0. This post is a sequel to Truthmaker Maximalism Questioned.
1. On one acceptation of the term, a nominalist is one who holds that everything that exists is a concrete individual. Nominalists accordingly eschew such categories of entity as: universals, whether transcendent or immanent, Fregean propositions, Castaneda's ontological operators, mathematical sets, tropes (abstract particulars, perfect particulars), and concrete states of affairs. Nominalists of course accept that there are declarative sentences and that some of them are true. Consider the true
1. Peter is hungry.
Nominalists cheerfully admit that the proper name 'Peter' denotes something external to language and mind, a particular man, which we can call the 'ontological correlate' of the subject term. But, ever wary of "multiplying entities beyond necessity," nominalists fight shy of admitting an ontological correlate of 'hungry,' let alone a correlate of 'is.' And yet, given that (1) is true, 'hungry' is true of Peter. (In a simple case like this, the predicate is true of the the referent of the subject term iff the sentence is true.) Now philosophers like me are wont to ask: In virtue of what is 'hungry' true of Peter? Since 'hungry' applies to Peter in the way in which 'leprous,' 'anorexic,' and other predicates do not, I find it reasonable to put the same question as follows: What is the ontological ground of the correct application of 'hungry' to Peter?
2. In answering this question I introduce two posits that will enrage the nominalist and offend against his ontologcal parsimoniousness. First of all, we need an o-correlate of 'hungry.' I admit of course that 'hungry' in our sample sentence functions differently than 'Peter.' The latter is a name, the former is what Frege calls a concept-word (Begriffswort). Nevertheless, there must be something in reality that corresponds to 'hungry,' and whatever it is it cannot be identical to Peter. Why not? Well, Peter, unlike my cat, is not hungry at every time at which he exists; and for every time t in the actual world at which he is hungry, there is some possible world in which he is not hungry at t. Therefore, Peter cannot be identical to the o-correlate of 'hungry.'
We are back to our old friend (absolute numerical) identity which is an equivalence relation (reflexive, symmetrical, transitive) governed by the Indiscernibility of Identicals and the Necessity of Identity.
3. But why do we need an o-correlate of 'hungry' at all? I asked: in virtue of what is 'hungry' true of Peter? One sort of nominalist, the 'ostrich nominalist,' will say that there is nothing in virtue of which 'hungry' is true of Peter. For him is is just a 'brute fact,' i.e., an inexplicable datum, that 'hungry' correctly applies to Peter. There is no need of an ontological ground of the correctness of this application. There is no room for a special philosophical explanation of why 'hungry' is true of Peter. It just applies to him, and that's the end of the matter. The ostrich nominalist of course grants that Peter's being hungry can be explained 'horizontally' in terms of antecedent and circumambient empirical causes; what he denies is that there is need for some further 'philosophical' or 'metaphysical' or 'ontological' explanation of the truth of 'Peter is hungry.'
If a nominalist says that 'hungry' is true of Peter because Peter is hungry, then I say he moves in a circle of embarrasingly short diameter. What we want to understand are the ontological commitments involved in the true sentence, 'Peter is hungry.' We need more than Peter. We need something that grounds the correctness of the application of 'hungry' to him. To say that 'hungry' is true of Peter because Peter is hungry presupposes what we are trying to understand. Apart from this diversionary tactic, the ostrich nominalist is back to saying that there is nothing extralingusitic that grounds the correct application of 'hungry' to Peter. He is denying the possibility of any metaphysical explanation here. He is saying that it is just a brute fact that 'hungry' applies to Peter.
4. As for my second posit, I would urge that introducing an o-correlate for 'hungry' such as a universal tiredness does not suffice to account for the truth of the sample sentence. And this for the simple reason that Peter and tiredness could both exist withough Peter being tired. What we need is a concrete state of affairs, an entity which, though it has Peter and tiredness as constituents, is distinct from each and from the mereological sum of the two.
5. Now one can argue plausibly against both posits. And it must be admitted that both posits give rise to conundra that cast doubt on them. But what is the alternative? Faced with a problem, the ostrich sticks his head in the sand. Out of sight, out of mind. Similarly. the ostrich nominalist simply ignores the problem. Or am I being unfair?
Perhaps the issue comes down to this: Must we accept the truth of sentences like (1) as a 'brute fact,' i.e. as something insusceptible of explanation (apart, of course, from causal explanation), OR is there the possibility of a philosophical account?
6. Finally, it is worth nothing that the nominalist blunders badly if he says that Peter is hungry in virtue of 'hungry''s applying to him. For that is a metaphysical theory and an absurd one to boot: it makes Peter's being hungry depend on the existence of the English predicate 'hungry.' To avoid an incoherent, Goodmanaical, linguistic idealism, the nominalist should give no metaphysical explanation and be content to say it is just a brute fact that Peter is hungry.
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