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The Reason's Proper StudyEssays towards a Neo-Fregean Philosophy of Mathematics$
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Bob Hale and Crispin Wright

Print publication date: 2001

Print ISBN-13: 9780198236399

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198236395.001.0001

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To Bury Caesar . . .

To Bury Caesar . . .

(p.335) 14 To Bury Caesar . . .
The Reason's Proper Study

Bob Hale (Contributor Webpage)

Crispin Wright (Contributor Webpage)

Oxford University Press

In this paper, Bob Hale and Crispin Wright discuss the Caesar Problem, which raises the worry that abstraction principles––like the Direction Equivalence and Hume's Principle ––are subject to an indeterminacy of reference which leaves them incapable of excluding the possibility that Caesar is the Number 3. They review––and deem implausible––an attempt by Richard Heck to finesse the Caesar Problem by recasting Hume's Principle in a two‐sorted language. Drawing on considerations by Michael Dummett (Frege: Philosophy of Mathematics, 1991) and Gideon Rosen (”Refutation of Nominalism(?)”, 1993), they then address the question whether a coherent nominalist response to Fregean abstraction––which is supposed to involve a distinctively realist ontology––can be provided. A section is devoted to a discussion of two criticisms––launched by respectively Dummett and Potter and Sullivan––of Wright's solution to the Caesar Problem in Frege's Conception of Numbers as Objects (1983), based on an inclusion principle for sortal concepts. While Hale and Wright disagree with Dummett, they find that a consideration close to the Potter‐Sullivan line of thought shows that Wright's earlier proposal stands in need of modification––and provide a modified solution centred around the notions of sortal concept, category, and criterion of identity.

Keywords:   Caesar Problem, category, criterion of identity, Dummett, Heck, Potter, Rosen, sortal, sortal inclusion principle, Sullivan

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