Ray Lee on Nostr: c'mon lemme have a little bit of infinite, as a treat — I worked hard this week! I ...

c'mon lemme have a little bit of infinite, as a treat — I worked hard this week!

I fear I speak all the mathematical disciplines with a ComSci accent, but I just regard these different axiomatic foundations as different hats we can try on. Or perhaps lenses with which to project a problem against. Much in the same way we can (usually) write the same program in wildly different languages.

I was a bit surprised the Quanta article you posted elsewhere said Choice was controversial. But I guess they mean historically; my knowledge of math history is terrible. The article ends on a practical note I liked, that mathematicians have extended the assembly instruction set -- sorry, axioms -- with C because it's useful.

The axioms may expand again with a choice about the continuum hypothesis. I think it would be fun to allow it to be decided both ways simultaneously, see what consequences fall out of each, and which landscape looks more inviting for a given problem. (Which, to be fair, is what people seem to be doing?, though in service of choosing one outcome to make the canonical extension to ZFC.)

I think it'd be a poorer mathematical multiverse if we limited ourselves to only working inside the dominant p̶r̶o̶c̶e̶s̶s̶o̶r̶ ̶a̶r̶c̶h̶i̶t̶e̶c̶t̶u̶r̶e̶ axiomatic basis. Though it is convenient that ZFC has a massive standard library of tools.

Apologies for resurrecting a necrothread.

John Carlos Baez (npub1nf4…nqe4)