Axiomatics and the mathematical-type Sciences

Paul Sfetcu
National Institute for Research and Development in Informatics, ICI Bucharest

Abstract: In this paper we follow the way the axiomatic concept evolved and we are going to put it in contrast with the Ancient Greek thinking – namely Aristotle, Plato and their followers, the scholastics. Modern scientists, especially mathematicians conceived Axiomatics only as an imitation of the real structure of a genuine science as it was conceived by Aristotle in Organon. Since data volume increases exponentially in a science based on empiricism there is no doubt that this structuring of scientific data has a ranking function in mastering the modern data explosion but it cannot bring any theoretical contribution concerning the foundations of Mathematics and modern thought.

Keywords: science, truth and false, axiomatization, formalization, axiom and postulate, formal system, axiomatic group, Gödel’s arithmetization, demonstration and transformation

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Paul Sfetcu, Axiomatics and the mathematical-type Sciences, Romanian Journal of Information Technology and Automatic Control, ISSN 1220-1758, vol. 20(3), pp. 13-32, 2010.