Timeline for Regarding my question: "Can only the constructible sets be proven to exist in $ZF$...."
Current License: CC BY-SA 3.0
15 events
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| Aug 26, 2017 at 1:10 | comment | added | Thomas Benjamin | @NoahSchweber: Thank you so much for your honesty and your answer--both very helpful. | |
| Aug 26, 2017 at 1:05 | comment | added | Todd Trimble Mod | It's also a good classroom technique: taking what is sometimes a suboptimal question and finding a useful lesson to extract for the world at large. All that preaching aside: you could well be right about the general trend of the OP's questions, and I hope he will reflect on everything you've said. I think this has been in many ways a useful discussion, and I thank you (again) for your honesty and forthrightness. | |
| Aug 26, 2017 at 1:02 | comment | added | Todd Trimble Mod | I didn't get subquestion (ii) here either. But the question did have a happy ending in the small respect that I myself gained some understanding. :-) So extrapolating from that: it might be useful on occasion to think of addressing not just the OP directly but the community at large: what the issues seem to be, what the resolutions are. Speaking over the head of the OP to the crowd out there (to be polite to Thomas: not saying he's incapable of understanding, but rather that it's a community question). I get the sense this is what Joel David Hamkins is often doing: speaking to the community. | |
| Aug 26, 2017 at 0:59 | comment | added | Noah Schweber | @ToddTrimble Wrapping up, I think my tldr response to your comment is: (i) I think the question is a bad one both because it is fundamentally unclear and because I don't think that in the near future it can receive an answer the OP will find satisfying. (ii) I regret the tone of the discussion at the question, which as you quite correctly pointed out is at points unconstructive. (iii) I think that the advice the OP should take to heart is structural: to reframe the focus of their future questions, and work to master the basics so that they can ask clear versions of the questions they want. | |
| Aug 26, 2017 at 0:53 | comment | added | Noah Schweber | that in some sense $\mathcal{P}_{def}$, or rather the appropriate iteration of $\mathcal{P}_{def}$, gives us a notion of powerset sufficient for ZF - but I'm not confident that that's what is really being asked, since that is a trivial consequence of the consistency of ZFC+V=L, which the OP knows. Or rather, they know the statement of that fact, but I don't know if they really understand what it means and I have no better sense now than I did before of what the OP does and does not understand. I bring up philosophy, but leaving that aside: I don't think this question can have a happy ending. | |
| Aug 26, 2017 at 0:47 | comment | added | Noah Schweber | Subquestion (ii) is a good example of this for me. I don't understand what the hereditarily finite sets have to do with anything, or what notion of predicativity the OP is using, or (and this is the important one) what criteria they are using to judge what the "right" powerset notion of a theory should be. There's a mass of mathematical and philosophical content implicit here, and before we can even get to that we need to address the OP's question (i), which already I don't think is a question they are ready to ask at the moment. Now on some level I think I do know what's being asked here - | |
| Aug 26, 2017 at 0:43 | comment | added | Noah Schweber | (cont'd) Specifically, it's easy for logic questions to be somewhat inherently subjective (and I've asked plenty myself with large subjective components), but then the appropriateness of such a question on mathoverflow depends in part on the OP's ability to engage the issue of what they really mean. This is really my problem here: my impression from this question and elsewhere is that the kinds of question the OP really wants to ask are not ones they are currently able to ask in a productive way, and that trying to do so is not helpful. As a specific example from this question: (cont'd) | |
| Aug 26, 2017 at 0:40 | comment | added | Todd Trimble Mod | Fair enough. Actually, I didn't think of you as being intolerant here. | |
| Aug 26, 2017 at 0:40 | comment | added | Noah Schweber | (I'd like to clarify, by the way, that here I am criticizing the OP's question - I am not trying to defend the tone of all participants involved. I can be frustrated by multiple things at once.) This is a difficult sort of thing to say, since it really can't help but risk having a chilling effect, but I think it's important for the OP to hear. This is not to say, by the way, that philosophy-heavy questions don't have their place on this site; as long as they have sufficient math content, I think they do. But I also think that to ask such questions well, one has to have very solid basics. | |
| Aug 26, 2017 at 0:33 | comment | added | Noah Schweber | Or at least, that's what comes through based on their engagement in this question (and in others). The confusions the OP is having are meaningful ones (incidentally in response to your comment let me just point out that I have in fact answered a large number of the OP's questions in the past - I don't think it's fair to paint me as intolerant of confusion in general or of the OP in particular); what I object to in this question, and in some others, is the way in which the OP goes about trying to resolve those confusions or responds to them being pointed out. (cont'd) | |
| Aug 26, 2017 at 0:22 | comment | added | Noah Schweber | @ToddTrimble "I think also there was just some simple honest confusion, and some of the tone I saw seemed a tad impatient about the confusion (I felt this personally when I tried to ask a question at the thread)." That is quite true and regrettable (especially the spillover to you). And I hope my own tone has been better. But at the same time, I stand by what I've said in my answer. In particular, I don't quite mean that there's a philosophical agenda here (although I do think there is); rather, the OP is interested more in doing philosophy than in understanding the mathematics here (cont'd) | |
| Aug 26, 2017 at 0:20 | comment | added | Todd Trimble Mod | Oh, yeah, let me add: +1. Thanks for your answer here. | |
| Aug 26, 2017 at 0:14 | comment | added | Todd Trimble Mod | "Mathematics is a process of staring hard enough with enough perseverence at at the fog of muddle and confusion to eventually break through to improved clarity. I'm happy when I can admit, at least to myself, that my thinking is muddled, and I try to overcome the embarrassment that I might reveal ignorance or confusion. Over the years, this has helped me develop clarity in some things, but I remain muddled in many others. I enjoy questions that seem honest, even when they admit or reveal confusion, in preference to questions that appear designed to project sophistication." | |
| Aug 26, 2017 at 0:13 | comment | added | Todd Trimble Mod | Noah, you may be right about there being philosophical agenda getting in the way here. But speaking as someone outside set theory, I think also there was just some simple honest confusion, and some of the tone I saw seemed a tad impatient about the confusion (I felt this personally when I tried to ask a question at the thread). I would like to quote Bill Thurston here, from his MO profile (continued next comment). | |
| Aug 25, 2017 at 22:50 | history | answered | Noah Schweber | CC BY-SA 3.0 |