“Reality” and “Construction” as Equivalent Evaluation-Functions in Algebra of Formal Axiology: A New Attitude to the Controversy between Logicism-Formalism and Intuitionism-Constructivism

Abstract

In this paper hitherto missed (neglected) formal-axiological meanings of the
words “reality”, construction” and “algorithm” are considered as
evaluation-functions (in the proper mathematical meaning of the word
“function”). These functions are precisely defined by tables and a strict
definition of formal-axiological equivalence (among the functions in question)
is given as well. Thus quite a new attitude to the formalism of D. Hilbert, the
“logicism” of B. Russel and the intuitionism of L.E.J. Brouwer and A. Heyting is
submitted. The paper presents a basic (twovalued) variant of discrete
mathematical simulation of axiology which investigates the system of values of
human activity in general. Algebra of formal axiology is reduced to its
particular case – algebra of formal ethics. Then algebra of ethics is used for
illuminating the ethical aspect of mathematical activity. This exotic (very
unusual) kind of investigating philosophical foundations of mathematics may be
called “ethicism” (in philosophy of mathematics).