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nLab > Latest Changes: ETCS

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  1.  
    • CommentRowNumber1.
    • CommentAuthorDavid_Corfield
    • CommentTimeJun 4th 2018

    I corrected the date of publication from 1965 to 1964.

    diff, v48, current

    • CommentRowNumber2.
    • CommentAuthorThomas Holder
    • CommentTimeFeb 1st 2021

    Added a reference to

    • ∅ystein Linnebo, Richard Pettigrew, Category theory as an autonomous foundation , Phil. Math. 19 (2011) 227–254.

    diff, v51, current

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 2nd 2021

    That sounds interesting, but it’s paywalled. Can anyone send me a copy?

    • CommentRowNumber4.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 2nd 2021

    Just sent it to you.

    • CommentRowNumber5.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 2nd 2021

    There are also preprint versions around, I’ll link to one

    • CommentRowNumber6.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 3rd 2021

    Corrected the first code point of Øystein Linnebo’s name from 0x2205 EMPTY SET to 0xD8 LATIN CAPITAL LETTER O WITH STROKE. (-:

    diff, v52, current

    • CommentRowNumber7.
    • CommentAuthorMike Shulman
    • CommentTimeFeb 3rd 2021

    Thanks! I think that’s actually a really good paper. I’m glad to see philosophers finally understanding the points being made about ETCS by category theorists, and I finally feel like I have some feeling for why some philosophers find it less convincing of a foundation than ZFC.

    • CommentRowNumber8.
    • CommentAuthorDavid_Corfield
    • CommentTimeFeb 3rd 2021

    So how would HoTT fare according to their three criteria: logical autonomy, conceptual autonomy, and justificatory autonomy? I guess for them it would hinge on “whether the objects for a foundation of mathematics can or indeed should be specified” only up to equivalence.

    Ladyman and Presnell take on the autonomy of HoTT here claiming that:

    the presentation of HoTT given in the HoTT Book is not autonomous since it explicitly depends upon other fields of mathematics, in particular homotopy theory.

    They then argue that a reformulation avoids this debt. I think they were misled by talk of paths.

    • CommentRowNumber9.
    • CommentAuthorDavidRoberts
    • CommentTimeFeb 3rd 2021

    Added link to preprint version (pdf) of Linnebo and Pettigrew’s paper.

    diff, v54, current

1 to 9 of 9

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