Indian Journal of Science and Technology
DOI: 10.17485/ijst/2011/v4i12.35
Year: 2011, Volume: 4, Issue: 12, Pages: 1786-1789
Original Article
Temur Z. Kalanov
Home of Physical Problems, Pisatelskaya 6a, 100200 Tashkent, Uzbekistan
[email protected] , [email protected] , [email protected]
Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that the generally accepted foundations are based on the logically erroneous concepts of “increment as variable quantity”, “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative” and, consequently, represent incorrect basis of mathematics.
Keywords: Foundations of mathematics, Philosophy of science.
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