As for realists in truth-value but not ontology, I must admit that it’s a bit puzzling to me too. However, I think a hermeneutic fictionalist strategy makes some sort of sense of this position, as does a purely syntactically-based logicism, or Dummettian intuitionism. On such an account, to be “true” just means to be provable, and no mathematical entities (except the proofs, which might actually be concrete) need exist.

]]>Plentiful platonism is an interesting view from a modal realist point of view. There may be counterparts of numbers that are not exactly like numbers in this universe (assuming there are such things) which allow us to talk about possibilities and counterfactual situations regarding actual numbers. Most people think the intrinsic properties of numbers (if there are any) are necessary, but that might not be the case.

Maybe that is sort of off-topic or irrelevant. Probably.

]]>Yasha Eliashberg, contact geometer at Stanford, once defined not only “mathematically worthwhile” but “interesting” as “useful for string theory.” This is not the sense in which you mean it, but it may not be _too_ far off, ne? Yasha called on that definition when trying to dissuade me from studying Nonstandard Analysis. (Thing is, I’m pretty sure that NSA holds the tools / ways to think about correctly atomizing space-time.)

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