Aristotle (384-322 bc) T. H. Irwin Routledge Encyclopedia of Philosophy, Version 0

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15 Universals, Platonic Forms, mathematics

These disputes partly concern Aristotle’s attitude to the reality of universals. One-sided concentration on some of his remarks may encourage a nominalist or conceptualist interpretation. (1) He rejects Plato’s belief (as he understands it) in separated universal Forms, claiming that only particulars are separable. (2) In Metaphysics VII 13-16 he appears to argue that no universal can be a substance. (3) He claims that the universal as

object of knowledge is - in a way - identical to the knowledge of it (On the Soul 417b23).
Other remarks, however, suggest realism about universals. (4) He claims they are better known by nature; this status seems to belong only to things that really exist. (5) He believes that if there is knowledge, then there must be universals to be objects of it; for our knowledge is about external nature, not about the contents of our own minds.
Aristotle’s position is consistent if (1)-(3) are consistent with the realist tendency of (4)-(5). The denial of separation in (1) allows the reality of universals. Similarly, (2) may simply say that no universals are primary substances (which are his main concern in Metaphysics VII). And (3) may simply mean (depending on how we take ‘in a way’) that the mind’s conception of the extra-mental universal has some of the features of the universal (as a map has some of the features of the area that it maps). While Aristotle denies that universals can exist without sensible particulars to embody them, he believes they are real properties of these sensible particulars.
He offers a rather similar defence of the reality, without separability, of mathematical objects (Physics II 2; Metaphysics XIII 3). While agreeing with the Platonist view that there are truths about, for example, numbers or triangles that do not describe the sensible properties of sensible objects, he denies that these truths have to be about independently-existing mathematical objects. He claims that they are truths about certain properties of sensible objects, which we can grasp when we ‘take away’ (or ‘abstract’) the irrelevant properties (for example, the fact that this triangular object is made of bronze). Even though there are no separate objects that have simply mathematical properties, there are real mathematical properties of sensible objects.

16 Metaphysics: God

When Aristotle claims that first philosophy is also theology (see §11), he implies that the general discussion of being and substance is the basis for the special discussion of divine substance. (Hence later writers distinguish ‘special metaphysics’, dealing with God, from ‘general metaphysics’, dealing with being in general.) The different features of substance explained in Metaphysics VII-IX are included in the divine substance of XII. (1) Primary substance is to be identified in some way with form rather than with matter or with the compound of form and matter; divine substance is pure form without matter. (2) Primary

substance is in some way numerically one, a ‘this’ rather than a ‘such’; divine substance is completely one and indivisible. (3) Primary substance is in some way actuality rather than potentiality; divine substance is pure actuality with no potentiality. (4) Primary substance is soul rather than body (see §17); divine substance is pure intellect without sense or body.
In each case the properties of primary substance are found in a sensible substance (an animal or a plant) only in so far as they belong to an object that also has other properties; hence primary substance in sensible reality is the form and actuality of an object (a horse, for example) that also has matter and potentiality. In divine substance, however, each feature is found in separation from these other properties; that is why a divine substance lacks matter, multiplicity, parts or potentiality. Aristotle argues that a substance with these pure substantial properties must exist if any sensible substances are to exist; for the existence of potentialities that can be actualized presupposes the existence of an actuality that does not itself include any potentiality (to avoid an infinite regress).
Since this primary type of substance is divine, it is what traditional belief in the Olympian gods was about, what the Presocratics were talking about when they spoke of ‘the divine’, and what Plato was talking about in speaking of a supreme god. Aristotle mentions the traditional Olympian gods without committing himself to acceptance of the

traditional conception of them. He rejects anthropomorphic views of the gods, but he speaks of the divine nature as a kind of mind. He believes that there is something divine about the order and workings of nature, and still more divine in the heavenly substances (Parts of Animals I 5). Although he continues to speak of gods in the plural, he also speaks of one divine mind as the ultimate cause of the whole universe; these remarks help to justify the later interpreters who take him to speak of the one God who is the subject of (for example) Aquinas’ ‘Five Ways’ (Summa Theologiae 1a q.2 a.3).

Aristotle’s God is the ultimate cause of the physical universe, but not its creator (as Plato’s demiurge is), since Aristotle believes the universe is eternal. Nor does Aristotle suggest that God has providence or foreknowledge concerned with future contingent events. But he believes that the physical universe is dependent on God. In Physics VIII he

argues that the explanation of motion requires recognition of a first cause of motion, and in Metaphysics XII this first cause is identified with divine, immaterial, substance. This first mover is itself unmoved; it initiates motion only as an object of love initiates motion by attraction. It is the ultimate final cause of the various movements in the universe.

In treating the divine substance as a god, and hence as a being with a soul and an intellect, Aristotle attributes some mental life to it. But since it would be imperfect if it thought of objects outside itself (because it would not be self-sufficient), it thinks only of its own thinking. This restriction, however, is not as severe as it may seem, since Aristotle believes that the various objects of thought are in some way identical to the mind that thinks them (see §15). In so far as God thinks of his own mind, he thereby also contemplates the order of the universe as a whole; this is the order that the different movements in the universe seek to embody.
Sometimes (as in Physics VIII) Aristotle argues for a single first mover. In Metaphysics XII, however, he argues that an unmoved mover must be postulated for each of the distinct movements of the heavenly bodies. This astronomical interpretation of his theological doctrine is difficult to reconcile with his belief, reaffirmed in Metaphysics XII 10, that in some way the universe is unified by a single first unmoved mover.

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