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 finite 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 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
    • CommentTimeNov 20th 2011

    I felt that we needed an entry titled proof. I added something, but maybe somebody else feels like turning it into a genuine entry.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2012
    • (edited Sep 5th 2012)

    I used to be very unhappy with the entry proof. Now I read Robert Harper’s little exposition Extensionality, Intensionality, and Brouwer’s Dictum and now I am happy. I moved some of this into the entry.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 6th 2012

    Your definition of formal proof only works in a specific context, so I generalised it and then noted its implications for that context.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2012

    Okay, thanks.

    I remember I was wondering about this point re Gödel’s theorem when reading in Martin-Löf’s lecture notes the piece where he emphasizes in great length that

    true \Leftrightarrow has a proof

    which is of course the whole point of all of constructivism/ type theory. Still, put this way a Gödel-alarm bell tends to go off.

    So it’s good to know how to switch that alarm off:

    true \Leftarrow has formal proof

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeAug 6th 2022
    • (edited Aug 6th 2022)

    added pointer to:

    diff, v34, current

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeJan 19th 2023

    found this an interesting read, worth recording here:

    Can’t really judge the main conclusion, but if nothing else this presents some interesting statistics on existing formal proofs.

    diff, v36, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeAug 5th 2023

    added (here) a remark on the meaning of “formal” in “formal proof”

    (prodded by discussion in another thread)

    diff, v38, current

    • CommentRowNumber8.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 5th 2023

    Ah good; thanks.