Substances are predicate-bearers. Yesterday I found myself in a philosophical discussion with a friend online who argued that to say that something has a Substance or has the property of being predicate-bearing was vacuous, since if two different substances had all and only the same predicates they would not only be indistinguishable, but identical. I argued that such a critique was based on the principle of the identity of indiscernibles, though I myself accept that principle (tentatively). However, his argument was pressed in the following way: he argued that the claim that there could be a distinction between two things in light not of predicates/properties but in light only of being discrete substances was entirely vacuous to him. At first blush it seemed to me that we fundamentally disagreed, but on further reflection I do think that it is vacuous to say that two substances can be differentiated, or even can be different, by some reason other than at least one antithetic predicate between them. It is not logically possible for at least two predicates in the same logically possible world to share all and only the same predicates.
So, the ‘substance’ is not something to which one can ostensibly point (in any manner of speaking), and thus it is not something by reason of which differentiation can be either observed or conceived. However, does this entail that substances do not exist, since they do not differentiate one thing from another? No, I think not.
It is not logically possible that predicates exist without belonging to predicate bearers (i.e., that the world have properties without having any ‘things’ to which belong properties). So long as Leibniz was right about this, that it is incoherent to imagine a world without substances (things, predicate-bearers, etc.), then even if one cannot differentiate one thing/substance from another merely by it’s being not the same substance as the other (independent of considerations having to do with its predicates), one cannot go the other way and argue that substances do not exist. It is not coherent to posit that in some logically possible world there are not things/substances – or more precisely it is incoherent to argue that in some logically possible world there is not at least one substance/thing.
It must be observed that there is no such thing as ‘having’ a substance, nor can ‘substance’ ever stand in the place of a predicate. Rather some thing is some substance, and a substance is just a predicate-bearing thing (to avoid circularity, a predicate-bearer). We cannot conceptually differentiate one thing from another by imagining two discrete substances simpliciter, but can only differentiate substances by imagining different predicates. However, we can’t do away with the category as vacuous since it is not possible to conceive of properties except by presupposing substances (i.e., literally not logically possible). Differentiation and Identity are concepts inexorably bound up with predicates, but without substances even Differentiation and Identity are incoherent ideas, because predicates cannot be conceived of as anything but properties possibly had by a thing/substance.