Sets, not Masses

This work uses sets, not masses.

Why sets? Sets are free over a universe of individuals. While they may not have the ultimate expressive power, they are therefore an inevitable structure which can be used for logic. The other free gadgets are vector spaces, and we leave that treatment for future work.

Why not masses? Masses can be expressed using plural logic; see la guskant for a complete foundation, including metaphysics. However, plural logic is equiconsistent with monadic second-order logic, given a predicate for masses. Since we treat the full semantics of second-order logic, we see a commitment to masses as simultaneously vague and limiting. That said, there are important use cases to address, and I propose discursive logic as a way to build a form of plural logic on top of standard set-theoretic foundations. I also give the axioms for mereology, using {pagbu} as the main predicate.