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nLab > Latest Changes: Gell-Mann principle

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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2022

    Just to record some references, prodded by discussion in another thread (here).

    From people’s question around the fora (e.g. Physics.SE:q/15339) I gather that the principle is referenced prominently in popular physics books by “Penrose, Hawking, Greene, etc.”, but I haven’t tracked those paragraphs down yet.

    v1, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 3rd 2022

    Anything that is not compulsory is forbidden

    But Kragh points out (p. 3) that this is the converse of what one wants:

    The statement Gell-Mann associated with a totalitarian state is not what is usually known as the TP. On the contrary, it is the converse of it.

    We want

    Anything that is not forbidden is compulsory.

    • CommentRowNumber3.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 3rd 2022
    • (edited Oct 3rd 2022)

    Although, perhaps one should see them as equivalent (classically) (¬C→F\neg C \to F iff ¬F→C\neg F \to C).

    In modal terms, we might have

    not compulsory AA implies forbidden AA, as ¬□A→□¬A\neg \Box A \to \Box \neg A

    and

    not forbidden AA implies compulsory AA, as ¬□¬A→□A\neg \Box \neg A \to \Box A

    The latter, classically, is ◊A→□A\lozenge A \to \Box A, which tallies with the possibility = necessity idea.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2022
    • (edited Oct 3rd 2022)

    Not the converse, but the contrapositive. [edit: oh, we overlapped]

    (I have added that term, and a few more references.)

    diff, v2, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeOct 3rd 2022

    Re #3:

    I’ll want to add the formulation in linear-modal-logic to this and related entries, but first to finish polishing up the entry quantum circuits via dependent linear types which will provide the justification.

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