Second nature. For a liberal naturalism of mathematics

The term “naturalism” has, over the course of the history of philosophy, taken on different and changing meanings, so we can apply it to a large number of philosophical areas, all having in common only an unspecified reference to the field of nature. Fortunately, contemporary naturalism has changed in recent years, with less erratic and ambiguous connotations, thus allowing for the possibility of identifying two distinct meanings: “scientific naturalism” and “liberal naturalism”, respectively. In this paper, we shall demonstrate how the distinction between different types of naturalism may more or less positively affect the field of numbers and arithmetic properties.