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nLab > Latest Changes: Boolean category

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  1. This is my first hook to the n-lab, I am pretty sure that isomorphism is an overly strong condition, and that any is a too weak restriction.

    Please see the wikipedia article on the principle of bivalence. https://en.wikipedia.org/wiki/Principle_of_bivalence

    I am unsure as how to proceeed.

    vukovinski

    diff, v4, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2019

    Hi vukovinski,

    welcome to the nLab. Before diving into editing entries, maybe best to first participate a bit in discussion here, so that we get to know each other.

    The sentence you just added to the entry Boolean category seems to require a bit of work still. For the moment I have rolled back the entry and am copying your sentence to here. It was:

    Many-valued logics can be reduced to Boolean logic, ie. any coherent category is isomorphic to the Principle of Bivalence.

    I trust that some logic expert here recognizes what you were trying to say and will lend a hand with putting it properly.

    • CommentRowNumber3.
    • CommentAuthorvukovinski
    • CommentTimeJun 5th 2019
    • (edited Jun 5th 2019)
    What is missing is a series of decision procedures sharing mutable state, that is a program denoting the structure of the reduction. A compiler that would translate this program must contain a free logic generator? for each part of the program containing descriptions of infinitary sums.
    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeJun 5th 2019

    I’m sorry, but I cannot make any sense out of either the sentence you added to the page or your subsequent comment.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 6th 2019

    Nor I.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019

    Hm, might this be auto-generated text?

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeJun 6th 2019

    Certainly I don’t see how

    any coherent category is isomorphic to the Principle of Bivalence

    can be considered a coherent piece of category theory.

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019
    • (edited Jun 7th 2019)

    At that point I was still benevolent and thought some poor soul might have tried to say something like that a coherent category is equivalent to one that satisfies the “principle of bivalence”, hence a Boolean category.

    But then we got #3 and this sounds like it’s auto-generated text trained on nLab keywords. And we should cut this all out here.

    • CommentRowNumber9.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 6th 2019

    Perhaps someone is checking to see if they can use mLab-style generation of pages as a Sokalian hoax.

    • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeJun 6th 2019
    • (edited Jun 6th 2019)

    Yeah, that might also explain the term “Spirited Systems Redesigner” at vukovinski. Looks like some kids are getting a bit carried away with their cunningness.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 8th 2019

    If this in the other thread is true, Filip Vukovinsky just scored on a co-Turing test, and I have to apologize for suspecting unnamed script kids for playing lame jokes on us. Apparently no cunningness involved here.

    In any case, best to let this rest unless we hear back anything intelligible.

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