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masque wrote (edited )

We would lose out on everything but the "formal sciences" (math, logic, theoretical CS, etc.) and certain branches of philosophy.

If you want to know about the natural world as it actually exists, you need your reasoning to be based to some extent on observations of the world. And while I mostly find the natural sciences quite boring when compared to math, CS, etc., I will begrudgingly admit that understanding how the actual world works is probably a good and useful thing.

EDIT: I will say, however, that I am a lot more confident in the knowledge gained through mathematics than in any empirical science (e.g. I am more confident in Kuratowski's Theorem than in the existence of electrons).

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