# Repository | Book | Chapter

(2015) *From logic to practice*, Dordrecht, Springer.

In mathematical literature, it is quite common to make reference to an informal notion of naturalness: axioms or definitions may be defined as "natural," and part of a proof may deserve the same label (i.e., "in a natural way…"). Our aim is to provide a philosophical account of these occurrences. The paper is divided in two parts. In the first part, some statistical evidence is considered, in order to show that the use of the word "natural," within the mathematical discourse, largely increased in the last decades. Then, we attempt to develop a philosophical framework in order to encompass such an evidence. In doing so, we outline a general method apt to deal with this kind of vague notions – such as naturalness – emerging in mathematical practice. In the second part, we mainly tackle the following question: is naturalness a static or a dynamic notion? Thanks to the study of a couple of case studies, taken from set theory and computability theory, we answer that the notion of naturalness – as it is used in mathematics – is a dynamic one, in which normativity plays a fundamental role.

Publication details

DOI: 10.1007/978-3-319-10434-8_14

Full citation:

San Mauro, L. , Venturi, G. (2015)., Naturalness in mathematics, in G. Lolli, M. Panza & G. Venturi (eds.), * From logic to practice*, Dordrecht, Springer, pp. 277-313.

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