Timeline for Ontological status of some "sets" in ZFC
Current License: CC BY-SA 3.0
9 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jun 2, 2016 at 21:23 | comment | added | user13113 | One thing I think is conspicuously lacking is the possibility of a many-valued but boolean truth; $\varphi \vee \neg \varphi$ is true, but that does not imply that true and false are the only possibilities for $\varphi$. I suppose, though, that this could be viewed as plural realism in disguise. | |
| Jun 5, 2013 at 9:47 | comment | added | Godot | Joel, I decided to choose your answer since it is philosophy- oriented and informative. I like your idea of the multiverse, very interesting. | |
| Jun 5, 2013 at 9:41 | vote | accept | Godot | ||
| Jun 5, 2013 at 1:29 | comment | added | Noah Schweber | Nor do I - but then, I think of "the reals" as also ambiguous. | |
| Jun 5, 2013 at 0:48 | comment | added | Joel David Hamkins | Noah, I find your description fine for particularly simple definitions, but I don't regard, say, "the reals, thought of as Dedekind cuts in the rationals" as a constant definition across set-theoretic universes, since different set-theoretic universes can have different collections of such cuts (not to mention different sets of rational numbers). | |
| Jun 5, 2013 at 0:26 | history | edited | Joel David Hamkins | CC BY-SA 3.0 |
added 1496 characters in body
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| Jun 5, 2013 at 0:02 | comment | added | Noah Schweber | A quick side note about plural realism in this context: under that view, definitions of sets can now be thought of as "meta-functions" assigning to each universe a set in that universe. Then the distinction between "ambiguous" and "unambiguous" definitions is just the distinction between "non-constant" and "constant" functions. (The use of the word "function" here might, to be fair, be inappropriate!) | |
| Jun 4, 2013 at 23:50 | history | answered | Joel David Hamkins | CC BY-SA 3.0 |