Questions tagged [foundations-of-mathematics]

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Relation of Mathematical Propositions to Natural Language

Treating Natural Language as a language game, what role does it play in our understanding of mathematics? Does natural language provide meaning to mathematics? Does a proof of a conjecture, say FLT,...
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Are the foundations of mathematics “doomed” to be set-theoretic in nature?

Let's say we want to come up with a foundational theory for all of mathematics and let's say that it is embedded in first-order logic. Note that the machinery of first-order logic is described with ...
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The nature of Nominalist Formalism

In this entry in the stanford encyclopedia of philosophy, it is stated that the theory of nominalist formalism deals with the metatheory problem of formalism as follows: Commendably, Goodman and ...
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What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and elementhood?

An excerpt from a question at Math SE (Bounty of 100 available for an answer): What goes wrong if we explain Russell's paradox as resulting from an overly rigid link between property satisfaction and ...