Not signed in (Sign In)

Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

  • Sign in using OpenID

Site Tag Cloud

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf sheaves simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

Welcome to nForum
If you want to take part in these discussions either sign in now (if you have an account), apply for one now (if you don't).
    • 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) (¬CF\neg C \to F iff ¬FC\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


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

    The latter, classically, is AA\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.