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Certain propositions can be meaningless. How do we know if "Are there abstract mathematical entities (platonism)?" a meaningful question, and not an abuse of language?

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  • It is unclear what you are asking, I am afraid. We do not need two possibilities A and B to be mutually exclusive or exhaustive to ask if one of them holds, even asking if a single one non-exhaustive possibility holds is a "logically valid" question. And it needs no "argument for validity". Of course, it could happen that neither holds, or both in part, and that would be the answer. And there are plenty of alternatives to both Platonism and constructivism, as well as blends of the two.
    – Conifold
    Oct 29, 2019 at 20:36
  • Platonism is at his roots a generalization of mathematics, imho, For historical reasons it became more widely known and that created the inverted illusion of mathematics being platonic.
    – sand1
    Oct 30, 2019 at 9:29
  • @Conifold Let me rephrase in terms of if, then argument. I ask IF Platonism and Constructivism are mutually exhaustive, exclusive, and meaningful concepts (in our World, i think this to be the case -since either something exists independently of us, or we create it), THEN, is it logically valid to apply this distinction to anything (and in this case, to foundations of mathematics)?
    – Ajax
    Oct 30, 2019 at 14:14
  • Your "if" is rather obviously false, just look over what SEP has on philosophy of mathematics. Or think of a hammer or any other artifact, it exists independently of us, yet we created it. But if we did have a valid dichotomy we could obviously apply it. So the question seems doubly moot.
    – Conifold
    Oct 30, 2019 at 17:53
  • @Conifold As for hammer, it exists independently of us, but it was created by us, so in this case, it strictly belongs to Constructivism. As for a valid dichotomy, my query resolves to IF existence of a 'valid dichotomy' can serve as a concrete (necessary and sufficient) argument in favor of asserting that Platonism vs Constructivism is not a nonsensical thing to discuss in context of foundation of mathematics.
    – Ajax
    Oct 31, 2019 at 5:10

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I think mathematics has both platonic and constructive aspects. If we view mathematics as a language for describing patterns evident in numbers, sets, etc., then these patterns might exist in some platonic sense, but the language used to name and describe them has been purposely constructed.

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