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«Axiom» (Greek ἀξίωμα — postulation, statement) — statement which is accepted as being true without a proof and which further serves as a “foundation” of a proof development within the frameworks of a theory, discipline, etc.

Big Soviet Encyclopedia

Perception is the heart of cognitive theory which requires cognizing forms and their interrelation as a goal of scientific cognition which is conditioned by the combination of induction with deduction; the truth of cognition consists in the correspondence of statements with external circumstances. The main thing is the development of metascience and classification on the basis of «Axioms – proofs – structures». Information received from things may be brought to main forms or categories: 1) essence as in the sense of substance, 2) quantity, 3) quality, 4) relation, 5) place, 6) time, 7) manner, 8) suffering. The key point of the final conclusion consists in syllogism, «imposing defined» method of proving in accordance of which in some special sciences (e.g. geometry) all particular propositions follow from their obvious axioms.

Aristotle , 384-322 BC. e .

«Axiom» (Greek axíōma — honored, accepted statement, from axióō — I consider it worthy), a statement of a certain theory which during deductive formation of such theory is not proven in it, but is taken as an initial, starting statement which lies at the root of proof of other statements of the theory. One normally takes as an Axiom statements of theory at issue which are knowingly true or may be considered as true within such theory.

Big Soviet Encyclopedia

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