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-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-geometry computable-mathematics computer-science constructive cosmology deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry differential-topology digraphs duality elliptic-cohomology enriched fibration finite foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry goodwillie-calculus 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 homology 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 monads monoidal monoidal-category-theory morphism motives motivic-cohomology newpage nforum nlab noncommutative noncommutative-geometry number-theory object 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 simplicial space spin-geometry stable-homotopy-theory string string-theory 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.
    • CommentAuthorjonsterling
    • CommentTimeMar 5th 2018
    • (edited Mar 5th 2018)

    Currently, the page Tools for the advancement of objective logic says that the described paper discusses the “concrete particular”, but this paper does not discuss “concrete particular”.

    [For context, Lawvere regards “concrete particular” as a category error, as he has stated elsewhere—basically to Lawvere, the abstract and the concrete are two aspects of a universal/general concept, and not to be discussed at the level of particulars. The passage from the particular to the universal/general is marked by choosing a subclass of observables about the particular as definitive—this generates the abstract general, and thence the concrete generals. The connection between the particulars and the concrete general comes from the fact that each particular can be observed in the ways specified by the abstract general, and that the abstract generals embed as representables into the concrete generals.]

    To be precise, the 1994 paper talks about the particular, and then the abstract and concrete general.

    However, I haven’t edited the page yet because I believe that in order to keep the nlab internally consistent, one may need to also update the page abstract general, concrete general and concrete particular; however, I am aware of a significant discussion elsewhere in the nforum, and I see that maybe some consensus was already reached there in favor of the notion of the “concrete particular”.

    The latter page contains the nlab’s synthesis of these ideas which does not quite match Lawvere’s—which is generally fine, but I think we should be careful about attributing this interpretation to Lawvere himself (which we are in danger of doing in the page on the 1994 paper).

    Do you all have any thoughts on how to proceed?

    • CommentRowNumber2.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 5th 2018

    FWIW, there is a pdf copy here of Lawvere’s paper.

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeMar 6th 2018

    I have modified these keywords, also added a pointer to the pdf.

    Please feel invited to edit this and other pages.

    • CommentRowNumber4.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 6th 2018

    I wasn’t sure about linking to the pdf given its grey status as far as legality goes, else I would have jumped at the opportunity :-)

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeMar 6th 2018

    I wasn’t sure about linking to the pdf

    You did link to the pdf in #2.

    • CommentRowNumber6.
    • CommentAuthorDavid_Corfield
    • CommentTimeMar 6th 2018

    Do people here who have read the article mostly understand the article? Section 4 in particular I find obscure.

    • CommentRowNumber7.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 6th 2018

    I meant as an “official nLab link”. Toby, in the past, expressed hesitation about linking to such grey sources from nLab pages. I certainly don’t feel comfortable linking to Sci-Hub for papers, for instance, even though it gives wider access than the publisher would.

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeMar 6th 2018

    What is it that makes this version of the paper “grey” (as opposed to “black”, i.e. a copyright violation)?

    • CommentRowNumber9.
    • CommentAuthorDavidRoberts
    • CommentTimeMar 7th 2018

    Ah, I suppose it’s ’black’, but no worse than eg the late Andrew Rainicki’s personal stash of papers that happen to be visible to the open web, as opposed to living on some website declared illegal and taken to court of millions of copyright violations.

    • CommentRowNumber10.
    • CommentAuthorMike Shulman
    • CommentTimeMar 7th 2018

    A quick search suggests to me that it’s probably not legally dangerous to link to a copyright violation, but is also probably worth avoiding. So I would lean towards not doing it as well.

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)