Timeline for "Introduction to mathematical logic" book from a formalist perspective
Current License: CC BY-SA 3.0
8 events
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| Jan 29, 2014 at 19:50 | comment | added | user43263 | @Burak Thanks for the link, that was a good tip (as was your advice)! | |
| Jan 27, 2014 at 16:41 | comment | added | Burak | Dear user43263, The following answer and question (mathoverflow.net/a/23096/33039) might seem irrelevant to your question at first sight, but I believe it is not. At its core, your question and concerns are really about the question in which formal system can we carry out logic. If you want to have a fixed metatheory and see formal details, just go and try to do it! For example, try to formalize "satisfaction" and "proves" relations in your favorite set theory. Once you see that these can be done, you will be no more disturbed by logicians' laziness to sweep these under the rug. | |
| Jan 26, 2014 at 22:17 | comment | added | Timothy Chow | I don't think that comfort with "intuitively clear" arguments has much to do with platonism vs formalism. It has more to do with whether the author expects the reader to have enough experience to formalize the argument, or whether the author feels the need to spell out more details. It's true that some authors get lazy and fail to spell out formalization details even in situations where it's important to check that a particular argument can be formalized in a particular formal system. But this has more to do with expository skill than with philosophical prejudice. | |
| Jan 26, 2014 at 11:53 | comment | added | user43263 | [...] work in, since he has some concept of "absolute truths" and can take that to be his metatheory - that would be a vague explanation of how I see the dichotomy (Timothy Chows answer explains this better). | |
| Jan 26, 2014 at 11:47 | comment | added | user43263 | I'm not sure if being a formalist necessarily means that the "details of formalizations and keeping proofs and arguments" have to look "closer to how they would 'formally'". If it's clear how to translate an informal argument into a formal one I don't see any objections to being informal. It seems to me that the difference lies rather in the fact that as a formalist one is more careful stating the setting in which one is working in the first place and avoiding "intuitively clear" arguments, whereas a platonist wouldn't be so much bothered by not being told, e.g., in which metatheory we [...] | |
| Jan 25, 2014 at 18:01 | history | edited | Burak | CC BY-SA 3.0 |
added 110 characters in body
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| S Jan 25, 2014 at 17:34 | history | answered | Burak | CC BY-SA 3.0 | |
| S Jan 25, 2014 at 17:34 | history | made wiki | Post Made Community Wiki by Burak |