Parts of Classes [antikvár]

Preface There is more mereology in set theory than we usually think. The parts of a class are exactly the subclasses (except that, for this purpose, the null set should not count as a class). The notion of a singleton, or unit set, can serve as the distinctive primitive of set theory. The rest is mereology: a class is the fusion of its singleton subclasses, something is a member of a class iff its singleton is part of that class. If we axiomatize set theory with singleton as primitive (added to an ontologically innocent framework of plural quantification and mereology), our axioms for 'singleton' closely resemble the Peano axioms for 'successor'. From these axioms, we can regain standard iterative set theory. Alas, the notion of a singleton was never properly explained: talk of collecting many into one does not apply to one-membered sets, and in fact introduces us only to the mereology in set theory. I wonder how it is possible for us to understand the primitive notion of singleton, if indeed we really do. In March 1989, after this book was mostly written, I learned belatedly that its main thesis had been anticipated in the vii