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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. St. Rev  ☯️ 🏴 😻‏ @St_Rev 1 May 2017
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      Replying to @St_Rev @Meaningness

      It seems likely that math at least ought to contain the rationals! Although the Greeks might have trouble even going that far.

      1 reply 0 retweets 0 likes
    2. St. Rev  ☯️ 🏴 😻‏ @St_Rev 1 May 2017
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      Replying to @St_Rev @Meaningness

      The problem with the rationals is they don't stick to themselves. You need some kind of glue for paths to hold together.

      1 reply 0 retweets 0 likes
    3. St. Rev  ☯️ 🏴 😻‏ @St_Rev 1 May 2017
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      Replying to @St_Rev @Meaningness

      Is the logical/set-theoretic/infinitary construction behind R really necessary, or is there some Q + glue construct we missed?

      3 replies 0 retweets 1 like
    4. David Chapman‏ @Meaningness 1 May 2017
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      Replying to @St_Rev

      Really interesting… I vaguely remember reading about a proof that you can’t do anything similar to real analysis unless you bite the bullet

      1 reply 0 retweets 0 likes
    5. David Chapman‏ @Meaningness 1 May 2017
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      Replying to @Meaningness @St_Rev

      > but I can’t remember any details of that. Failure of the Brouwer program is presumably relevant;t I don’t remember much about that either!

      1 reply 0 retweets 0 likes
    6. St. Rev  ☯️ 🏴 😻‏ @St_Rev 1 May 2017
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      Replying to @Meaningness

      You can do everything with nonstandard reals instead, but they're even worse.

      3 replies 0 retweets 1 like
    7. David Chapman‏ @Meaningness 1 May 2017
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      Replying to @St_Rev

      Yes, counting “worse” along that axis—I like nonstandard analysis better than ε/δ, but I like logic better than mathematics :)

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    8. Referent Of Self‏ @ReferentOfSelf 1 May 2017
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      Replying to @Meaningness @St_Rev

      synthetic differentiation and constructive analysis are better

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    9. David Chapman‏ @Meaningness 1 May 2017
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      Replying to @ReferentOfSelf @St_Rev

      I thought I’d read you can’t get far with that. Have a handy url for a summary?

      1 reply 0 retweets 0 likes
    10. Referent Of Self‏ @ReferentOfSelf 1 May 2017
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      Replying to @Meaningness @St_Rev

      For constructive analysis, there's http://www.springer.com/us/book/9783642649059 …. For synthetic differentiation, you can only do differential geometry

      2 replies 0 retweets 0 likes
      David Chapman‏ @Meaningness 1 May 2017
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      Replying to @ReferentOfSelf @St_Rev

      So, apparently you can’t prove the intermediate value theorem… which is sort of exactly what reals are for. https://en.m.wikipedia.org/wiki/Constructive_analysis …

      4:08 PM - 1 May 2017
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        2. Referent Of Self‏ @ReferentOfSelf 1 May 2017
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          Replying to @Meaningness @St_Rev

          because it gives the wrong intermediate value theorem. Replace the f(x) = c with another epsilon delta

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        3. Referent Of Self‏ @ReferentOfSelf 1 May 2017
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          Replying to @ReferentOfSelf @Meaningness @St_Rev

          The point is to rarely if ever use =, and instead use approximation

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