NOTES 38113 Medieval theories of relations is an interesting topic all by itself – one that would take
us far afield from our current concerns. Mark Henninger, Relations: Medieval Theories,
1250–1325 (Oxford: Clarendon Press, 1989) provides an excellent introduction.
14 Some member of the domain must also stand in this relationship only backwardly –
must depend on something else but nothing else depends on it.
15 At De Caelo XII 258 Aquinas offers a series of claims relevant to his Five Ways. It seems
worth including them here. Again, we begin with definitions:
Definition A: X has non-derivative necessary existence if and only if X
does not exist is self-contradictory.
Definition B: X has derivative necessary existence if and only if X
cannot naturally (without the action of an omnipotent being) cease to exist.
Definition C: X cannot naturally cease to exist if and only if X
contains no matter or the matter that X contains cannot have any essence
other than the one that it has.
Definition D: X has the power of not existing if and only if X is such that X exists
only if X has the essence it has but it is possible that the stuff that X is made
of come to have some other essence.
Definition E: X generates from Y at T if and only if There is a Y that exists at T-
1 and X at T contains the matter that was in Y at T.
Definition F: X corrupts at T if and only if There is a Y such that Y exists at T+1
and the matter that was in X at T is in Y at T+1.
Definition G: X is a natural body only if X is capable of generation and corruption.Aquinas tells us:1 If X always exists, then X has the power always to exist.
2 If X has the power always to exist, then X lacks the power not to always exist.
3 If X always exists then X lacks the power not to always exist. (from 1 and 2)4 If X lacks the power not to always exist then X does not generate or corrupt.
5 If X generates or corrupts then X does not lack the power not always to exist.
6 If X has the power not always to exist then X does not always exist.
7 If X generates or corrupts then X does not always exist.Also involved seems the idea that, in some sense, Necessarily, in any infinite
time all possibilities are realized, though it is difficult to think of any reading
of this claim on which it is true.
16 More fully: for X to change or move is for X to go from potentiality to actuality or from
actuality to potentiality regarding quantity, quality, or place.
17 The existence of something with causal powers – the actual capacity to bring about
changes in other things – that was not itself changed in so doing – might, by itself, have
slight religious relevance, but of course Aquinas has no intention of limiting himself to
this one conclusion.
18 And animal mind, if such there be – we need not enter into that matter here.
19 The notion of infinity is of course complex. A nice introduction to various relevant
notions is A. W. Moore, The Infinite (London: Routledge, 1991).
20 At Summa Ia 46 2–7.