Lesson 8: Abstraction and Separation

We have had occasion several times to dwell on the manner in which the theoretical sciences are distinguished from one another. The classical sources for this are found in various passages of Aristotle but there is a later text which is reminiscent of Aristotle but which has seemed to readers to convey a somewhat different doctrine from that of the Stagyrite. Boethius (480-524) is one of the most important figures in the history of philosophy. Living in Rome in parlous times, himself the beneficiary of an education that acquainted him with classical philosophy, he conceived the plan of turning all of Aristotle and all of Plato into Latin, thereby making them accessible to readers who had no Greek. Beyond this, Boethius hoped to show the fundamental agreement and complementarity of Plato and Aristotle. Boethius himself gives many indications of the influence of Neoplatonism.

Boethius had not made much headway on his translation project before he was accused of treason by Theodoric the Ostrogoth and sentenced to death. The Consolation of Philosophy was written as he awaited execution. Its influence on subsequent times can be gauged by the number of copies that have survived. That work, along with a handful of theological treatises -- Boethius was a Catholic -- drew the fascinated attention of later generations. In the thirteenth century, early in his Parisian career, Thomas Aquinas commented on two of the Boethian treatises, the work called by the medievals De hebdomadibus and another called On the trinity. Thomas's commentary on the latter is incomplete, coming to an abrupt stop shortly after he has discussed the statement of the distinction between physics, mathematics and theology found at the beginning of Chapter Two of On the Trinity. This incomplete commentary has been known by students of Thomas from the beginning, but the study of the holograph -- Thomas's own handwritten version -- of the work, along with discarded paragraphs which nonetheless survived in the manuscript tradition, triggered in recent years a spate of works, some of which professed to find in the Boethian commentary a vision of metaphysics quite different from Aristotle's.

I simply allude to the scholarly cadenza that can be descried here. A first set of questions turn on the relationship between Boethius and his sources: is he a Platonist or is he an Aristotelian? Neoplatonists give a quite different account of the distinction of the sciences than Aristotle did, and we find a version of this presented with apparent approval by Boethius in one of his commentaries on the Neoplatonist Porphyry. [There is as well the vexed problem of universals, occasioned by another Boethian commentary on Porphyry, something to which we will return.] Next, the question arises as to the relation between Thomas and Aristotle and Boethius -- does Thomas hold views that set him at odds with his great predecessors? Such questions have an attraction all their own and they are not without importance for the deeper understanding of the matters before us. But here we touch on them only insofar as the discussion casts light on the nature of metaphysics.

Thomas's commentary or exposition of the De trinitate, observes the original demands of the genre. The first task was to explicate the text, display its division and order. This is called the divisio textus. That being done, the commentator might then formulate the questions raised by the text and proceed to discuss them as such, that is, without further reference to the text that occasioned them. In his commentary on the Sentences of Peter Lombard, both these moments will be found, as well as a third, when Thomas returns to the text and resolves difficulties found in it, an exercise which benefits from the intervening discussions. [It might be mentioned that all these tasks are melded into one in such commentaries as Thomas wrote on Scripture and on Aristotle.] In the Boethian commentary that interests us, we find after an analysis of the opening of Chapter Two, two great questions raised and discussed, first, the division of the sciences, second, the mode or manner of the different sciences. In the modern ordering of the work, these are knows as Questions 5 and 6. In 1948, Wyser published an edition of these questions, but without the preceded divisio textus. It was with reference to it, as well as to the still unpublished rejected paragraphs, that a lively discussion went on. Subsequently, Bruno Dekker published the complete text of the uncompleted commentary and included in the appendix the versions that Thomas had scrapped. This edition provides the student with all he needs fully to assimilate the teaching of Thomas in this text, something desirable because of the light it cases on our subject, the nature of metaphysics and the way in which it differs from the other sciences. Father Armand Mauer's Thomas Aquinas: Faith, Reason and Theology, Toronto, 1987, complements his earlier Division and Method of the Sciences. The latter is a translation of the Wyser edition of Questions 5 and 6 of the commentary, whereas the former translates the first four questions, as well as the literal commentary of the divisio textus.

In Question 5, article 1, Thomas gives the division of the theoretical sciences and, in subsequent articles, takes up seriatim the philosophy of nature [article 2], mathematics [article 3] and divine science [article 4]. It is the discussion in article 3 that has received the most attention of late. Before turning to that, let us quickly review the content of article 1.

Alluding to the distinction between theoretical and practical thinking -- theoretical thinking aims at the perfection of thinking as such, that is, at truth, whereas practical thinking has an aim beyond thinking, in doing or making -- Thomas labels the concern of theoretical or speculative thinking the speculabile. The formal notes of the speculable object are derived, first, from the immaterial character of intellectual activity and, second, from the demands of science, that is, necessity. The necessary is that which cannot be otherwise, which is incapable of change. The speculabile, accordingly, will be characterized by removal from matter and change.

