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Atrium > Mathematics, Physics & Philosophy: Girard's 'Transcendental Syntax'

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    • CommentRowNumber1.
    • CommentAuthortonyjones
    • CommentTimeJan 26th 2014
    Hi guys, been following discussions here and on the cafe for a long time now and just wondered if anybody has seen Girards recent work on what he calls transcendental syntax? Seeing as theres been alot of discussion here on linear logic (and its type-theoretic incarnation) and Hegel. He draws on Kantian and Hegelian ideas. Just thought it might be of interest to some of you:
    http://iml.univ-mrs.fr/~girard/TS2.pdf
    also check out 'Transcendental Syntax and GoI: interplays between logic and philosophy' - V.M. Abrusci, P. Pistone (the link to the paper is broken but the HTML version works on google scholar) http://scholar.google.co.uk/scholar?cluster=2835623818545577955&hl=en&as_sdt=0,5
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJan 26th 2014
    • (edited Jan 26th 2014)

    Thanks for the pointer.

    I keep finding when reading that I tend to have trouble spotting the focus in Girard’s writing. For instance when I open that document “Transcendental syntax 2.0” (pdf) on pages 27-28, the paragraph headlined “dependent types”, then I read it again, and then I still could not reproduce the intended message. What I do get away with is somebody expressing strong opinions, but I am not always sure what the opinion actually is.

    • CommentRowNumber3.
    • CommentAuthortonyjones
    • CommentTimeJan 26th 2014
    He can be frustratingly obscure and abstruse (and offensive!) but he has some deep ideas. He's exploring how logic can emerge (in an hegelian fashion), about the possibility of logic (much like how kant explored the possibility of experience, the constitution of objectivity by a subject). Pistone/abrusci had a some slides of a talk which discusses this with far greater clarity than girard but they seem to be unavailable at the moment. I think there is something deep in these ideas and worth exploring.
    • CommentRowNumber4.
    • CommentAuthorTodd_Trimble
    • CommentTimeJan 26th 2014

    Well, I also get the impression that he’s often talking to an in-crowd of people who can follow and are willing to discuss and debate his allusions (and jokes).

    Sometimes he does hard mathematics too, and indeed his original Linear Logic paper has some hard combinatorics in it (cf. the ’long trip’ criterion for the correctness of a proof net). I’m probably not alone in finding that material quite useful and important.

    So Tony, if you’re up on your Girard and know of places where he (or somebody else) proves actual theorems relevant to GoI, etc., that might be very useful for us here to sink our teeth in.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJan 27th 2014

    I see Todd’s point, we have been somewhat excessively increasing the ratio of philosophical over mathematical discussion as of late and it would be good to re-balance that a bit. Nevertheless, given the title of this thread here, if you could give me a summary of what that “transcendental syntax” is supposed to be about, I’d really appreciate it. In the little spare time that I have I briefly looked through Girard’s note, but I didn’t get much out of it yet.

    • CommentRowNumber6.
    • CommentAuthortonyjones
    • CommentTimeJan 27th 2014
    • (edited Jan 27th 2014)
    Im only starting to learn this stuff myself (i come from more of a philosophy baclground) and was hoping you guys might help me! haha! Just thought this might be something worth looking at given the kinds of ideas floating around on here in recent months. its all so tantalizing!
    From the transcendental paper:
    ''Kant explains the coherence of perception — an experimental fact — by its transcendental conditions, i.e., the hypotheses that make it possible. Whether these conditions are necessary is a delicate question that may lead to unwelcome conclusions; but there is no problem with sufficiency. I propose to do the same for logic: coherence — not limited to consistency which is but the poor man’s coherence i.e., cut-elimination, Church-Rosser, the disjunction property, are not accounted for by semantics...The question is thus ''what makes logic coherent?'' the only possible answer being in the language itself: logical artifacts are constructed so as to ensure coherence. To find the hypotheses making logic
    possible, this is transcendental syntax''
    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeMay 23rd 2014
    • (edited May 23rd 2014)

    A kind soul pointed out to me that this recent thesis here may be a helpful read for transcendental syntax:

    I have added that to new entry transcendental syntax which I gave a mini-minimum of an Idea-section. Experts (if any?) please expand!

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