Timeline for Are the models of infinitesimal analysis (philosophically) circular?
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Aug 1, 2023 at 9:42 | comment | added | Nico | @MichaelBächtold Yes, although one could say that "smooth space" is a primitive of SDG (one should think of all objects as being automatically equipped with a smooth structure). It just so happens that not all "sets" of SDG are manifolds. | |
| Jan 20, 2023 at 9:27 | comment | added | Michael Bächtold | SDG does not "take manifolds as primitives". It takes nilpotent real numbers as primitives. Manifolds are a defined concept in SDG. | |
| Jan 19, 2023 at 4:29 | comment | added | Timothy Chow | @Qfwfq "Need to" is a strong term that I personally would avoid. But yes, ETCS is one approach to a categorical foundation of mathematics, and it does not try to avoid set theory. What I'm referring to is the idea one sometimes hears of categorical foundations without set theory. From the point of view of a working mathematician, it's not clear why you would want to eliminate sets entirely. But let's say you wanted to, because you don't trust sets. It would be hard (though maybe not impossible) to avoid sets completely. | |
| Jan 19, 2023 at 3:23 | comment | added | Qfwfq | A question: categorical foundations of mathematics need to axiomatize the category of sets, not of arbitrary categories, is this correct? If this is true, I feel like categorical foundations would just give us a "structural" (some would say "non-evil") way to talk about sets, not really a different basic idea. | |
| Jan 19, 2023 at 2:52 | history | answered | Timothy Chow | CC BY-SA 4.0 |