Use this URL to cite or link to this record in EThOS: http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.691331
Title: Methods, goals and metaphysics in contemporary set theory
Author: Rittberg, Colin Jakob
ISNI:       0000 0004 5917 6676
Awarding Body: University of Hertfordshire
Current Institution: University of Hertfordshire
Date of Award: 2016
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Abstract:
This thesis confronts Penelope Maddy's Second Philosophical study of set theory with a philosophical analysis of a part of contemporary set-theoretic practice in order to argue for three features we should demand of our philosophical programmes to study mathematics. In chapter 1, I argue that the identification of such features is a pressing philosophical issue. Chapter 2 presents those parts of the discursive reality the set theorists are currently in which are relevant to my philosophical investigation of set-theoretic practice. In chapter 3, I present Maddy's Second Philosophical programme and her analysis of set-theoretic practice. In chapters 4 and 5, I philosophically investigate contemporary set-theoretic practice. I show that some set theorists are having a debate about the metaphysical status of their discipline{ the pluralism/non-pluralism debate{ and argue that the metaphysical views of some set theorists stand in a reciprocal relationship with the way they practice set theory. As I will show in chapter 6, these two stories are disharmonious with Maddy's Second Philosophical account of set theory. I will use this disharmony to argue for three features that our philosophical programmes to study mathematics should have: they should provide an anthropology of mathematical goals; they should account for the fact that mathematical practices can be metaphysically laden; they should provide us with the means to study contemporary mathematical practices.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID: uk.bl.ethos.691331  DOI: Not available
Keywords: Philosophy of mathematical practice ; set theory ; Penelope Maddy ; second philosophy ; Ultimate-L ; Methodology ; Mathematical goals
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