Chapter

Implicit Definition and the a Priori

Bob Hale and Crispin Wright

in The Reason's Proper Study

Published in print March 2001 | ISBN: 9780198236399
Published online November 2003 | e-ISBN: 9780191597565 | DOI: http://dx.doi.org/10.1093/0198236395.003.0006
Implicit Definition and the a Priori

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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

Chapter.  17943 words. 

Subjects: Philosophy of Mathematics and Logic

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