fossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 3 months agoTheories on Theoriesmander.xyzimagemessage-square114linkfedilinkarrow-up12arrow-down10
arrow-up12arrow-down1imageTheories on Theoriesmander.xyzfossilesque@mander.xyzM to Science Memes@mander.xyzEnglish · 3 months agomessage-square114linkfedilink
minus-squaresparkyshocks@lemmy.ziplinkfedilinkEnglisharrow-up0·3 months ago I see philosophy as a place to make nonrigorous arguments. Wait do you think Bertrand Russell and Alan Turing and Kurt Gödel weren’t making philosophical arguments?
minus-squarepfried@reddthat.comlinkfedilinkEnglisharrow-up0·3 months agoThey are clearly mathematical. Starting with definitions and axioms and deriving from there using mathematical statements.
minus-squarelemonwood@lemmy.mllinkfedilinkEnglisharrow-up0·3 months agoThey all debated the question what being mathematical means there whole lives.
minus-squarepfried@reddthat.comlinkfedilinkEnglisharrow-up0·3 months agoAnd we determined that the resulting incompleteness proofs are valid mathematical proofs whose logical correctness has been verified by computer. https://formalizedformallogic.github.io/Catalogue/Arithmetic/G___del___s-First-Incompleteness-Theorem/#goedel-1
minus-squaresparkyshocks@lemmy.ziplinkfedilinkEnglisharrow-up0·3 months ago They are clearly mathematical. Sure. But they’re also philosophical. The categories aren’t mutually exclusive. Basic set theory (which is both mathematics and philosophy).
Wait do you think Bertrand Russell and Alan Turing and Kurt Gödel weren’t making philosophical arguments?
They are clearly mathematical. Starting with definitions and axioms and deriving from there using mathematical statements.
They all debated the question what being mathematical means there whole lives.
And we determined that the resulting incompleteness proofs are valid mathematical proofs whose logical correctness has been verified by computer. https://formalizedformallogic.github.io/Catalogue/Arithmetic/G___del___s-First-Incompleteness-Theorem/#goedel-1
Sure. But they’re also philosophical. The categories aren’t mutually exclusive. Basic set theory (which is both mathematics and philosophy).