St· Thomas Aquinas Î787 THE DIVISION AND METHODS OF THE SCIENCES Questions V and VI of his Commentary on the De Trinitate of Boethius translated with Introduction and Notes 2- ARMAND MAURER. C.S.B. THE PONTIFICAL INSTITUTE OF MEDIAEVAL STUDIES TORONTO, CANADA 1953 Cum permissu Superiorum E. J. McCorkell, C.S.B. Superior General Nihil obstat F. A. Orsini, C.S.B., J.C.D. Censor Deputatus Imprimatur ►J*James C. Cardinal McGuigan Archbishop of Toroni m ** τχ T y 77 m f Copyright X by The Pontifical Institute of Mediaeval Studies 1953 Printed in Canada By Garden City Press Co-Operative, Toronto CONTENTS Introduction ............................................................................ vii Question Five. The Division of Speculative Science. Article 1. Is Speculative Science Appropriately Di­ vided into these Three Parts: Natural, Mathematical and Divine? ......... 3 Article 2. Does Natural Philosophy Treat of What Exists in Motion and Matter? ... 17 Article 3. Does Mathematics Treat Without Motion and Matter of What Exists in Matter? . 24 Article 4. Does Divine Science Treat of What Exists Without Matter and Motion? . 36 I Question Six. The Methods of Speculative Science. Article 1. Must We Proceed according to the Mode of Reason in Natural Science, according to the Mode of Learning in Mathematics, and according to the Mode of Intellect in Divine Science? .......................... 46 Article 2. Must We Entirely Abandon the Imagina­ tion in Divine Science? ............ 60 Article 3. Can Our Intellect Behold the Divine Form Itself? ............................................................ 66 Article 4. Can Our Intellect Behold the Divine Form by Means of Some Speculative Science? .... 73 Appendix I. The Division of the Sciences in St. Thomas’ Commentary on the Ethics . 79 Appendix Π. Metaphysics as a Science: Introduction to St. Thomas’ Commentary on the Meta­ physics .................................. 80 Appendix III. The Order of Learning the Sciences 83 Bibliography ........................................................................... 86 Index ....................................................... -............................. INTRODUCTION I T. THOMAS AQUINAS gives his views on the hierarchy the in several his works, sciences and their methods of Sbutof his most extensive and penetrating treatment of these sub­ jects is to be found in the two Questions translated in this little book. They are taken from his unfinished Commentary' on Boethius’ De Trinitate. Question Five deals with the division of the speculative sciences, Question Six with their methods. The Questions were w-ritten early in St. Thomas’ career, very likely between 1255 and 1259,1 so that they are not always his last word on the subject; what he says in them should be studied along with his statements in his later works. Yet, because he never again took up the problems in such detail, they are of exceptional value in giving us an appreciation of his views on these topics. It may appear strange that St. Thomas treats of the division and methods of the sciences while commenting on Boethius’ book on the Trinity. However, he is simply taking his cue from Boethius himself, who, before considering the mystery of the Trinity, touches upon certain preliminary points con­ cerning faith, theology and the place of theology in the scheme of the sciences. A few brief remarks of Boethius about the division of the speculative sciences and their methods of pro­ cedure form the basis of St. Thomas’ lengthy discussions on these points. 1. See Thomas ton Aquin, In Librum Boethii de Trinitate. Quaestiones Quinta et Sexta, ed. P. Wyser, Einleitung, pp. 17-18. M. D. Chenu proposes the date 1256. See his La date du commentaire de sair.t Thomas sur le De Trinitate de Boece Rerue des sciences philos­ ophiques et théoloffiques, 1941-42. pp. 432-434.2 2. See Boethius, De Trinitate 2 *PL 64. 1250AB). viü DIVISION AND METHODS OF THE SCIENCES The circumstance of the Commentary also helps to explain the limited perspective of St. Thomas in the two Questions. In the first place, they are concerned specifically with the speculative and not with the practical sciences. It is true that he has some important things to say in them about practical knowledge and science, but these are incidental to his main theme. They are simply meant to throw more light on the nature of speculative science. No attempt is made to give the hierarchy of practical science? Moreover, the nature of theology as the science of Sacred Scripture is not considered in these Questions. They contain a few incidental remarks about it, but these are only to con­ trast it with metaphysics. St. Thomas had already treated the science of Sacred Scripture in the earlier Questions (I-II1). Here his perspective is that of the sciences attainable through the natural light of reason. In order to appreciate the aim and significance of the present work, the reader must understand St. Thomas’ notion of science. It will be apparent at once that it differs significantly from that 1 current in our own day. The very fact that he uses the terms science and philosophy as synonyms warns us of this and at the same time points to his ideal of science. Today, no one would think of equating philosophy and science, even though there is little agreement as to what the distinction between them is. Science in general is thought of as any reasoned knowledge that is universal and systematic. The ideal of scientific knowledge is to be found in an exact science such as mathematical physics, which uses precise mathematical calculations and a highly refined method involving experimentation, formation of hypo­ theses and their verification.* Whatever philosophy may be, it obviously does not answer to this description. X On this subject, see J. Maritain. Les Degrés du aavoir, pp. 618-627; Annexe VU, pp, 873-896. 4. On the modern notion of science and its method, see Claude Bernard. An Introduction to the Study of Experimental Medicine; Henri Poincaré. The Foundations of Science; Albert Einstein, On the Method of Theoretical Physics; A. Einstein and Leopold Infeld. The Evolution of Physics; Max Planck, “The Meaning and Limits of Exact INTRODUCTION ix St. Thomas’ ideal of science is quite different. For him, science in general is knowledge of things through their causes? As Aristotle said before him, it is knowledge, not only of fact, but of reasoned fact? It reaches its ideal, not simply when it records observable connections in nature and calculates them in mathematical terms, but rather when it accounts for observable phenomena and the properties of things by bringing to light their intelligible relations to their causes. Metaphysics reaches this goal when, for example, it explains the contingent uni­ verse through God, mathematics when it explains the proper­ ties of a triangle through its definition, natural philosophy when it accounts for change through efficient and final causes and the intrinsic principles of bodies, matter and form. In other words, scientific inquiry for St. Thomas at its best is philosophical. It does not aim simply at empiriological knowledge gained through controlled observation and measure­ ment of the physical world, but rather at knowledge of the very being and essential structure of things. Its goal is onto­ logical rather than empiriological knowledge.' It is true that St. Thomas was acquainted with genuine empiriological inquiry, although its range was very limited and its methods remained simple and undeveloped. During his lifetime, St. Albert the Great carried out observations in biology and zoology which still evoke the admiration of the scientist, Peter of Maricourt wrote his treatise on the magnet, and Roger Bacon observed and measured the rainbow and Science”, Scientific Autobiography and Other Papers, pp. 80-120. For varying appreciations of modern science by philosophers, see A. N. Whitehead, Science and the Modem World; Philipp Frank, Modern Science and its Philosophy; Morris Cohen and Ernest Nagel, Ah Introduction to Logic and Scientific Method; Jacques Maritain, Les Degrés du savoir; Vincent Smith, Philosophical Physics. 5. See Contra Gentiles I, 94 6. See Posterior Analytics I, 2, 71b8ff; I, 13. T. For a Further explanation of the meaning of these terms, see J. Maritain Philosophy of Nature, pp. 73S. By contrasting these two types of knowledge we do not mean to imply that ontological knowledge is in no sense the result of experience and observation. All our knowledge begins in the senses, although the type of experi- X DIVISION AND METHODS OF THE SCIENCES other phenomena of light/ It is not surprising, then, to find St. Thomas’ description of the method of natural science quite correctly laying stress on the role of the senses in such knowl­ edge, on the verification of its judgments in sense data, and on reasoning from signs and effects to causes.* 89 What is more, he gives us the best analysis of physico-mathematical science written in the Middle Ages. He knew of this type of science in a very rudimentary form from the ancients and also from his contemporaries, such as Robert Grosseteste, Roger Bacon and Witelo, who cultivated it chiefly in the field of astronomy and the mathematical study of light (optics). He calls these intermediary sciences because they are situated between mathematics and physics and partake of the character of both.10 Sciences of this sort, however, remained largely unde­ veloped in the Middle Ages and their method was not ade­ quately understood. They play a very minor role in St. Thomas’ scheme of the sciences. The center of attraction for St. Thomas and his contempor­ aries was not empiriological or mathematical science, but ence and observation used in philosophy is different from those used in the other sciences. In brief we can say that philosophical analysis of sensible reality begins in the senses and ascends towards intelli­ gible being, while empiriological analysis begins in the senses and descends, in the resolution of its concepts, towards the observable and the measurable as such. See J. Maritain, op. cit., pp. 74-76. The growth in modem times of empiriological science, as distinct from philosophy in its formal object and method, renders impossible a physical theory which would be applicable in a univocal way to both. Such a theory, which denies the distinction between ohilosophical and empiriological analysis, has been proposed by R. Nogar. "Towards a Physical Theory.” The New Scholasticism. Oct., 1951. pp. 397-438. 8. See G. Sartan. Introduction to the History of Science Π; for St Albert, pp. 934-944; for Peter of Maricourt 'Petrus Peregrinus), pp. 1030—1032; for Roger Bacon, pp. 952-967. St. Albert’s emphasis on personal observation in the sciences is particularly worthy of note. He writes: "What I have to say (on the various plant species) is partly proven by experience (experimento), and partly taken from the reports of those whom I have discovered^ do not readily make statements that are not proven by experience." De Vegetabilibue et Plantis VI, L L ed. A. Borgnet (Paris, 1891), voL 10, pp. 159-160. 9. See below, pp. 52-53. 10. See below, pp. 33-35. INTRODUCTION xi rather ontological or philosophical knowledge, which attains the very being and intelligible structure of things. Indeed, so great was the attraction towards this type of knowledge in the Middle Ages that the other sciences suffered from it. Not only did they fail to flourish and to achieve their independence as distinct kinds of knowledge, but all too frequently prob­ lems which can be solved only by their methods were ap­ proached with the methods of ontological science or philoso­ phy. In general there was too great an optimism in the mind’s ability to understand the ontological structure of things ot their intelligible natures. The consequence of this optimism was the extension of philosophical analysis to areas in which it fails to achieve results. We know all too well the conse­ quences of this; the corpse of mediaeval physics is there to warn us against the error.11 The beginning of the modern era witnessed a revolt against the physics of the Middle Ages. The empiriological and physico-mathematical sciences gradually established themselves as distinct scientific ways of knowing and their scope and methods w'ere carefully defined. At first these sciences were taken as a substitute for the napiral philosophy of the Middle Ages. Newton, for example, called his monumental work "The Mathematical Principles of Natural Philosophy.” It was only much later, indeed within the last century, that their non-philosophical character has been clearly recognized. This clarification not only benefits the scientist, who no longer takes bis work to be a philosophical one, but it also helps the philosopher to appreciate better the limits of his own disci11. Mediaeval physics included, parts which properly belong to the philosophy of nature and parts which belong to the science of nature. I am here referring to the latter and not to the former, at least in so far as they were not contaminated by incorrect science. The analysis of changeable beings in terras of form and matter, and of change itself in terms of act and potency, are examples of a sound philosophical explanation of nature. On the other hand, the medi­ aeval attempt to explain the particular movements in nature through tendencies towards natural places (See Q. 5. a. 2. note 25) is an instance of the misuse of the philosophic method in the domain of science. xii DIVISION AND METHODS OF THE SCIENCES pline. As a result, he too benefits from the separation of science from philosophy. The tragedy was that the revolt against mediaeval physics turned against, not only the bad physics of the Middle Ages, but against philosophy itself.12 .The methods of the sciences of controlled observation and measurement were hailed as the only ones -which enable us to understand maqjrtid. the universe. The method of ontological analysis, proper to philosophy, was denied all validity. The advent of positivism, with its repudia­ tion of any ontological implication in science and its glorifi­ cation of the positive sciences as the only valid method of knowing, gave these notions definite form and fixed them indelibly in the modern mind. It should be added, however, that a reaction to positivism began as early as the nineteenth century, led by such philosophers as Emile Meyerson13 and Edmund Husserl, the founder of phenomenology. With positivism the modern world had its revenge on the Middle Ages, but not without itself suffering a loss. For if the methods of empiriological science are successful in dealing with many problems