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’. Pophyry (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.

Full-text access is restricted to subscribers. Log in to obtain additional credentials. For subscription information see Subscription & Price.


Van Benthem, J.
1988A manual of intensional logic. Center for the Study of Language and Information, Stanford.Google Scholar
Boolos, G.
1971The iterative conception of a set. The Journal of Philosophy 68: 215–231. DOI logoGoogle Scholar
Bealer, G. & U. Mönnich
1989Property theories. In D. Gabbay & F. Guenthner (eds.) Handbook of philosophical logic 4: 133–251. DOI logoGoogle Scholar
Carnap, R.
1956Meaning and necessity. University of Chicago Press.  BoPGoogle Scholar
Chierchia, G.
1985Formal semantics and the grammar of predication. Linguistic Inquiry 16: 417–443.Google Scholar
Chierchia, G. & R. Turner
1988Semantics and property theory. Linguistics and Philosophy 11: 261–302. DOI logoGoogle Scholar
Chierchia, G., B. Partee & R. Turner
1989Properties, types and meaning, 2vols. Kluwer. DOI logoGoogle Scholar
Church, A.
1941The calculi of lambda conversion. Princeton University Press.Google Scholar
Cocchiarella, N.
1988Predication versus membership in the distinction between logic as language and logic as calculus. Synthese 77: 37–72. DOI logoGoogle Scholar
1989Conceptualism, realism, and intensional logic. Topoi 8: 15–34. DOI logoGoogle Scholar
Frege, G.
1949[1892] On sense and nominatum. In H. Feigl & W. Sellars (eds.) Readings in philosophical analysis: 85–102. Appelton Century Crofts.Google Scholar
Gamut, L.T.F.
1991Logic, language and meaning, vol. 2. University of Chicago Press.Google Scholar
Heny, F.
(ed.) 1981Ambiguities in intensional contexts. Reidel. DOI logo  BoPGoogle Scholar
Hintikka, J.
1969Models for modalities. Reidel.Google Scholar
Hintikka, J. & M. Hintikka
1989The logic of epistemology and the epistemology of logic. Reidel.Google Scholar
Montague, R.
1974Formal philosophy. Yale University Press.  BoPGoogle Scholar
Niiniluoto, I. & E. Saarinen
1982Intensional logic. Acta Philosophica Fennica 35.Google Scholar
Russell, B.
1940An inquiry into meaning and truth. Allen & Unwin.Google Scholar
Thayse, A.
(ed.) 1989From modal logic to deductive databases, vol. 2. Wiley.Google Scholar
Tichy, P.
1978Two kinds of intensional logic. Epistemologia 1: 143–162.Google Scholar
Vergauwen, R.
1993A metalogical theory of reference. University of America Press.Google Scholar
Zalta, E.
1988Intensional logic and the metaphysics of intensionality. MIT Press.Google Scholar