Foundations of Science 14 (4):351-360 (2009)

This paper considers the role of mathematics in the process of acquiring new knowledge in physics and astronomy. The defining of the notions of continuum and discreteness in mathematics and the natural sciences is examined. The basic forms of representing the heuristic function of mathematics at theoretical and empirical levels of knowledge are studied: deducing consequences from the axiomatic system of theory, the method of generating mathematical hypotheses, “pure” proofs for the existence of objects and processes, mathematical modelling, the formation of mathematics on the basis of internal mathematical principles and the mathematical theory of experiment.
Keywords Mathematics  Heuristic function  Knowledge  Experiment  Theory
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DOI 10.1007/s10699-009-9162-2
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Non-Standard Analysis.Abraham Robinson - 1961 - North-Holland Publishing Co..
The Best Explanation: Criteria for Theory Choice.Paul R. Thagard - 1978 - Journal of Philosophy 75 (2):76-92.
Mathematics, the Loss of Certainty.Morris Kline - 1980 - New York, NY, USA: Oxford University Press, Usa.

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