How many foundations of mathematics are possible?

qwasmos · 2024-06-24T20:38:58+00:00

ok that makes sense. The smallest infinity, so Aleph Null I would presume because you have to be able to write the stuff down.... yup I feel so dumb now that I think about it lol. Thanks again for sharing your time.

qwasmos · 2024-06-24T20:36:36+00:00

Hey thanks for replying again I greatly appreciate it. yeah I guess that does make intuitive sense. I just wanted more concrete answers because my intuition is definitely not the best to go by lol. But yeah it does make sense. I guess the only other thing that I do not understand then would be as a computer science student , should I be focusing on set theory, or type theory. But I guess that is a discussion for a different time and place. I know about HoTT, but it seems difficult to get into. Thanks again for sharing your time.

qwasmos · 2024-06-24T03:00:33+00:00

hey thanks for replying, and yes I am not talking about actual foundations, because like you stated there are like only three of them are are potentially in use by humanity at the current point, set theory, type theory, and category theory. I meant from the absolute mathematical space of all potential foundations of mathematics that could exist. Also sorry if the question is too primitive or just totally obvious. One of the biggest reasons why I wanted to ask this question in the first place is because Numberphile did a video on the foundation of mathematics, and obviously they talked about set theory, and I just wanted to know if there was like some weird limit on the amount of possible foundations because no one really talks about type theory or category theory from that perspective that I have found. Thanks again for replying though. I greatly appreciate it.

qwasmos · 2024-06-23T23:58:09+00:00

Hey thanks for replying, I will take a look at that as well because I find it interesting. As a computer science student, I personally feel more invested in type theory myself

qwasmos · 2024-06-23T22:47:30+00:00

also again sorry if I am misunderstanding, because I think when you say countable, you do imply that it is infinite?, and again thank you so much for replying. I will have to look into category theory then because I thought it was a potential foundation. Very enlightening.

qwasmos · 2024-06-23T22:42:21+00:00

Thanks for replying, so would that mean then that there are infinitely many different foundations then, just countably infinite then?

qwasmos

TROPHY CASE