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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeNov 20th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI felt that we needed an entry titled [[proof]]. I added something, but maybe somebody else feels like turning it into a genuine entry.

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

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeSep 5th 2012
   • (edited Sep 5th 2012)
   • PermaLink
   Author: Urs
   Format: MarkdownItexI used to be very unhappy with the entry _[[proof]]_. Now I read Robert Harper's little exposition _[Extensionality, Intensionality, and Brouwer’s Dictum](http://existentialtype.wordpress.com/2012/08/11/extensionality-intensionality-and-brouwers-dictum/)_ and now I am happy. I moved some of this into the entry.

   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.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeSep 6th 2012
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexYour definition of formal proof only works in a specific context, so I generalised it and then noted its implications for that context.

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

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeSep 6th 2012
   • PermaLink
   Author: Urs
   Format: MarkdownItexOkay, 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

   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

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 6th 2022
   • (edited Aug 6th 2022)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded pointer to: * [[Jean-Yves Girard]] (translated and with appendiced by [[Paul Taylor]] and [[Yves Lafont]]), *Proofs and Types*, Cambridge University Press (1989) &lbrack;[ISBN:978-0-521-37181-0](), [webpage](http://www.paultaylor.eu/stable/Proofs+Types.html), [pdf](https://www.paultaylor.eu/stable/prot.pdf)&rbrack; <a href="https://ncatlab.org/nlab/revision/diff/proof/34">diff</a>, <a href="https://ncatlab.org/nlab/revision/proof/34">v34</a>, <a href="https://ncatlab.org/nlab/show/proof">current</a>

   added pointer to:

   • Jean-Yves Girard (translated and with appendiced by Paul Taylor and Yves Lafont), Proofs and Types, Cambridge University Press (1989) [ISBN:978-0-521-37181-0, webpage, pdf]

   diff, v34, current

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJan 19th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexfound this an interesting read, worth recording here: * Scott Viteri, Simon DeDeo, *Epistemic Phase Transitions in Mathematical Proofs*, Cognition **225** (2022) 105120 &lbrack;[arxiv:2004.00055](https://arxiv.org/abs/2004.00055), [doi:10.1016/j.cognition.2022.105120](https://doi.org/10.1016/j.cognition.2022.105120)&rbrack; Can't really judge the main conclusion, but if nothing else this presents some interesting statistics on existing formal proofs. <a href="https://ncatlab.org/nlab/revision/diff/proof/36">diff</a>, <a href="https://ncatlab.org/nlab/revision/proof/36">v36</a>, <a href="https://ncatlab.org/nlab/show/proof">current</a>

   found this an interesting read, worth recording here:

   • Scott Viteri, Simon DeDeo, Epistemic Phase Transitions in Mathematical Proofs, Cognition 225 (2022) 105120 [arxiv:2004.00055, doi:10.1016/j.cognition.2022.105120]

   Can’t really judge the main conclusion, but if nothing else this presents some interesting statistics on existing formal proofs.

   diff, v36, current

7. • CommentRowNumber7.
   • CommentAuthorUrs
   • CommentTimeAug 5th 2023
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded ([here](https://ncatlab.org/nlab/show/proof#MeaningOfTheWordFormal)) a remark on the meaning of "formal" in "formal proof" (prodded by discussion in [another thread](https://nforum.ncatlab.org/discussion/16990/generalized-global-symmetry/?Focus=111924#Comment_111924)) <a href="https://ncatlab.org/nlab/revision/diff/proof/38">diff</a>, <a href="https://ncatlab.org/nlab/revision/proof/38">v38</a>, <a href="https://ncatlab.org/nlab/show/proof">current</a>

   added (here) a remark on the meaning of “formal” in “formal proof”

   (prodded by discussion in another thread)

   diff, v38, current

8. • CommentRowNumber8.
   • CommentAuthorTodd_Trimble
   • CommentTimeAug 5th 2023
   • PermaLink
   Author: Todd_Trimble
   Format: MarkdownItexAh good; thanks.

   Ah good; thanks.