Substances, Properties, and Ontological Dependency

Clearly, a crucial notion in metaphysics is that of one object depending for its existence upon another object—not in a merely causal sense, but in a

deeper, ontological sense. (The kind of dependency in question must also be distinguished from any kind of logical dependency, because logical relations, strictly speaking, can only obtain between propositions, not between concrete objects, nor between abstract objects which are not propositional in nature.) Thus a substance is often conceived to be an object which does not depend for its existence upon anything else.¹⁷⁹Again, properties are often said to depend for their existence upon the objects which possess them.¹⁸⁰So how should this relationship of existential dependency be defined? An obvious proposal would be to say, quite simply:

(D1) x depends for its existence upon y = df Necessarily, x exists only if y exists.

The definiens here is equivalent, of course, to ‘Necessarily, if x exists, then y exists', so that according to (D1) the existential dependency of x upon y amounts to the strict implication of y's existence by x's existence. Note that (D1) implies that everything depends for its existence upon itself—but, while the desirability of this implication may be disputed, I shall let the matter pass for the time being and return to it later. (It would, of course, be easy enough to modify (D1)’s definiens to read ‘y is not identical with x and, necessarily, x exists only if y exists’, but that would have the disadvantage of precluding anything from depending for its existence upon itself.)

On the face of it, (D1) seems to capture precisely the intuitive notion of existential dependency. For example, when it is said that a particular event, such as the assassination of Caesar, depends for its existence upon Caesar, (D1) seems to explicate this appropriately in terms of the fact that the assassination could not have existed if Caesar had not existed to be assassinated. Some other assassination could have existed at that very time and place, but for that very assassination to have existed, Caesar himself had to exist. Incidentally, I speak here and later of events existing, whereas ordinary usage prefers talk of their occurring: but I think that this is a matter of idiom rather than one of genuine ontological import. I am inclined to take the view that to say that x exists is just to say that there is

179 Thus Descartes, in the Principles of Philosophy (I. 51), asserts that ‘by substance we can understand nothing other than a thing which exists in such a way as to depend on no other thing for its existence’. See The Philosophical Writings of Descartes, ed. John Cottingham et al. (Cambridge: Cambridge University Press, 1985), i. 210.

180 Thus Descartes, once again, remarks in the Second Set of Replies (Definition V) that ‘we know by the natural light that a real attribute cannot belong to nothing’. See The Philosophical Writings of Descartes, ii. 114.

something that is identical with x: and this applies as much to events as to entities of other ontological categories.

(Note, however, that this does not restrict existence to entities possessing fully determinate identity-conditions—what I called ‘individual objects’ in Chapter 3—provided one is prepared to say, as I am, that any entity whatever must at least be self-identical. Incidentally, in what follows, I shall often use the term ‘object’ rather less precisely than I did in Chapter 3, understanding it to extend to what I there called ‘quasi-objects’ and ‘quasi-individuals’. More precision than this is not called for at present.)

But how well does the conception of substance adverted to earlier fare under the assumption of (D1)? According to that conception, a substance may be defined as follows:

(D2) x is a substance =dfThere is nothing y such that y is not identical with x and x depends for its existence upon y.

Substituting the definiens of (D1) into (D2) gives the theorem:

(T1) x is a substance if and only if there is nothing y such that y is not identical with x and, necessarily, x exists only if y exists.

But presumably we want to allow that substances may be composite objects, that is, that they may possess proper parts:

and yet isn't it the case that any composite object is such that, necessarily, it exists only if its proper parts exist? So are we not compelled to give up either (D1) or (D2)? Perhaps not, for we may instead deny that a composite substance depends for its existence upon its proper parts, on the grounds that it may undergo a change of its parts without ceasing to exist. It may be true that a mere collection of things, such as a pile of stones, depends for its existence upon the things in question, but for that very reason such a collection may be deemed not to be a true substance. By contrast, a living organism may survive a change in any of its parts (provided the change is effected in a non-disruptive manner). It is true, of course, that such an organism must have parts if it is to exist, but which objects those parts are is inessential—and consequently it is not the case that it depends for its existence (in the sense defined by (D1)) upon any one of those parts. (We shall see later, however, that it is possible to define another sense of existential dependency in which it is true to say that a composite substance depends for its existence upon its proper parts: see (D1g) below.) Let us now, for the time being, leave the notion of substance and turn to that of property. Earlier it was pointed out that properties are commonly said to depend for their existence upon the objects which possess them. We may state this in the form of an axiom, as follows:

(A1) If x is a property and y is an object possessing x, then x depends for its existence upon y.

This time, substituting the definiens of (D1) into (A1) gives us:

(T2) If x is a property and y is an object possessing x, then, necessarily, x exists only if y exists.

But (T2) might also be challenged. For even if one subscribes to an ‘Aristotelian’ (as opposed to a ‘Platonic’) view of universals, according to which there can be no unexemplified properties (that is, no properties not possessed by objects),¹⁸¹one may still contend that a given property, x, possessed by a particular object, y, would exist even if y did not, provided that some other object then possessed x. However, to this challenge it might be replied that it misconceives how (T2) is to be interpreted: (T2), it may be said, is not intended to apply to properties understood as universals, but only to so-called particularized properties (otherwise variously known as property instances, individual accidents, tropes, or—my own preferred term—modes). These are supposed items such as the particular redness of a particular apple, conceived of as an entity distinct from the redness of any other apple, no matter how well matched in colour to the first.¹⁸² On this interpretation, (T2) has considerable plausibility, complying as it does with the intuition that particularized properties cannot ‘migrate’ from one object to another. (Actually, (T2) itself does not quite imply this, though it does imply that a particularized property cannot migrate from one object to another when the first object ceases to exist.)

