Article/Publication Details

Mathematical Models as Abstractions

(Mathematical Models as Abstractions)
Organon F, 2018, vol. 25, No 2, pp. 244-264.
File to download: PDF
BibTex EndNote Tagged EndNote XML RIS
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.

Contact

Institute of Philosophy SAS, v.v.i.
Klemensova 19
811 09 Bratislava 1
Slovak Republic
Tel.: +4212 5292 1215
E-mail: sekretariat.fiu@savba.sk
Home page

Address for correspondence:

Filozofický ústav SAV, v. v. i.
P. O. Box 3364
813 64 Bratislava
Slovak Republic

Journal Filozofia

Institute of Philosophy SAS, v.v.i.
Filozofia Editorial Office
Klemensova 19
811 09 Bratislava 1
Slovak Republic
Tel.: +4212 5292 1215
E-mail: redakcia.filozofia@savba.sk
Home page

Address for correspondence:

Filozofický ústav SAV, v. v. i.
Filozofia Editorial Office
P. O. Box 3364
813 64 Bratislava
Slovak Republic

Journal Organon F

Institute of Philosophy SAS, v.v.i.
Organon F Editorial Office
Klemensova 19
811 09 Bratislava 1
Slovak Republic
Tel.: +4212 5292 1215
E-mail: organonf@gmail.com
Home page

Address for correspondence:

Filozofický ústav SAV, v. v. i.
Organon F Editorial Office
P. O. Box 3364
813 64 Bratislava
Slovak Republic