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I'm a philosophy novice that's trying to wrap my head around nominalism. In my current thinking there is a big difference between two categories of things that don't exist: non-actual concepts and logical contradictions. For example:

  • unicorns, Harry Potter, vs
  • married bachelors, four sided triangles.

These are different categories because we can say things about non-actuals (unicorns have one horn on their head, are sometimes rainbow coloured, etc), whereas we can't say anything meaningful about a four side triangle.

Would nominalism say that both of these categories don't exist in the same way, or would they distinguish them somehow?

SEP notes that there are two independent types of nominalism: "Thus there are (at least) two kinds of Nominalism, one that maintains that there are no universals and one that maintains that there are no abstract objects." I think I understand what abstract objects are (and I think unicorns would qualify?), but I'm still a little vague on universals. Would these different types of nominalism give different answers to my question, or would they agree and say that unicorns and married bachelors both don't exist?

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  • Unicorn is a coherent concept about which it makes sense to ask the existence question, married bachelor is not, so the question is nonsensical. The abstract vs universal divide is a modern reincarnation of platonism (w/ a separate realm of forms) vs Aristotelian hylomorphism (with forms fused with matter in this realm), but it makes little difference to the sensibility question.
    – Conifold
    Sep 7, 2022 at 2:03
  • @Conifold Do you mean that nominalists would say that married bachelors neither exist not don't exist because existence makes no sense to apply to logical contradictions?
    – curiousdannii
    Sep 7, 2022 at 2:23
  • At least classically, yes, see Impossible Worlds. But everything is pragmatic and relative these days, one could lump non-referring terms and non-terms unless they have a special reason to exclude inconsistent descriptions (in Russellian approach) syntactically. If they are only interested in a particular kind of possibility (stronger than logical) they would have little reason to. Besides, in possible worlds we are dealing with joint possibility, individually consistent may be jointly inconsistent, so the distinction is blurry.
    – Conifold
    Sep 7, 2022 at 3:05
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    Indeed there's a subtle difference between these two types of nominalists where the in re universal nominalist would claim they don't exist inside space and time while the other would claim they even don't exist outside space and time...
    – Double Knot
    Sep 7, 2022 at 6:26
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    If you got married on a drunk night out in Las Vegas, and don't remember the next morning, it is justifiable to say that you are still a bachelor. With "logical impossibilities" you'd have to be very careful whether they are indeed impossible. And abstract logical impossibilities like a "four sided triangle" are a completely different category from unicorns.
    – gnasher729
    Sep 7, 2022 at 12:56

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To contradict the parts of the contradiction have to be able to exist. A unicorn is never real so a pink unicorn has no more or less unreality than any other unicorn. But we do know what marriage is and what a bachelor is in reality so we know that a married bachelor can't exist.

But don't overlook the fact that in your examples like 4-sided triangle you are using essences. esp in something non-material , to be talking about a 4-sided triangle you are referring to essences and not anly particular example hence nominalism would have nothing to say about that.

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