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REFERENCE IN ARITHMETIC

Published online by Cambridge University Press:  14 January 2018

LAVINIA PICOLLO
LAVINIA PICOLLO*
Affiliation:
Ludwig-Maximilian University of Munich
*
*MUNICH CENTER FOR MATHEMATICAL PHILOSOPHY LMU MUNICH MUNICH, GERMANY E-mail: Lavinia.Picollo@lrz.uni-muenchen.de
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Abstract

Self-reference has played a prominent role in the development of metamathematics in the past century, starting with Gödel’s first incompleteness theorem. Given the nature of this and other results in the area, the informal understanding of self-reference in arithmetic has sufficed so far. Recently, however, it has been argued that for other related issues in metamathematics and philosophical logic a precise notion of self-reference and, more generally, reference is actually required. These notions have been so far elusive and are surrounded by an aura of scepticism that has kept most philosophers away. In this paper I suggest we shouldn’t give up all hope. First, I introduce the reader to these issues. Second, I discuss the conditions a good notion of reference in arithmetic must satisfy. Accordingly, I then introduce adequate notions of reference for the language of first-order arithmetic, which I show to be fruitful for addressing the aforementioned issues in metamathematics.

Keywords

03-XXreferencearithmeticself-referencediagonalization
Type
Research Article
Information
The Review of Symbolic Logic , Volume 11 , Issue 3 , September 2018 , pp. 573 - 603
Copyright
Copyright © Association for Symbolic Logic 2018 

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