Ricerc@Sapienza

This article aims to suggest that a promising step towards the elaboration of an adequate naturalist account of mathematics and mathematical knowledge may be to take the method of mathematics to be the analytic method rather than the axiomatic method. Indeed, it seems impossible to naturalize mathematics without challenging at least some crucial aspects of the traditional view of mathematics, according to which mathematical knowledge is certain and the method of mathematics is the axiomatic method.

How should one conceive of the method of mathematics, if one takes a naturalist stance? Mathematical knowledge is regarded as the paradigm of certain knowledge, since mathematics is based on the axiomatic method. Natural science is deeply mathematized, and science is crucial for any naturalist perspective. But mathematics seems to provide a counterexample both to methodological and ontological naturalism. To face this problem, some naturalists try to naturalize mathematics relying on Darwinism.

The concept of human identity is generally built upon the view that human beings are somehow central and unique among all the other living beings. Nonetheless, presumed human uniqueness is no longer tenable after the “revolution” caused by Darwin’s theory. According to the scientific image produced by Darwinian biology human beings can no longer be understood as the outcome of a project. Furthermore, cognitive ethology undermines also the idea that Homo sapiens is equipped with unique capacities and shows unique behaviors.