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Plinz's profile
Joscha Bach
Joscha Bach
Joscha Bach
@Plinz

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Joscha Bach

@Plinz

FOLLOWS YOU. Artificial Intelligence, Cognitive Architectures, Computation. The goal is integrity, not conformity.

San Francisco, CA
bach.ai
Joined April 2009

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    1. Matthew Mirman‏ @mmirman 23 Sep 2018
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      Replying to @mmirman @Plinz @vgr

      what saves us is that proofs are text, and thus there are countably many proofs for any logic we might agree upon, where checking a proof is correct is decidable, and thus for any axioms we culturally agree on, a computer will be able to come up with all the proofs we would.

      1 reply 0 retweets 0 likes
    2. Joscha Bach‏ @Plinz 23 Sep 2018
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      Replying to @mmirman @vgr

      I don't like the idea that "we" "culturally agree" on axioms. If by "we" you include non-mathematicians, you are probably wrong in most cases, and if you characterize mathematics as a culture instead of a formal exercise, you miss its point.

      2 replies 0 retweets 0 likes
    3. Matthew Mirman‏ @mmirman 23 Sep 2018
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      Replying to @Plinz @vgr

      no, we doesn't include non-mathematicians. Mathematics is a culture. This is what gödel's thms actually show: there are provably infinitely many possible independent axioms forming a hierarchy of logics by relative consistency, and at the top assuming all of them is inconsistent

      3 replies 0 retweets 1 like
    4. Joscha Bach‏ @Plinz 23 Sep 2018
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      Replying to @mmirman @vgr

      How do you define "culture"?

      1 reply 0 retweets 0 likes
    5. Matthew Mirman‏ @mmirman 23 Sep 2018
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      Replying to @Plinz @vgr

      A group of people with mutually accepted and practiced customs, or the customs themselves

      1 reply 0 retweets 1 like
    6. Joscha Bach‏ @Plinz 24 Sep 2018
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      Replying to @mmirman @vgr

      It seems to me that there is an ideal way to do mathematics (I know that this is a crass oversimplification), and the customs of mathematicians are not cultural but pragmatic approximations of this. Deforming them into an idiosyncratic culture perverts mathematics.

      1 reply 0 retweets 0 likes
    7. Joscha Bach‏ @Plinz 24 Sep 2018
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      Replying to @Plinz @mmirman @vgr

      (I think that a set of policies and behaviors only counts as a culture if it involves a choice, and is not imposed by the rules of the game one has to play.)

      1 reply 0 retweets 0 likes
    8. Matthew Mirman‏ @mmirman 24 Sep 2018
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      Replying to @Plinz @vgr

      There are a few choices for mathematicians: 1. Which logic to use for their metalogic 2. What axioms should be made explicit: Most papers don't declare "we now use modus ponens" 3. What level of detail to present their arguments: what is acceptable as a pragmatic approximation

      1 reply 0 retweets 0 likes
    9. Joscha Bach‏ @Plinz 24 Sep 2018
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      Replying to @mmirman @vgr

      It seems to be a good approximation when we say that are no fundamental disagreements between mathematicians. There seem to be merely different areas and levels of expertise. In my view, philosophy is a culture (or several ones), because philosophers have tremendous disagreements

      2 replies 0 retweets 0 likes
    10. Matthew Mirman‏ @mmirman 24 Sep 2018
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      Replying to @Plinz @vgr

      As for "mathematicians don't have fundamental disagreements" - Gödel's theorems came from a disagreement between him and hilbert. Forcing came from the dissatisfaction with the continuum hypothesis as an axiom which and is still contentious.

      1 reply 0 retweets 0 likes
      Joscha Bach‏ @Plinz 24 Sep 2018
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      Replying to @mmirman @vgr

      The disagreement between Gödel and Hilbert was a mathematical and not a cultural one, and it was resolved by mathematics, not by culture.

      1:19 PM - 24 Sep 2018
      1 reply 0 retweets 0 likes
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        2. Matthew Mirman‏ @mmirman 24 Sep 2018
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          Replying to @Plinz @vgr

          It is only resolved if you assume every axiom in the hierarchy but doing so is inconsistent. i.e. hilbert thought mathematics was consistent and wanted a proof. Gödel thought it was impossible to know, but proved (lots of people rly) that he couldn't prove that he couldn't know

          1 reply 0 retweets 0 likes
        3. Joscha Bach‏ @Plinz 24 Sep 2018
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          Replying to @mmirman @vgr

          Yes, but the point is that in principle (and to a surprisingly large degree in practice) mathematicians can know and agree that this is the case.

          1 reply 0 retweets 0 likes
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