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I think the title and body questions are subtly different. Here I'm going to address the title question, which I'll paraphrase for clarity as: What sort of "mathematical truth" can a non-Platonist make sense of? I think this is less strange than it may first appear, since there is an existing parallel: "sharp" vs. "fuzzy" referents in natural language. ...


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The decision is about formal systems. So the problem arises only within Formalism. It is possible to deny Platonism and still not anchor mathematics in axiomatic systems. The program that led to Goedel's completeness competes with more radical reactions to the gap in Frege's work. The first among these is the original form of Intuitionism proposed by ...


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The Many Worlds interpretation of quantum mechanics happily enfolds any kind of time travel, because any way that the alternative timeline might play out was already a possible state of events, and all possible states of events are already simultaneously 'real', at least in the sense that they exert power over the universal wave function and therefore are ...


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Yes - the key term is "generalized quantifiers." They are studied in the contexts of both natural language and in mathematical logic. I'll focus on the logic side, about which I know more. A name which crops up in both contexts is Jon Barwise, and this article of Vaanaanen describes much of Barwise's work on generalized quantifiers; this paper of Barwise on ...


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