Timeline for Were Bourbaki committed to set-theoretical reductionism?
Current License: CC BY-SA 4.0
10 events
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| Jan 20, 2023 at 8:04 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
abstract group is a set with a binary relation ] ---> [ abstract group is a set with a binary law
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| Jan 20, 2023 at 7:50 | history | edited | Duchamp Gérard H. E. | CC BY-SA 4.0 |
Eliminated repetition "the the"
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| Jan 12, 2010 at 4:14 | comment | added | Harry Gindi | I'd like to direct all of you to an example that gives a good deal of substance to both Pete's claims and my own: mathoverflow.net/questions/11425/a-categorical-question/… This description is spot on. | |
| Jan 11, 2010 at 3:02 | comment | added | Pete L. Clark | @FGD: My comments were qualified: I didn't say whether I personally viewed Bourbaki as proto-categorical, only "some have argued". (To be fair, I do think there is some merit in this view, or I wouldn't have repeated it.) I agree with your comment about the a posteriori reading of Bourbaki -- in my defense, I cannot truly read it in any other way. I think you're absolutely right that the familiarity of the structuralist approach to mathematics is largely due to Bourbaki's influence. What I was saying was the part where they define structure is not very compelling or essential. | |
| Jan 11, 2010 at 1:42 | comment | added | François G. Dorais | I agree with your characterization of Bourbaki as "structuralist" rather than "reductionist" but I think some of your arguments rely on an a posteriori reading of Bourbaki. For example, when you talk about "structure preserving maps" being "clear from context." It seems to me that this clarity may be due to Bourbaki and how they shaped mathematics. It is possible that Bourbaki viewed precise definitions of "structures" as much more essential than you and I do now. If so, that would make Bourbaki much less "proto-categorical" than you describe. Anyway, that was my two cents. | |
| Jan 10, 2010 at 18:09 | comment | added | Jeremy Shipley | I take the point about group elements not needing to be sets to be a good one that helps to clarify that the basic issue is not actually about basic ontology (as I'd put it). I suppose I'd be more interested to know whether group, etc. operations are identified with sets. This would help to distinguish (as I'd put it following Corry) "informal structures on sets" from "formal set structures". | |
| Jan 10, 2010 at 17:33 | vote | accept | Jeremy Shipley | ||
| Jan 10, 2010 at 13:07 | comment | added | Chandan Singh Dalawat | It might interest you to visit the Bourbaki archive : mathdoc.emath.fr/archives-bourbaki | |
| Jan 10, 2010 at 12:52 | comment | added | Harry Gindi | Speaking of the unfinished works of Bourbaki, I'd be very interested in seeing some of them. Does anyone know where they are? I'd guess, based on Bourbaki's perfectionism, that "not ready to be published" means that not everyone had agreed that it was ready to be published, and it's probably better than most books previously published on the subject. | |
| Jan 10, 2010 at 12:32 | history | answered | Pete L. Clark | CC BY-SA 2.5 |