Timeline for Formulas for the liar paradox
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2010 at 15:28 | comment | added | Joel David Hamkins | Tomate, thanks for accepting my answer. About the question in your comment, every statement has a definite truth value in the standard model of arithmetic, even if we don't know which occurs. What the Incompletness Theorem asserts is that for any formal axiomatic system, there will be statements that are neither provable nor refutable in that system. Such a statement will have a definite truth value, and so there will be true unprovable statements. | |
| Jun 12, 2010 at 15:13 | comment | added | tomate | Thanks for the clear answer. It's quite articulated, so let me see if I get this straight. Tarsky's theorem states that a truth predicate T cannot be defined for all sentences; were it definable, THEN (and only then) we could show that there exists a sentence \psi (the liar paradox) such that \psi\iff\neg T(\langle\psi\rangle) Let me ask you another question then. Does Goedel theorem state that - there exist sentences which have a definite truth value but are neither provable nor disprovable or only the weaker - there exist sentences which are neither provable nor disprovable ? | |
| Jun 12, 2010 at 15:11 | vote | accept | tomate | ||
| Jun 11, 2010 at 15:10 | comment | added | Joel David Hamkins | Ketil, thanks very much! I have now corrected this. | |
| Jun 11, 2010 at 15:09 | history | edited | Joel David Hamkins | CC BY-SA 2.5 |
deleted 11 characters in body
|
| Jun 11, 2010 at 14:50 | comment | added | Ketil Tveiten | Minor quibble: I think you want to say $\psi$ is equivalent to $\phi(|\psi|)$, not $\phi(|\phi|)$. | |
| Jun 10, 2010 at 12:30 | history | answered | Joel David Hamkins | CC BY-SA 2.5 |