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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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Implicit Definition and the a Priori

Implicit Definition and the a Priori

Chapter:
(p.117) 5 Implicit Definition and the a Priori
Source:
The Reason's Proper Study
Author(s):

Bob Hale (Contributor Webpage)

Crispin Wright (Contributor Webpage)

Publisher:
Oxford University Press
DOI:10.1093/0198236395.003.0006

This paper discusses the idea, labelled as “the traditional connection” that implicit definitions aim to found a priori knowledge of logic and mathematics. In the first part, it discusses and rejects a specific understanding of certain constraints (existence, uniqueness, possession problem, and explanation problem) on the theory of implicit definitions, as suggested by Horwich, on the basis of it being committing to some robust Platonist version of meaning facts. In contrast, it motivates further new constraints on the success of implicit definitions, such as arrogance, conservativeness, Evan's generality constraint, and harmony. Then, the standard view of implicit definitions for scientific terms, which appeals to so called Carnap Conditionals is discussed and an alternative model, i.e. the inverse Carnap Conditional is proffered. Lastly, this latter model is then applied to Hume's Principle and the conditionalized version of Hume's Principle as offered by Field is rejected. Furthermore, the problem of the ontological commitments of Hume's Principle and its status as a meaning––conferring successful stipulation are further discussed.

Keywords:   a priori, arrogance, Carnap Conditional, conservativeness, Hartry Field, Horwich, Hume's Principle, implicit definitions, traditional connection

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