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

Synthese 170 (3):349 - 369 (2009)
Abstract
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
Options
 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
Our Archive


Upload a copy of this paper     Check publisher's policy     Papers currently archived: 26,804
Through your library
References found in this work BETA
The Limits of Abstraction.Kit Fine - 2002 - Oxford University Press.
Nominalist Platonism.George Boolos - 1985 - Philosophical Review 94 (3):327-344.

View all 22 references / Add more references

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

Add more citations

Similar books and articles
What If the Principle of Induction Is Normative? Formal Learning Theory and Hume's Problem.Daniel Steel & S. Kedzie Hall - 2010 - International Studies in the Philosophy of Science 24 (2):171-185.
Aristotelian Logic, Axioms, and Abstraction.Roy T. Cook - 2003 - Philosophia Mathematica 11 (2):195-202.
Neo-Fregeanism: An Embarrassment of Riches.Alan Weir - 2003 - Notre Dame Journal of Formal Logic 44 (1):13-48.
The Logic in Logicism.Bird Alexander - 1997 - Dialogue 36 (2):341--60.
Mixed Feelings, Mixed Metaphors: Hume On Tragic Pleasure.A. Merivale - 2011 - British Journal of Aesthetics 51 (3):259-269.
Hume = Small Hume.Jeffrey Ketland - 2002 - Analysis 62 (1):92–93.
Finitude and Hume's Principle.Richard G. Heck Jr - 1997 - Journal of Philosophical Logic 26 (6):589 - 617.
Bad Company Tamed.Øystein Linnebo - 2009 - Synthese 170 (3):371 - 391.
Is Hume's Principle Analytic?Crispin Wright - 2001 - In Bob Hale & Crispin Wright (eds.), Notre Dame Journal of Formal Logic. Oxford University Press. pp. 307-333.

Monthly downloads

Added to index

2009-01-28

Total downloads

71 ( #72,973 of 2,158,920 )

Recent downloads (6 months)

2 ( #193,038 of 2,158,920 )

How can I increase my downloads?

My notes
Sign in to use this feature


Discussion
Order:
There  are no threads in this forum
Nothing in this forum yet.

Other forums