Applying the Results of the Eliminative Method to Alpha Generally

Now, what else is achieved in Aquinas's application of the method, and how well do those results apply to Alpha as delineated so far?

end p.117


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In Aquinas's application of the eliminative method in chapters 15-28 there are more than eighty arguments that are intended to eliminate nineteen predicates from the concept of Alpha—that is, to show, in the following order, that Alpha could not be

(A) anything that begins or ceases to exist (15.121, 123-5)

(C) dependent for its existence on anything other than itself (15.124)

(D) anything that has any passive potentialities (16.128-33)

(E) matter, or anything material (17.134-6)

(F) the universal material cause (prime matter) (17.137-40)

(H) subject to anything unnatural, violent, or coercive (19.149-52)

(I) corporeal, whether a body or a power in a body (20.154-86) (J) other than its own essential nature (21.197-201)

(K) anything whose being is other than its nature (22.203-8) (L) anything that has any accidental characteristics (23.214-19) (M) specified by differentiae (24.223-6)

(N) classified within any genus or category (25.228-32, 235-6) (0) defined (25.233)

(P) the subject of an a priori demonstration (25.234) (Q) a universal formal cause (26.238-47) (R) the form of any particular thing (27.251-8) (S) imperfect (28.259-66). I believe that all nineteen of these predicates are properly eliminable from the concept of Alpha. And, of course, if I'm right about that, then Alpha gets much more sharply delineated as a consequence of all those eliminations. I'll look more or less briefly at each of them, less briefly at the more controversial or more illuminating ones. I can't claim to offer full support for any of them now, but working on them has led me to think that the material Aquinas supplies in his several arguments for each elimination can be made to yield at least a very plausible case for each. It's clear that the elimination of some of these predicates has the effect of making Alpha look more like God. But it remains to be seen whether or not eliminating even all of them could count as unveiling Alpha to reveal God unmistakably.

In Chapter Three I said all I think I need to say about the elimination of predicates A and C. I said less there about M, N, and end p.118


© Copyright Oxford University Press, 2006. All Rights Reserved

O, but there's nothing unexpected or controversial in the observation that anything that could count as the ultimate explanation of the observable world could not be classified or defined by means of categories, genera, and differentiae—the taxonomic devices we've found to be indispensable to our detailed understanding of the things and events that make up the observable world. As for the closely associated predicate P, Aquinas derives its elimination immediately from the elimination of predicate O on the basis of an Aristotelian technicality. The entity under consideration cannot be the subject of an a priori demonstration 'because the starting-point of [such] a demonstration is the definition of whatever is the subject of the demonstration' (25.234). But the rest of what he says on this score in that same passage is untechnical and readily acceptable regarding Alpha at this stage of the investigation, when it is cognized only indirectly. He says that we can't frame any demonstration regarding the ultimate explanatory principle except on the basis of its effects, and so, if it can be the subject of demonstrative argumentation at all, it can be the subject of only a posteriori


5 25.234: Patet etiam quod non potest demonstratio de ipso fieri, nisi per effectum:

quia principium demonstrationis est definitio eius de quo fit demonstratio.

Aquinas argues for the elimination of predicate B, temporality, on the grounds of immutability. Temporality is ruled out by immutability only if immutabilty is understood super-strictly, the way Parmenides seems to have understood it, as ruling out getting older even when that sort of change involves no other sort of change in the thing that is getting older—the way Caesar's assassination is getting older. But the immutability justifiably associated with Alpha at this stage seems not obviously super-strict, and the mode of existence that really should be eliminated from Alpha here is spatio-temporality. It may be eliminated on the grounds that to be spatio-temporal is to be subject to this world's natural laws, a condition that can't characterize whatever it is that is supposed to account for this world's natural laws (in some way yet to be disclosed). And if Alpha could not be spatio-temporal, then, clearly, Alpha could not be matter, or anything

material (E), or corporeal, whether a body or a power in a body (I).

6 Ch. 20, 'God is not a body', is much the longest of the chapters in which the eliminative method is applied. It contains ten arguments, more than any other chapter, but most of the chapter is devoted to one very complex argument (20.161-84). It's not clear to me why Aquinas takes the elimination of corporeality so seriously (especially since the elimination of predicate I is never invoked as a premiss in chs. 21-8), or why none of his arguments for it rely on the earlier elimination of E, since eliminating materiality seems to be the most obvious basis on which to eliminate corporeality. Does he, perhaps, avoid using the materiality-corporeality connection because the universal hylomorphism maintained by some of his contemporaries requires incorporeal matter and so would reject that connection?

The elimination of E

end p.119


© Copyright Oxford University Press, 2006. All Rights Reserved leads naturally, perhaps irresistibly, to the elimination of F, the possibility that Alpha is the universal material cause of things. But I want to consider F later, in another connection.

Since Aquinas's concept of matter is the Aristotelian concept of it as passive potentiality, it isn't surprising that the route he takes to the elimination of E runs through the elimination of D, passive potentiality. In the elimination of D itself two kinds of passive potentiality are at issue. One kind is potentiality for existence and for non-existence, dependence on something else for beginning to exist and for continuing to exist: 'everything that has potentiality mixed into its substance can, to the extent to which it has potentiality, not exist' (16.128). This kind of passive potentiality is eliminated, naturally, on the basis of Alpha's absolutely independent

existence, which was argued for in G6.

7 Arguments against potentiality for existence and non-existence occur in 16.128,

129, 130, and 133. (For 16.128, see n. 4 above; for 16.130, see sect. 4c below.)

The other kind is passive potentiality in an existing thing, regardless of the necessity or contingency of its existence: 'Just as anything whatever is naturally suited to act [or to move something] in so far as it is in an actualized state, so is it naturally suited to be affected [or to be moved] in so far as it is in a state of potentiality' (16.132). In other words, mutability varies directly with passive potentiality. Following Aquinas in adopting this unproblematic Aristotelian principle, we may conclude with him that Alpha 'has no potentiality—that is, no passive potentiality—at all' (ibid.), since Alpha's immutability is one of the starting-points of the eliminative method.

On that basis it's easy to eliminate H as well, since an entity with no passive potentiality at all is clearly an entity invulnerable to anything violent, s coercive, or otherwise unnatural to it.

8 Aquinas doesn't employ the elimination of D directly in the elimination of H, arguing instead from the elimination of G (19.149), from perse necessity (19.150 and 151), and from immutability in the form of the condition of being altogether immovable (19.152). The elimination of D has an indirect role, however, since it was used to support the elimination of G (18.141).

Moreover, an entity without passive potentiality must likewise be without end p.120

Kretzmann, Norman , (deceased) formerly Susan Linn Sage Professor Emeritus of Philosophy, Cornell University, New York

The Metaphysics of Theism

Print ISBN 9780199246533, 2001 pp. [ 121]-[ 125]

components of any kind, since composition by its very nature entails a theoretical susceptibility to decomposition, which is a kind of passive potentiality (18.141). And since anything theoretically susceptible to decomposition can cease existing, anything that exists necessarily through itself must be simple, not composite in any way (18.143). And so predicate G can apparently also be eliminated from the concept of Alpha.

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