### “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).

#### Keywords

philosophy; 20th century philosophy; reality; construction; action; good; bad; morality; evaluation function; formal axiological equivalence; two-valued; algebra of formal axiology

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