Wide Sets, ZFCU, and the Iterative Conception

Journal of Philosophy 111 (2):57-83 (2014)
Download Edit this record How to cite View on PhilPapers
The iterative conception of set is typically considered to provide the intuitive underpinnings for ZFCU (ZFC+Urelements). It is an easy theorem of ZFCU that all sets have a definite cardinality. But the iterative conception seems to be entirely consistent with the existence of “wide” sets, sets (of, in particular, urelements) that are larger than any cardinal. This paper diagnoses the source of the apparent disconnect here and proposes modifications of the Replacement and Powerset axioms so as to allow for the existence of wide sets. Drawing upon Cantor’s notion of the absolute infinite, the paper argues that the modifications are warranted and preserve a robust iterative conception of set. The resulting theory is proved consistent relative to ZFC + “there exists an inaccessible cardinal number.”
PhilPapers/Archive ID
Revision history
Archival date: 2013-01-18
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
Modality and Paradox.Uzquiano, Gabriel
Modal Set Theory.Menzel, Christopher
Worlds and Propositions Set Free.Bueno, Otávio; Menzel, Christopher & Zalta, Edward N.

View all 9 citations / Add more citations

Added to PP index

Total views
812 ( #4,095 of 50,349 )

Recent downloads (6 months)
78 ( #6,637 of 50,349 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.