Timeline for Intuitive and/or philosophical explanation for set theory paradoxes
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| Jun 19, 2010 at 12:14 | comment | added | Carl Mummert | @Neel: I think there are two reasons. The first is that set theory was developed before semantics for intuitionistic logic were known. Kripke models were first studied in the 1950s, and the BHK interpretation was not widely known before the 1930s. Second, some set theorists I know feel that a key goal of set theory is to study the intended model, which consists of "all sets" (disquotationally). That model, from their point of view, cannot possibly grow larger. Let's leave the discussion on the validity of that view for another day; I'm just pointing out it's common among set theorists. | |
| Jun 19, 2010 at 10:34 | comment | added | Neel Krishnaswami | What surprises me about this story is that the logic of sets is taken to be classical rather than intuitionistic. If you assume that the domain of quantification (eg, the universe of sets) can grow, and you want true propositions to remain true in future domains, then you get a Kripke model. So why isn't the logic of sets intuitionistic? Or at the very least, why don't sets have an open/closed distinction as in topology...? | |
| Jun 19, 2010 at 7:46 | history | answered | Péter Komjáth | CC BY-SA 2.5 |