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Meaningness's profile
David Chapman
David Chapman
David Chapman
@Meaningness

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David Chapman

@Meaningness

Better ways of thinking, feeling, and acting—around problems of meaning and meaninglessness; self and society; ethics, purpose, and value.

meaningness.com/about-my-sites
Joined September 2010

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    1. David R. MacIver‏ @DRMacIver 25 Nov 2019
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      David R. MacIver Retweeted The Great Natsby

      The fact that people get hung up on the truth or falsehood of set theoretic axioms like Choice or CH is a weird messy holdout of mathematical platonism and we should be taking Godel's completeness theorem more seriously. (No, not his incompleteness theorem. The other one)https://twitter.com/nex3/status/1199086783222255616 …

      David R. MacIver added,

      The Great Natsby @nex3
      controversial opinions stress me out so please quote-tweet this with your most OBSCURE opinion instead
      Show this thread
      3 replies 2 retweets 26 likes
      Show this thread
    2. David R. MacIver‏ @DRMacIver 25 Nov 2019
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      I mean not that you actually need the completeness theorem for this - we can construct models of all these things perfectly well without it - but it's funnier if I put it that way.

      1 reply 0 retweets 5 likes
      Show this thread
    3. David R. MacIver‏ @DRMacIver 25 Nov 2019
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      Also topology should be taught as part of a first course on set theory and logic and real analysis should be taught assuming it as a foundation.

      3 replies 0 retweets 5 likes
      Show this thread
    4. David Chapman‏ @Meaningness 25 Nov 2019
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      Replying to @DRMacIver

      That would have saved me a year’s worth of existential crisis when I was 19

      1 reply 0 retweets 1 like
    5. David R. MacIver‏ @DRMacIver 25 Nov 2019
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      Replying to @Meaningness

      Go on...

      1 reply 0 retweets 0 likes
    6. David Chapman‏ @Meaningness 25 Nov 2019
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      Replying to @DRMacIver

      I was existentially incapable of continuing with math until I could find out what a real number was, which my analysis teacher refused to tell me. After six months of clinical depression I found the answer in the library and life became livable again.

      2 replies 0 retweets 3 likes
    7. Nathaniel‏ @Nathani02617995 25 Nov 2019
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      Replying to @Meaningness @DRMacIver

      What’s the answer

      2 replies 0 retweets 0 likes
    8. David Chapman‏ @Meaningness 25 Nov 2019
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      Replying to @Nathani02617995 @DRMacIver

      Well the answer I *got*, which seemed completely satisfactory at the time, was “Dedekind cuts/Cauchy sequences.” This turns out to be wrong, but I didn’t figure that out until MUCH later, >

      1 reply 0 retweets 0 likes
    9. David Chapman‏ @Meaningness 25 Nov 2019
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      Replying to @Meaningness @Nathani02617995 @DRMacIver

      and by then I’d developed a meta-rational view so I didn’t have to freak out when rationality broke down.

      1 reply 0 retweets 0 likes
    10. David R. MacIver‏ @DRMacIver 25 Nov 2019
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      Replying to @Meaningness @Nathani02617995

      "The object satisfying these axioms (which we prove exists and is unique up to isomorphism), pick your favourite implementation" is sufficiently standard fare literally everywhere in mathematics that I'm not sure it's reasonable to count it as a breakdown of rationality.

      2 replies 0 retweets 0 likes
      David Chapman‏ @Meaningness 25 Nov 2019
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      Replying to @DRMacIver @Nathani02617995

      Wait I haven’t done this stuff in 35 years, but the nonstandard reals are a model for the reals axioms, and not isomorphic, right? Or am i misremembering?

      3:37 PM - 25 Nov 2019
      1 reply 0 retweets 0 likes
        1. New conversation
        2. David R. MacIver‏ @DRMacIver 25 Nov 2019
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          Replying to @Meaningness @Nathani02617995

          The nonstandard reals are not a model for the real axioms - they don't satisfy the completeness property. They satisfy all the same first-order sentences, but the real axioms involve quantifying over sets of reals, which is not a first order sentence.

          1 reply 0 retweets 1 like
        3. David Chapman‏ @Meaningness 25 Nov 2019
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          Replying to @DRMacIver @Nathani02617995

          Ugh, it’s been a long time… if you go beyond fopc, you’ve got a ton of big new philosophical problems if my memory isn’t completely rotten

          1 reply 0 retweets 1 like
        4. 9 more replies

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