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WHAT IS INTELLIGIBLE MATTER? pAUL O'REILLY St. Anseim Ooiiege Marwhester, New Hampshire A ER ST. THOMAS' commentary on Boethius' De Trinita.te, another discussion on the nature of intelligible matter might ·seem unnecessary. In question five, article three of that work he argues that mathematics is the study of quantity and since no accident can be understood apart from substance, one must understand mathematics to have some substrate. This he calls intelligible matter. But what is intelligible matter? St. Thomas, along with Aristotle, recognises only two kiinds of substance: natuml composites ·and pure forms. Neither of these could be identified with intelligible matter. One could also ask what does the term " intelligible matter " mean. In a couple of plaices St. Thoma.s appears to call the substrate of mruthematica1ls intelligible matter because it is substance and substance can only he grasped by the intellect.1 Yet, manother text he explains that it is because mathematioals are held in the imagination, and rthe ·imagination is sometimes : referred to as intellect, that the matter of mathematicals is called intelligible.2 And then there are the te:x;ts in which both Aristortle and St. Thomas refer to this same subjecrt ais the continuum; iis the continuum the same thing as substance? We should further note thart several modern Arisrtotelian commentators describe 1 Cf. St. Thomas Aquinas, Ewpositio Super Librum Boethii de Trinitate, Q.5, a.3, pg. 184, n.16-18. (Bruno Decker) E. J. Brill, 1959, a.nd also Summa Theoloqiae, Prima Pars, Q.85, a.I, ad 2. (Texts of St. Thomas are taken from the Marietti editions unless otherwise indicated.) 2 Cf. St. Thomas, In Metaphysicorum, L.VII, l.X, n. 1495. 74 WHAT IS INTELLIGIBLE MATTER( 75 intelligible matter as the continuous, or as space or extension; are all these positions consistent? These, then, are some of the problems ·associated with the doctrine of intelligible matter. It tis important to determine what intelligible mrutter is for a few reasons. If one undel"stands it as the substance that is found in :the natural o;rder then mathematics will become a branch of physics, a consequence that is untenable for a Thomist. Whereas iit is ridiculous to think that the substance that is separa..te from ,sensible mrutter, viz. pure ,furms like angels, is the subject of mathematicals. Furthermore, there are other A:cistotelian-Thomist doctrines that could be implicated if one were to dismiss the traditional posiition on intelligible matter. For example, both these great thinkers recognise that every accident ·is dependent on substance for its being and its definition, but iif intelligible matter iis not substance, ais might seem to he the case if there ·are only the two kinds of substances mentioned before, then this assertion is not universal. A synthesis of St. Thomrus' position will, therefore, be valuable. The mathematician (at least the classical mathematician, if not all his modern counterparts) may consider this question irrelev;ant. A~ter all, the mathemartician does not stop to wonder about the kind of matter that composes mathematical figures. More than that, he could maintain that the notion of matter in mathematics is repugnant. For the marthematician, as Aristotle himself says,3 studies rthe figures of quantity and their properties and does not treat of that which is quantified. (The modern mathemartician does not even appear to grant this supposition, for him the mathematical object is relation not quantity.) The investigation into the nature of the subject of mathematical beings is not in the mathematician's domain . No science questions its own principles since to do so would require these very same principles. A more universal discipline will seek the answers to the questions we have raised; that discipline is metaphysics. a .Aristotle, Metaphysics, Bk. I.3, 106la29-36. 76 PAUL O'REILLY Although the notion of matter seems at first to have no place in mathematics, reflection reveals that some 'SON of matter is required in O['der to fully explain mathematical entities. For instance, how does one account for the many individuals of the same species that one finds in mathematics? Seveml triangles do not differ from each other because of what they are, ,all...

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