about the physical universe, they are equally unsuccessful in handling many others, and these indeed the most important of all, such as the very intelligibility of the universe, the nature of man, his ultimate origin and destiny, good and evil, and God. In fact, the methods of these sciences do not even enable us to investigate the meaning and value of science itself, and to evaluate the various types of knowledge and science. There is need, then, for a better understanding and apprecia­ tion of the ontological or philosophical method of knowing. And it is just for this reason that the philosophy of St. Thomas, and the present work in particular, are well worth our atten­ tion today. His analysis of the hierarchy of the sciences and of their methods is itself an excellent example of the ontologi12. See J. Maritain, Philosophy of Nature, pp. 41 fl· “The Conflict of Methods at the End of the Middle Ages . The Thamist, Oct, 1941 pp. 527-533. IX See his De FExpÜcaüon dans l«s sciences. INTRODUCTION xiü cal method. It is not his aim to draw up a detailed and complete classification of the sciences, but rather to exhibit the main divisions of the sciences known in his day in the light of the causes, both on the side of the object and on the side of the subject, which give rise to them. In fine, his inquiry is a strictly philosophical one. The product of an age quite different from our own, it does not always give us ready-made answers to our problems. St. Thomas knew nothing about our new types of science, and so his analysis of the sciences and their methods could not take them into account. But he sets before us a model of how such an analysis should be made, as well as the broad principles of being and knowing which, because they are true, are as relevant today as they were in his century. II In this brief Introduction it would be impossible to comment on all the topics considered in these questions and the many problems they raise. The topics include such important ones as logic,1 the liberal arts,* ethics,3 practical science in general,4 the subalternation of science,5 and intermediate science/ Here we will confine our remarks to the two central themes of the Angelic Doctor: the hierarchy of the speculative sciences and their methods. St. Thomas divides these sciences into three branches: natural philosophy or science, mathematics, and theology or divine science. It will be noticed that he uses the terms natural science, physics and natural philosophy as synonyms. T ike all ancient and mediaeval philosophers, he makes no L See below, Q. 5, a. L Reply to obj. 2 and 3, pp. 9-10. 2. Loc. cit. Reply to obj. 3, pp. 10-12. X 4. 5. 6. Ibid. Loc. cit. Reply to obj. 4. pp. 12-14. Loe. cit. Reply to obj. 5, p. 14. See below. Q- 5, a. X Reply to obj. 6 and 7, pp. 34-35. introduction DIVISION AND METHODS OF THE SCIENCES distinction between them.7 By theology is here meant first philosophy or metaphysics, not theology in the sense of the science of Sacred Scripture.89 This threefold division of the speculative sciences stems from Aristotle? It was handed down to the Middle Ages by Boethius and adopted by St. Thomas. Each of these sciences is defined by its subject of inquiry and by its method of pro­ cedure. St. Thomas followed Boethius on this point too, but not without significant additions and alterations.^According UxBoethius, the sciences are concerned with forms, and the hierarchy of the sciences corresponds exactly to the hierarchy of forms in the real world in various degrees of separation from matter. 6Thus natural science studies the forms of bodies along with the bodies themselves in which they exist. Mathematics studies apart from matter forms of bodies which must exist in matter (e.g. lines, circles, numbers). Theology studies forms which are entirely separate from matter (e.g. God).1011 It is clear from this that Boethius’ division of the sciences, to some extent like that of Plato,11 is based upon an objective division of reality. <9Tach science has for its object a type of form more or less independent of matter. xThe branches of science exactly correspond to the order of forms themselves arranged in the real world according to their separation from matter. In such a view, there is little need to investigate the subjective acts by which the different objects of the sciences are grasped. AThe intellect follows more or less passively the division of forms it finds ready-made in the world. TOnly in 7. Indeed, as late as the nineteenth century bocks in physics were railed treatises on natural philosophy. Since then. the scope and method of science in the modern sense have been more clearly distinguished from those of natural philosophy. See J. Mari tain. ' Philosophy of Nature; Let Degrés du savoir, pp. 11Û-112, 120-123. 265-397 Science and Wisdom, pp. 34-69. 8. For the distinction between the two meanings of theology, see below Q. 5. a. 4, pp. 41-42. 9. See Aristotle, Metaphysics XI. 7, 1064bl-6. 10. See Boethius, De Trinitate 2 (PL 64, 1250A>. 11. See Plato, Republic VI, 509-511. the case of mathematics is there opportunity for discussing the act whereby the object of the science is attained, for, while existing in matter, mathematical forms are considered separate from matter. Yet Boethius does not exploit this opportunity, as St. Thomas does in his important third Article of Question Five. In this Article St. Thomas shows the essential role played by the operations of the intellect in the determination of the subjects of the sciences.ri^The sciences are no longer considered as differentiated according to a distinction of forms ready-made in the world, but according to distinctions the mind itself makes in the course of its investigation of reality. - Thus he changes the very notion of the object of a science. It is no longer a form in the Boethi an sense, even though he sometimes uses the language of Boethius. Each science is said to have its own subject (subjectum), which differentiates that science from every other. By the subject of a science St. Thomas does not simply mean the things considered by the science, or its subject-matter. ^The term also designates the formal per­ spective (ratio) under which these things are considered in the science.13 The analogy which St. Thomas sees between a science and its subject and a faculty of the soul or a habitus and its object may help to clarify this point.'Α-He says, "The relation between a science and its subject is the same as that between a faculty or a habitus and its object. Now, properly speaking the object of a faculty or a habitus is that under whose formal perspective (ratio) all things are referred to that faculty or habitus; as man and stone are referred to sight in that they are colored. Hence ’colored thing' is the proper object of 12 The pages which follow (xv-xxvii) are an analysis of this Article. The reader should also consult St. Thomas. In. I P^ys. L m 1-3; In Meta. Prooemium, trans, below, PP-Meta-_,Yect: V’ Jb 158 ΓΠ lect. 7 n 405. XI. lech 7, n. 22a9-22S7; Summa Theol. I, 40, U “U?'*’, 7; a sàeAce see SV The mas. In I Post. Anal. lect. 2. I? » 5a "S Sn.2; ta ««·» Prooemium. »» Mo». pp~ 30-83. - xvi DIVISION AND METHODS OF THE SCIENCES sight.”14 Completing this analogy, we can say that the subject■ of a science is that under whose formal perspective all things | are studied in that science; as in metaphysics all things are I considered from the point of view of being. Consequendy, the subject of metaphysics is being according as it is being. Once this viewpoint of the subject of science is adopted, it becomes imperative to study the operations of our intellect and the different distinctions it makes in considering reality(1.Now the human intellect, St. Thomas says, has basically two opera­ tions. The first is the understanding or apprehension of intelligible objects, by which we know more or less distincdy what things are, or in other words their essences. The second operation is judgment, by which we compose or divide what we have grasped in simple apprehension. For instance, having understood what green and grass are, we unite the two in affirming, "Grass is green”; or having grasped what man and stone are, we divide the two by denying, "Man is not a stone.” In judgment, then, the intellect does not simply know what things are; rather, it grasps them in their very existence. For when we affirm that grass is green, we under­ stand how grass exists, namely as green; and when we judge that man is not a stone, we understand how man does not exist, namely as a stone. ‘'That is why St. Thomas says that the first operation of the mind is directed to the essence of a being, whereas judgment is directed to its existence.15 ) '"Xj Now, St. Thomas goes on to say, we can distinguish or ab­ stract through both these operations of the intellect.16 Abstrac­ ti. Summa Theol. I, 1, 7. 15. See below, Q. 5. a. 3. pp. 26. 27. See also In I Sent. 19, 5, I. ad 7”; 38, 1. 1 Also J. Maritain. Existence and the Existent, pp. 10-19; E. Gilson. Being and Some Philosophers, pp. 190-215; G. B. Phelan, “Venun Sequitur Esse Rerum”, Mediaeval Studies, 1939, pp. 11-22. 16. See below, Q. 5, a. 3, pp. ZIfL Also Summa Theol, I, 85, 1, ad 1", 2“. Abstraction has both a negative and positive aspect. It involves a detaching or separating, but primarily it is a positive concentration of the mind on some intelligible object or aspect of a thing without considering other objects or aspects of the same thing. Ta abstract is not primarily to leave something out, but to take something in, and this is the reason why abstractions are knowledge." E. Gilson, The Unity of Philosophical Experience, pp. 144-fc>. See J. Mantain, A INTRODUCTION xvii tioQ through simple apprehension is the absolute consideration of some intelligible essence or nature; for instance, the con­ sideration of animality in man without considering his rationality. This way of abstracting, connected as it is with simple apprehension, takes no account of the existence or non­ existence of these objects of thought. It is simply concerned with them as distinct intelligible natures. The second way of abstracting, however, does take existence into account, for it is accomplished through judgment. Thus if we judge, "Man is not a stone,” we abstract or separate man from stone in such a way that we deny their identity, not simply as intelligible objects of thought, but in existence. "k Once we grasp this distinction in the ways the intellect abstracts, it is not difficult to see that the laws of abstraction differ in the two cases. Obviously, the intellect cannot abstract or separate in judgment what is united in reality. This would be contrary to the truth, for in order that judgment be true, it must conform to the way things are. But if we judge, "The man is not white,” separating in this way white from man, although in reality the man exists as white, then our judgment is false. As a consequence, we can only unite in our judg­ ments what is united in existence, and separate or abstract in our judgments what is separate in existence. This is not true, however, of abstraction through simple apprehension. In this operation of the intellect, we can, at least in some cases, abstract what is not separate in reality. As long as the intelligible object can be conceived apart, it can be considered by itself, even though it does not and cannot exist separately. For example, it is possible to consider human nature without considering the various individual men in whom that nature exists. For human nature is an intelligible object which ran be conceived apart from individual men, although it cannot exist separately from them in reality. In St. Thomas’ view, the Platonic doctrine of separated Forms resulted from a confusion of these two modes of Preface to Metaphysics, p. 87. xviii DIVISION AND METHODS OF THE SCIENCES abstraction. Because the intellect can consider a nature or essence without thinking of the individuals whose nature it is. Plato thought that it must exist separate from them. So he confused the order of intelligibility and the order of existence. Because an object of thought is intelligible in itself, Plato thought that it must exist in itself. In fact, what is one in existence can be conceived in multiple fashion in simple apprehension. Only in negative judgment do we grasp the separation of one thing from another in existence. So the fact chat we can consider a nature without considering the individuals in which it exists is no indication of the separate existence of that nature. The immediate relevance, however, of the distinction between abstraction through apprehension and judgment goes beyond a refutation of Plato’s theory of separate Forms. It enables us to distinguish between the subjects of natural philosophy and mathematics on the one hand, and that of metaphysics on the other. For according to St. Thomas the former grasp their subjects through abstraction in simple apprehension, while the latter attains its subject through a kind of abstraction accomplished in a negative judgment. In order to emphasize this difference he calls the latter sort of abstraction separation, reserving the term abstraction in the proper sense for that effected through simple apprehension.’ Let us now examine briefly the subjects of these sciences and the operations of the intellect whereby they are grasped.1’ The abstraction of the natural philosopher is described as the abstraction of a whole: abstractio totius. By this is meant the absolute consideration of some essence without considering the individuals whose nature it is. The individuals are, as it were, "parts” from which the nature as a "whole” is abstracted. An abstraction of this sort is legitimate because these parts are accidental to the whole, in the sense that individuals as such are not contained in the definition of the nature. St. 17. See beîow. Q. 5. a. 3, p. 31. B. See, In Meta. Prooemium; trans, below, pp. 80-83, In I Phu*, Ie. pp. 335-33«. xxiv DIVISION AND METHODS OF THE SCIENCES between the intellectual operations by which the metaphysician lays hold of his subject and those by which the natural philosopher and mathematician lay hold of theirs. The direction in which St. Thomas’ mind was moving in these various redactions is clear. He was progressively realizing the central role of judgment and existence in the solution of his problem, as well as the eminently existential character of the subject of metaphysics. In recent years historians of St. Thomas’ philosophy have become more fully conscious of these aspects of his thought which for a long time remained quite obscured and forgotten.2’ Indeed two of his outstanding followers in the sixteenth and seventeenth centuries, Cajetan and John of St. Thomas, taught a doctrine of abstraction and division of the sciences based on it which leaves out of consideration the very features St. Thomas took such pains to emphasize: the role of judgment and existence. They distinguish between "total abstraction” and "formal abstraction.” What is abstracted in the former is as a universal whole with respect to that from which it is abstracted; what is abstracted in the latter is as a form of that from which it is abstracted. All the sciences, they add, use total abstraction, but they are diversified according to modes of formal abstraction.” it is beyond the scope of this Introduction to attempt an adequate study of their doctrine and an evaluation of it as a faithful continuation of St. Thomas’. But this at least should be pointed out: For St. Thomas, abstraction of a whole, although common to all the sciences, is especially character­ istic of natural philosophy, whereas for Cajetan and John of » ■^in that act. Only here does he establish the basic difference; „—/St. Thomas, total abstraction is used by all die sciencesVbut^ 28. Among other works, see E. Gilson, Le Thomisme, pp. 43-SL, 123-139: Being and Some Philosophers. J. Maritain, A Preface to Metaphysics; Existence and the Existent. J. de Finance, Etre et agir dans la philosophie de s. Thomas. G. B. Phelan. “Being and the Meta­ physicians”, From an Abundant Spring, pp. 423-447.29 29. See Cajetan, In De Ente et Essentia, Prooemium, Q. 1, n. 5, pp. β, 7; De Nominum Analogia 5, p. 50. John of St. Thomas, Ars Logica Π, Q. 27, a. L pp. 818-830. INTRODUCTION XXV properly defines none of them. Again, for St. Thomas abstraction of form is proper to mathematics, while for his two commentators formal abstraction belongs to all the sciences, which are diversified by its various modes.30 Finally, and most important of all, these commentators fail to explain the essential role negative judgment plays in St. Thojnas’ memphysics, and the existential character of its subject. There are grounds to suspect, therefore, that behind the difference in the terminology of St. Thomas and his commentators there is a difference of doctrine.31 This much at least is certain: without a direct contact with the works of St. Thomas, especially with his Commentary on the De Trinitate, it is impossible to appreciate his authentic teaching. St. Thomas’ conception of abstraction and the hierarchy of the sciences owes much to Aristotle. Yet it should be pointed out that he adds notions of his own and that even the ones he borrows from the Greek philosopher generally take on a quite original meaning in the context of his philosophy. This is not the place to attempt an elaborate exposition of Aristotle’s doctrine in comparison with that of St. Thomas. Aristotle’s views on these subjects are extremely difficult to understand and no brief account could do them justice. However, it might be helpful to the reader to say a few words on this topic. Some suggested readings will help him to carry on the study for himself.33 It should be remarked, first of all, that when Aristotle uses the term "abstraction” in connection with the sciences, it does not have the analogical character it has for St. Thomas. There 30. The terms themselves (“formal abstraction”, “total abstraction”) are not equivalent to St Thomas’ “abstraction of a whole” and “abstrac­ tion of a form.” Total and formal qualify the act of abstraction; of a whole and of a form designate the object of the abstraction. 3L See L. M. Régis, art. cit., pp. 138-140. The opposite view is expressed by J. Maritain, Existence and the Existent, p. 30, note; also by Μ. V. T^roy “Le Savoir spéculatif”, Jacques Maritain, son oeuvre philosophique, pp. 328-339. 32. See M. D. Philippe, “Abstraction, addition, séparation dans la philosoohie d’Aristote”, Revue Thomiste 48 (1948), pp. 461-479. J Owens The Doctrine of Being in the Aristotelian Metaphysics, pp. 239-24L xxvi DIVISION AND METHODS OF THE SCIENCES is no doctrine of "degrees” of abstraction in Aristotle’s philo­ sophy of the sciences.33 For him, abstraction in the technical sense means the act by which mathematical entities are grasped; namely those which are not separate from sensible things, but which are considered by the mathematician as separate. The mathematician subtracts and leaves out of consideration sensible forms, retaining only quantity.34 The natural philosopher, on the other hand, attains his object by addition; for in his science forms are grasped, not as separated, but as immanent in the matter which they determine. Hence they must be understood with the addition of matter, which enters into the definition of the objects of this science.35 To appreciate the import of addition in Aristotle’s philoso­ phy, we must realize that for him the form or essence of a material thing does not include matter. Only the concrete entity does. e And since it is this concrete entity or substance which is defined by the natural philosopher, an act of addition is required to grasp form and matter together. St. Thomas, however, does not require such an operation, for according to him the essence of a material thing at once includes both form and matter.37 Aristotle is not so explicit in designating the intellectual 33. See J. Owens, op. cit., p. 240. 34. See M. D. Philippe, art. cit., pp. 461-466; J. Owens, op. cit., p. 239. 35. See M. D. Philippe, art. cit., pp. 466-469: J. Owens, op. cit., pp. 239-240. 36. See Aristotle, Metaphysics VII. 7. 1032bl-2. b!4; 10, 1035al7-22: 11, 1037a25-29. See also J. Owens, op. cit., pp. 222-225. 37. See below. Q. 5. a. 2, p. 19 and note 16. St. Thomas refers to addition when commenting on Aristotle (See In III De Caelo et Mundo. lect. 3, n. 4). It finds no place, however, in his personal doctrine. St. Thomas’ conception of essence is not identical with that of Aristotle. The Mediaeval Arabian philosopher Averroes followed Aristotle’s notion of essence as form without matter. (See Averroes, In VU Meta. t c. 21, fol. 1711; t. c. 34, fol. 1S4D). St. Thomas criticizes Averroes for teaching that the whole essence of a species is the form alone without matter, but he does not recognize this doctrine as Aristotelian. Rather, he benignly interprets Aristotle’s doctrine as in accord with his own. See St. Thomas. In VII Meta. lect. 9. n. 1467-1469. See also A. Maurer. "Form and Essence in the Philosophy of St Thomas ”, Mediaeval Studies. 1951. pp. 165-176. INTRODUCTION xxvii activity characteristic of primary philosophy or metaphysics. However, he does describe it as an act of contemplation; and this act w’ould seem to imply a separation, for its object is either separated in reality from the material world, like the separated substances, or it is at least capable of being separated in thought, like being, act, potency, etc.38 Nothing explicit is said, however, about these objects being attained through a negative judgment of separation; and they lack the existential character which they have in St. Thomas’ metaphysics. These observations should put us on our guard against speaking without qualification of an "Aristotelico-Thomistic” doctrine of abstraction and scheme of the sciences. Although St. Thomas owes much to Aristotle on these points, to link together in this way the views of the two philosophers is a simplication wrhich loses sight of important divergences in doctrine.19 ***** We come now to the main theme of Question Six: the special methods of the speculative sciences. This will give us a new criterion for distinguishing these sciences: they not only have distinct subjects of inquiry; they also have their own characteristic methods of procedure in harmony with their subjects. It will be noticed at once that St. Thomas adopts a pluralist attitude towards scientific method; he does not propose one method for all sciences. He recognizes, of course, that they have a common method in that they follow the same basic laws of logic;40 but besides this he maintains that each science has its own special way of inquiring after truth. Because scientific methods are not equal in the certitude they yield, there will always be a temptation to deny this and to extend one method to all the sciences because of its excellence. St. Thomas saw that there is a particular temptation to single 38. See M. D. Philippe, art. cit., pp. 469-479; J. Owens, op. cit., pp. 240-241. 39. See the remarks of L. M. Régis, art. cit., pp. 128-138. 40. See St Thomas, In II Meta, lect 5, n. 335; also below. Q. 5, a. 1. Reply to obj. 2 and 3, pp. 9-11: Q. 6, a. 1. Reply to obj. 3, p 56. . ιλ ι» · xxvüi DIVISION AND METHODS OF THE SCIENCES out the mathematical method for this role, since it is the most exact and certain. But he warns against this, insisting on the specificity of method in each of the sciences.41 The physico-mathematical sciences are no exception to this rule. Although they were merely in their infancy in the thirteenth century, St. Thomas recognized their epistemological type and describes it with a greater acumen than anyone else in his day. He calls them "intermediate sciences” because they are located between natural science and mathematics and thus share the characteristics of both. He names astronomy, optics and harmony or music as examples. Sciences of this sort study the physical universe, but by means of mathematics. So mathematics plays a formal role in their structure, while physical reality plays a material role.42 But even though the rule of analysis and deduction in these sciences is mathematical, their method is not simply that of mathematics. Since they are physical sciences on their material side, they must be fed through a contact of the senses with material things. As a result, they have a method distinct from that of natural science and mathematics, although it shares to some extent in the methods of both. In describing the methods of the main branches of the sciences, St. Thomas adopts the classical terminology of Boethius. The philosophy of nature, he says, proceeds rationabiliter, mathematics disciplinabiliter, and metaphysics intellectualiter.*3 For want of better terms, these Latin words have been translated respectively: "according to the mode of 4L See In II Meta. led. 5, n. 335-337; also below, Q. 6, a. 2, p. 65: “ . . . they are in error who try to proceed in the same way in these three parts of speculative science.” Here St. Thomas opposes the notion, which has become prevalent in our day, that science is essentially one, with the same scientific method. Descartes did much to introduce this conception into modern thought. See J. Marita in, The Dream of Descartes, pp. 48-57; also E. Gilson, The Unity of Philosophical Experience, pp. 142-151. The latter is an his­ torical study of what happened to philosophy when methods other than its own were applied to it. 42. See below, Q- 5, a. 3, Reply to obj. 5, 6 and 7, p. 33, and note 19. 43. See below. Q. 6. a. L P· 46. and note 2. INTRODUCTION xxix reason” or "rationally,” "according to the mode of learning,” and "according to the mode of intellect,” or "intellectually.” Some explanation of these terms, however, is required. The terms "reason” and "intellect,” with which the methods of the philosophy of nature and metaphysics are respectively related, are almost synonyms, although we associate reason more particularly with the power of drawing conclusions from principles and intellect with the power of simply knowing or understanding. For St. Thomas, reason and intellect are not really distinct powers of man. They are one and the same in­ tellectual power by which we know in different ways. Through reason we move from the known to the unknown, advancing from one thing to another in our conquest of truth. Through intellect we grasp an intelligible truth simply and intuitively, without any movement or discourse of the mind. So the act of reason is compared to that of intellect as movement to rest, or as the reaching out for something to the actual possession of it. Again, they are compared as the imperfect to the perfect, as a circle to its centre, as time to eternity.44 Reasoning is especially characteristic of man, for he must acquire knowledge through inquiry and discovery. That is why he is properly a rational animaL But he also knows by understanding. Indeed every movement of his reason begins and ends in understanding, just as every step we take in walking begins and ends at a position of rest. And just as every step we take brings us closer to our goal, so the move­ ment of reason leads to a deeper understanding of truth, which is the object of our intellect. It is quite different with the angels. They do not have to reason. Intellectual beings by nature, they grasp intuitively a multitude of truths in the unity of a single idea.41 In this respect they resemble God, who simply by knowing His essence knows all things. Human reason, on the other hand, as the most imperfect of all intellects, must grasp unity in multiplicity rather than multiplicity in unity. Human know44. See St Thomas, Summa Theol. I, 79, 9. 45. See St Thomas, op. cit., I, 58, X XXX DIVISION AND METHODS OF THE SCIENCES ledge begins in the senses, which present reason with a vast variety of data; but in this multiplicity it sees unity and thus gathers simple truths from it. At the end of its reasoning, therefore, the human mind approaches the angelic intellect in gathering up a multitude of truths in the unity of simple principles or ideas. St. Thomas says: . . it is distinctive of reason to disperse itself in the consideration of many things and then to gather one simple truth from them.” And he quotes with approval the words of Dionysius the pseudoAreopagite: ' Souls have the power of reasoning in that they approach the truths of things from various angles, and in this respect they are inferior to angels; but inasmuch as they gather a multiplicity into unity they are in a way equal to the angels.”40 It is against the background of this distinction of reason and intellect that we must understand St. Thomas’ views on the methods of the sciences. Natural philosophy, he tells us. uses a method most in harmony with our natural way of knowing as rational beings.47 For this reason its method is properly called rational. To begin with, this science deals with the changing sensible world, which is our first and most congenial object of knowledge: the one which our reason is best adapted to understand. It stays closest to this world in its changing and sensible character, and in the multiplicity of data it presents to us. Hence the very method it uses is characterized by the analysis of manifold data and by move­ ment and progression from one thing to another. Then too, as rational beings, all of whose knowledge originates in the senses, we must investigate the properties of things and their sensible appearances in order to know their natures. We must inquire into effects in order to discover their causes. This movement of reason from effect to cause, from sign to thing signified, is particularly characteristic of natural philosophy and most connatural to us as rational animals. What is more, unlike mathematics, natural philosophy does not move simply 46. See below, Q. 6, a. 1. Reply to the Third Question, p. 57. 