TY - JOUR T1 - Mathematical Models as Abstractions JF - Organon F Y1 - 2018 A1 - Zámečník, Lukáš KW - Abstraction KW - dynamic systems theory KW - Explanation KW - formal grammar idealization KW - mathematical model KW - Morrison KW - Philosophy of science AB - 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. VL - 25 UR - http://www.klemens.sav.sk/fiusav/doc/organon/2018/2/244-264.pdf M3 - State U2 - Articles U3 - 244264 ER -