The Asymmetry of Existential Dependency

As it happens, however, I think that there are independent reasons for not adopting (D2**) anyway. More particularly, I think that it is a mistake to respond to the problem raised by Socrates' life by modifying (D2*) in this way, because the real source of the problem lies with (D1), the definition of existential dependency. The case of Socrates' life demonstrates that definition (D1) permits the possibility of mutual existential dependency between non-identical things. But there is something very unsatisfactory about this implication because, I believe, our (primary) intuitive notion of ontological dependency is of a distinctly asymmetrical relation (though I

186 Cf. Rosenkrantz and Hoffman, ‘The Independence Criterion of Substance’, and Substance Among Other Categories, 67–9.

shall shortly modify this claim in a minor way). Take, indeed, the relationship between Socrates and his life. According to (D1), Socrates is quite as much existentially dependent upon his life as his life is upon him. And yet there is a strong intuition that, quite to the contrary, Socrates' life is the truly dependent entity here, while Socrates is a wholly independent existent (a substance). We want to say that Socrates' life only exists because Socrates does, whereas it would be putting the cart before the horse to say that Socrates exists because his life does. Now, the conjunction ‘because’ is asymmetrical, because it expresses an explanatory relationship and explanation is asymmetrical. Two distinct states of affairs cannot explain each other. (There may, quite conceivably, be self-explanatory states of affairs, so I only want to urge that non-identical states of affairs cannot be mutually explanatory; technically, this means that I should strictly describe explanation as an ‘antisymmetric’ rather than as an asymmetric relation—a point to which I shall return, though I shall ignore it for the time being.) The asymmetry of explanation is, of course, intimately related to the unacceptability of circular arguments. (Note here that while two distinct propositions may entail one another—at least according to a reasonably fine-grained criterion for the individuation of propositions—none the less, in so far as those entailments are exploited to argue for the truth of one or other of those propositions, one must make an exclusive choice as to which proposition is to be regarded as premiss and which as conclusion: one cannot have it both ways.)

All this suggests that (D1) should be replaced, at least to a first approximation, by something like:

(D1*) x depends for its existence upon y = _df Necessarily, x only exists because y exists.

Here it is important that the presence of the word ‘only’ in (D1*)'s definiens should not be understood as implying that an object x may not depend for its existence upon two (or more) different things, y and z. Thus the particularized relation of Mary's loving Tom—supposing such an entity to exist—plausibly only exists because Mary exists, but plausibly also only exists because Tom exists. Furthermore, I am assuming that it is not an implication of (D1*) that a composite substance depends for its existence upon its proper parts, that is, that it is not the case that it ‘only exists because they exist’—on the grounds that it could still exist in the absence of those particular parts, provided suitable alternative parts were substituted for them. (Thus (D1*) is quite unlike (D1g) in its implications for part–whole dependency relations, as far as substances are concerned.) For the same reason, I assume that (D1*) does not imply that an ‘Aristotelian’

universal depends for its existence upon its particular exemplars.

Indeed, I take it that the definiens of (D1*) entails the definiens of (D1)—though not vice versa, of course—so that the following is a theorem:

(T3) If, necessarily, x only exists because y exists, then, necessarily, x exists only if y exists.

However, despite these clarifications, it must be conceded that the locution ‘x only exists because y exists’ is hardly very perspicuous, either as to its logical form or as to its exact meaning. Moreover, precisely because I have introduced the conjunction ‘because’ as an explanatory conjunction, it may be felt that it is not well-suited to the ontological role now being devised for it. There are perhaps two sources of worry here: first, that this approach invites a confusion between metaphysics and epistemology; and secondly (but relatedly) that contexts governed by the conjunction ‘because’ are opaque (in the technical sense of the term, in which it implies the non-applicability of Leibniz's law).

Although I think that these latter worries can be allayed, I accept that (D1*) as it stands does not constitute anything like a satisfactory definition of existential dependency, conceived as an objective metaphysical relation between entities, because it is insufficiently perspicuous. Even so, the considerations which led us away from (D1) and towards (D1*) may still have served to point us in the right direction. The fact that (T3) but not its converse is plausibly taken to be a theorem indicates that what we need to seek for a satisfactory definition of existential dependency is a perspicuous relation between x and y stronger than (entailing but not entailed by) ‘necessarily, x exists only if y exists’. This should moreover be (for reasons discussed earlier) an asymmetrical relation—or, more accurately, an antisymmetric relation, that is, a relation R such that if xRy and yRx, then x = y (this is to allow that an object may depend for its existence upon itself, but that where it depends for its existence upon something else, that other thing does not in turn depend for its existence upon the first object).

As we shall see in a moment, a relation of just the sort we seek is the relation of identity-dependence, to be explained below. But first I should digress for a moment to dismiss the suggestion that the relation we seek might be expressed in terms of the one-sided holding of the relation defined in (D1). According to this suggestion, we would have:

(D1+) x depends for its existence upon y =df(i) necessarily, x exists only if y exists and (ii) it is not the case that, necessarily, y exists only if x exists.

Notice that the relation thus defined is asymmetric rather than antisymmetric: it doesn't permit any object to be existentially dependent upon

itself. This alone does not render such a definition unsuitable for deployment in conjunction with a definition of substance along the lines of (D2) and (D2*), though it would render otiose the clause ‘y is not identical with x’ in those definitions. A much more serious problem is that such a definition does nothing to resolve the difficulty raised by the example of Socrates' life: for it will prevent us from saying that either Socrates or his life is existentially dependent on the other, since in neither case is clause (ii) of the proposed definition satisfied.