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Podnieks, Karlis and Tabak, John (2011) The Nature of Mathematics – an interview with Professor Karlis Podnieks. In: John Tabak. Numbers: Computers, Philosophers, and the Search for Meaning. Revised edition. Facts on File, USA, pp. 188-197. ISBN 0816049572

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Abstract

Many people think that mathematical models are built using well-known “mathematical things” such as numbers and geometry. But since the 19th century, mathematicians have investigated various non-numerical and non-geometrical structures: groups, fields, sets, graphs, algorithms, categories etc. What could be the most general distinguishing feature that would separate mathematical models from non-mathematical ones?

I would describe this feature by using such terms as autonomous, isolated, stable, self-contained, and – as a summary – formal. Autonomous and isolated – because mathematical models can be investigated “on their own” in isolation from the modeled objects. And one can do this for many years without any external information flow. Stable – because any modification of a mathematical model is qualified explicitly as defining a new model. No implicit modifications are allowed. Self- contained – because all properties of a mathematical model must be formulated explicitly. The term “formal model” can be used to summarize all these features.

Item Type:Book Section
Uncontrolled Keywords:mathematics, philosophy of mathematics, modeling, large numbers, inconsistency, inventing, discovering
Subjects:B Philosophy. Psychology. Religion > B Philosophy (General)
Divisions:University of Latvia > F1 Faculty of Computing
ID Code:192
Deposited By:Prof. Karlis Podnieks
Deposited On:09 Dec 2011 10:40
Last Modified:09 Dec 2011 14:07

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