Hume's big brother: Counting concepts and the bad company objection

Synthese 170 (3):349 - 369 (2009)
A number of formal constraints on acceptable abstraction principles have been proposed, including conservativeness and irenicity. Hume’s Principle, of course, satisfies these constraints. Here, variants of Hume’s Principle that allow us to count concepts instead of objects are examined. It is argued that, prima facie, these principles ought to be no more problematic than HP itself. But, as is shown here, these principles only enjoy the formal properties that have been suggested as indicative of acceptability if certain constraints on the size of the continuum hold. As a result, whether or not these higher-order versions of Hume’s Principle are acceptable seems to be independent of standard (ZFC) set theory. This places the abstractionist in an uncomfortable dilemma: Either there is some inherent difference between counting objects and counting concepts, or new criteria for acceptability will need to be found. It is argued that neither horn looks promising.
Keywords Frege  Neo-logicism  Abstraction  Arithmetic  Higher-order logic  Bad company objection
Categories (categorize this paper)
DOI 10.1007/s11229-007-9264-8
 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: 24,442
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
George Boolos (1985). Nominalist Platonism. Philosophical Review 94 (3):327-344.

View all 22 references / Add more references

Citations of this work BETA
Beau Madison Mount (2015). Higher‐Order Abstraction Principles. Thought: A Journal of Philosophy 4 (4):228-236.

Add more citations

Similar books and articles
Alan Weir (2003). Neo-Fregeanism: An Embarrassment of Riches. Notre Dame Journal of Formal Logic 44 (1):13-48.
Richard G. Heck Jr (1997). Finitude and Hume's Principle. Journal of Philosophical Logic 26 (6):589 - 617.
Crispin Wright (2001). Is Hume's Principle Analytic? In Bob Hale & Crispin Wright (eds.), Notre Dame Journal of Formal Logic. Oxford University Press. pp. 307-333.

Monthly downloads

Added to index


Total downloads

69 ( #70,651 of 1,925,098 )

Recent downloads (6 months)

22 ( #23,081 of 1,925,098 )

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.