Project description

Description It is common to say that we know today that Fermat’s Last Theorem is true, although we still do not know whether Goldbach’s conjecture is. Obviously, such knowledge ascriptions are implicitly attributed to the mathematical community or a subgroup thereof. But what is the nature of such collective knowledge? Is it simply reducible to the sum of the knowledge of individual mathematical agents, or shall the mathematical community be conceived as a full- fledged social epistemic subject? What are the mechanisms ensuring the reliability of collective knowledge in mathematics, and thus the stability of the mathematical edifice? Although the social dimensions of mathematics have received increasing attention within the so-called philosophy of mathematical practice, we are still lacking clear philosophical proposals to answer the above set of questions. The general aim of this research project is to contribute to fill this gap by developing an account of collective knowledge in mathematics. Our focus will be specifically on the notion of collective justification and how it is acquired by a group of mathematicians through proofs. We'll also be concerned with characterizing groups of mathematical agents as epistemic subjects in their own right. The notions thus developed will be used to address the fundamental epistemological issue of the reliability of mathematical knowledge. Finally, implications for epistemology and general philosophy of science will be spelled out and discussed.

Collective Knowledge in Mathematics: Proofs, Collective Justification, and Reliability — Vrije Universiteit Brussel (vub.be)