4L See below, Q. 6, a. L Reply to the First Question, pp. 52-53. INTRODUCTION xxxi from one object of thought to another logically distinct object of thought. It is concerned with existing changing beings in their diversity and interrelations. In other words, it not only demonstrates by way of formal causes, but also through efficient and final causes, one of which is entirely external to the other. On this score, too, it uses a method which is rational in the proper sense of the word, for it follows most closely the human reason’s natural way of knowing. St. Thomas also attributes a major role to reasoning in mathematics.48 In this respect it is like natural philosophy. The difference in their methods lies in the causes employed in reasoning. Mathematical demonstrations begin with defini­ tions and principles, from which conclusions are deduced by way of formal causality. For example, a certain property of the triangle is shown to follow from its very definition. Unlike natural philosophy, mathematics does not demonstrate through final or efficient causes. Following Boethius and a long-established tradition, St. Thomas says that mathematics proceeds "according to the mode of learning” (disciplinabiliter). This does not describe the mathematical method intrinsically, as "rational” describes that of natural philosophy. It simply designates that the mathe­ matical sciences are the easiest to learn, for they are most exact and certain. The antiquity of this notion is indicated by the very etymology of the word "mathematics”. It comes from the Greek matbein which means "to learn”. Its equivalent in Latin is discere, from which disciplina and the English "dis­ cipline” are derived. St. Thomas always maintained that we achieve our greatest certitude in mathematics.49 It is more certain than natural philosophy because it abstracts from motion and the sensible qualities of material things. Natural philosophy must take 48. See below, Q. 6, a. 1, Reply to the First Question, p. 53; Reply to obj. 4 of Second Question, p. 57. 49. See below, Q. 6. a. 1, Reply to the Second Question; also In II Meta. lect. 5, n. 336. From the point of view of the simplicity of its objects, metaphysics is the most certain science (See In I Meta. xxxii DIVISION AND METHODS OF THE SCIENCES all of these into account, and so it is more difficult and less certain. The demonstrations of this science often hold good only in the majority of cases: there are exceptions because of the contingency of matter. Furthermore, although natural philosophy studies material things, we do not know their substantial essences in them­ selves. Whatever knowledge we can have of them is attained through their accidental characteristics—their quantity, quali­ ties, operations, etc — which are simply signs of their essential properties. In other words, the natural philosopher knows his objects of study very imperfectly through their sensible appear­ ances.50 This is why St. Thomas qualifies so strictly the type of certitude we can expect in natural science. He does not deny that some of its reasonings furnish adequate proof and are true demonstrations; but others are simply "suppositions”, which explain sensible appearances without being necessarily true. For example, St. Thomas considers that although the Ptolemaic system of astronomy "saves the appearances”, it is not necessarily true, since the appearances of the stars might conceivably be "saved” in still another way not yet known to man.51 The mathematical method is also more certain than that of metaphysics, but for another reason. The objects of meta­ physics, like God, the angels, being, goodness, truth, are too lofty for the human reason. They can be known only with lect 2, n. 47). It is not the most certain science, however, with reference to us, or subjectively, owing to the weakness of our intellects. For the different meanings erf certitude, see St Thomas, Summa TheoL Π-Π, 4, 8. 50. See St Thomas, De Ente et Essentia S; Eng. trans, p. 52: ‘Out even in the case of sensible things the essential differences themselves are unknown to us; hence, we have to signify them by the accidental differences which arise from the essential, as we designate a cause by its effect.** See also De Spiritualibus Creaturis 11, ad 3”, Eng. trans. p. 132; Summa Theol. I, 29, 1, ad 3m; I, 77, 1, ad 7“; In I De Anima, lect. 1, n. 15, Eng. trans, pp. 49-50; Contra Gentiles I, 3. See J. Maritain, Les Degré» du savoir, pp. 347-350; 407-414. 5L See St Thomas. In I De Caelo et Mundo, lect 3, n. 7; 11, lect 17, n. 2; Summa Theol. L 32. L ad 2“. See also J. Maritain, Les Degree du savoir, p. 123, note; Réflexions sur I’intelligence, p. 195, note. INTRODUCTION xxxiü the greatest difficulty and hence with a lesser degree of certi­ tude than mathematical entities. However, there is this consolation for the metaphysician: the little he can know about these most lofty matters is of greater value than the vast amount that can be known about those that are mundane.52 Indeed, in the realm of metaphysics the human intellect is strained to its utmost and is forced to adopt a method little congenial to it: the method of intellectual insight. For in this science it deals with objects, some of which transcend itself, and all of which are purely intelligible and as such do not fall under the senses or the imagination. In knowing these objects it must use a method which is not rational, but rather resembles that of the angelic intelligences. The method of metaphysics, St. Thomas says, is properly intellectual because it stays closest to the mode of knowing characteristic of intellect, as the method of natural philosophy is properly rational because it stays closest to the mode of knowing proper to reason.'3 By this he does not mean that metaphysics makes no use of reasoning, or that natural philosophy makes no use of intellectual insight. It is simply a question of greater emphasis on one or the other phase of human knowledge. In natural philosophy the movement of reason predominates, in metaphysics the unwavering grasp of fundamental truths through simple insight or intuition.'4 If metaphysics uses discursive reasoning, and moves from principles to conclusions, its conclusions are closest to its principles and so its reasoning most closely resembles intellectual intuition. Its method is accordingly more simple and less complicated than that of either natural philosophy or mathematics. It is a method 52. See St. Thomas, Expositio super Librum de Causis, lect. 1; trans, below, p. 84. 53. See below, Q. 6, a. 1, Reply to the Third Question, p. 57. 54. As a consequence, natural philosophy progresses in a different way than metaphysics. Movement from one thing to another and change of doctrine are more accentuated in natural philosophy than in metaphysics, which develops rather by penetrating more and more deeply into the same truths which are ever ancient and ever new. J. Maritain remarks that a treatise on natural philosophy can at the most endure a lifetime, and even then it must be periodically revised xxxiv DIVISION AND METHODS OF THE SCIENCES of synthesis rather than analysis, for it is not so much a gleaning of simple truths from a multitude of data, as seeing a multitude of truths in the unity of simple truths. For metaphysics comes at the end of man’s natural knowledge as its crown and completion, just as intellectual insight comes at the end of reasoning. The analytic movement of reason in all the sciences finds its ultimate term in the intellectual insights of metaphysics, whether the object under consideration is God as the first cause of all things, or being and the properties of being as being as the most universal of all conceptions. ,! St. Thomas throws further light on the methods of the speculative sciences in Article Two of Question Six. The specific problem raised there is whether metaphysics must in any way use the imagination; but the solution involves the more general problem of the relation of the sciences to the senses, imagination and intellect. In resolving this problem, he points out first that all our knowledge begins in the senses. So the starting-point of all the sciences must be the same: they must all originate in the senses. Our knowledge, however, ends in an intellectual judgment, and this judgment is made in different ways in the different sciences. In natural philosophy the judgment "ter­ minates” in the senses. By this St. Thomas means that the judgment is made in the light of what the senses reveal: their evidence is the final court of appeal for the veracity of the scientific judgment. In mathematics the judgment "terminates" in the imagination, in the sense that the mathematical judgto take into account new data. This is not true of metaphysics, ■whose rythmn of development is different because of its greater independence of the natural sciences. On the other hand, science in the modern sense moves and changes in its theories with a greater rapidity than natural philosophy. The distinction between the methods and development of natural philosophy and metaphysics is verified proportionately between philosophy as a whole and science in the modern sense of the word. See J. Maritain, Science and Wisdom, p. 64, A Preface to Metaphysics, pp. 2-16. 55. In the sense in which these terms are defined below. Q. 6, a. 1. Reply to the Third Question, p. 58. 56. See below, Q. 6, a. L Reply to the Third Question, pp. 58-59. INTRODUCTION XXXV ment looks to the evidence presented by the imagination. When he says this, St. Thomas is thinking of such mathe­ matical sciences as Euclidean geometry, in which the mathe­ matical entities are directly imaginable, and the judgment of the mathematician is directly verified by an appeal to the imagination. The problem of non-Euclidean geometries, in which a direct appeal to the imagination is impossible, did not arise in his day.37 Finally, the judgment of the meta­ physician "terminates” in the intellect alone. It could not possibly terminate in the senses or the imagination, for these faculties grasp things under their qualitative and quantitative aspects, whereas the objects of metaphysics are separated from matter and material conditions both in existence and in thought. Its objects are purely intelligible; and it is only the intellect which apprehends things under this aspect. Of course the metaphysician must use his senses and imagination as the source of his knowledge, but he makes his judgments in the light of what the intellect reveals about things, not according as they are grasped by the lower faculties of the soul. This final observation gives us a new criterion for distinguishing the speculative sciences from each other, and it offers new evidence that it would be a mistake to think that they must all use the same method. In broad outline this is the picture of the hierarchy of the speculative sciences and of their methods drawn by St. Thomas in the present work. We leave the reader to fill out the many details by a careful reading of the text, including the illuminating answers to objections. Abundant notes are appended to direct him to other writings of the Angelic Doctor for additional clarification of his doctrines. Reference is also made wherever possible to works on St. Thomas’ philosophy 57. The conclusions of non-Euclidean geometries are not directly veri­ fiable in the intuition of the imagination. but only indirectly and analogically. The mathematical entities of Euclidean geometry and arithmetic are real beings, in the sense that their concepts have an immediate foundation in reality. The entities of non-Euclidean geometries are beings of reason (entia rationis), constructed on the foundations of the Euclidean and translatable in terms of them. See J. Maritain, Les Degrés du savoir, pp. 107-110, 285, 325-326. xxxvi DIVISION AND METHODS OF THE SCIENCES which throw light on the more difficult passages. With their assistance it is hoped that the modern reader will be able to make contact with his thought and share in its order and wisdom. ' The translation has been made from the edition of the autograph manuscript of St. Thomas’ Commentary on Boethius’ De Trinitate, published by Father Paul Wyser, O.P.58 I wish to thank Father Wyser and the Société Philosophique de Fribourg for granting permission to use their edition. I am also grateful to Dr. Anton C. Pegis, President of the Pontifical Institute of Mediaeval Studies, for his generous assistance in preparing the translation. There is an old saying that a translator is a traitor (traduttore traditore). If I am in any measure innocent of this quite justifiable charge, it is largely due to his constant criticism and correction. 58. Thomas von Aquin, In Librum Boethii de Trinitate, Quaestiones Quinta et Sexta, ed. Paul Wyser, Fribourg and Louvain, 1948. QUESTION FIVE The Division of Speculative Science There are two questions here.1 The first concerns the division of speculative science which the text proposes,- the second the methods it attributes to the parts of speculative science. With regard to the first question there are four points of inquiry: Is speculative science appropriately divided into these three parts: natural, mathematical and divine? 2. Does natural philosophy treat of what exists in motion and matter? 1. 3. 4. Does mathematics treat without motion and matter of what exists in matter? Does divine science treat of what exists without matter and motion? ARTICLE ONE Is Speculative Science Appropriately Divided Into These Three Parts: Natural, Mathematical and Divine.9 H e proceed thus to the first article: It seems that speculative science is not appropriately divided into these three parts. Objection 1. For the parts of speculative science are those habits perfecting the contemplative part of the soul. But the Philosopher says in the Ethics3 that the scientific part of the soul, which is its contemplative part, is perfected by three 1. The beginning of Chapter 2 of Boethius' De Trinitate (PL 64. 1250A), the point St. Thomas has reached in his Commentary. 