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    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 27th 2016

    I started a page logicality and invariance. In Bristol the other day, Steve Awodey was promoting the thought that HoTT is a realisation of that thrust to understand logic as maximally invariant.

    What would it be to take that seriously? If invariants are picked up by dependent product in some BAut\mathbf{B} Aut context, could there be a useful context BAut(𝒰)\mathbf{B} Aut(\mathcal{U}) for the universe 𝒰\mathcal{U}?

    • CommentRowNumber2.
    • CommentAuthorDavid_Corfield
    • CommentTimeSep 27th 2016

    An attempt to work things out for a form of type theory:

    • Johan van Benthem, Logical constants across varying types, Notre Dame J. Formal Logic 30 (1989), no. 3, 315–342, (pdf)
    • CommentRowNumber3.
    • CommentAuthorAnthony Durity
    • CommentTimeOct 17th 2016
    • (edited Oct 17th 2016)

    Maybe include this quotation from that Tarski paper? [bottom of page 8]

    Now suppose we continue this idea, and consider still wider classes of transformations. In the extreme case, we would consider the class of all one-one transformations of the space, or universe of discourse, or ’world’, onto itself. What will be the science which deals with the notions invariant under this widest class of transformations? Here we will have very few notions, all of a very general character. I suggest that they are the logical notions, that we call a notion ’logical’ if it is invariant under all possible one-one transformations of the world onto itself.

    It is quite succinct and as Corcoran says in footnote 5, “Apart from Mautner 1946, which Tarski seems not to have known, this is, I believe, the first attempted application in English of Klein’s Erlanger Programm to logic.”

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2016

    Yes, by all means include that quote.

    Slightly odd wording by Corcoran. Why not say

    Apart from Hillary and Tenzing 1953, Ernst Reiss and Fritz Luchsinger were the first men to climb Everest?

    I don’t see what Tarski’s ignorance of Mautner has to do with it. The latter hardly hid his intentions:

    F. I. Mautner, An Extension of Klein’s Erlanger Program: Logic as Invariant-Theory

    Apart from a billion or so people, I’m the fastest man alive.

    • CommentRowNumber5.
    • CommentAuthorAnthony Durity
    • CommentTimeOct 17th 2016
    • (edited Oct 17th 2016)

    Regarding Corcoran’s wording. Noted.

    I’ve made the edit. As it’s my first on this site can you check it to make sure that it is alright? Thanks! Should I add the DOI of Tarski’s paper? I have a copy of the PDF but it is copyrighted so I ought not link to it I guess.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 17th 2016

    Looks fine to me, but David C is more of an expert in the subject matter. I went ahead and took the liberty of adding the doi myself.

    • CommentRowNumber7.
    • CommentAuthorDavid_Corfield
    • CommentTimeOct 17th 2016

    Another factor in Mautner’s favour for you, Anthony, is that he was working in Dublin at the time.

    Let’s give him a page Friederich Mautner.

    • CommentRowNumber8.
    • CommentAuthorAnthony Durity
    • CommentTimeOct 17th 2016

    Thank you David R! Interesting factoid David C! I must get to know a bit about Mautner.

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