Timeline for Are proper classes objects?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 13, 2016 at 20:02 | comment | added | user99916 | Let us continue this discussion in chat. | |
| Nov 13, 2016 at 19:56 | comment | added | user99916 | @MikeShulman: Of course I also think that everybody can think what he/she wants; but I'm afraid that Blass's view isn't compatible with the practice of mathematicians, since proper classes are used all the time, right? I expected that therefore, the majority of people would have your opinion. What do you make of the fact that his answer is accepted and has more likes than yours? | |
| Nov 13, 2016 at 19:41 | comment | added | Mike Shulman | (This sort of philosophical "existence", of course, must be distinguished from purely mathematical questions of existence, on which all mathematicians should agree. I agree entirely that inside ZFC it is a true statement that proper classes "do not exist"; I just resist the identification of this mathematical statement with the philosophical one.) | |
| Nov 13, 2016 at 19:40 | comment | added | Mike Shulman | @Nullachtfünfzehn well, this is philosophy, not mathematics, so you can believe whoever you want, or you can invent your own opinion. In math we can prove theorems to convince people they are wrong, but in philosophy no questions can ever be definitely resolved, people just keep arguing forever. (-O | |
| Nov 13, 2016 at 11:05 | comment | added | Mike Shulman | @Nullachtfünfzehn - In my opinion, Blass's argument fails at "If proper classes were objects, they should be included among the sets", which simply begs the question by assuming that all "objects of mathematics" are sets. | |
| Nov 12, 2016 at 17:07 | comment | added | user99916 | @MikeShulman: Can you refute the philosophical argument given by Blass that tries to show that proper classes do not exist? | |
| Nov 12, 2016 at 16:24 | comment | added | user99916 | @StefanGeschke: Are you believing that all of mathematics has to take place in ZFC? Shulman wrote: "I'm guessing the insistence that proper classes are "not objects" stems from a belief that all of mathematics takes place in ZF." | |
| Aug 3, 2011 at 3:56 | comment | added | Mike Shulman | @Stefan: We can say it just fine, in a perfectly technical and precise sense. We just can't formalize it as a single statement inside the model of ZF in question. But "the class of all sets in this model of ZF is a model of ZF" is a perfectly true (though somewhat tautological) statement about any model of ZF, in any context in which one can talk about a model of ZF. | |
| Aug 2, 2011 at 5:49 | comment | added | Stefan Geschke | This will sound like splitting hairs, but in a technical sense we cannot say that "the class of all sets is a model of ZF". This is because the model relation can only be defined for structures that are sets. Otherwise we run into problems with Tarski's undefinability of truth. We do, however, usually assume that all axioms of ZF hold in the the class of all sets, but that is a metamathematical statement. | |
| Aug 2, 2011 at 4:31 | history | answered | Mike Shulman | CC BY-SA 3.0 |