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Montague/Hintikka: for him it was mostly about a framework for general meaning analysis.
Possible World/Hintikka: Montague would need all linguistic (semantic, analytical) possible worlds. But it would require stronger arguments than the ones that Montague had available to limit them so that they would be less than the logically possible worlds.
This makes his use of non-standard semantics even more puzzling in the later work.
Quantifier/Quantifiers/Natural Language/HintikkaVsMontague: his theory is not appropriate because of its treatment of quantifiers.
Terminology: "PTQ": Montague: "The proper treatment of quantification in Ordinary English".
(i). Meaning entities are functions of possible worlds on extensions.
(ii). Semantic objects ((s) words) are linked to meaningful expressions by rules that correspond one-by-one to the syntactic rules by which the expressions are composed. That is, the semantic rules work from the inside out.
(iii) quantifiers: e.g. "a girl", e.g. "every man"...
...behave semantically as singular terms. That is, "John is happy" and "Every man is happy" are on the same level.
Hintikka: ad (i) is based on the semantics of possible worlds. (It is a generalization of Carnap's approach).
Ad (ii) is a form of the Frege principle (compositionality principle).
Ad (iii) has been anticipated by Russell in Principia Mathematica.
Individual Area/Possible Worlds/Montague/Hintikka: Thesis: Montague assumes a constant range of individuals.
HintikkaVsMontague: precisely this leads to problems. Especially in religious contexts.
Jaakko and Merrill B. Hintikka
The Logic of Epistemology and the Epistemology of Logic Dordrecht 1989
J. Hintikka/M. B. Hintikka
Untersuchungen zu Wittgenstein Frankfurt 1996