Abstract
The paper gives a theory of intensional objects somewhat along the lines of Montague's higher type intensional logics. The theory is rich enough to deal with the problems of philosophy and linguistics discussed by Montague. It is shown to include its own semantics in a sense analogous to the way ZF has natural set theoretic models for any finite sub-theory. The theory does not quantify over possibilia χ, or over associated essences of χ, nor are these required for its semantics. Strong axioms of infinity are formulated in the framework of the theory.
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