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