Mark van Atten: Brouwer and the Mathematics of the Continuum

[@kamilziemian995]

Fascinating lecture.

[@Urdatorn]

Thanks, Mark! Fabulous to have a lecture on this ravishing but often overlooked subject.

[@annaclarafenyo8185]

What Brouwer meant by 'intuition' is now captured in the concept of 'computation'. The computer had not been created when he wrote. The point Brouwer is making is that the objects of mathematics which we have experience with and manipulate in our 'intuitions' are all computable. This is why his logic gives a computable interpretation. The notion of computer was in part derived from intuitionistic deduction calculus, which is a programming language, like lambda calculus, but earlier.

[@watcher8582]

Brouwers mathematics contains lawless sequences (that's a technical term there) that are not recursive in the computable function sense. In Russian constructivism, all functions can be taken to be computable, but that's not consistent with Brouwers world.

[@annaclarafenyo8185]

@@watcher8582 That's later Brouwer, after he introduced bar-induction.

[@lucassiccardi8764]

A critique of the intuitionist subject should be the next target of constructivism: states of consciousness are numbers.

[@CandidDate]

Are you a robot, too? I'm a robot, two?

[@teset_feedback-ue3bo]

@lucassiccardi8764 i always love when circular reasoning is employed to push ideology

[@MindForgedManacle]

Is there a higher resolution upload of this anywhere? I don't see any on KZbin.

[@CandidDate]

I'm a big FAN of intuitionism, I want to go to a BAR and think myself into a twisted mindfuck

[@LogicFoundationsMathematics]

[@johnstfleur3987]

"ZERO."