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By proof of a statement S we mean any process which the subject of knowledge accepts as the evidence that S is true and is ready to use S for predictions on the basis of which to make decisions.

There are two cases of proof which can never arise any doubt because they do not base on any assumptions: verification and direct refutation.

When a statement cannot be directly verified or refuted, it is still possible that we take is as true relying on our intuition. For example, consider a test process T the stages of which can be represented by single symbols in some language. Let further the process T develop in such a manner that if the current stage is represented by the symbol A, then the next stage is also A, and the process comes to a successful end when the current stage is a different symbol, say B. This definition leaves us absolutely certain that T is infinite, even though this cannot be either verified, or refuted. In logic we call some most immediate of such statements axioms and use as a basis for establishing the truth of other statements. In natural sciences some of the self-evident truths serve as the very beginning of the construction of theories.

Copyright© 1991 Principia Cybernetica - Referencing this page

V. Turchin,

Sep 1991


Metasystem Transition Theory




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