MoL-2010-05: Non-Standard Models of Arithmetic: a Philosophical and Historical perspective

MoL-2010-05: Giorgio, Nicola Di (2010) Non-Standard Models of Arithmetic: a Philosophical and Historical perspective. [Report]

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Abstract

Over the last fifty years, the study of non-standard models of arithmetic has become a fertile and highly technical mathematical branch. Nevertheless, surprising as it might seem today, the topic of non-standard models was born as a genuine philosophical issue. My work sets out to investigate the philosophical and historical significance of non-standard models of arithmetic. Not only has non-standard models of arithmetic encountered a scarce success in what concerns philosophy, but also a detailed presentation on the beginnings of the topic has never been written. In particular, I will discuss the origins of non-standard models of arithmetic with respect to the pioneering work of Richard Dedekind and Thoralf Skolem, and strive to shed light on the relationship between philosophy, logic and mathematics in what concerns arithmetical theories and foundational studies in mathematics.

Item Type: Report
Report Nr: MoL-2010-05
Series Name: Master of Logic Thesis (MoL) Series
Year: 2010
Uncontrolled Keywords: Non-standard models, intended model, descriptive use of logic, Peano Arithmetic, Dedekind, Skolem, Tennenbaum’s Theorem, foundations of mathematics.
Subjects: Logic
Date Deposited: 12 Oct 2016 14:38
Last Modified: 12 Oct 2016 14:38
URI: https://eprints.illc.uva.nl/id/eprint/830

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