2. The text of Boethius, ibid. 3 Aristotle. Niconiachean Ethics VI, 1, 1139al2ff; 3. 6 and 7, 1139b 14 ff. 1140b31ff. 1141a9ff. 4 DIVISION AND METHODS OF THE SCIENCES habits, namely, wisdom, science and understanding. Therefore these are the three divisions of speculative science, not those proposed in the text.4 Objection 2. Again, Augustine says5 that rational philos­ ophy, or logic, is included under contemplative or speculative philosophy. Consequently, since no mention is made of it, it seems the division is inadequate. Objection 3. Again, philosophy is commonly divided into seven liberal arts, which include neither natural nor divine science, but only rational and mathematical science. Hence natural and divine should not be called parts of speculative science. Objection 4. Again, medicine seems to be the most opera­ tive science, and yet it is said to contain a speculative part and a practical part. By the same token, therefore, all the other operative sciences have a speculative part. Consequently, even though it is a practical science, ethics or moral science should be mentioned in this division because of its speculative^ part. Objection 3. Again, the science of medicine is a branch of physics, and similarly certain other arts called ‘'mechanical”, like the science of agriculture, alchemy, and others of the same sort. Therefore, since these sciences are operative, it seems that natural science should not be included without qualification under speculative science. Objection 6. Again, a whole should not be contradistin­ guished from its part. But divine science seems to be a whole in relation to physics and mathematics, since their subjects are parts of its subject. For the subject of divine science or first philosophy is being; and changeable substance, which the natural scientist considers, as well as quantity, which the mathematician considers, are parts of being. This is clear in the Metaphysics? Therefore, divine science should not be contradistinguished from natural science and mathematics. 4. The text of Boethius, ibid. 5. St. Augustine, De Civitate Dei VUI. 4 fCSEL 40, L 359). 6. Aristotle. Metaphv«« ΠΙ. 2, 996bl4-23; see VI, 1, 1025b26-28. 1026a7-16; XI, 3. 1061b4-U; 4, 1061bl7-33. QUESTION V, ARTICLE 1 Objection 7. Again, as it is said in the De Anima,1 sciences are divided in the same manner as things. But philosophy concerns being, for it is knowledge of being, as Dionysius says.8 Now being is primarily divided with reference to potency and act, one and many, substance and accident. So it seems that the parts of philosophy ought to be distinguished by such divisions of being. Objection 8. Again, there are many other divisions of beings studied by sciences more essential than the divisions into mobile and immobile and into abstract and inabstract: for example, the divisions into corporeal and incorporeal and into living and non-living, and the like. Therefore differences of this sort should be the basis for the division of the parts of philosophy rather than those mentioned here. Objection 9. Again, that science on which others depend must be prior to them. Now all the other sciences depend on divine science because it is its business to prove their principles. Therefore Boethius should have placed divine science before the others. Objection 10. Again, mathematics should be studied before natural science, for the young can easily learn mathematics, but only the more advanced natural science, as is said in the Ethics.9 This is why the ancients are said to have observed the following order in learning the sciences: first, logic; then mathematics before natural science; after that moral science; and finally the mature studied divine science. Therefore, Boethius should have placed mathematics before natural science. And so it seems that this division is unsuitable. On the contrary, the Philosopher proves the appropriateness of this division in the Metaphysics,10 where he says, There will be three philosophical and theoretical sciences: mathe­ matics, physics and theology.” 7. 8. 9. 10. Aristotle. De Anima HL 8, 431b24. Pseudo-Dionysius, Epistola VU, 2 (PG 3, 1080B). Aristotle, Nicomachean Ethics VL 8, 1142all-19. Aristotle, Metaphysics VI, L 1026al8. «J 6 QUESTION V, ARTICLE 1 DIVISION AND METHODS OF THE SCIENCES Moreover, in the Physics'1 three methods of the sciences are proposed which indeed seem to belong to these three. Moreover, Ptolemy also uses this division in the beginning of his Almagest.'2 Reply: The theoretical or speculative intellect is properly distinguished from the operative or practical intellect in this, that the speculative intellect has for its end the truth under consideration, while the practical intellect directs the truth under consideration to operation as to its end. So the Philosopher says in the De Anima ' that they differ from each other with regard to their end. And he says in the Meta­ physics, “ "The end of speculative science is truth, while the end of practical science is action”. /Now since the matter must be proportionate to the end} the subject matter of the practical sciences must be those things which can be achieved through our own efforts, so that we can direct the knowledge of them to operation as to an end. On the other hand, the subject matter of the speculative sciences must be those things which are nor produced through our efforts, so our investigation of them cannot be directed to operation as to an end. And it is according as these things are distinguished from each other that the speculative sciences ; must be divided. Now we must understand that when habits or powers are ^distinguished according to their objects, they are not dis­ tinguished according to just any differences of objects, but according to those which essentially characterize rhe objects as objects. * For instance, to be either an animal or plant is , Î 11 Aristotle. Physics Π. 2 193b23ff; 194514. 12 Claudius Ptolemaeus. Syntaxis Mathematica I, 1 (Opera Omnia I, 5,13 16 15 14 13. Aristotle. De Anima ΠΙ. 10. 433aI4. 14. Aristotle. Metaphysics H, 1 993520. 15. For the distinction between speculative and practical knowledge St. Thomas, Summa Theol. I. 1 4; I. 14. 16; De Veritate 2 8; 13· In I Eth. lect. 1 and 2 See also J. Maritain. Les Degrés du savoir pp. 618-625: Annexe VII pp. 879-896; Yves Simon. Critique de la connaissance morale. 16. For the distinction of powers and habits according to objects. f 7 acddental to a sensible thing as sensible; and so the distinction of the senses is not taken from this difference, but rather from the difference of color and sound. Consequently, the specula­ tive sciences must be distinguished according to the differences among objects of speculation precisely as objects of specula­ tion. Now an object of this kind—that is to say, an object of a speculative power—possesses one characteristic on the side of the intellectual power and another on the side of the habit of science perfecting the intellect. On the side of the intellect it belongs to it to be immaterial, because the intellect itself is immaterial. On the side of the habit of science it belongs to it to be necessary, because science is of the necessary, as is proved in the Posterior Analytics.'1 Now whatever is neces­ sary, is as such immobile; for, as is said in the Metaphysics,'* everything which is moved, in so far as it is moved, can be or not be, either absolutely or in a certain respect. Therefore, separation from matter and motion, or connection19 with them, essentially belong to an object of speculation, which is the object of speculative science. Consequently the speculative sciences are distinguished according to their disposition (ordinem) with reference to separation from matter and motion. Now there are some objects of speculation which depend on matter with respect to their existence, for they can only exist in matter. And there is a distinction among these. Some depend on matter both with respect to their existence and their concept. This is the case with those whose definition contains sensible matter and which, therefore, cannot be under­ St Thomas. Summa Theol. I, 77, 3; Ι-Π, 54, 2 In I Phys. lect. L nn. 1-3. Eng. trans, p. 13. 17. Aristotle, Posterior Analytics I, 6, 7455-75alî. 13. Aristotle, Metaphysics IX, 8, 1050511-15. See St Thomas, In IX Meta. lect 9. n. 1869. ArmPcatio St Thomas here refers to the connection or relation Ctween the universal natures considered by natural science and 7? individual things from which they are abstracted. This cwiknown through an act of reflection, is necessary for See below. Q. 5, a. 2 and Reply to obj. 4. p. 22 8 DIVISION AND METHODS OE THE SCIENCES stood without sensible matter; as, for instance, it is necessary to include flesh and bones in the definition of man. Physio or natural science studies things of this sort. There are some objects of speculation, however, which although depending on matter with respect to existence, do not depend on it with respect to their concept, because sensible matter is not included in their definitions. This is the case with lines and numbers— the sort of things mathematics studies. There are still other objects of speculation which do not depend on matter with respect to their existence because they can exist without matter. This is true, whether they never exist in matter, e.g., God and the angels, or whether they exist in matter in some things and in others do not, e.g., substance, quality, being, potency, act, one and many, and the like. Theology or divine science (so called because God is the principal thing known in it) deals with all these. It is called by another name "metaphysics”, that is to say, "transphysics”, because in the order of learning it comes after physics for us who must rise from sensible things to what is beyond the sensible. It is also called first philosophy”30 in so far as all the other sciences take their principles from it21 and so come after it. It is impossible, however, for some things to depend on matter with respect to their concept and not with respect to their existence, for the intellect by its very nature is immaterial. So there is no fourth kind of philosophy besides the ones mentioned. 20. For a similar explanation of the three names of this science, see the Prooemium to St. Thomas’ Commentary on the Metaphysics. trans, below p. 83. Divine science and theology are here used as synonymous with metaphysics. They are not the theology of Sacred Scripture. as St. Thomas explains below in Q. 5, a. 4. p. 41. Aristotle himself calls this science primary philosophy or theology. The name “metaphysics” does not come from him, but from either Andronicus of Rhodes or some earlier editor of Aristotle’s works in the first century RC. who placed the treatises on primary philosophy after the Physics and therefore called them the treatises after the Physics. It is also possible that the name was coined to signify that metaphysics goes beyond the order of physics. See W. Ross. Aristotle's Metaphysics I. pp. xxxi-xxxii; W. Jaeger, Aristotle pp. 378-379. 21. Of course the other sciences have their own proper principles, which can be known without an explicit knowledge of the principles QUESTION V, ARTICLE 1 9 Reply to obj. 1. In the Ethics,22 the Philosopher considers the intellectual habits in so far as they are intellectual virtues. Now they are called virtues from the fact that they perfect the intellect in its operation; for virtue makes its possessor good and renders its work good. So he differentiates between virtues of this sort according as such speculative habits perfect the intellect in different ways. Now, in one way the speculative part of the soul is perfected by understanding, which is the habit of principles, through which some things become known of themselves. In another way it is perfected by a habit through which conclusions demonstrated from such principles are known, whether the demonstration proceeds from inferior causes, as in science, or from the highest causes, as in wisdom. But when sciences are differentiated in so far as they are habits, they must be distinguished according to their objects, that is, according to the things of which the sciences treat. And it is in this way that both here and in the Metaphysics23 speculative philosophy is distinguished into three parts. Reply to obj. 2. As is evident in the beginning of the Metaphysics,2* the speculative sciences concern things the knowledge of which is sought for their own sake. However, we do not seek to know the things studied by logic for them­ selves, but as a help to the other sciences. So logic is not included under speculative philosophy as a principal part but as something brought under speculative philosophy as fur­ nishing speculative thought with its instruments, namely, of metaphysics. Hence these sciences do not directly depend on metaphysics; they are autonomous in their own spheres. Yet the principles of metaphysics are the absolutely universal and primary principles. AH the others can be resolved into them. It is in this sense that all the other sciences are said to take their principles from metaphysics, and that this science is said to explain the principles of all the sciences. See below, Reply to obj. 9. p. 16; Q. 6, a. L Reply to the Third Question, p. 59. See also In I Post. Anal. lect. 17, rm. 4-5; J. Maritain, Introduction to Philosophy, pp. 113-114. 22. Aristotle, Nicomachean Ethics VI, 3β. 1139bl4ff. 23. Aristotle, Metaphysics VI. L 1026al8. 24. Aristotle, op. eit. L L 981b21. 982al; 2, 982al4-17. 10 DIVISION AND METHODS OF THE SCIENCES syllogisms, definitions and the like, which we need in the speculative sciences. Thus, according to Boethius,2 logic is not so much a science as the instrument of science. Reply to obj. 3. The seven liberal arts do not adequately divide theoretical philosophy; but, as Hugh of St. Victor says,2* seven arts are grouped together, leaving out certain other ones, because those who wanted to learn philosophy were first instructed in them. And the reason why they are divided into the trivium and quadrivium27 is that "they are as paths introducing the eager mind to the secrets of philosophy”.