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an immediate inference within the formalism of traditional logic, usually used in conjunction with the conversion of judgments. In an obversion, the quality of a premise is changed at the same time the predicate term is replaced by its opposite, as in “The book is new, therefore it is not old.” The semantic basis of obversion is the dichotomous division of attributes, and its logical basis is the law of the excluded middle and the law of double negation. The rules of obversion for what are known as categorical syllogistic premises are as follows: (1) “All S are P” (“Some S are P”) implies “No S are not-P” (“Some S are not not-P”), and conversely; (2) “No S are P” (“Some S are not P”) implies “All S are not-P” (“Some S are not-P”), and conversely.

Obversion, like other types of immediate inferences, was of special interest to medieval philosophers, who undertook a logical and grammatical analysis of the position of negation in a sentence in dealing with the equipollence of propositions. Although obversion has no independent value within the formalism of mathematical logic, this does not lessen its usefulness in meaningful thought. In particular, obversion is used—usually implicitly—in the “language of the researcher” to translate the traditional symbolism of categorical judgments into the symbolic language of modern predicate logic.


Logika. Moscow, 1956. Pages 130–31.