(2014) Philosophia Scientiae 18 (1).

Facets and levels of mathematical abstraction

pp. 81-112

Mathematical abstraction is the process of considering and ma­nipulating operations, rules, methods and concepts divested from their refe­rence to real world phenomena and circumstances, and also deprived from the content connected to particular applications. There is no one single way of per­forming mathematical abstraction. The term “abstraction” does not name a unique procedure but a general process, which goes many ways that are mostly simultaneous and intertwined; in particular, the process does not amount only to logical subsumption. I will consider comparatively how philosophers consi­der abstraction and how mathematicians perform it, with the aim to bring to light the fundamental thinking processes at play, and to illustrate by signifi­cant examples how much intricate and multi-leveled may be the combination of typical mathematical techniques which include axiomatic method, invariance principles, equivalence relations and functional correspondences.

Publication details

DOI: 10.4000/philosophiascientiae.914

Full citation:

(2014). Facets and levels of mathematical abstraction. Philosophia Scientiae 18 (1), pp. 81-112.

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