They all debated the question what being mathematical means there whole lives.
Comment on Theories on Theories
pfried@reddthat.com 5 weeks agoThey are clearly mathematical. Starting with definitions and axioms and deriving from there using mathematical statements.
lemonwood@lemmy.ml 5 weeks ago
pfried@reddthat.com 5 weeks ago
And we determined that the resulting incompleteness proofs are valid mathematical proofs.
lemonwood@lemmy.ml 5 weeks ago
They already knew that. You’re treading an old work out logical positivist path, that was inspired by Wittgenstein who worked closely with Russell (both mathematicians and philosophers) and he later saw his error, rejected his positivist followers and explained how truth is not a correspondence to facts, rather meaning is derived from use in language. This applies to all languages, formal and informal, including math and logic.
sparkyshocks@lemmy.zip 5 weeks ago
Sure. But they’re also philosophical. The categories aren’t mutually exclusive. Basic set theory (which is both mathematics and philosophy).