Extension and Intension
While it is commonly held that the notions of extension and intension originate with the Port Royal logicians, a lively oral tradition has it that they are found explicitly in ARISTOTLE. In several passages of the Organon, ARISTOTLE does speak of the extension of the universals genus and species, often expounding, on the same occasion, the principle that the species is predicated of fewer things than the genus, and giving as example the genus “animal” and the species “man”. He also asserts that the genus is predicated of the species, but not conversely. It can be reasonably argued that these assertions constitute the original formulation of the familiar relation between extension and intension, known as the law of inverse ratio: the extension of the genus contains the extension of the species, while the species comprehends or grasps more of the essence of a thing than does the genus.
KeywordsBoolean Algebra Proof Theory Incompleteness Theorem Entailment Relation Modern Logic
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