Article/Publication Details

Mathematical Models as Abstractions

(Mathematical Models as Abstractions)
Organon F, 2018, vol. 25, No 2, pp. 244-264.
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The paper concerns a contemporary problem emerging in philosophy of science about the explanatory status of mathematical models as abstractions. The starting point lies in the analysis of Morrison’s discrimination of models as idealizations and models as abstractions. There abstraction has a special status because its non-realistic nature (e.g. an infinite number of particles, an infinite structure of fractal etc.) is the very reason for its explanatory success and usefulness. The paper presents two new examples of mathematical models as abstractions – the fractal invariant of phase space transformations in the dynamic systems theory and infinite sets in the formal grammar and automata theory. The author is convinced about the indispensability of mathematical models as abstraction, but somehow disagrees with the interpretation of its explanatory power.

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Slovak Academy of Sciences
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Journal Organon F

Institute of Philosophy
Slovak Academy of Sciences
Klemensova 19
813 64 Bratislava, Slovak Republic
Tel.:(+4212) 5292 1215
Fax: (+4212) 5292 1215
E-mail: organonf@gmail.com
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