Pragmatic Insights into Set-Theoretic Independence

Summary

Many believe mathematical truth is indisputable. However, the set-theoretic independence phenomenon challenges this idea. Certain statements about infinite sets, like the continuum hypothesis, are neither true nor false according to the standard axioms. While philosophers have offered various diagnoses of this problem, this book posits that the set-theoretic community is key to solving the issue, proposing a pragmatic approach. It presents the first extensive empirical study, featuring interviews with 28 set theorists from varied backgrounds. It explores the spectrum of disagreement and agreement among practitioners, predicting whether the community will adopt new axioms. Overall, this book demonstrates the potential of empirical research for philosophical purposes, also contributing to debates in social epistemology. It addresses a complex problem, applies a novel sociological method, and reveals much about the inner workings of a scientific community in the foundations of mathematics.

Keywords

Search publication

Bibliographic data

Publication year

2025

Publication date

26.02.2025

ISBN-Print

978-3-465-04643-1

ISBN-Online

978-3-465-14643-8

Publisher

Klostermann, Frankfurt am Main

Series

Studies in Theoretical Philosophy

Volume

12

Language

English

Pages

236

Product type

Book Titles