·' This is also in harmony with what the Philosopher says in the Metaphysics,-* that we must investigate the method of scientific thinking before the sciences themselves. And the Commentator says in the same place31* that before all the other sciences a person should learn logic, which teaches the method of all the 25. Boethius, In Isagogen Porphyrii Comm., ed. secundae, I, 3 (CSEL 48, 142) ; Eng. trans, p. 77. Sometimes St. Thomas calls logic a science because it proceeds by demonstration. (See In I Perih. lect. 1, n. 2; In I Post. AnaL lect 1, n. 2; In IV Meta. lect. 4, n. 576). At other times he calls it an art. because it involves the construction of syllogisms and the like, and it has a practical purpose, namely the direction of the human reason in its movement towards truth. Art is defined as the determined ordination of reason by which human actions through determined means arrive at their due end. Logic is the art by which reason directs itself so that it will reach its due end, which is, truth. Indeed, it is the “art of arts”, because it directs reason itself, from which in turn all the arts proceed. See In I Post. Anal. lect. L nn. 1-3; John of St Thomas, Ars Logica Π, Q. 1, a. 2, pp. 256 ff; J. Maritain. Introduction to Philosophy, pp. 142-148. See also below, note 40. 26. Hugh of St Victor, Didascalion HI, 3, p. 52, L 29-p. 53, L 8. 27. The trivium includes grammar, rhetoric and logic; the quadrivium arithmetic, geometry, astronomy and music. Inherited from the classical culture of Rome through the writings of Cicero and Quintillian. they became the foundation of mediaeval education. See L. J. Paetow, The Arts Course at Mediaeval Universities icith Special Reference to Grammar and Rhetoric; Hastings Rashdall. The Univer­ sities of Europe in the Middle Ages, ed. by F. M. Powicke and A. B. Emden. I. pp. 34-37; G. Paré, A. Brunet P. Tremblay, La Renaissance du rti’ siècle, pp. 98-108; R. McKeon. “Rhetoric in the Middle Ages ” Speculum. <1942). pp. 1-32. 28. Hugh of St Victor, ibid. 29. Aristotle, Metaphysics II, 3, 995a 12-14. 30. Averroes, In II Meta. X t. e. 15, fol. 35FG. QUESTION V, ARTICLE 1 11 sciences; and the trivium belongs to the domain of logic. The Philosopher further says in the Ethics31 that the young can know mathematics, but not physics, which requires experience. So we are given to understand that we should learn mathe­ matics, to whose domain the quadrivium belongs, immediately after logic. And so these are as paths preparing the mind for the other philosophic disciplines. We may add, too, that these are called arts among the other sciences because they not only involve knowledge but a certain work which is directly a product of reason itself; for example, producing a composition, sy llogism or discourse, numbering, measuring, composing melodies and reckoning the course of the stars. Other sciences, like divine and natural sciences, either do not involve a work produced, but only knowledge, and so we cannot call them arts, because, according to the Metaphysics,32 art is called "productive reason”; or they involve a material product, as in the case of medicine, alchemy and other sciences of this sort. These latter, then, cannot be called liberal arts because such actions belong to man on the side of his nature in which he is not free, namely, on the side of his body.31 And although moral science is 3L Aristotle, Nicomachean Ethics VI, 8, 1142all-19. 32. Aristotle, Metaphysics VI. I, 1025b22. Aristotle defines art as a habit which is directed to making and which involves a true course of reasoning. (See Nichomachean Ethics VI, 4. 1140al0). Following Aristotle. St. Thomas defines it as an operative habit accompanied by right reason. (See In VI Ethic, lect. 3, n. 1153). Again, he says that art is nothing else than right reason about works to be made. (See Summa Theol. Ι-Π. 57, 3). On this point, consult J. Maritain, Art and Scholasticism, p. 9. Alchemy is the art of transmuting base metals into pure ones, such as silver and gold. For the history of alchemy and its relation to rhemictry, see F. Sherwood Taylor, The Alchemists, Founders of Modem Chemistry. St Thomas’ views on alchemy are treated on pp. 96-100, but they are drawn from the Commentary on Book ΠΙ of the Meteors which is not the work of St Thomas but of his disciple, Peter of Auvergne. (See St. Thomas. Opera Omnia ed. Leonine ΙΠ o xxxiii). Lvnn Thorndike draws from the same source in describing St Thomas’ views on alchemy. See his A History of Magic and Experimental Science Π, p. 607. For this reason they are called mechanical or servile arts, in d:stinct’on to the liberal arts, which, although they involve a work produced directly by reason itself, do not exist for the sake of that J 12 DIVISION AND METHODS OF THE SCIENCES directed to action, still that action is not the act of the science but rather of virtue, as is clear in the Ethics.* 3536 So we cannot call moral science an art; but rather in these actions virtue takes the place of art. Thus, as Augustine says,38 the ancients defined virtue as the art of noble and well-ordered living. Reply to obj. 4. As Avicenna says,37 the distinction between theoretical and practical is not the same when philosophy is divided into theoretical and practical, when the arts are divided into theoretical and practical, and when medicine is so divided. For when we distinguish philosophy and likewise the arts into theoretical and practical we must do so on the basis of their end, calling that theoretical which is directed solely to work, but rather are ordained to knowledge. St. Thomas says, “Only those arts are called liberal which are ordained to knowledge. Those ordained to some utility to be achieved through action are called mechanical or servile.” (In I Meta. lect. 3, n. 59). “Even in speculative matters there is something by way of work: e.g., the making erf a syllogism or of a fitting speech, or the work of counting or measuring. Hence whatever habits are ordained to such works of the speculative reason are, by a kind of comparison, called arts indeed, but liberal arts, in order to distinguish them from those arts that are ordained to works done by the body; for these arts are, in a fashion, servile, inasmuch as the body is in servile subjection to the soul, and man, as regards his soul, is free [liber].” Summa Theol. Ι-Π, 57, 3. Reply to obj. 3. See M. D. Chenu, “Arts ‘mécaniques’ et oeuvres serviles,” Revue des sciences ph.il. et théol., 1940. pp. 313-315. 35. Aristotle. Nicomachean Ethice VI, 13, 1144bl7-30. There is a distinc­ tion between the moral science of right conduct and the moral virtues, which are the proximate principles of right conduct. Moral science or ethics is a practical science because its purpose is to direct human action; but it guides man only in a remote way, because as a science it deals with human actions in general and not directly with the particular action to be done here and now. The moral virtue of prudence is the immediate guide to action in the moral order. See J. Maritain, Les Degrés du savoir, pp. 618-624: Annexe VU, pp. 878-896; Introduction to Philosophy, pp. 264-267. 36. St Augustine. De Civitate Dei IV, 21 (CSEL 40, L 188); XIX, 1 (CSEL 40, Π. 364). Referring to this statement of St. Augustine. J. Maritain says that the virtue of prudence, “which discerns and applies the means orf attaining our moral ends,” can be called an art only metaphorically. For art in the proper sense of the word, is directed to the good work which the artist produces, whereas the virtue of prudence is directed to the good of the agent. See J. Maritain, Art and Scholasticism, p. 14. 37. Avicenna. Canon Medicinae I, fen. 1, doctr. L prologus (Venice, 1608. I, 6, a 33-40). knowledge of the truth, and that practical which is directed to operation. However, there is this difference when we distinguish the whole of philosophy and the arts on this basis: We divide philosophy with respect to the final end or happiness, to which the whole of human life is directed. For, as Augustine says,38 following Varro, "There is no other reason for a man philosophizing except to be happy.” And since the philosophers teach that there is a twofold happiness, one contemplative and the other active, as is clear in the Ethics,33 they have accordingly also distinguished between two parts of philosophy, calling moral philosophy practical and natural and rational philosophy theoretical. But when they call some arts speculative and some practical, this is on the basis of some special ends of those arts; as when we say that agriculture is a practical art while dialectic is theoretical.40 However, when we divide medicine into theoretical and practical, the division is not on the basis of the end. For on that basis the whole of medicine is practical, since it is directed to practice. But the above division is rather made according as what is studied in medicine is proximate to, or remote from, practice. Thus we call that part of medicine practical which teaches the method of healing, for instance, that medicines of such and such a kind should be given for such and such abscesses. On the other hand, we call that part theoretical which teaches the principles directing a man in his practice, although not proximately; for instance, that there are three virtues,41 and that there are so many kinds of 38. St Augustine, De Civitate Dei XIX, 1 (CSEL 40, Π, 366). St. Augustine refers to Varro’s Laber de Philosophia, which is not extant 39. Aristotle, Nicomachean Ethics X, 7-8, H77al2 ff. 40 Logic or dialectic is not properly a speculative science, but rather a liberal art, sine*» it is ordained to knowledge and it involves the construction of syllogisms, definitions, etc. (See above, note 34). But its special end is to serve the speculative sciences of which it is the instrument. Hence it can be called speculative or theoretical by reduction. (See above, note 25). 41 St Thomas refers to the classical division of virtues in medicine MMM 13 UVMVM QUESTION V, ARTICLE 1 14 DIVISION AND METHODS OF THE SCIENCES fever. Consequently, if we call some part of a practical science theoretical, we should not on that account place that part under speculative philosophy. Reply to obj. 5. One science is contained under another in two ways: In one way, as its part, because its subject is part of the subject of that other science, as plant is a part of natural body. So the science of plants is also contained under natural science as one of its parts. In another way, one science is contained under another as subalternated to it. This occurs ■when in a higher science there is given the reason for what a lower science knows only as a fact/2 This is how music is contained under arithmetic. Medicine, therefore, is not contained under physics as a part, for the subject of medicine is not part of the subject of natural science according to that character (ratio) by which it is the subject of medicine. For although the curable body is a natural body it is not the subject of medicine in so far as it is curable by nature, but in so far as it is curable by art. But because art is nature’s handmaid in healing (in which art too plays a part, for health is brought about through the power of nature with the assistance of art), hence it is that the reason for the practices used in the art must be understood from the properties of natural things. So medicine is subalternated to physics, and for the same reason so too are alchemy, the science of agriculture, and all sciences of this sort. We conclude, then, that in itself and in all its parts physics is speculative, although some practical sciences are subalternated to it. into vital, natural and animal. See Avicenna, Canon Medicinae I. _ fen. L doctr. 6 (Venice, 1608, I, TO b 40-44). 42. When one science is subalternated to another, it is inferior to it and borrows principles from it as from a superior science. It cannot explain those borrowed principles by itself. Only the higher science can do that. It assumes that they are true without knowing why they are true. For St Thomas’ doctrine of the subalterna to., of science, see In Boetium de Trinitate Π. 2. Reply to obj. 5; In I Sent. ProL Q. I. a. 3, quest 3, sol. 2; In I Post. Anal. lect 25. See also John of St Thomas. Ari Loffica II. 36. 2. pp. 795-802. QUESTION V, ARTICLE 1 15 Reply to obj. 6. Although the subjects43 of the other sciences are parts of being, which is the subject of metaphysics, the other sciences are not necessarily parts of metaphysics. For each science treats of one part of being in a special way distinct from that in w'hich metaphysics treats of being. So its subject is not properly speaking a part of the subject of metaphysics, for it is not a part of being according to that character (ratio) by which being is the subject of metaphysics. But from the point of view of this character it is a special science distinct from the others. However, the science treating of potency, or that treating of act or unity or anything of this sort, could be called a part of metaphysics, because these are considered in the same manner as is being, which is the subject of metaphysics. Reply to obj. 7. These parts of being require the same manner of consideration as being in general (ens commune) because they too are independent of matter. For this reason the science dealing with them is not distinct from the science of being in general. Reply to obj. 8. The other diversities of things mentioned in the objection do not differentiate those things essentially as objects of knowledge. So the sciences are not distinguished according to them. Reply to obj. 9. Although divine science is by nature the first of all the sciences, with respect to us the other sciences come before it.44 For, as Avicenna says,49 the order of this science is that it be learned after the natural sciences, which explain many things used by' metaphysics, such as generation, corruption, motion, and the like. It should also be learned after mathematics, because to know the separate substances metaphysics has to know the number and disposition of the heavenly spheres, and this is impossible without astronomy, 41 For the meaning of the subject of a science, see above, Introduction. pp. xv, xvi. 44. The punctuation of this sentence in the Wyser edition has been slightly changed. 45. Avicenna, Metaphysics I, 3, fol. 16 DIVISION AND METHODS OF THE SCIENCES flcmnn î Jîïk îw ü k JO ajusotoi which presupposes the whole of mathematics;48 while other sciences, like music, ethics, and the like, contribute to its fulness of perfection. Moreover, that this science presupposes some things as proved in the other sciences while it itself proves the principles of those other sciences, does not necessarily involve a vicious circle. For the principles which another science (such as natural philosophy) takes from first philosophy do not prove what the same first philosopher takes from the natural philosopher. Rather, they are proved through other selfevident principles. Similarly the first philosopher does not prove the principles he gives the natural philosopher by principles he receives from him, but by other self-evident principles. So there is no vicious circle in defining. Moreover, in the beginning the sensible effects from which the demonstrations of natural science proceed are more evident to us. But when through them we come to know the first causes, from these latter there will become evident to us the reason for the effects on which the proof of the demonstrations of fact (quia)*7 rest. In this way natural ' * ■ 46. According to Aristotle, the separate substances or intelligences are the movers of the heavenly spheres and are equal in number to them. • See Metaphysics XI, 8, 1073a32ff). Although St Thomas thought that the angels move the heavenly bodies, he does not restrict their number to the number of those bodies. See Summa Theot. I, 50. 