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Since a statement is a generator of predictions, it is true if it generates only true predictions. A statement that does not produce any predictions is, by this definition, true -- vacuously. Most important statements can produce infinitely many predictions; we call such statements theories. We cannot directly verify such a statement -- we have to believe that it is true. Karl Popper stressed that we can never prove a theory, we only can reject it when it gives us false predictions. Creation of theories is, essentially, an evolutionary process. They arise as products of the creative human mind and compete for survival. Those producing more important predictions (and promising to give even more) are selected for usage; the others perish. (See Evolutionary approach to Epistemology and Epistemological Constructivism.) There is no criterion of truth other than its power to give predictions. Since powers, like multidimensional vectors, are hard to compare, there is no universal and absolute criterion of truth.

Proclamation of any truth as absolute because of being given through a "revelation" is sheer self-deception.

It is natural to test the validity of this approach to knowledge, meaning and truth in the field which does not allow imprecision and vagueness but requires a complete formalization and inambiguity, -- in mathematics. This is done in V.Turchin's Cybernetic foundation of mathematics. This approach gives answers to the century old questions about foundations of mathematics; in particular, a new and constructive interpretation of the full set theory is proposed there.

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V. Turchin,

Oct 6, 1997 (modified)
Sep 1991 (created)


Metasystem Transition Theory



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Statement of infiniteness

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