The Mereological Foundation of Megethology

In this chapter we show how, assuming the existence of a pairing function on atoms, as the unique assumption non expressed in a mereological language, a mereological foundation of set theory is achievable within first order logic. Furthermore, we show how a mereological codification of ordered pairs is achievable with a very restricted use of the notion of plurality. Finally, in the last section of this chapter we show that, adopting a relativistic notion of atom, according to which any individual can play the role of atom, one can reconstruct Cantor’s theorem and prove that, given any infinite, mereology with plural quantification (MPQ) guarantees the existence of large and large infinities. This result seems in conflict with the alleged ontological innocence of MPQ.