Here's one way of bringing out the problem.
Assuming there are universals, then:
- 1. Either (a) universals exist extramentally or (b) they do not exist extramentally.
- 2. If (b), then nominalism or conceptualism, QED.
- 3. If (a), then either (i) they only exist in the objects that have them, or (ii) they sometimes exist outside of the objects that have them.
- 4. If (i), then that is Armstrong's view.
- 5. If (ii) then that is Platonism.
- 6. So if (a) is true, then either Armstrong's view or Platonism is true, and so moderate realism either reduces to Armstrong's view or Platonism.
- 7. If Armstrong's view holds, then universals depend on the objects that have them, and therefore cease to exist if the objects do.
- 8. But if the universals cease to exist, then statements about non-existent things, like "dinosaurs are big creatures", do not require universals to be true, and so universals are superfluous.
- 9. So if Armstrong's view holds, then universals are superfluous.
That only leaves Platonism, and there are huge problems with Platonism.
To be fair, I am leaving much unsaid here, and I am not making any distinctions within "Platonism." But ultimately I think this is basically correct; the way Platonism is construed in modern times basically just is the view that there are non-mental, objective, necessarily existent, universals.
The problem, from the Thomist perspective, is that you take universal to be a thing rather than a mode of a thing. For Thomas the fundamental thing at play here is not a universal, but a form that qua form is neither universal nor particular. The form is particular when composing an individual, and universal when abstracted from matter by a rational agent.
Forms are postulated to address is the classical problem of the one and the many, not the modern question of the existence of referents in referencing sentences and propositions. The idea with the immanent forms of Aristotle (which Thomas espouses) is that two things resemble each other (exhibit unity or oneness) insofar was they are composed of matter determined in the same way, which determination is form. Considered in this way, there are two particularised forms, one in each individual. Our intellect then abstracts the matter away from each individual, resulting in a single abstract form which, at this point, is universal. This universal (abstracted form) is that by which things are referred to in our sentences and propositions: what we say applies to individuals insofar as they instantiate a form that when abstracted agrees with this universal. (This is, of course, merely a very brief summary of how the Thomist would see this working. For a detailed discussion I can recommend Lonergan's two books "Verbum" and "Insight".)
Now, the claim that dinosaurs are big creatures is true only in virtue of the forms that characterise dinosaurs. But so long as the word "are" isn't taken in a sense committing us to the current existence of dinosaurs, the relevant forms needn't currently exist in the sense of actually characterising particular individuals. They exist only in an abstracted way in our intellect. I can refer to things that don't now exist because my intellect can arrive at abstract forms in ways other than direct abstraction from particular sensations.
Nevertheless, the Thomist is not committed, by virtue of his theory of forms, to the metaphysically necessary existence of forms. Before there were any humans there was no individual composed with the human form.
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