Timeline for The Importance of ZF
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 29, 2012 at 20:54 | comment | added | Todd Trimble | "Friedman is right to say that categorical logicians (among others) have not presented a genuinely independent ontology for mathematics that achieves what modern set theory does." I am afraid I don't understand what is trying to be said here. "Genuinely independent" in particular sound like weasel words to me, and the use of the word "ontology" is not very clear to me. Insofar as there are structural set theories which have the same strength as membership-based set theories, can you clarify what precisely is lacking in structural set theories? (Only saw this after > 2.5 years; sorry.) | |
| Jun 10, 2010 at 11:27 | comment | added | Charles Stewart | @Todd: I did not find the discussion shallow, and I did not find Friedman to be hostile, although I entirely agree that Simpson framed the whole issue in a pointlessly divisive manner: the list-1 vs. list-2 distinction was presented almost as a matter of moral character. I agree that justice was not done to the structuralist viewpoint, but I still think that Friedman is right to say that categorical logicians (among others) have not presented a genuinely independent ontology for mathematics that achieves what modern set theory does. | |
| Jun 7, 2010 at 16:14 | comment | added | Todd Trimble | I didn't see Friedman's sense of "foundationally complete" from the link provided (and actually, I was actively following the FOM discussions during that time). The responses to categorical/structuralist foundations (advocated by McLarty, Awodey, and others) by Friedman, Simpson, and others committed to materialist foundations were, IMO, disappointingly shallow and ridiculously emotional (hostile). The question Friedman raises about V(w+w) is very interesting however (and particularly interesting for the question of adequacy of Mac Lane's set theory!). | |
| Jun 7, 2010 at 9:12 | comment | added | Charles Stewart | @David: Maclane's categorical set/type theories are not foundationally complete, in Friedman's sense. | |
| Jun 7, 2010 at 6:41 | comment | added | David Roberts♦ | "simplest" probably the most complicated to define. ZF is not finitely axiomatisable, but some category theoretical variants are. If an axiom schema only 'counts' as much as an axiom, then ZF has a shorter list of axioms+schemas, but... | |
| Jan 15, 2010 at 12:25 | history | answered | Charles Stewart | CC BY-SA 2.5 |