Timeline for "Introduction to mathematical logic" book from a formalist perspective
Current License: CC BY-SA 3.0
6 events
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| Jan 26, 2014 at 22:02 | comment | added | Timothy Chow | (continued) Once students get over that hurdle, then there is, as you say, another hurdle later, when one needs to verify that specific arguments can be formalized in specific systems. Sometimes this is glossed over, and it is fair to ask for more details than are usually given. But again in my experience, people who have a clear understanding of the general setup and just want more technical details tend to phrase their request rather precisely, and in particular recognize that formalism vs platonism isn't the real issue. | |
| Jan 26, 2014 at 21:56 | comment | added | Timothy Chow | @Nik: Everything you say is accurate. However, in my experience, students who say (in effect) that they are formalists and not platonists tend to be bothered by something more basic. They freeze up when they see talk of "truth" or "the standard natural numbers" and can't follow the reasoning. This really has nothing to do with formalism or even with technical concerns about the precise metatheoretical strength needed for specific arguments, although their complaints can sound like that. | |
| Jan 26, 2014 at 16:28 | comment | added | Nik Weaver | I'm puzzled about why this answer is getting votes. The difference is that in logic the subject matter is the formal systems themselves, so you can't just reason naively and say, for instance, "we know PA is consistent" and leave it at that. The consistency of PA is not provable in PA and this matters. The point is that the choice of metatheory is more relevant in logic than elsewhere, so I wouldn't be so quick to dismiss the OP's concerns. | |
| Jan 26, 2014 at 11:38 | comment | added | user43263 | I want to thank you very much - it felt as if you could read my mind with a part of what was bothering a set me straight! | |
| S Jan 26, 2014 at 4:32 | history | answered | Timothy Chow | CC BY-SA 3.0 | |
| S Jan 26, 2014 at 4:32 | history | made wiki | Post Made Community Wiki by Timothy Chow |