The Epistemic Role of Social Values in Mathematics

(Logic, )

n social epistemology, ``social'' values concern an agent's social, moral or political background, or they involve the agent in a crucial way. They are different from the values that are *internal* to the scientific enterprise (such as empirical adequacy and consistency). In mathematics, studies of mathematicians' practices describe how agents turn to social values to fulfil various epistemic tasks. For example, considering a conjecture's purported ``beauty'' is taken as an indicator of its truth, the authority of a proof's author is taken as an indicator of its correctness. Social values seem to complement the epistemic role of internal values. But how can social values be epistemically reliable?

In the talk, we shall suggest a reductive explanation. We proceed in three steps. Firstly, we describe a set of (potentially) epistemically relevant social values. Mathematicians do not take any social value to be epistemically relevant, but only a subset that includes, among others, beauty and authority. Secondly, we define the epistemic effect of these values as truth-indicative. Mathematicians rely on these values because they take them to indicate mathematical truth. Thus, to explain why social values are epistemically reliable, one needs to explain the connection between the relevant values (identified in the first step) and mathematical truth. Thirdly, we argue for a weak dependency claim. If a mathematician believes that *p* is a mathematical truth, because she believes that *p* is beautiful (in addition to other beliefs concerning *p*), her belief that *p* is beautiful needs to be partly grounded in the mathematical properties of the mathematical entity that corresponds with *p*. That is, only if the relevant social values partly depend on mathematical properties, and only on the right subset thereof, social values can be epistemically reliant. We conclude by sketching some consequences if the weak dependency claim is accepted and some possible problems.

Chair: Larissa Bolte

Zeit: 14:40-15:10, 11. September 2021 (Samstag)

Ort: SR 1.006

Paul Hasselkuß

(Heinrich Heine University Düsseldorf, Deutschland)

Paul Hasselkuß is a PhD student at Heinrich Heine University Düsseldorf. His research interests concern the philosophy of mathematics and social epistemology.

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