Timeline for Completeness or soundness? Understanding a claim by Gödel
Current License: CC BY-SA 4.0
4 events
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| Sep 14, 2019 at 3:57 | history | edited | YCor | CC BY-SA 4.0 |
removed capitals, formatting
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| Sep 14, 2019 at 2:18 | comment | added | Mallik | What support is there for interpreting "disproof of A" in the sense of showing A to have no models, as opposed to being syntactically inconsistent? | |
| Sep 13, 2019 at 19:22 | comment | added | Peter LeFanu Lumsdaine | I’m not familiar enough with his writing at the time to be certain without checking more context, but I would guess that his “informal” there means (in modern terms) “meta-theoretic”, and so by “an informal disproof of A”, he means “a proof in the meta-theory that A cannot hold [in models]”, i.e. “a meta-theoretic proof that A is not satisfiable”. So the implication he’s considering is “if (we can prove meta-theoretically that) A is not satisfiable, then there is a proof (in the object theory) of $\lnot A$”, which is indeed a form of completeness, not soundness. | |
| Sep 13, 2019 at 15:24 | history | asked | Mallik | CC BY-SA 4.0 |