Exploring the Weak Objectivity of Mathematical Knowledge

Philosophers of science and mathematics typically account for the success and intersubjective character of mathematical knowledge in terms of its objective character. On this view, what is objective is taken to be independent (or to exist independently) of human thought, as opposed to something that depends (or whose existence is not independent) of human intellectual activity. Call this notion ‘strong objectivity’. Strong objectivity is commonly used to identify mathematics as a body of mind-independent, absolute and necessary truths. With my project EWOMK (Exploring the Weak Objectivity of Mathematical Knowledge) I shall investigate a different way to conceive the objectivity of mathematical knowledge. I shall shape and test a notion of objectivity that, although not ontologically loaded because not dependent on the existence of mathematical objects and the truth of mathematical theories, is nonetheless capable to account for the intersubjective character of mathematics and its evolution. The main goal of the project is to assess the viability of such a notion (weak objectivity) and see how it can make justice of the way in which mathematical and scientific practices evolve.