Ah good; thanks.

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

(prodded by discussion in another thread)

]]>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.

]]>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]

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

formalproof

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

]]>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.

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

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