That is not the business of pure mathematics, but of applied mathematics within all the other sciences--including philosophy. — aletheist
Mathematics in general does not require a "foundation" at all, and certainly need not be treated as Platonic, as if its objects "exist" in some immaterial realm. That was my point in giving Peirce's definition of it as the science of drawing necessary conclusions about hypothetical states of affairs. The key to its practical applications is formulating those hypotheses in a way that captures the significant relations among the real phenomena of interest.In other words what's desired is a foundation for applicable mathematics, and not just pure platonic mathematics. — Zuhair
Mathematics in general does not require a "foundation" at all, and certainly need not be treated as Platonic, as if its objects "exist" in some immaterial realm. — aletheist
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