About Logic interview with Giovanni Sambin
You can read notes on Martin-Löf's lecture given in Padua in 1980 here: Giovanni Sambin's notes on Per Martin-Löf's Intuitionistic Type Theory . My comment : 40:32 Thorsten "You only need the notion of a type... Then I can explain a proposition,..." I remember when you did that a few weeks ago , and you explained it, but did anybody actually understand your explanation? I know I didn't! 30:38 On intensional and extensional theories and "running them in parallel". I wonder how far you could get by modelling functions with bijections between pairs, i.e. permutations on graphs. I did something like this once in the iterative construction I described in this post: Brady Haran interview with Terence Tao . It produced some very interesting constructions full of amazing symmetries. See also Category Theory May Actually be a Disease and Emma Tye on Martin-Löf Type Theory . What I did was construct something like a closure operator on an abstract algeb...