Timeline for What does Godels Incompleteness theorem "true but unprovable" mean?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 16, 2015 at 6:12 | vote | accept | advocateofnone | ||
| Nov 16, 2015 at 6:11 | comment | added | Yuval Filmus | @sasha Right, the proof is valid in the metalanguage but not in the language. The metalanguage knows (or rather assumes) that the language is consistent, but the language itself doesn't know it. | |
| Nov 16, 2015 at 3:53 | comment | added | advocateofnone | @YuvalFilmus Sorry, but i would lastly like to ask that, the reasoning given that $\psi$ is true is indeed a proof but the proof can't be expressed as statements belonging to $Th(\mathbb{N},+,*)$. Am I understanding it correctly ? | |
| Nov 15, 2015 at 23:26 | comment | added | user12859 | @sasha : Also, note that one can reach a stronger conclusion by replacing "π ( if" with "π such that for all ρ, if ρ is shorter than π then D does not accept $\langle \hspace{-0.02 in}$ρ,¬φ$\hspace{-0.02 in}\rangle$ (if". | |
| Nov 15, 2015 at 23:11 | comment | added | Yuval Filmus | Use your favorite search engine on the phrase "Gödel's second incompleteness theorem". There are many resources. | |
| Nov 15, 2015 at 23:07 | comment | added | advocateofnone | I don't come from a maths background. Could you point out resource(s) for a beginner ? I don't mind learning starting from the basics of mathematical logic. | |
| Nov 15, 2015 at 22:31 | history | answered | Yuval Filmus | CC BY-SA 3.0 |