Comment on Theories on Theories

woodenghost@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

Math: here’s a theorem, if it’s proven, it’s true until someone finds an error in the proof or in the compiler, if it’s a computer assisted proof (and the compiler can never be proven not to be flawed - Turing) or in one of the assumptions or in their proofs or until the axiomatic system used is proven inconsistent (and it can never be proven not to be inconsistent - Goedel) or until you decide you need to work in a different systems or technically if we stay in the system, but language or culture shifts and we change what we mean by the specific words and symbols used in the theorem.

Even if it’s true, unless you’re a platonist, it’s not true in the sense that it corresponds to a factual state of affairs in the world (there are no triangles). It’s only true within the system you’re using, just like the sentence: “Sherlock Holmes lives in Baker Street” is only true in the fictional world of the novels by Arthur Conan Doyle. Or even less so, because unlike novels, math statements are tautologies, reducible to a small number of axioms or axiom schemes.

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