3: De Substantiis Separatis Π, η. 12, p. 13L See also below, Q. 5, a. 4, note 28. In general, metaphysics uses the inferior sciences and in this sense depends on them. But this dependence is purely materiaL As the supreme science in the natural order, metaphysics is inde­ pendent in its own sphere and does not exist for the sake of the other sciences. It is supremely free. See St. Thomas, In I Meta, lect 3, n. 58; J. Maritain. An Introduction to Philosophy, p. 118.47 47. A demonstration quia is one which proves the existence of something from its effect without revealing the very nature of that thing or giving the reason why it is. Only a demonstration propter quid does that Thus the demonstrations of the existence of God based on the sensible world are demonstrations quia, not propter quid. "Demonstrations can be made in two ways: One is through the cause, and is called propter quid, and this is to argue from what is prior absolutely. The other is through the effect, and this is called a demonstration quia; this is to argue from what is prior relatively only to us.” Summa TheoL I. 2, 2. See Contra Gentiles Ϊ, 12; In I Post. AndL lect. 21 See also G. Smith, Natural Theolopy, pp. 55-59. QUESTION V, ARTICLE 2 17 sdence contributes something to divine science and never­ theless it is divine science which explains its principles. That is why Boethius48 places divine science last, because it is the last relatively to us. Reply to obj. 10. Although we should learn natural science after mathematics because the extensive data it is grounded upon require experience and time, still, since natural things fall under the senses, they are naturally better known than the mathematical entities abstracted from sensible matter. ARTICLE TWO Does Natural Philosophy Treat of What Exists in Motion' and Matter? We proceed thus to the second article: It seems that natural science does not treat of what exists in motion and matter. Objection I. For matter is the principle of individuation. Now, according to Plato’s doctrine, which is found in Porphyry,2 no science treats of individual things but only of universals. Therefore, natural science does not treat of what is in matter. Objection 2. Again, science pertains to the intellect. But the intellect knows by abstracting from matter and from the conditions of matter. Therefore, no science can treat of what is not abstracted from matter. Objection 3. Again, as is clear in the Physics,3 the First Mover is considered in natural science. But the First Mover 48. Boethius, De Trinitate 2 (PL 64, 1250A). L Motion (motus), as used throughout the article, means not only change of place, but change in general, including qualitative, quan­ titative and substantial change. For St Thomas doctrine of change, see I* ΙΠ Phys. lect. 1-5; Eng. trans, pp. 7, 28-49. , Pru-τΛντν Isaaoae (Commentaria in AristotL Graeca TV/l, p. 6. IL 1 5-16).Philebus 1SC-D, ITO; Laches 198D. 3. Aristotle. Physics VOL 5, S6a4-257a33. wjwesjw at jrrn r Γί?.κ tw 18 DIVISION AND METHODS OF THE SCIENCES is free from all matter. Therefore, natural science does not treat only of what is in matter. Objection 4. Again, every science has to do with what is necessary. But whatever is moved, as such is contingent, as is proved in the Metaphysics* Therefore, no science can treat of what is subject to motion; and so neither can natural science. Objection 5. Again, no universal is subject to motion; for as is said in the beginning of the Metaphysics,5 it is not man in general who is healed, but this man. But every science concerns that which is universal. Therefore natural science does not treat of what is in motion. Objection 6. Again, some of the things with which natural science deals are not subject to motion; for instance, the soul, as is shown in the De Anima,'' and the earth, as is proved in the De Caelo et Mundo.1 What is more, all natural forms neither come into being nor perish, and for the same reason they are not subject to motion except accidentally. This is shown in the Metaphysics* Therefore not everything that physics considers is in motion. Objection 7. Again, every creature is mutable, for, as Augustine says,9 immutability naturally belongs to God alone. So if it is the task of natural science to consider what is in motion, it will be its business to consider all creatures; which clearly appears to be false. On the contrary, it is the work of natural science to reach conclusions about natural things. Now, natural things are those in which there is a principle of motion; and, as the 4. Aristotle. Metaphysics IX. 8. 1050bll-15. 5. Aristotle. Metaphysics I. 1, 981al8-20. 6. Aristotle. De Anima I, 3, 4O5b31-407bl2. 7. Aristotle. De Caelo et Mundo Π, 14, 256a24-297a8. bility of the earth, see below, note 25. For the immo­ 8. Aristotle. Metaphysics VTl, 8. 1033b5. 9. St. Augustine. De Civitate Det XI, 10 (CSEL 40, L 525). QUESTION V, ARTICLE 2 19 Metaphysics says,!0 wherever there is motion there must be matter. So natural science treats of what is in motion and matter. Moreover, there must be some speculative science dealing with what is in matter and motion, for otherwise the teaching of philosophy, which is knowledge of being, would be incomplete. Now no other speculative science treats of these things, for neither mathematics nor metaphysics does so. Therefore, natural science treats of them. Moreover, the fact is clear from the statements of the Philosopher in the Metaphysics" and the Physics1* Reply: It was the difficulty involved in this problem that drove Plato to posit ideas. For, as the Philosopher says,13 he believed all sensible things to be always in flux, following the opinion of Cratylus and Heraclitus, and so he thought that there can be no science concerning them. As a consequence, he asserted the existence of substances separated from the sensible world, which might serve as the objects of science and of definitions. Now he made this mistake because he failed to distinguish what is essential from what is accidental. Thus it happens that accidentally even the wise frequently fall into error, as is said in the Sophistic Refutations.1* Now, as is shown in the Metaphysics,'3 we find in a sensible substance both the whole or the composite itself, and also the nature (ratio), that is, its form;18 and it is the 10. IL 12. 11 14. 15. 16. Aristotle, Metaphysics IX, 8, 1050b22; see VII. 8, 1033bl8. Aristotle, Metaphysics VI,. 1, 1025b26-28. Aristotle, Physics Π, 2, 193b22-134al2. Aristotle, Metaphysics I, 6, 987a32-34. Aristotle, Sophistic Refutations I» 6. 164b6. Aristotle, Metaphysics VII, 8, 1033bl7ff. Form, as used here by St Thomas, means the whole nature or of a thing. It is the ratio of a thing, or that which its defini­ tion signifies. For example, humanity is the essence of Peter; con­ sequently it is his form or ratio. Notice that form in this context does not mean substantial form, for instance in man. his soul. The difference between these two meanings of the word "form” is expre^sed by the terms forma zotius (form of the whole) and forma 20 DIVISION AND METHODS OF THE SCIENCES composite which is essentially generated and corrupted and not the nature or form except accidentally. As the Metaphysics says,1 "It is not house that comes into existence, but this house.” Now anything can be considered apart from whatever is not essentially related to it. Consequently, the forms and natures of things, though they be forms and natures of things existing in motion, are without motion according as they are considered in themselves. Therefore, as the Philosopher says,” they can be the objects of sciences and definitions. As he proves,* 19 the sciences of sensible things are not grounded on 18 17 a knowledge of certain substances separated from the sensible world. Now, when we consider without motion natures (rationes) of this kind, which are the objects of the sciences of things, we must consider them without the characteristics according to which motion belongs to mobile things. But since every motion is measured by time, and the first motion is local motion, without which there is no other motion present, it must be that a thing is subject to motion according as it exists here and now; and this belongs to a mobile thing itself according as it is individuated by matter existing under determined dimensions.20 Therefore, natures of this sort, by 17. 18. 19. 20. pnrtij (form of the part). The former is the whole essence, including both form and matter in a material substance. The latter is a part of the essence and excludes matter. See St. Thomas. De Ente et Essentia 3. pp. 31-32. Eng. trans, p. 28 and note 7, pp. 37-38: In VII Me tn. lect. 9, nn. 1467-1469. See also A. Maurer, “Form and Essence in the Philosophy erf St Thomas.” in Mediaeval Studies, 1951, pp. 16-17«. Aristotle, Metaphysics VII, 15, 1039b25. Aristotle, Metaphysics VII, 15, 1039b27-1040a2. Aristotle shows here that there is neither scientific definition nor demonstration about sensible individual substances because they are contingent and can either be or not be. Science deals primarily only with the necessary, that is. with the natures of things as defined in universal concepts. See St. Thomas, In VII Meta. lect. 15. For the way in which the individual is known in natural science, see below, Q. 5, a. 2, Reply to obj. 4, p. 22. Aristotle. Metaphysics VU 14. 1039a21ff. For St. Thomas’ doctrine of individuation of form by matter, see Roland-Gosselin, Le “De Ente et Essentia" pp. 10£ff. By determinate matter (materia signata) is meant particular matter, for instance QUESTION V, ARTICLE 2 21 reason of which there can be sciences of mobile things, must be considered without determined matter and everything consequent upon such matter, but not without undetermined matter, because the notion of the form which determines matter to itself depends on this notion of undetermined matter. That is why the nature of man, which his definition signifies, and which is the object of science, is considered without this flesh and these bones, but not absolutely without flesh and bones. And since, as the Metaphysics says,21 individual things include determined matter in their nature while universals include common matter, we do not call this simply an abstraction of form from matter, but of the universal from the particular. Natures of this sort, abstracted in the above manner, can be considered in two different ways: In one way in themselves, and then they are considered without motion and determined matter, and such a consideration befalls them only because of the existence they have in the intellect. In another way they can be considered in relation to the things of which they are the natures, which things indeed exist in matter and motion. In this way they are principles whereby we know those things, since everything is known through its form. Thus in natural science we have knowledge of mutable and material things existing outside the soul through natures of this sort, which are immobile and considered without particular matter. Reply to obj. 1. Matter is the principle of individuation only in so far as it exists with determined dimensions; and in this sense natural science indeed abstracts from matter. Reply to obj. 2. The intelligible form is a thing s quiddity, for, as the De Anima says,22 the object of the intellect is the this flesh or these bones. By indeterminate matter is meant common matter, for instance flesh and bones. The natures studied by natural sciences abstract from the former, but not brom the latter kind of matter. See Summa Theol. I, 85. 1. Reply to obj. 2. a. Aristotle, Metaphysics VTL 10, W35027-31. Aristotle De Anima HL < 429619. See St Thomas, In ΠΙ De Anima, 22. led 8. nn. 705-717; Eng. trans, pp. 414-419. 22 DIVISION AND METHODS OF THE SCIENCES u'bat of a thing. Now, as is said in the Metaphysics,23 the quiddity of a universal composite, like man or animal, includes within itself common, but not particular, matter. So the intellect regularly abstracts from determined matter and its conditions; but in natural science it does not abstract from common matter, although matter itself is considered in natural science only in relation to form. For this reason the natural scientist is more concerned with form itself than he is with matter. Reply to obj. 3. Natural science does not treat of the First Mover as of its subject or as part of its subject, but as the end to which natural science leads. Now the end does not belong to the nature of the thing of which it is the end, but it has a relation to it; as the end of a line is not the line but is related to it. So also the First Mover is of a different nature from natural things, but it is related to them because it moves them. So it falls under the consideration of natural science, not in itself, but in so far as it is a mover. Reply to obj. 4. Science treats of something in two ways: In one way, primarily and principally; and in this sense science is concerned with universal natures, which are its very foundation. In another way it treats of something secondarily, as by a sort of reflection; and in this sense it is concerned with the things whose natures they are, inasmuch as, using the lower powers, it relates those natures to the particular things possessing them. For a knower uses a universal nature both as a thing known and as a means of knowing. For through the universal nature of man we can judge of this or that particular man. Now, all universal natures of things are not subject to motion and so, in this respect, all science is con­ cerned with what is necessary. But some of the things possessing those natures are necessary and immobile, and others are contingent and subject to movement; and in this respect sciences are said to be concerned with the contingent and mobile.-1 23 Aristotle. Metapliyaica VII, 10, 1035b28-30. 