The Philosophical Implications of the Four-Color Problem (1980) [pdf]

Re:The Philosophical Implications of the Four-Color Problem ... by amw-zero on Thursday November 26, 2020 @02:43AM (#25217821)

Of course math is a formal system. If you take Zermelo-Frankel Set Theory as the foundation of math, it has a very clear, formal set of axioms.

And we do not know for certain that math is objective truth. If we did, there would be no philosophy of mathematics.

Reasoning within mathematics is objective, because math is a formal system. But to think that we know anything about anything is frankly pure arrogance. We don’t know why we are here or what our universe even is at a fundamental level. Math is a human-imposed construct that we use to try and make sense of it all.

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Re:The Philosophical Implications of the Four-Color Problem ... by povik on Thursday November 26, 2020 @08:05AM (#25219687)

> But to think that we know anything about anything is frankly pure arrogance.

It would be arrogant to conflate a model and the subject being modeled, but we have some pretty successful models for physical reality, and you won't bring me to say we don't know anything about it.

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Re:The Philosophical Implications of the Four-Color Problem ... by amw-zero on Thursday November 26, 2020 @08:52AM (#25220003)

Yes that’s fair. We know things that are within the model (i.e. math). Some models are very useful, after all.

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