Timeline for Russell's paradox as understood by current set theorists
Current License: CC BY-SA 4.0
6 events
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| Sep 17, 2020 at 18:59 | comment | added | Rodrigo Freire | Thanks, I have given just a rough sketch of the beginning of an answer. Many things must be addressed. But I believe those things can be at least partially addressed. I also believe that the alternative view of set theory as being about an extramathematical model or a collection of extramathematical models really introduces the dichotomy, (and alienates mathematical truth from its practice, making mathematics somewhat speculative or based on some private intellectual intuition which is much more mysterious than the mathematical practice that it presumably explains.) | |
| Sep 17, 2020 at 17:56 | comment | added | Pace Nielsen | That said, it seems to me that most mathematicians don't follow the advice of only reasoning about $\Omega$ intensionally. Rather, ${\rm Ord}$ is treated as an object that one can reason about (perhaps only in the meta-theory, but still a concrete object), create models of, etc... It's like we mathematicians want to have our cake, and eat it too. | |
| Sep 17, 2020 at 17:25 | comment | added | Pace Nielsen | This is an excellent answer. I really like your rephrased question "should there be a dichotomy...". | |
| Sep 17, 2020 at 14:35 | history | edited | Rodrigo Freire | CC BY-SA 4.0 |
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| Sep 17, 2020 at 10:05 | history | edited | Rodrigo Freire | CC BY-SA 4.0 |
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| Sep 17, 2020 at 3:02 | history | answered | Rodrigo Freire | CC BY-SA 4.0 |