Individuals enough for classes

Abstract
This paper builds on the system of David Lewis’s “Parts of Classes” to provide a foundation for mathematics that arguably requires not only no distinctively mathematical ideological commitments (in the sense of Quine), but also no distinctively mathematical ontological commitments. Provided only that there are enough individual atoms, the devices of plural quantification and mereology can be employed to simulate quantification over classes, while at the same time allowing all of the atoms (and most of their fusions with which we are concerned) to be individuals (that is, urelements of classes). The final section of the paper canvasses some reasons to be committed to the required ontology for other than mathematical reasons.
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