Workshop: Mathematical Indispensability in Philosophy

Idea & Motivation

The application of formal methods has been a hallmark of analytic philosophy since its inception. It then flourished broadly during the post-war period, not just in the traditionally more technical disciplines of philosophy of logic and language (Quine, Kreisel, Kripke, Montague, Lewis), but also in philosophy of science (Carnap, Hempel, Putnam), epistemology (von Neumann, de Finetti, Jeffrey, Hintikka), ethics (von Wright, Harsanyi), and social choice (Arrow, Sen). A notable consequence is that these subjects are now developed using techniques and results not just from logic but from core mathematics.

The integration of mathematical methods into philosophical methodology is widely regarded as having been fruitful, giving rise to sub-developments such as formal semantics, formal epistemology, axiomatic theories of truth, and logical philosophy of science. But at the same time, the reception of mathematical results within philosophy has been largely unsystematic and non-critical — e.g. in regard to the framework by which philosophical principles and mathematical theorems are combined, the logical principles required for the derivation of the latter, and their appropriateness within different philosophical contexts. Contemporary formal philosophy has thus developed in relative isolation from the concerns of both mathematical logic and philosophy of mathematics — e.g. in regard to axiomatically calibrating the strength of core mathematical theorems required to sustain philosophical arguments or assessing the acceptability of axioms relative to foundational considerations.

The general goal of this workshop will be to highlight mathematical results which find applications in philosophy. More specific questions to be addressed include the following: Is it possible to provide an axiomatic characterization of “philosophically applicable” mathematics? How does this compare with the characterization of “empirically applicable” mathematics? Are there instances in which mathematical results are explicitly required as premises in philosophical arguments? If so, does this suggest that some portion of mathematics is indispensable for the development of certain philosophical positions or theories? To what extent can the methods and results of Reverse Mathematics and computability theory be used to clarify these questions?

More details can be found on the workshop´s homepage.