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ec429 comments on The Apparent Reality of Physics - Less Wrong
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Yes, but I'm actually going somewhere with this: EY doesn't believe that "infinite sets exist" (loosely put). So I'm trying to deduce constraints on what "exist" can mean and still be coherent; at this point I don't think we can even claim that lavalamp's kangaroos "don't exist".
So if you've ever read Probability Theory, by E.T. Jaynes, I suspect he's just a convert to the position that, in order to make sense when applied to the real world, infinite things have to behave like limits of finite things. Using "exists" can be avoided.
I haven't; I probably should.
Is this "limits" in the sense of analysis (epsi-delta limits), or is it "limit points" (like ω)? If the former, then that position involves not believing that arithmetic makes sense when applied to the real world. If the latter, then the position doesn't seem different from what most mathematicians believe, because allowing limit points gets you transfinite induction... but then, as I intend to show, that gets you the first uncountable ordinal, by the power of 'scary dots'. So... either EY doesn't believe arithmetic applies to the real world, or EY doesn't know the logical consequences of his beliefs, or EY doesn't believe the above position, or I've made an error. Of course, at this point the last of those is rather likely, which is exactly why I want to formalise my argument and lay it out as coherently as possible.
Also, if I can't say "exists", how come you can talk about "the real world"? Double standards if you ask me ;)
Well, you can say exists, it just seems to be digging you into a hole.
Has EY articulated a position on "infinite set atheism" outside of a few off-hand comments, that are possibly jokes? You might be preparing to rebut a position that he hasn't taken.
Well, I've seen him go into quite some detail in comment threads about uncountable ordinals; it looks to me very much as though there is a position there that he's taking (it's fairly clear that it's more than just a joke). OTOH, I haven't seen an article by him setting out his position in a rigorous or articulated fashion, though if there is one I'd like to know about it.