Kalanov, Temur Z.
July 1, 2021
formal logic, mathematical logic, pure mathematics, philosophy of mathematics, methodology of mathematics, history of mathematics, higher education; history of science;, dialectics, epistemology
The critical analysis of the starting point of mathematical (symbolic) logic is proposed. Methodological basis of the analysis is the unity of formal logic and rational dialectics. It is shown that mathematical logic represents incorrect mathematical theory. Arguments are as follows. (1) Pure mathematics operates on mathematical quantity. Pure mathematics and mathematical (symbolic) logic ignore the correct methodological basis (i.e., criterion of truth) of science. (2) Mathematics and mathematical (symbolic) logic abolishes (deletes) essence (central point) of formal logic: concept and proposition (as a logical form of verbal expression (statement) of thought). But thought without words does not exist. If concepts and propositions as meaning contents are removed from consideration, then formal logic is destroyed. (3) Mathematical (symbolic) logic replaces proposition by the property of proposition: “truth” or “false”. But the concepts “proposition” and “property of proposition” are not identical. In this case, the formal logic is destroyed. In addition, the concepts “proposition” and “property of proposition” do not represent mathematical quantities, and the concepts cannot be in mathematical formalism. (4) The starting point of mathematical (symbolic) logic represents several symbols that connect (join, unite) the words “truth” and “false” in truth tables.../...