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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2011

    I felt that we needed an entry titled proof. I added something, but maybe somebody else feels like turning it into a genuine entry.

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeSep 5th 2012
    • (edited Sep 5th 2012)

    I used to be very unhappy with the entry proof. Now I read Robert Harper’s little exposition Extensionality, Intensionality, and Brouwer’s Dictum and now I am happy. I moved some of this into the entry.

    • CommentRowNumber3.
    • CommentAuthorTobyBartels
    • CommentTimeSep 6th 2012

    Your definition of formal proof only works in a specific context, so I generalised it and then noted its implications for that context.

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeSep 6th 2012

    Okay, thanks.

    I remember I was wondering about this point re Gödel’s theorem when reading in Martin-Löf’s lecture notes the piece where he emphasizes in great length that

    true \Leftrightarrow has a proof

    which is of course the whole point of all of constructivism/ type theory. Still, put this way a Gödel-alarm bell tends to go off.

    So it’s good to know how to switch that alarm off:

    true \Leftarrow has formal proof

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