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    • CommentRowNumber1.
    • CommentAuthorMike Shulman
    • CommentTimeJul 20th 2012
    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 21st 2012

    In the bullet item referreing to structural set theory I made “type” hyperlinked. I am wondering if at this point an explicit reference to type theory would be useful, and a comment on how it achieves something similar to the “stratification” mentioned earlier (as far as I understand).

    Also maybe the Idea-section at type theory would conversely want to point to Russel’s paradox for motivation?

    I could try to add some such comment, but maybe it is better you do so right away, if you have a second, instead of needing to improve on my formulation afterwards :-)

    • CommentRowNumber3.
    • CommentAuthorMike Shulman
    • CommentTimeJul 23rd 2012

    I was going to say that Russell’s paradox just doesn’t make any sense in type theory, but I guess that really is basically the same thing that happens in structural set theory. So I added a comment to that bullet point. Thanks!

    • CommentRowNumber4.
    • CommentAuthorTobyBartels
    • CommentTimeJul 23rd 2012

    Historically, there is more connection; the first explicit ‘type theory’ was Russell’s, a direct response to his paradox and the foundation used in Principia Mathematica. It’s really a sort of typed material set theory, not the type theory that we use today.

    • CommentRowNumber5.
    • CommentAuthorMike Shulman
    • CommentTimeJul 24th 2012

    Yeah… I generally try to avoid talking about Russell’s “type theory” as much as possible, to avoid confusing people, since it’s so unlike what is nowadays called “type theory”.

    • CommentRowNumber6.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 24th 2012
    • (edited Jul 24th 2012)

    Isn’t the theory of Russell types more like NF? (also relevant: this MO question of mine http://mathoverflow.net/questions/27793/russell-and-whiteheads-types-ramified-and-unramified)

    • CommentRowNumber7.
    • CommentAuthorTobyBartels
    • CommentTimeJul 24th 2012

    I added a few remarks inspired by responses to David’s MO question.

    • CommentRowNumber8.
    • CommentAuthorDavidRoberts
    • CommentTimeJul 25th 2012

    @Toby - to the page Russell’s paradox?

    • CommentRowNumber9.
    • CommentAuthorTobyBartels
    • CommentTimeJul 25th 2012

    Yes.

    • CommentRowNumber10.
    • CommentAuthorTim_Porter
    • CommentTimeSep 23rd 2012

    I have added some links to Bertrand Russell.

  1. added Curry’s paradox to related ideas section

    Anonymous

    diff, v25, current

    • CommentRowNumber12.
    • CommentAuthorNikolajK
    • CommentTimeOct 11th 2022

    The original one page letter from the second reference is also online here.

    • CommentRowNumber13.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 11th 2022

    @Nikolaj

    I typeset Russell’s letter, we should probably put a clean pdf of it on the nLab.

    • CommentRowNumber14.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 11th 2022

    Added link to paper discussing Zermelo’s pre-Russell version of the result, and link to copy of the letter.

    diff, v26, current

    • CommentRowNumber15.
    • CommentAuthorDavidRoberts
    • CommentTimeOct 11th 2022

    Added note about and date of pre-Russell paper record of Zermelo’s proof.

    diff, v26, current