Hilary Putnam argues that while empirical science allows for a "correspondence view" of truth—where we use our sense organs to verify that our ideas match the physical world—mathematics offers no such biological bridge. Because mathematical entities like numbers and sets are abstract objects rather than physical ones, humans lack a "mathematical sense organ" to perceive them directly. This creates a profound epistemological gap: if mathematical objects exist independently of us (Platonism), we cannot explain how we "see" or interact with them to verify our knowledge, yet if they don't exist, we struggle to explain why mathematics describes the world so perfectly, leaving the discipline as a puzzle where "no theory works very well."
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"mathematics describes the world so perfectly" = false.
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I do agree with you. I want to point out that it would be more interesting to pose the question of whether or not mathematics is discovered or created. Does math already exist in the universe or do we make it, which is still quite hotly debated in the philosophy of science community
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Marco =
Here is the philosophy to answer it. If numbers exist, then philosophy (exists). It is very simple to digest. The complexity of numbers is that numbers to reflect nature of reality cannot impact us. Even if numbers change in some fixed reality we are unaware of, how would we know. Therefore, numbers cannot act for what we already know. Unknown variables are the quest for both mathematical or philosophical formulae. Truth is our only constant. Which is a concept. Numbers do NOT form conceptual ideas. If we cannot instruct how numbers inform us on a quantitative level. Mathematical ablatively must be made more accessible rather than abstract. What I mean is: for mathematics to be better understood requires concepts that we can interpret on a meaningful level. I'm not saying it's not probable. I am saying our knowledge may only be incomplete unless we qualify what mathematics does.
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