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 comma 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 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.
    • CommentAuthorThomas Holder
    • CommentTimeAug 23rd 2016
    I've sorted out some references at infinite judgement. Despite all the verbosity, my sympathies lie with Lotze's view here! Well, from a linguistic point of view something reasonable could probably still been said about predicate term negation but otherwise I am rather at a loss.
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeAug 23rd 2016
    • (edited Aug 23rd 2016)

    I have added cross-links with judgment and made infinite judgment a redirect (omitting an “e”) (also made redirects for the plural versions)

    • CommentRowNumber3.
    • CommentAuthorTim_Porter
    • CommentTimeAug 24th 2016

    Why omit the e'?Judgement’ is the traditional spelling. ;-)

    • CommentRowNumber4.
    • CommentAuthorMike Shulman
    • CommentTimeAug 24th 2016
    • CommentRowNumber5.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 24th 2016
    • (edited Aug 24th 2016)

    Similarly, being born and raised in America, I write ’acknowledgment’, not ’acknowledgement’.

    In HowTo, it is advised to use American spelling in page titles (in the text body, spell whichever way you prefer). I think the original reason given was that of the three original Café founders, John and Urs use American English spellings (and David British); the current reason focuses on Urs: “Most of this is written by Urs Schreiber, who use American English spelling.”

    Although I’m not sure of the extent that’s true (I thought I recently saw Urs write ’neighbourhood’, for example).

    • CommentRowNumber6.
    • CommentAuthorTim_Porter
    • CommentTimeAug 24th 2016
    • (edited Aug 24th 2016)

    As English comes from England, I do feel the Americanisation of spelling is usually not necessarily a good thing,Putting that aside, however, there is one solid point here and that is that both spellings are being used in this page and that does seem a bit odd. (NB ’Americanisation’ not ’Americanization’, and again ;-))

    • CommentRowNumber7.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 24th 2016

    As English comes from England, I do feel the Americanisation of spelling is usually not necessarily a good thing

    There is an awful lot that could be said on that score, but let us please not go there.

    both spellings are being used in this page and that does seem a bit odd

    Actually, that both American and British spellings appear on the same page can be frequently observed throughout the nLab. It can look a little odd, yes, but I’ve gotten used to it. (I’m not in favor, or favour, of the alternative which is to enforce one or the other.)

    • CommentRowNumber8.
    • CommentAuthorMike Shulman
    • CommentTimeAug 24th 2016

    I barely even notice any more which spelling is being used in anything I read. I think rather than regarding one spelling as “American” and one as “British” (what about all the other English-speaking countries?) it would be more 21st-century to regard them all as “correct variants”. And now that we have redirects, there’s not even an especially compelling reason to choose one over the other in page titles.

    • CommentRowNumber9.
    • CommentAuthorTodd_Trimble
    • CommentTimeAug 24th 2016
    • (edited Aug 24th 2016)

    Still off the opening topic, but I guess I can’t resist. :-)

    what about all the other English-speaking countries

    Correct me if I’m wrong, somebody, but I thought most British Commonwealth (now apparently called Commonwealth of Nations) countries use spellings that are closer to those used in the UK. I was just using “British English” as a rubric for those.

    it would be more 21st-century to regard them all as “correct variants”

    I agree! Live and let live.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeAug 25th 2016
    • (edited Aug 25th 2016)

    Live and let live.

    Todd, I was not suggesting otherwise, merely teasing you all. ;-) I certainly was not intending to proclaim a “judgement” or “judgment”.

    • CommentRowNumber11.
    • CommentAuthorDavidRoberts
    • CommentTimeAug 25th 2016

    Didn’t Ænglisc come from the low countries/northern Europe? Them foreigners coming here and giving us their subtly inflected language… >:-(

    • CommentRowNumber12.
    • CommentAuthorUrs
    • CommentTimeAug 25th 2016
    • (edited Aug 25th 2016)

    To come back on topic: all I meant to do in #2 is recall that for every entry you create, you should please check to add redirects to all possible spelling variants that people might use, as well as to their plural versions. This is independent of whether you yourself plan to use any of these spelling variants or plurals. Instead it us to serve the robustness of the nnLab link structure, as it guarantees that other users find your entry and don’t accidentally create duplicates, just with different spelling.

    • CommentRowNumber13.
    • CommentAuthorTim_Porter
    • CommentTimeAug 25th 2016

    Urs: your point was well made. Unfortunately a contributor does not always see all the alternative spellings. (e.g. the one in question here ‘judgment’ was one that I have rarely seen.) Plurals are, of course, simpler to handle.

    Thanks,

    Tim

    • CommentRowNumber14.
    • CommentAuthortonyjones
    • CommentTimeSep 6th 2016

    Related work by van Lambalgen (most well known for work in computability theory and randomness) and Achourioti.

    Kant’s Logic Revisited

    ”Kant considers his Critique of Pure Reason to be founded on the act of judging and the different forms of judgement, hence, take pride of place in his argumentation. The consensus view is that this aspect of the Critique of Pure Reason is a failure because Kant’s logic is far too weak to bear such a weight. Here we show that the consensus view is mistaken and that Kant’s logic should be identified with geometric logic, a fragment of intuitionistic logic of great foundational significance.”

    A Formalisation of Kant’s Transcendental Logic

    ”Although Kant envisaged a prominent role for logic in the argumentative structure of his Critique of pure reason [12], logicians and philosophers have generally judged Kant’s logic negatively. What Kant called ‘general’ or ‘formal’ logic has been dismissed as a fairly arbitrary subsystem of first order logic, and what he called ‘transcendental logic’ is considered to be not a logic at all: no syntax, no semantics, no definition of validity. Against this, we argue that Kant’s ‘transcendental logic’ is a logic in the strict formal sense, albeit with a semantics and a definition of validity that are vastly more complex than that of first order logic. The main technical application of the formalism developed here is a formal proof that Kant’s Table of Judgements in §9 of the Critique of pure reason, is indeed, as Kant claimed, complete for the kind of semantics he had in mind. This result implies that Kant’s ’general’ logic is after all a distinguished subsystem of first order logic, namely what is known as geometric logic.”

    • CommentRowNumber15.
    • CommentAuthorThomas Holder
    • CommentTimeSep 6th 2016
    • (edited Sep 9th 2016)

    Thanks for reminding me of these! Actually, Peter Wolfendale had made a similar remark on another thread . For the time being I still try to figure out what Kant had on his mind but it certainly would be nice if someone could add a section on the Achourioti-Lambalgen approach.