Timeline for Is "all categorical reasoning formally contradictory"?
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| May 6, 2010 at 2:30 | comment | added | algori | Joel -- I seriously doubt that Cartier was talking of an actual formal contradiction, since none have been discovered so far. So I think this statement should be taken as a figure of speech, which is why I mentioned something which may look like a contradiction without actually being one. Another option would be that the phrase "formal contradiction" is the interviewer's interpretation of something else or that it simply appeared in translation (if things can get lost in translation, presumably they can appear as well:). | |
| May 5, 2010 at 18:53 | history | edited | algori | CC BY-SA 2.5 |
added a sentence
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| May 5, 2010 at 18:33 | comment | added | Joel David Hamkins | Although it is true that universes have a large cardinal strength, as you say, this doesn't make their use contradictory. So I doubt that this is what Cartier meant when he said that catogorical reasoning is formally contradictory. After all, neither the category theorists nor the set theorists believe that the existence of large cardinals or universes is inconsistent. Rather, I believe that Cartier was referring to the fact that much of category-theoretic reasoning uses a version of naive set theory that skirts very close to or even allows the Russell contradiction. | |
| May 5, 2010 at 13:19 | history | answered | algori | CC BY-SA 2.5 |