Mathematics is megethology

Philosophia Mathematica 1 (1):3-23 (1993)
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Abstract

is the second-order theory of the part-whole relation. It can express such hypotheses about the size of Reality as that there are inaccessibly many atoms. Take a non-empty class to have exactly its non-empty subclasses as parts; hence, its singleton subclasses as atomic parts. Then standard set theory becomes the theory of the member-singleton function—better, the theory of all singleton functions—within the framework of megethology. Given inaccessibly many atoms and a specification of which atoms are urelements, a singleton function exists, unique up to isomorphism. (This article is partly abridged from my Parts of Classes, partly a sequel.).

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Author's Profile

David K. Lewis
PhD: Harvard University; Last affiliation: Princeton University

Citations of this work

Mereology.Achille C. Varzi - 2016 - Stanford Encyclopedia of Philosophy.
Against quidditism.Robert Black - 2000 - Australasian Journal of Philosophy 78 (1):87 – 104.
Plural quantification exposed.Øystein Linnebo - 2003 - Noûs 37 (1):71–92.

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References found in this work

The Structure of Appearance.Nelson Goodman - 1956 - Studia Logica 4:255-261.

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