If immateriality and immobility are of the essence of the speculable, variations in these notes will provide us with a formal way to distinguish the sciences that bear on things so distinguished. The reader finds himself in familiar territory. The definitions of natural philosophy, while they include matter, include common not singular matter, bones and flesh, in Aristotle's favorite illustration, not these bones and this flesh. The definitions of mathematics exclude sensible matter, common as well as singular, but they do not commit us to the view that mathematics exist as they are considered. Finally, a third science defines its objects without any matter but with the added note that they are taken to exist as they are defined, that is, apart from matter and motion.

The previous lesson made clear why definition should play such a crucial role in science, even though definition is the product of the first operation of the mind, not the third, where discourse is engaged in. Just as judgments, propositions presuppose the definitions produced by the first operation of the mind, so discourse presupposes propositions and definitions. In the demonstrative syllogism par excellence in which a predicate is shown to express the property of the subject, the definition of the subject, its nature or essence, serves as the middle term. A property is an accident that it inheres in a subject because of what the subject is, its nature.

The stage is thus set by article 1 for subsequent detailed discussions of the various theoretical sciences. Let us turn to the third article which has generated so much discussion.

In approaching the way in which our mind grasps things and distinguishes them as it does so, we should first recall that there are two quite different mental acts. First, the mind's grasp of the nature of a thing, what it is, which is expressed in a definition or account. Second, a mental act which can be contrasted with the first as the complex is contrasted with the simple. This second act combines in affirmative and negative judgments what the mind has grasped. The mind distinguishes one thing from another, abstracts A from B, according to the first kind of mental act when it defines A without mentioning B in the definition when A and B are found together, exist together. Thus, given AB, one speaks of A without speaking of B: call this abstracting A from AB or distinguishing A from B. On the other hand, we might judge that A is not found with B and distinguish them in a negative propositions, "A is not B."

The difference between these lies in the fact that in the first mental act, to consider apart does not involve any assertion that what is so considered exists apart. For example, in defining "man" I make no mention of the singular features of this man or that -- I leave aside this flesh and these bones -- and express only what is essential to and thus found in any man. But this, pace Plato, does not entail that there is some man who exists apart from this man or that, from singular men. No more does the definition and discussion of triangle, which leaves our and abstracts from all sensible matter, entail that there are subsisting triangles apart from matter and motion.

In this article, Thomas proposes that we use "to abstract" or "abstraction" in a narrow sense to cover only cases where we think apart things which do not exist apart, when from AB, I abstract A without suggesting that A exists apart from AB. On the other hand, when we abstract one thing from another by way of a negative judgment, "A is not B," Thomas proposes to use the term "to separate" or "separation." Both of these terms can be used either broadly or narrowly; used broadly, they can be synonyms. Used narrowly, they are quite distinct.

In introducing the two mental acts on which this distinction is based, Thomas says that the first looks to essence or nature, while the second looks to the existence of the thing: respicit ipsum esse rei. It is that that caught the eye of many. They noticed the absence of this from the discarded drafts and then its appearance, which enabled Thomas to move swiftly on and complete the article. Given the view among many Thomists -- a view not shared by Thomas himself -- that the distinction between essence and existence is both peculiar to Thomas and the key to his thought, it is not surprising that the link of separation with esse did not escape attention. But there is more. The distinction between abstraction and separation is referred to the distinction of science -- hardly surprising when we remember that the distinction was made precisely in the course of a discussion of the division of the sciences.

There are two kinds of abstraction in the narrow sense, what Thomas calls abstractio totius -- abstraction of the whole -- and abstractio formae -- abstraction of form. The first of these is found in philosophy of nature and is common to all the sciences. That should be so is clear when we see that it is in effect the abstraction of the common nature from the individuals that have that nature. Abstraction of form is said to characterize mathematics. Two things are necessary to understand the phrase. First, accidents are to substance as forms to matter; second, the accidents inhere in substance in a certain order. For example, only an extended surface can be colored. On the basis of these two facts, considering extension apart from color and other sensible qualities, is called abstraction of form -- that is abstracting quantity from the sensible qualities which are subsequent to it. The matter corresponding to form here is, again, substance and, since substance as such is grasped by mind and not by sense, substance is said to be the intelligible matter of quantity.

Separation in the narrow sense is taken to characterize metaphysics. In the narrow sense, separation is the consideration of A without B when A exists apart from B, something captured in the judgments, "A is not B" or "A is separate from B." Now, struck by the fact that separation in the narrow sense is associated with the second act of mind and equally struck by the phrase respicit ipsum esse rei as characterizing this act, and struck further by Thomas's linking of separation and metaphysics, Thomists who saw the distinction between essence and existence as a defining achievement of St. Thomas were tempted to think that all this was pointing in the direction of saying that the distinction between essence and existence is crucial for the constitution of metaphysics, as if the science begins on the basis of this distinction. Pursued, such thinking leads in the direction of thinking that while natural philosophy and mathematics are concerned with essence, metaphysics is concerned with existence.

