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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 choi
by ysofunny 2y ago
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?
- MathMonkeyMan 2y agoI 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?
- deleted 2y ago[deleted]
- reuben364 2y agoNot 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.
- ysofunny 2y agoi 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.