24. Individual things are thus indirectly and secondarily the object of QUESTION V, ARTICLE 2 25 Reply to ohj. 5. Although a universal is not moved, it is levertheless the nature of a mobile thing. Reply to obj. 6. Although the soul and other natural forms are not themselves subject to motion, they are moved accidentally, and they are moreover the perfections of mobile things; and for this reason they come within the domain of natural science. But even though the earth as a whole is not moved (for it happens to be in its natural place, where a thing is at rest in virtue of the same nature through which it is moved to a place), nevertheless, when its parts are outside their proper place, they are moved to a place.* 25 Thus the earth falls within the domain of natural science both by reason of the immobility of the whole earth and by reason of the movement of its parts. Reply to obj. 7. The mutability characteristic of all crea­ tures is not with respect to any natural motion, but with respect to their dependence on God, separation from whom entails destruction of their very being. And that dependence falls under the consideration of metaphysics rather than natural philosophy. Spiritual creatures, moreover, are mutable only with regard to choice; and this sort of motion is not the concern of the natural philosopher but rather of the metaphysician. science. See above. Reply, p. 20; also Summa Theol. I, 86, 1; 86, 3. 25. According to mediaeval physics, each of the four elements, earth, water, air and fire,has its naturalplace in the universe, with earth at the center. Byvirtue of its nature, each of the elements rests in its proper place in the order in which they are listed above, or if removed from that place tends to move back to it That is why a stone, in which the element of earth predominates, tends to fall, and fire tends to rise. See St Thomas, Γη I De Caelo et Mundo, lect. 17-18. See also J. de Tonquédec, Questions de cosmologie et de physique chez Aristotle et saint Thomas, pp. 8-16. For the immobility of the earth in the center of the universe, see st Thomas, In Π De Caelo et Mundo, lect 21. ARTICLE THREE Does Mathematics Treat Without Motion and Matter of What Exists in Matter? We proceed thus to the third article: It seems that mathematics does not treat of what exists in matter without matter. Objection 1. For since truth consists in the adequation of thing to intellect, there must be falsehood whenever we think of something otherwise than it is. If then in mathematics we consider what is in matter without matter, we will consider it falsely; and so mathematics will not be a science, for every science is concerned with what is true. Objection 2. Again, as the Philosopher states,1 every science has the task of considering a subject and the parts of that subject. Now in actual existence matter is a part of all material things. So it is impossible for a science to treat of what is in matter without treating of matter. Objection 3. Again, all straight lines are specifically the same. But the mathematician treats of straight lines by numbering them; otherwise he would not treat of the triangle and the square. It follows that he considers lines as specifically the same and numerically different. But it is clear from the above that matter is the principle differentiating things specifically the same. So the mathematician treats of matter. Objection 4. Again, no science completely abstracting from matter demonstrates through a material cause. But in mathe­ matics some demonstrations are made which can only be reduced to a material cause, as when we demonstrate something about a whole by its parts. For, as the Physics says? parts are the matter of the whole. Thus in the Posterior Analytics1 23 the demonstration that the angle in a semicircle is a right angle from the fact that each of its two parts is half of a right angle, 1. Aristotle, Posterior Analytics I. 28. 87a38ff. 2. Aristotle. Physics Π. 3. 195a20. 1 Aristotle. Posterior Analytics Π, IL 94a28-34. i QUESTION V, ARTICLE 3 25 is reduced to a material cause. Therefore, mathematics does not entirely abstract from matter. Objection 5. Again, motion cannot exist without matter. But the mathematician ought to consider motion, because, since motion is measured relative to space, to consider the quantity of space, which pertains to the mathematician, and the quantity of motion, has the same nature and belongs to the same science. Therefore, the mathematician does not entirely leave matter out of consideration. Objection 6. Again, astronomy is a part of mathematics and so too is the science of the moved sphere, the science of weights, and music;4 all of which treat of motion and mobile things. So mathematics does not entirely abstract from matter and motion. Objection 7. Again, natural science is entirely concerned with matter and motion. But some conclusions are demon­ strated alike by the mathematician and the natural scientist; for instance, whether the earth is round and whether it is in the middle of the universe. Therefore, it is impossible that mathematics entirely abstract from matter. If it be said that mathematics abstracts only from sensible matter, the contrary seems true, for sensible matter seems to be particular matter, because what the senses perceive are particular things, and all the sciences abstract from this kind of matter. So mathematical investigation should not be called more abstract than that of the other sciences. Objection 8. Again, the Philosopher says3 that there are three branches of study: the first of what is mutable and corruptible, the second of what is mutable and incorruptible, and the third of what is immutable and incorruptible. As 4. See St Thomao’ reply to the objection for the sense in which these sciences are *=»*4 to be parts of mathematics. By the science of the moved sphere (sphaera mota) is meant the general study of the movement of soherical bodies. See St Thomas. In VI Phys. lect 12. a. 3; see also ttv» references to “moved sphere” in the Index to St. Thomas’ Commentary on the De Caelo et Mundo in the Leonine edition, p. 443. 5. Aristotle, Physics Π, 1, 138a28-3L 16 DIVISION AND METHODS OF THE SCIENCES Ptolemy explains,6 the first is natural science, the third divine science, and the second mathematics. Therefore, mathematics concerns what is mutable. On the contrary there is what the Philosopher says in the Metaphysics.' Moreover, some things, although existing in matter, do not contain matter in their definition; for instance, the curved, which differs in this respect from the snub. Now philosophy should treat of all beings. Hence some part of philosophy must consider beings of this sort; and this is mathematics, for this does not belong to any other part. Moreover, what is prior from the point of view of the intellect can be considered without what is posterior. Now mathematicals are prior to natural things existing in matter and motion, for the latter are so related to mathematicals that they add something to them, as is said in the De Caelo et Mundo* Therefore, mathematical investigation can be without matter and motion. Reply: In order to throw light on this question we must understand how the intellect in its operation is able to abstract.* We must realize that, as the Philosopher says,10 the intellect has two operations, one called the ''understanding of indi­ visibles,” by which it knows what a thing is; and another by which it composes and divides, that is to say, by forming affirmative and negative enunciations. Now' these two opera­ tions correspond to two principles in things. The first operation has regard to the nature itself of a thing, in virtue of w'hich the known thing holds a certain rank among beings, whether it 6. Claudius Ptolemaeus, Syntaxes Mathematica I, 1, (Opera Omnia I 5, B-6, 5). 7. Aristotle. Metaphysics VI, 1, 1026a7-10, 14. 8. Aristotle. De Caelo et Mundo ill. 1, 299alfiff. 9 For the meaning of abstraction and the modes of abstraction, see above. Introduction. pp. xvi-xxvii. 1Û. Aristotle. De A aima III, 6, 430a26; b26ff. QUESTION V, ARTICLE 3 17 be a complete thing, as some whole, or an incomplete thing, as a part or an accident. The second operation has regard to a thing's act of existing (esse), which results from the union of the principles of a thing in composite substances, or, as in the case of simple substances, accompanies the thing’s simple nature. Now, since the truth of the intellect results from its conformity with the thing, clearly in this second operation the intellect cannot truthfully abstract what is united in reality, because the abstraction would signify a separation with regard to the very existence of the thing. For example, if I abstract man from whiteness by saying, "Man is not white,” I signify that there is a separation in reality. So if in reality nun and whiteness are not separated, the intellect will be false. Through this operation, then, the intellect can truth­ fully abstract only those things which are separated in reality, as when we say, "Man is not an ass.” Through the first operation, however, we can abstract things which are not separated in reality; not all, it is true, but some. For since everything is intelligible in so far as it is in act, as the Metaphysics says,11 we must understand the nature itself or the quiddity of a thing either inasmuch as it is a certain act (as happens in the case of forms themselves and simple substances); or by reason of that which is its act (as we know composite substances through their forms); or by reason of that which takes the place of act in it (as we know prime matter through its relationship to form, and vacuum through the absence of a body in place). And it is from this that each nature is given its definition. Now, when that through which the intelligibility (ratio)'2 of a nature is constituted and through which the nature itself IL Aristotle, Metaphysics IX, 9. 1051a29-32. < 12. The ratio of a thing is its definition, or, in other words, the concept which expresses what a thing is. By extension, the term also signifies the intelligible nature of a thing corresponding to its definition. More" generally. ratio is simply what the intellect grasps of the mean­ ing of any name. See St Thomas. Iit I Sent. 2. 1, 3; 33, 1. L Reply to obj. 3. £8 DIVISION AND METHODS OF THE SCIENCES is understood, has a relation to, and a dependence on, some­ thing else, clearly we cannot know the nature without that other thing. This is true whether they are connected as a part is united to a whole (as we cannot know foot without knowing animal, because that whereby foot has the nature of foot depends on that whereby animal is animal)’, or whether they are connected as form is united to matter, as one part to another part, or as accident to subject (as we cannot know the snub without nose); or even whether they are separated in reality (as we cannot know father without knowing son, although these relationships are found in different things). But if one thing does not depend on another with regard to what constitutes the intelligibility of the nature, then the intellect can abstract it from that other thing so as to know it without that other. This is true not only if they are separated in reality, as man and stone, but also if they are united in reality, whether they are joined as part and whole (as letter can be understood without syllable, but not vice versa, and animal without foot but not conversely); or even if they are joined as form is united to matter and accident to subject (as whiteness can be understood without man and vice versa). Accordingly, in its various operations the intellect dis­ tinguishes one thing from another in different ways. In the operation by which it composes and divides, it distinguishes one thing from another by understanding that the one does not exist in the ocher. In the operation, however, by which it understands what a thing is, it distinguishes one from the other by knowing what one is without knowing anything of the other, either that it is united to it or separated from it. So this distinction is not properly called separation, but only the first. It is correctly called abstraction, but only when the things, one of which is known without the other, are one in reality. For if we consider animal without considering stone, we do not say that we abstract animal from scone. It follows that since, properly speaking, we can only abstract things united in reality, there are two sorts of abstraction corresponding to the two modes of union mentioned above. QUESTION V, ARTICLE 3 29 namely, -fbe union of part and whole, and the union of form and matter. The first is that in which we abstract form from matter, and the second is that in which we abstract a whole from its parts. Now that form can be abstracted from some matter, the intelligibility of whose essence does not depend on matter of that sort; but the intellect cannot abstract form from the sort of marær on which the intelligibility of the essence depends. Consequently, since all accidents are related to substance as form to matter, and since the nature of every accident is to depend on substance, any accidental form cannot possibly be separated from substance. Accidents, however, befall sub­ stance in a definite order. Quantity' comes first, then quality, then passions and motion. So quantity can be considered in substance before the sensible qualities, in virtue of which matter is called sensible, are understood in it. Quantity, then, does not depend on sensible matter with regard to the nature of its substance, but only on intelligible matter.'3 For, after accidents have been excluded, substance remains intelligible only to the intellect, because the sense powers do not reach a comprehension of substance. And it is mathematics, which considers quantities and the properties of quantities, such as figures and the like, which treats of abstract entities of this sort. Furthermore, we cannot abstract a whole from just any parts whatsoever. For there are some parts on which the nature of the whole depends, that is, when to be such a whole 13. The matter which is the subject of mathematics is called “intelligible because it is not perceived by the external senses, like “sensible matter”, but by the imagination, which was sometimes called “in­ tellect” by the mediaevals. See St. Thomas, In VII Meta. lect. 13. nn 1494-1496: In IB De Anima, lect. 10. n. 745; Eng. trans, p. 432. ~ Intelligible matter is defined as “substance as subject to quantity. See Summa Theol. 1, 85, 1, Reply to obj. 2; In II Phys. lect 3. n. 5. However St. Thomas sometimes speaks of the subject of mathematics as simply quantities and their properties, such as figures, surface the like «See In VII Meta. lect 11. n. 1508). It should be noticed that according to St Thomas mathematics does in a sense n,