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Publication Details

On the Nature of the World of Mathematics

(Original title: O povahe sveta matematiky)
Filozofia, 50 (1995), 3, 131-144.
Type of work: Papers
Publication language: Slovak

The paper is concerned with the epistemological analysis of mathematical language. Together with symbolic languages of arithmetics, algebra and of predicate calculus it decsribes also the iconic languages of synthetic, analytical and fractal geometry. Explaining geometric figures as terms and Euclid’s axioms as formative rules of the iconic language makes conceiving of the geometric intuition, as precise as the formal symbolism of algebra or arithmetics, possible. The historical variations of mathematics, in which intuitive, resp. calculative moments prevailed, thus could be seen as the development of language. An interesting regularity was revealed by this approach, showing that the higher form of symbolic or iconic language has always been achieved thruough a mediating stage of a language of the opposite kind.

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