Approached in this way, the point of the text is quickly lost. What is the constitutive negative judgment, the separation, which metaphysics presupposes in order to begin. The context can leave little doubt that it is precisely the judgment that there is something, a substance, which exists apart from matter and motion. The second operation looks to the ipsum esse rei because the negative judgment expresses the real, existential separation of what is considered apart. The first operation of the mind considers apart what does not exist apart -- the nature apart from individuals, for example. When Thomas asks whether abstracting is falsifying, he further clarifies the distinction. The passage I am about to quote at some length is from the Summa theologiae, Ia, q. 85, a. 1, the reply to the first objection. This text was written some years after that in the exposition of Boethius's De trinitate, but the teaching is the same. You will notice that Thomas simply distinguishes two senses of abstracting here -- the narrow and broad senses -- and does not dub them abstrahere and separare, respectively, as he eventually did in the earlier text. It is doubtful that anyone would be tempted into existential excess by the passage in the Summa.

Dicendum quod abstrahere contingit duplicter. Uno modo, per modum compositionis et divisionis: sicut cum intelligimus aliquid non esse in alio, vel esse separatum ab eo. Alio modo, per modum simplicis et absolutae considerationis; sicut cum intelligimus unum, nihil considerando de alio. Abstrahere igitur per intellectum ea quae secundum rem non sunt abstracta, secundum primum modum abstrahendi , non est absque falsitate. Sed secundo modo abstrahere per intellectum quae non sunt abstracta secundum rem, non habet falsitatem; ut in sensibilibus manifeste apparet. Si enim intelligamus, vela dicamus colorem non inesse corpori colorato, vel esse separatum ab eo, erit falsitas in opinione vel in oratione. Si vero consideremus colorem et proprietatem eius, hihil considerantes de pomo colorato; vel si quod intelligimus, voce exprimamus, erit abseque falsitate opinionis vel orationis. Pomum enim non est de ratione coloris; et ideo nihil prohibet colorem intelligi, nihil intelligendo de pomo.

It should be said that there are two ways in which abstracting takes place. In one way, by composition and division, as when we understand a thing not to be in another or to be separated from it. In another way, in the manner of a simple and absolute consideration, as when we understand one thing without considering anything of another. Therefore, to abstract with intellect things which are not abstracted in reality, in the first way of abstracting, is not without falsity. But for the mind to abstract in the second way things not abstracted in reality does not involve falsity; as is manifest in sensible things. For if we should understand or say that color is not in the colored body, or that it is separated from it, there will be falsity both in opinion and speech. If if we should consider color and its properties without considering the colored apple at all; or if we should say what we think, there will be falsity of both opinion and speech. For apple is not of the essence of color, and that is why nothing prevents color from being understood while not thinking at all of apple.

Similiter dico quod ea quae pertinent ad rationem speciei cuiuslibet rei materialis, puta lapidis aut hominis aut equi, possunt considerari sine principiis individualibus, quae non sunt de ratione speciei. Et hoc est abstrahere universale a particulari, vel speciem intelligibilem a phantasmatibus: considerare scilicet naturam speciei, absque consideratione individualium principiorum, quae per phantasmata repraesentantur.

Cum igitur dicitur quod intellectus est falsus, qui intelligit rem aliter quam sit, verum est si ly aliterreferatur ad rem intellectam. Tunc enim intellectus est falsus, quando intelligit rem esse aliter quam sit. Unde falsus esset intellectus si sic abstraheret speciem lapidis a materia, ut intelligeret eam non esse in materia, ut Plato posuit. Non est autem verum quod proponitur, si ly aliter accipiatur ex parte intelligentis. Est enim absque falsitate ut alius sit modus intelligentis in intelligendo, quam modus rei existendo: quia intellectum est in intelligent immaterialiter, per modum intellectus; non autem materialiter, per modum re materiale.

So too I say that what pertains to the nature of any material thing, for example, a stone, a man or a horse, can be considered apart from the individuating principles which are not of the notion of the species. This is to abstract the universal from the particular, or the intelligible species from phantasms: namely to consider the nature of the species without a consideration of its individuating principles, which are represented by phantasms.

Therefore when it is said that the understanding is false which grasps the thing otherwise than as it is, this is true if otherwise is taken to refer to the thing understood. For the understanding is false when it understands the thing to be otherwise than as it is. Thus the intellect would be false if he should abstract the species of stone from matter and understand it not to be in matter, as Plato thought. But the claim is not true if otherwise is taken on the side of the one understanding. That the thing is understood in a way different from the way it exists does not involve falsity, because what is understood is in the thinker immaterially, not materially as in the material thing.

Suggested Reading Assignment

Selected Writings of Aquinas, the commentary on the De hebdomadius, lesson 2 [Selection 7].

Suggested Writing Assignment

While abstraction and separation in their broad senses are found in all the sciences, Thomas assigns each of them a narrow sense which enables him to distinguish metaphysics from mathematics and natural philosophy. Explain.


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