Logo Logo
Hilfe
Hilfe
Switch Language to English

Picollo, Lavinia (14. Januar 2018): Reference in Arithmetic. In: The Review of Symbolic Logic: 1–31 [PDF, 434kB]

[thumbnail of Reference in Arithmetic.pdf]
Vorschau
Eingereichte Version
Download (434kB)
[thumbnail of 42199.pdf]
Vorschau
Veröffentlichte Version
Download (260kB)

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.

Dokument bearbeiten Dokument bearbeiten