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

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?

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?

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.

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.