Timeline for Difference between provability and the existence of a proof?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 12, 2023 at 16:15 | answer | added | godelian | timeline score: 0 | |
| Jun 12, 2023 at 15:49 | answer | added | PW_246 | timeline score: 1 | |
| Jul 24, 2022 at 0:58 | vote | accept | Glubs | ||
| Jul 23, 2022 at 19:51 | history | became hot network question | |||
| Jul 23, 2022 at 18:31 | comment | added | Timothy Chow | Another way to see that provability does not imply truth is that the consistency of the system is not provable; i.e., we can't rule out that $X$ and $\neg X$ are both provable, whereas we can certainly rule out that $X$ and $\neg X$ are both true. | |
| Jul 23, 2022 at 12:43 | answer | added | Will Sawin | timeline score: 12 | |
| Jul 23, 2022 at 12:33 | comment | added | Glubs | @Wojowu I think you may have it. I was reading propositions as "a proof of", not "is true". This makes a lot more sense. | |
| Jul 23, 2022 at 12:30 | comment | added | Paul Siegel | I think the historical origin of the distinction between "provable" and "proved" is Godel's first incompleteness theorem. Very roughly, this encodes the observation that a consistent formal system F cannot prove the statement "This statement is not provable in F". But the fact that F cannot prove the statement means that the statement is true in some broader sense. | |
| Jul 23, 2022 at 12:30 | comment | added | Wojowu | The way $\Box X\to X$ should be read is "if X is provable then X is true". Alternatively, "if we have a proof that X is provable, then we have a proof of X". That such implications fail is a fairly well-established phenomenon in logic. | |
| Jul 23, 2022 at 12:30 | history | edited | Glubs | CC BY-SA 4.0 |
added 281 characters in body
|
| Jul 23, 2022 at 12:13 | history | edited | Glubs |
edited tags
|
|
| S Jul 23, 2022 at 11:50 | review | First questions | |||
| Jul 23, 2022 at 13:48 | |||||
| S Jul 23, 2022 at 11:50 | history | asked | Glubs | CC BY-SA 4.0 |