Timeline for Meta$^{n{-}th}$ mathematics [duplicate]
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 28, 2014 at 12:30 | vote | accept | Joseph O'Rourke | ||
| Jun 28, 2014 at 12:02 | history | closed |
Bjørn Kjos-Hanssen Felipe Voloch Andrés E. Caicedo Stefan Kohl♦ Emil Jeřábek |
Duplicate of Interesting meta-meta-mathematical theorems? | |
| Jun 28, 2014 at 3:51 | comment | added | Christian Remling | Metamathematics is really mathematics (of mathematics, or more precisely certain formalizations of it), and the meta is just a (useful) linguistic device to help us distinguish the investigation from the object being investigated. This precaution is peculiar to logic, and indeed we need not call the investigation of groups meta-group-theory (but we could): one only rarely mistakes a proof of Lagrange's theorem for a group. | |
| Jun 28, 2014 at 3:26 | answer | added | Joel David Hamkins | timeline score: 36 | |
| Jun 28, 2014 at 2:28 | answer | added | The Masked Avenger | timeline score: 8 | |
| Jun 28, 2014 at 1:51 | comment | added | Steven Landsburg | @JosephO'Rourke: Is the four-color theorem "just a theorem of mathematics?" Is the Pythagorean theorem "just a theorem of mathematics"? Is there some relevant sense in which these differ from Godel's theorems? | |
| Jun 28, 2014 at 1:43 | comment | added | Asaf Karagila♦ | @Andreas: I believe this was discussed before; on the StackExchange network, the meta operator is idempotent. | |
| Jun 28, 2014 at 1:41 | review | Close votes | |||
| Jun 28, 2014 at 12:12 | |||||
| Jun 28, 2014 at 1:39 | comment | added | Joseph O'Rourke | @BjørnKjos-Hanssen: Thanks for that reference---I agree that I unwittingly nearly duplicated that recent question, which has informative responses. | |
| Jun 28, 2014 at 1:37 | comment | added | Andreas Blass | @Asaf I agree with your comment, but doesn't it belong on the meta-meta-site? | |
| Jun 28, 2014 at 1:30 | comment | added | Asaf Karagila♦ | Shouldn't this question be asked on the meta site? :-) | |
| Jun 28, 2014 at 1:27 | comment | added | Burak | @Joseph O'Rourke: Eventhough I would like to agree with that, I cannot see how to make the distinction precise. Say, for example, you are doing your Gödel numbering in such a way that sentences starting with $\exists$ are always assigned to even numbers. Is the statement "there exist infinitely many even numbers" a metamathematical fact? It tells you that there exist infinitely many sentences starting with $\exists$. But it also tells you that, well, there are infinitely many even numbers. | |
| Jun 28, 2014 at 1:22 | comment | added | Joseph O'Rourke | @Burak: I would say that it is difficult to maintain the position that, say, Gödel's incompleteness theorems are just theorems of mathematics. | |
| Jun 28, 2014 at 0:58 | comment | added | Burak | This might be a naive question but don't metamathematical theorems, once you formalize them, become mathematical and therefore meta-metamathematical theorems are simply metamathematical? For example, you can prove theorems like "the theory T proves that the theory S proves...etc.", which you might consider meta-meta-meta-...-mathematical, but isn't this just metamathematics? | |
| Jun 28, 2014 at 0:35 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |