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
U2 - Articles
U3 - 244264
ER -