I have in mind an interpretation of mathematics as intuitionalism, where intuitions are subjective (built from personal experience), but subjective experience is ultimately explained “objectively” a la naturalism. So a kind of weak emergence, where math as we know it is a human tool that can be continually expanded to model the world. Thus mathematicians can describe objective reality because human experience and intuition are wholly explained naturalistically. Naturalism means humans are not blinded a priori to the world like Kant’s a priori ungraspable neumena. So math can capture real truths about the world, but it is not Platonic because it is built from how we experience that reality, a natural process. And how we experience reality can be objectively explained naturalistically, no room for platonism. This seems ideal because math has no problem of the platonic gap and an explanation for why it is effective (transcendentally “reliable” empirical evidence via naturalism).

Now this does not guarantee humans can reach the naturalistic explanation for everything, so math and human knowledge may never be complete. So a current mathematical truth is objective in that it captures what a human understands. And human understanding is objectively explained by further principles. But there is no principle yet that limits such complete knowledge. No neumena of Kant.

Yet humans still experience and learn about the world through the lens of natural limitations. But this conception doesn’t have a dogmatic limit to expanding knowledge that Kant did. We may never travel to distant reaches of the galaxy, but maybe there are natural processes unknown that help us complete our understanding.

So I wonder where this fits. Is this like Sellars’ myth of the given and scientific and manifest image? Is it like Kant except for no hard and fast rule against knowing continually more?



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