By Dov M. Gabbay, Franz Guenthner
conceptual, realist) theories of predication. bankruptcy IV.4 facilities on an incredible classification of expressions used for predication in reference to amounts: mass expressions. This bankruptcy studies the main recognized ways to mass phrases and the ontological proposals on the topic of them. as well as quantification and predication, concerns of reference have constituted the opposite overriding topic for semantic theories in either philosophical good judgment and the semantics of typical languages. bankruptcy IV.5 of ways the semantics of right names and descrip offers an outline tions were handled in fresh theories of reference. bankruptcy IV.6 is anxious with the context-dependence of reference, specifically, with the semantics of indexical expressions. the subject of bankruptcy IV.7 is said to predication because it surveys the various primary difficulties of ascribing propositional attitudes to brokers. Chap ter IV.8 offers with the research of the most temporal points of average language utterances. jointly those chapters supply an excellent indication of the problematic complexities that come up as soon as modalities of 1 or the opposite type input at the semantic level. in philosophical bankruptcy IV.9 offers with one other famous subject good judgment: presupposition, a topic at the borderline of semantics and prag matics. the amount closes with an intensive examine of the Liar paradox and its many implications for the research of language (as for instance, self reference, fact strategies and fact definitions).
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Additional resources for Handbook of Philosophical Logic. Volume IV: Topics in the Philosophy of Language
But there is usually no point in allowing this generality. Moreover, there is a clear intuition. I think, that determiners are constants. We therefore lay down the following methodological postulate: (M P) Simplex DETs are constants: each one denotes a fixed quantifier (modulo, of course, lexical ambiguity. vagueness. ; cf. 4). (MP) allows us to dispense with the interpretation function for (simplex) DETs. 4, using boldface letter for quantifiers: Q denotes Q, most denotes most, some denotes some, etc.
Then it can be shown by induction that if X is universe-like and ¢ is an L-sentence, (REL) (M, X) ~ ¢(P) <=> MI X ~
Variable-binding is done with the abstraction operator '. Quantifier symbols are (certain) I-place DETs, and quantified formulas are of the form (*) D(1]) (J), where D is a DET and 1], J are set terms. There are the usual atomic formulas, plus formulas of the form 1](t), where 1] is a set term and t an individual term, and the formulas are closed under sentential connectives. DETs are interpreted as binary conservative quantifiers; the truth condition for (*) in a model is then obvious. The result is that logical form in L( GQ) corresponds more closely to syntactic form in the fragment than usual.
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