Timeline for Proving things about a formal logical system
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 2, 2021 at 18:24 | comment | added | user21820 | You may be interested to read about reverse mathematics. All known theorems about logic that have practical implications (e.g. Godel's semantic completeness theorem and syntactic incompleteness theorems) can be proven in ACA0, which is conservative over PA. This at least makes these theorems very convincing and not open to doubt. It also turns out that all practical applications of real analysis can be derived from theorems of ACA0, though it's not relevant to your question. | |
| Jan 20, 2021 at 7:17 | vote | accept | Wei | ||
| Dec 2, 2020 at 22:04 | answer | added | Peter Gerdes | timeline score: 2 | |
| Nov 12, 2020 at 4:55 | comment | added | Wei | That's a good point! I did have the impression that one of logicians' job was to create a formal foundation from scratch but soon realized the difficulty of not using mathematics and then the ambiguity of logical operations permitted to use. Now I understand, or at least, I can agree with your stand on this issue. | |
| Nov 11, 2020 at 23:09 | comment | added | Andrej Bauer | One point there is, why do you expect logicians to have different standard for doing mathematics than all the other mathematicians? Do you think it's somehow their task to "build a foundation"? I think that's a very misguided task. | |
| Nov 11, 2020 at 21:56 | comment | added | Wei | It helps. I understand the inevitability of leaving philosophical questions to philosophers and the methodology of thinking about and doing research in mathematical logic as one would in any mathematical discipline (cue: "mathematical" is the adjective in front of "logic") using human logic and ordinary mathematics. | |
| Nov 11, 2020 at 19:40 | comment | added | Andrej Bauer | Does this answer to a similar question help? (You might just read the last sentence first.) | |
| Nov 11, 2020 at 19:12 | review | Close votes | |||
| Nov 24, 2020 at 3:06 | |||||
| Nov 11, 2020 at 18:47 | review | First posts | |||
| Nov 11, 2020 at 20:06 | |||||
| Nov 11, 2020 at 18:45 | history | asked | Wei | CC BY-SA 4.0 |