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Everything Is Just Functions: 1 week with David Beazley and SICP

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389 points kurinikku | 4 comments | 17 Nov 24 15:07 UTC | HN request time: 0.001s | source
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ysofunny ◴[17 Nov 24 17:31 UTC] No.42165469[source]▶
alternative take: everything is just sets

both can be a foundation for mathematics, and hence, a foundation for everything

what's interesting is how each choice affects what logic even means?

replies(1): >>42168681 #
1. MathMonkeyMan ◴[18 Nov 24 00:45 UTC] No.42168681[source]▶
I learned functions in terms of sets. Domain and codomain are sets. Function is a set of ordered pairs between them.

How could we go the other way? A set can be "defined" by the predicate that tests membership, but then how do we model the predicates? Some formalism like the lambda calculus?

replies(3): >>42168696 #>>42171390 #>>42184908 #
2. ◴[18 Nov 24 00:48 UTC] No.42168696[source]▶
3. reuben364 ◴[18 Nov 24 11:08 UTC] No.42171390[source]▶
Not sure of details to make it a mathematical foundation but:

A category can be defined in terms of its morphisms without mentioning objects and a topos has predicates as morphisms into the subobject classifier.

4. ysofunny ◴[19 Nov 24 15:59 UTC] No.42184908[source]▶
i think predicates are functions returning booleans

lambda calculus would provide a computational way to determine the truth value of the predicate, any computable predicate that is.