not be read as opposed to Aristotle,426 but instead, when read in the context of his creative appropriation and expansion of the Aristotelian tradition,427 it can open the door to a greater self-understanding on the part of modern science. It is possible to contend therefore that Aristotelian methodology is not incompatible with, but rather illuminates and places in context, the achievement of modern science as "the addition of new methods and discoveries to the still valid ancient methods and discoveries."428 If, in the light of recent scholarship, it can be seriously contended that Galileo's contributions did not overturn Aristotle's Posterior Analytics, but were rather part of the 4 2 2 Wallace (1996), 300. In MS Gal. 46, difficulties in the De caelo et mundo and the De generatione et corruptione are treated in the light of books and lecture notes from Jesuits at the Collegio Romano: Wallace (1977), passim. 4 2 3 Cf. Galilei (1988), translated in Wallace (1992b). Wallace traces Galileo's use of the demonstrative regress throughout his career in Wallace (1992a), 194-295, and in Wallace (1996), 300-308, 334-350. 4 2 4 Wallace (1984), 347. 4 2 5 Wallace (1972), 184. 4 2 6 Wallace (1992a), 1-187. 197 Western tradition that draws sustenance from them, then it becomes imperative to understand this Aristotelian text, and its interpretations in history, in order to judge properly Aristotelian natural science and its validity. It was first Albertus Magnus, and then his student Thomas Aquinas, who gave the decisive impetus to the influence of Aristotle in the West, and made Aristotle fundamentally accessible for all subsequent Aristotelianisms,429 including those which shaped Galileo and those with which he contended.430 Aquinas is recognized as one of the best commentators on Aristotle, if not the best, and his comprehension of the Posterior Analytics informed all of his teaching, not just the structuring of the questions in his Summa Theologiae, but also his exposition of the structure of reasoning in all the Aristotelian works upon which he commented.431 7 Wallace (1992b), passim. 8 Weisheipl (1964), 86. 9 Wallace (1982), Weisheipl (1959), Weisheipl (1974), Weisheipl (1980a), Weisheipl (1980b). 0 Wallace (1981a), Wallace (1984), Wallace (1992a). 1 Wallace (1982), 15. 198 Appendix III: Aquinas and the River Forest School A recent school within the Thomist tradition, the River Forest school, has most emphasized the contribution of Aristotelian methodology to natural science. From 1939 to 1969, the Dominican Fathers of the Chicago Province operated the Pontifical Faculty of Philosophy of Aquinas Institute of Theology in River Forest, Illinois (a suburb of Chicago). William H. Kane worked there, with Raymond J. Nogar and Benedict M. Ashley, to found an Albertus Magnus Lyceum for the study of the relation between philosophy and science. From this school, William A. Wallace and James A. Weisheipl have produced especially compelling readings of Aquinas in his historical context, emphasizing the importance of Aristotelian methodology and natural science for an authentic understanding of Aquinas.432 The main theses of this school of Thomism can be summarized as follows:433 1. Aquinas' philosophy is found foremost in his commentaries on Aristotle. 2. Aquinas is a convinced Aristotelian, subjecting any Platonizing in epistemology or metaphysics to Aristotelian methodology. 3. Aquinas' order of the sciences is of paramount importance for correctly interpreting his metaphysics (i.e., natural philosophy must come first in the order of abstraction). 4. Any opposition between "empirical" science and "rational" philosophy inadequately appreciates Aquinas' natural science and, moreover, shows an 4 3 2 Ashley (1991), 1-2. 4 3 3 The following eight theses are our condensation of the summary in Ashley (1991), 2-15. We omit an account of the differing emphases of other schools of Thomism. We note that none of these theses are in 199 unhistorical understanding of modern science. 5. To understand Aristotle on natural science, one must properly understand the Organon, especially the Posterior Analytics, which is Aristotle's philosophy of science. Aquinas knew this well. 6. Galileo's polemics have created a confused self-understanding in modern science. Mathematical formal causes are emphasized, final causes denigrated, and efficient causality is conceived narrowly in terms of mechanism and measurement. Skepticism about genuine empirical certitudes is rampant. 7. The particular details of natural science in Aristotle and Aquinas are obsolete, but their general foundational analysis is not. 8. Neither metaphysics nor theology can rectify modern science's inadequate appreciation of its own foundation in Aristotelian logic and natural science. The inadequate appreciation of the difference between a priori and a posteriori deductions in natural science leads to confusion about mathematical physics' true place in the architectonic of knowledge and its level of certainty. Galileo himself, despite his genius in advancing the scientia media of mathematical physics,434 overestimated the level of certitude involved in his reasoning on Copernican astronomy and tidal theory, and unwittingly bequeathed a distorted view of Aristotelian methodology to modern 435 science. opposition to the "The Twenty-Four Thomistic Theses" of the Sacred Congregation of Studies (1914); they are, in our opinion, hermeneutical complements to those doctrinal norms. 4 3 4 Cf. Wallace (1998), passim. 4 3 5 Ashley (1991), 8-9. Cf. Wallace (1984), 348. 200 The illuminating exposition of Aristotelian methodology made in the River Forest school, however, places Galileo's achievements in their proper context within scientific demonstration, and we have adopted in our studies here this interpretation, which distinguishes between a priori and a posteriori demonstrations, and the role of definitions within them.436 4 3 6 Our analysis is based primarily upon the elucidation of definition and demonstration in Aristotle's Physics as treated in Smith (1952), passim, Wallace (1957), passim, Smith (1958), passim, and Wallace (1996), 280-308, 420-426. 201 

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