Collective Knowledge in Mathematics: Proofs, Collective Justification, and Reliability

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