Pragmatic Insights into Set-Theoretic Independence

Many believe mathematical truth is indisputable. However, the set-theoretic independence phenomenon challenges this idea. Certain statements about infinite sets, like the continu-um 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 inter-views with 28 set theorists from varied backgrounds. It ex-plores 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 de-bates 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 founda-tions of mathematics.