Abstraction and set theory

Notre Dame Journal of Formal Logic 41 (4):379--398 (2000)
The neo-Fregean program in the philosophy of mathematics seeks a foundation for a substantial part of mathematics in abstraction principles—for example, Hume’s Principle: The number of Fs D the number of Gs iff the Fs and Gs correspond one-one—which can be regarded as implicitly definitional of fundamental mathematical concepts—for example, cardinal number. This paper considers what kind of abstraction principle might serve as the basis for a neo- Fregean set theory. Following a brief review of the main difficulties confronting the most widely discussed proposal to date—replacing Frege’s inconsistent Basic Law V by Boolos’s New V which restricts concepts whose extensions obey the principle of extensionality to those which are small in the sense of being smaller than the universe—the paper canvasses an alternative way of implementing the limitation of size idea and explores the kind of restrictions which would be required for it to avoid collapse
Keywords abstraction principle   set   limitation of size   sortal concept   definiteness
Categories (categorize this paper)
DOI 10.1305/ndjfl/1038336882
 Save to my reading list
Follow the author(s)
My bibliography
Export citation
Find it on Scholar
Edit this record
Mark as duplicate
Revision history Request removal from index
Download options
PhilPapers Archive

Upload a copy of this paper     Check publisher's policy on self-archival     Papers currently archived: 23,280
External links
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
Through your library
References found in this work BETA

No references found.

Add more references

Citations of this work BETA
J. P. Studd (2016). Abstraction Reconceived. British Journal for the Philosophy of Science 67 (2):579-615.
Jonathan Payne (2013). Abstraction Relations Need Not Be Reflexive. Thought: A Journal of Philosophy 2 (2):137-147.

View all 9 citations / Add more citations

Similar books and articles

Monthly downloads

Added to index


Total downloads

24 ( #196,776 of 1,932,507 )

Recent downloads (6 months)

1 ( #456,270 of 1,932,507 )

How can I increase my downloads?

My notes
Sign in to use this feature

Start a new thread
There  are no threads in this forum
Nothing in this forum yet.