Timeline for Are the Foundations of Mathematical Logic Shaky?
Current License: CC BY-SA 3.0
16 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 5, 2012 at 13:24 | comment | added | Qfwfq | @A.Bauer, Re to a comment above: I think mathematics has more to do with "correctness" (in some formal sense concerning symbols) rather than with "truth" or "certainty". | |
| Nov 5, 2012 at 13:17 | comment | added | Qfwfq | I don't agree with Wittgenstein, if by "mathematics" we understand some formalizable entity. I would rather say: "Logic is the foundation of mathematics as the canvas is the support of the painting (and of course, you could paint on other surfaces if you have some at your disposal)". The problem with (formal) mathematics is that -almost by definition- there are no other "surfaces" on which to paint. On the other hand, I also agree with Wittgenstein if by "mathematics" here we intend the human activity of doing mathematics (which is not a formalizable entity). | |
| Oct 25, 2012 at 20:21 | comment | added | Andrej Bauer | I find myself agreeing with Wittgenstein a bit more every year. | |
| Oct 25, 2012 at 20:05 | comment | added | Alexander Woo | To condense Andrej's remarks, Wittgenstein said something like: "Logic is the foundation of mathematics only as the painted rock is the support of the painted tower." | |
| Oct 25, 2012 at 19:36 | comment | added | Andrej Bauer | Re Stefan Geschke: his is a very good answer, but I think he is answering a different concern, namely what do we need technically speaking, to get things going. The answer is something like "symbolic manipulation". But that leaves open the question how do we know that our manipulations are not arbitrary. I think I am trying to answer a different concern: what secures mathematics? (Surely not the bare fact that I can type letters into my computer.) The answer is: not logic. | |
| Oct 25, 2012 at 19:31 | comment | added | Andrej Bauer | I strongly disagree that at the beginning there is blind manipulation of symbols. It is extremely dishonest to claim such a thing. At the beginning you, the human who is actually doing all of this, has a pretty good idea how informal mathematics works. Those in search of "perfect certainly" are not going to find it in logic, or any other mathematical activity. Mathematics gives a high degree of certainty, but not the mystical kind that some seem to ask of it. | |
| Oct 25, 2012 at 17:36 | comment | added | Qfwfq | (...) I believe this answer by Stefan Geschke: mathoverflow.net/questions/62818/the-sets-in-mathematical-logic/… came close to be conclusive for this philosophical problem (you don't need to read my needlessly verbose answer to the same question!). If I interpret it correctly, when we want to break the circle there is no logic at the beginning: just blind manipulation of symbols. | |
| Oct 25, 2012 at 17:32 | comment | added | Qfwfq | As I did in your answer to the similar question, I don't agree with this viewpoint. Of course when you intend Logic simply as a branch of mathematics, it is not different from number theory or differential geometry. But you can also intend the word "Logic" as what determines the inferences in formal theories, and formal theories are -so far- the only method we have to provide a rigorous foundation to mathematics. (...) | |
| Oct 25, 2012 at 13:06 | comment | added | user9072 | @Asaf Karagila: well, yes, I also thought this quite likely. Hence my question that was not intended as rhetorical in any way. | |
| Oct 25, 2012 at 12:44 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
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| Oct 25, 2012 at 12:36 | comment | added | Andrej Bauer | Right, there it is. | |
| Oct 25, 2012 at 12:36 | history | edited | Andrej Bauer | CC BY-SA 3.0 |
added 1516 characters in body; added 15 characters in body
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| Oct 25, 2012 at 12:10 | comment | added | Asaf Karagila♦ | quid, I think he posted this so he could write a proper answer even if the question gets closed. | |
| Oct 25, 2012 at 12:06 | comment | added | user9072 | Do you plan to expand this? If not, you should, IMO, at least make this CW. | |
| Oct 25, 2012 at 11:55 | history | answered | Andrej Bauer | CC BY-SA 3.0 |