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Zalamea’s research may be interesting — I’m thinking of Synthetic Philosophy of Contemporary Mathematics as there’s a fair bit of analysis of the work of Grothendieck and other recent abstract/pure mathematicians, and also a pretty broad-ranging review of lots of other works that could be starting-points for investigating the philosophy of contemporary maths....


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Accounts of impossible worlds come in many flavors, but none seems to require that natural numbers obey the same laws in all possible worlds unless these laws count as "logical" to some (required) extent. Or one might posit numbers as dwelling in their own world(s), wherefore the question of variation becomes the question of something like the set-...


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The Dirac belt trick is simply experimental evidence that our universe has three macroscopic spatial dimensions. If our universe had more than three macroscopic spatial dimension then the belt trick would not work (although there are more direct ways of demonstrating this e.g. seeing how the volume of a sphere is related to its radius). And the belt trick ...


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Not sure if this helps with your confusion/skepticism, but natural language is full of under-determined sentences, e.g. Today is Tuesday. That statement is true if where you're at right now (time and space) is a Tuesday and false otherwise. Words like 'today' are known as indexicals in linguistics and the philosophy of language. Think of that formalized as ...


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