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AbstractionismEssays in Philosophy of Mathematics$
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Philip A Ebert and Marcus Rossberg

Print publication date: 2016

Print ISBN-13: 9780199645268

Published to Oxford Scholarship Online: January 2017

DOI: 10.1093/acprof:oso/9780199645268.001.0001

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A Framework for Implicit Definitions and the A Priori

A Framework for Implicit Definitions and the A Priori

Chapter:
7 (p.133) A Framework for Implicit Definitions and the A Priori
Source:
Abstractionism
Author(s):

Philip A. Ebert

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199645268.003.0007

The so-called traditional connection—a position defended by Bob Hale and Crispin Wright—aims to account for our knowledge of arithmetic by appeal to implicit definitions and stipulations. The resulting picture is one that does not draw on epistemic support from empirical evidence or from pragmatic considerations and thus regards our arithmetical knowledge as genuinely a priori. In this paper, I will offer a general framework for a theory of implicit definitions and locate therein the main tenets of the traditional connection while also highlighting the main challenges this approach faces.

Keywords:   implicit definition, stipulation, a priori knowledge, abstraction principles, entitlement

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