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.

References

Van Benthem, J.

1988A manual of intensional logic. Center for the Study of Language and Information, Stanford.

Boolos, G.

1971The iterative conception of a set. The Journal of Philosophy 68: 215–231.

Bealer, G. & U. Mönnich

1989Property theories. In D. Gabbay & F. Guenthner (eds.) Handbook of philosophical logic 4: 133–251.

Carnap, R.

1956Meaning and necessity. University of Chicago Press.

Chierchia, G.

1985Formal semantics and the grammar of predication. Linguistic Inquiry 16: 417–443.

Chierchia, G., B. Partee & R. Turner

1989Properties, types and meaning, 2 vols. Kluwer.

Church, A.

1941The calculi of lambda conversion. Princeton University Press.

Cocchiarella, N.

1988Predication versus membership in the distinction between logic as language and logic as calculus. Synthese 77: 37–72.

Cocchiarella, N.

1989Conceptualism, realism, and intensional logic. Topoi 8: 15–34.

Davidson, D.

1968–9On saying that. Synthese 19: 130–146.

Dowty, D., R. Wall & S. Peters

1981Introduction to Montague Semantics. Springer.

Frege, G.

(1949) [1892]On sense and nominatum. In H. Feigl & W. Sellars (eds.) Readings in philosophical analysis: 85–102. Appelton Century Crofts.

Gamut, L. T. F.

1991Logic, language and meaning, vol. 2. Intensional Logic and Logical Grammar. University of Chicago Press.

Heny, F.

(ed.)1981Ambiguities in intensional contexts. Reidel.

Hintikka, J.

1969Models for modalities. Reidel.

Hintikka, J. & M. Hintikka

1989The logic of epistemology and the epistemology of logic. Reidel.

Lambalgen, M.Van & F. Hamm

2005The Proper Treatment of Events.Blackwell.

Miller, D.

1991A Logic Programming Language with Lambda-abstraction, Function Variables and Simple Unification. Journal of Logic and Computation 1: 497–536.

Montague, R.

1974Formal philosophy. Yale University Press.

Moschovakis, Y.

1993Sense and denotation as algorithm and value. In J. Oikkonen & J. Väänänen (eds.) Lecture Notes in Logic: 210–249. Association for Symbolic Logic, A.K. Peters Ltd.

Moschovakis, Y.

1994Sense and Denotation as Algorithm and Value. Logic Colloquium 90 (Helsinki 1990), vol.2 of Lectures Notes in Logic: 210–249. Springer.

Muskens, R.

2005Sense and the computation of reference. Linguistics and Philosophy 28: 473–504.

Muskens, R.

2007Intensional Models for the Theory of Types. Journal of Symbolic Logic 72: 98–118.

2000Opacity and the Attitudes. In P. Kotatko & A. Orenstein (eds.) Knowledge, Language and Logic. Questions for Quine: 367–407. Kluwer.

Rijke, M.De

(ed.)1997Advances in Intensional Logic. Kluwer.

Russell, B.

1940An inquiry into meaning and truth. Allen & Unwin.

Salmon, N.

2002Puzzles about Intensionality. In D. Jacquette (ed.) A Companion to, Philosophical Logic: 73–85. Blackwell.

Tarski, A.

1956Logic, semantics, metamathematics. Oxford University Press.

Thayse, A.

(ed.)1989From modal logic to deductive databases, vol. 2. Wiley.

Thomason, R.

1980A Model Theory for Propositional Attitudes. Linguistics and Philosophy 4: 47–70.

Tichy, P.

1978Two kinds of intensional logic. Epistemologia 1: 143–162.

Vergauwen, R.

1993A metalogical theory of reference. University of America Press.

Wittgenstein, L.

(1960) [1921]Tractatus-logico-philosophicus, with a new Translation by D.F. Pears & B.F. McGuinness and with the Introduction by B. Russell. Routledge & Kegan Paul.

Zalta, E.

1988Intensional logic and the metaphysics of intensionality. MIT Press.