The context principle and implicit definitions : towards an account of our a priori knowledge of arithmetic

Dissertation, St. Andrews (2005)
  Copy   BIBTEX

Abstract

This thesis is concerned with explaining how a subject can acquire a priori knowledge of arithmetic. Every account for arithmetical, and in general mathematical knowledge faces Benacerraf's well-known challenge, i.e. how to reconcile the truths of mathematics with what can be known by ordinary human thinkers. I suggest four requirements that jointly make up this challenge and discuss and reject four distinct solutions to it. This will motivate a broadly Fregean approach to our knowledge of arithmetic and mathematics in general. Pursuing this strategy appeals to the context principle which, it is proposed, underwrites a form of Platonism and explains how reference to and object-directed thought about abstract entities is, in principle, possible. I discuss this principle and defend it against different criticisms as put forth in recent literature. Moreover, I will offer a general framework for implicit definitions by means of which - without an appeal to a faculty of intuition or purely pragmatic considerations - a priori and non-inferential knowledge of basic mathematical principles can be acquired. In the course of this discussion, I will argue against various types of opposition to this general approach. Also, I will highlight crucial shortcomings in the explanation of how implicit definitions may underwrite a priori knowledge of basic principles in broadly similar conceptions. In the final part, I will offer a general account of how non-inferential mathematical knowledge resulting from implicit definitions is best conceived which avoids these shortcomings.

Other Versions

No versions found

Links

PhilArchive

    This entry is not archived by us. If you are the author and have permission from the publisher, we recommend that you archive it. Many publishers automatically grant permission to authors to archive pre-prints. By uploading a copy of your work, you will enable us to better index it, making it easier to find.

    Upload a copy of this work     Papers currently archived: 104,706

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

Similar books and articles

Transmission of warrant-failure and the notion of epistemic analyticity.Philip A. Ebert - 2005 - Australasian Journal of Philosophy 83 (4):505 – 521.
Analyticity, Platonism, and A Priori Knowledge.Deke Gould - 2011 - Dissertation, Syracuse University
Against a priori knowledge of non-trivial truths.Carin Robinson - 2014 - Dissertation, University of Kwazulu-Natal
Knowing linguistic conventions.Carin Robinson - 2014 - South African Journal of Philosophy 33 (2):167-176.
Frege's context principle and reference to natural numbers.Øystein Linnebo - 2008 - In Sten Lindstr©œm, Erik Palmgren, Krister Segerberg & Viggo Stoltenberg-Hansen, logicism, intuitionism, and formalism - What has become of them? Berlin, Germany: Springer.

Analytics

Added to PP
2018-07-11

Downloads
44 (#560,142)

6 months
4 (#1,015,396)

Historical graph of downloads
How can I increase my downloads?

Author's Profile

Philip A. Ebert
University of Stirling

References found in this work

No references found.

Add more references