Not signed in (Sign In)

Start a new discussion

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-categories 2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry bundles calculus categories category category-theory chern-weil-theory cohesion cohesive-homotopy-theory cohesive-homotopy-type-theory cohomology colimits combinatorics comma complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality education elliptic-cohomology enriched fibration finite foundations functional-analysis functor galois-theory gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck 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 infinity integration integration-theory k-theory lie-theory limit limits linear linear-algebra locale localization logic manifolds mathematics measure-theory modal-logic model model-category-theory monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory 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 simplicial space spin-geometry stable-homotopy-theory string string-theory subobject superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory 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.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 19th 2019

    Jotted down some things. Leibniz should feature but perhaps another day.

    diff, v6, current

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 20th 2019

    Tweaked some more, and left some to do’s.

    diff, v8, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeJun 20th 2019

    Thanks for writing this. I have added pointer to this from synthetic mathematics, and maybe it should be pointed to from orher places, too.

    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJun 20th 2019

    Is one of the to-do’s to insert a link to whatever Martin-Löf wrote?

    • CommentRowNumber5.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 20th 2019

    Re #4, yes. I’ve just added a brief paragraph along this line.

    diff, v9, current

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 25th 2019

    Added a bit more of the story to show how to move from Descartes to Kant via Leibniz.

    diff, v10, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2019

    Great to see you add some philosophy content! I have given the entry now the Philosophy floating context menu.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 26th 2019

    I know I should add more. But then every concept or thesis is so thoroughly contested. History of philosophy, as with this one, is more straightforward.

    • CommentRowNumber9.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2019

    Right, but I suppose we have the magnificent option here to add an nnPOV to the usual stories, point out – you do here – which philosophical positions are reflected (or not) in which piece of foundations of maths, type theory, physics, etc. That would be the additional value not found on any other sites.

    • CommentRowNumber10.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 26th 2019

    Right, it should be a nnPOV view which makes it quite a blank state. Extraordinary that 50 years on from Adjointness in Foundations, next to no philosopher could tell you that quantifiers are adjoints.

    • CommentRowNumber11.
    • CommentAuthorUrs
    • CommentTimeJun 26th 2019

    Yes, exactly. This would change if they found more philosophy discussed on the nnLab.

    • CommentRowNumber12.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 26th 2019

    My immediate target is via a book I’m finishing off for Oxford UP – Modal homotopy type theory: The new new logic for philosophy (a play on Russell’s ’new logic’ as in the quotation at analytic philosophy). Sorting out the index as we speak.

    Unfortunately while there are plenty of pointers to the importance of modal HoTT for physics, there’s little content, but that’s perhaps another book.

    • CommentRowNumber13.
    • CommentAuthorDavid_Corfield
    • CommentTimeAug 9th 2019

    Added a quote from Kant employing terms in their original sense.

    diff, v13, current

Add your comments
  • Please log in or leave your comment as a "guest post". If commenting as a "guest", please include your name in the message as a courtesy. Note: only certain categories allow guest posts.
  • To produce a hyperlink to an nLab entry, simply put double square brackets around its name, e.g. [[category]]. To use (La)TeX mathematics in your post, make sure Markdown+Itex is selected below and put your mathematics between dollar signs as usual. Only a subset of the usual TeX math commands are accepted: see here for a list.

  • (Help)