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> How Gödel’s second incompleteness theorem shows that you can prove anything, That is not at all what it says. > They both can be useful or harmful, If a pr
by anon291 1y ago
> How Gödel’s second incompleteness theorem shows that you can prove anything,
That is not at all what it says.
> They both can be useful or harmful,
If a proof is admitted into lean, there is no doubt as to its truth. There is no way in which lean can be construed as harmful.
> The 2009 crash and gaussian copula as an example.
There is nothing mathematical about the economics behind the 2009 crash. Such things are statistical measurements, which admit the possibility of failure, not mathematical conclusions that are demonstrably true.
- nyrikki 1y ago> That is not at all what it says. Gödel's incompleteness theorems demonstrate that any computable system that is sufficiently powerful, cannot be both consistent and syntactically complete. Godel's second proved, a formula Con_κ associated with the consistency of κ is unprovable if κ is consistent. If it is not consistent, Ex falso quodlibet (principle of explosion) applies and finding that contradiction allows any proposition or the negation of that proposition to be proven. > They both can be useful or harmful It is not lean that is harmful, mistaking finding a proof as being the same as truth. A proof that verifies a theorem does not have to explain why it holds, and the mathematical assumptions that may have been statistical is exactly why that failed. Probability theory is just as much of a mathematical branch as λ-calculus. But we probably do differ in opinion on how "demonstrably true" much of mathematics is. But here is a fairly accessible document related to the crash. https://samueldwatts.com/wp-content/uploads/2016/08/Watts-Gaussian-Copula_Financial_Crisis.pdf https://samueldwatts.com/wp-content/uploads/2016/08/Watts-Ga...