For me, the heart of the matter is what is the purpose of logic and what is the purpose of math and what is their relationship?
There are semiotic situations that seem to violate the initial conditions of logic but there are ways of approaching them that do not reduce our brains to jelly from the getgo. C.S. Peirce, following on Aristotle’s negotiation of the boundary between logic and rhetoric, developed his theory of triadic sign relations in large part to manage just such problems.
I’m determined to keep my gnosis close to the grinstone for the time being, but here is a smattering of old notes that give a hint as to Peirce’s way of approaching the question: