Intensional logic

Paul Gochet
Table of contents

The distinction between intension and extension is rooted in the Aristotelian tradition. Aristotle built up a logic whose smallest units are general terms like ‘Man’, ‘Animal’, and ‘Mortal’. With each general term is associated a concept or characteristic property in virtue of which the term is ascribed to an individual. This is called the intension of the term. The set of individuals which happen to fall under the above-mentioned concept or to possess the corresponding property is called the extension of the term. The copula linking two general terms (‘Men are mortal’) can also be read intensionally or extensionally. Intensionally, the sentence could be paraphrased as ‘mortality belongs to humanity’. Extensionally, it means ‘the class of men is included in the class of mortals’. Porphyry (232–300) designed a tree which showed the possibility of inverting the intensional connection into an extensional one and anticipated the controversial law according to which extension and intension are in inverse ratio to one another.

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