Abstract
The idea of rejection originated by Aristotle. The notion of rejection was introduced into formal logic by Łukasiewicz. He applied it to complete syntactic characterization of deductive systems using an axiomatic method of rejection of propositions. The paper gives not only genesis, but also development and generalization of the notion of rejection. It also emphasizes the methodological approach to biaspectual axiomatic method of characterization of deductive systems as acceptance (asserted) systems and rejection (refutation) systems, introduced by Łukasiewicz and developed by his student Słupecki, the pioneers of the method, which becomes relevant in modern approaches to logic.
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Notes
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- 3.
Słupecki’s theorem is an immediate consequence of the following theorem of the theory recursion, which we quote from Grzegorczyk’s book [14, p. 355 in the Eng. ed.]: If the union of two recursively enumerable disjoint sets T and S is computable set, then the sets T and S are also computable.
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G. Bryll (as well as his book [2]) and T. Skura have been very helpful in verifying certain significant facts.
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It is saved in Łukasiewicz’s, so called Polish notation.
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Wybraniec-Skardowska, U. (2018). Rejection in Łukasiewicz’s and Słupecki’s Sense. In: Garrido, Á., Wybraniec-Skardowska, U. (eds) The Lvov-Warsaw School. Past and Present. Studies in Universal Logic. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-65430-0_40
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