But now another difficulty looms. What, in the light of our preceding remarks, are we to say about the ontological status of properties in the sense of universals? More specifically, do they qualify as substances according to the proposed definitions? For, even adopting the ‘Aristotelian’ view, whereby if a property x exists then some object must exist which exemplifies x, we are not compelled to say that there is any object y, exemplifying x, such that necessarily, x exists only if y exists. However, even if the universal x does not depend for its existence upon

181 Such a view of universals is defended by David Armstrong in Universals and Scientific Realism (Cambridge: Cambridge University Press, 1978).

182 See e.g. Keith Campbell, Abstract Particulars (Oxford: Blackwell, 1990), in which these items are called (following D. C. Williams) ‘tropes’. Described as ‘moments’

(following Husserl), the existence of such items is ably defended by Kevin Mulligan, Peter Simons, and Barry Smith in ‘Truth-Makers’, Philosophy and Phenomenological Research, 44 (1984), 287–321. For an illuminating discussion of Husserl's conception of moments as ‘dependent parts’, see Peter Simons, ‘The Formalisation of Husserl's Theory of Wholes and Parts’, in Barry Smith, ed., Parts and Moments: Studies in Logic and Formal Ontology (Munich: Philosophia Verlag, 1982).

any of the objects which exemplify it, perhaps it still depends for its existence upon something else and thereby fails to qualify as a substance. Yet there is a difficulty in seeing what sort of entity, quite generally, could be invoked to fulfil this role. Compound universals (such as conjunctive ones, and disjunctive ones if they exist) no doubt depend for their existence upon the universals out of which they are compounded. Likewise, if one believes that determinable universals exist in addition to determinate ones (for instance, red in addition to scarlet and crimson), one may argue that the determinate universals depend for their existence upon the determinable ones.¹⁸³(The reverse would be more difficult to argue for, because it is presumably not the case, for instance, that necessarily if red exists then scarlet exists—since it is possible for red to be exemplified, and so to exist, even if scarlet is not exemplified. Incidentally, one should, of course, concede that scarlet itself is only a determinable relative to a more specific shade of it, so that more accurately one should speak of a scale of determinateness from most to least.) However, simple and least determinate universals would not appear to depend for their existence upon any other universals—unless perhaps it can be argued that corresponding to any universal there is a higher-order universal which must exist if that first universal does (for example, that if the property of being red exists, then so must the property of being a colour-property).¹⁸⁴

Suppose, then, that we cannot exclude (all) universals from the category of substance according to (D2) in conjunction with (D1): what to do? A plausible move, which would not appear unduly ad hoc, would be simply to modify the definition of substance, (D2), to give:

(D2*) x is a substance =_dfx is a particular and there is no particular y such that y is not identical with x and x depends for its existence upon y.

After all, we have the respected precedent of Aristotle, who (in the Categories) only admitted particulars as ‘primary’

substances, while allowing some universals (the species and genera of primary substances) the status of ‘secondary’

substances.

183 Armstrong denies the existence of determinable universals: see Universals and Scientific Realism, ii. 118. There he also denies the existence of disjunctive universals, but accepts conjunctive ones.

184 An argument of this sort is advanced by Gary Rosenkrantz and Joshua Hoffman in ‘The Independence Criterion of Substance’, Philosophy and Phenomenological Research, 51 (1991), 835–52: see p. 845. See also their Substance Among Other Categories (Cambridge: Cambridge University Press, 1994), 97–8.

An alternative strategy that I should mention would be this. We could first define a ‘generic’ notion of existential dependency as follows:

(D1g) x depends for its existence upon objects of type T =df Necessarily, x exists only if something y exists such that y is of type T.

In this sense, both composite substances and ‘Aristotelian’ universals are existentially dependent objects, since the former require the existence of proper parts and the latter require the existence of particular exemplars. (Set T as

‘proper part of x’ and ‘particular exemplar of x’, respectively, in (D1g).) We could then define a substance as an entity which is existentially dependent only in virtue of requiring the existence of parts (bearing in mind here that even a non-composite substance must have itself as a part, albeit as an improper part):

(D2g) x is a substance = _dfx only depends for its existence upon objects which are parts of x.

(If we believe in the existence of universals, then we should clearly add to the definiens ‘and universals which are exemplified by x’.) This will then exclude universals from the category of substance because their particular exemplars—upon which they depend for their existence, in the sense defined by (D1g)—are not parts of them.

However, I shall not pursue this alternative strategy further here since the problems that we shall later discover to afflict (D2*) also afflict this alternative definition of substance. Moreover, this alternative definition has additional problems of its own: for instance, unless we are prepared to regard particularized properties as parts of the objects possessing them (which looks like a category mistake), or else to argue against their existence altogether, then we shall have to conclude that only ‘bare particulars—propertyless substrata—could qualify as substances. Similarly, unless we are prepared to regard places as parts of the objects occupying them, or again to deny their existence altogether, we shall have to conclude that only unlocated mental entities—immaterial souls, perhaps—could qualify as substances. (These problems could, no doubt, be evaded by adding appropriate clauses to (D2g), but because the terms introduced by those clauses—such as ‘particularized property’ and ‘place’—express concepts no more fundamental than that of substance itself, the resulting definition of substance would be philosophically unilluminating, even if extensionally correct. We shall encounter the same type of problem with another rival to (D2*) later: see the discussion of (D2**) below.)