By Dov M. Gabbay, Franz Guenthner
conceptual, realist) theories of predication. bankruptcy IV.4 facilities on a tremendous classification of expressions used for predication in reference to amounts: mass expressions. This bankruptcy experiences the main famous methods to mass phrases and the ontological proposals regarding them. as well as quantification and predication, concerns of reference have constituted the opposite overriding subject for semantic theories in either philosophical good judgment and the semantics of ordinary languages. bankruptcy IV.5 of the way the semantics of right names and descrip provides an summary tions were handled in contemporary theories of reference. bankruptcy IV.6 is anxious with the context-dependence of reference, particularly, 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 facets of common 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 bargains with one other famous subject common sense: presupposition, a subject at the borderline of semantics and prag matics. the quantity closes with an intensive learn of the Liar paradox and its many implications for the examine of language (as for instance, self reference, fact options and fact definitions).
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Additional resources for Handbook of Philosophical Logic. Volume IV: Topics in the Philosophy of Language
Still, one may ask what, if any, is the idea or intuition behind it. As for Barwise and Cooper, they seem to regard it mainly as a successful empirical generalization. 6. 2. l, III. We still have to deal with "there are" -sentences and with the semantics of more. 2. "there are"-sentences. Consider sentences such as (I) There are no flowers, (2) There are many patients waiting outside, (3) There are some philosophers who like logic, (4) There are a few errors in the text. I: QUANTIFIERS 39 where Q is the quantifier denoted by the DETand A is the set contributed, in a model M, by the expression following the DET.
L: QUANTIFIERS Two examples of vague DETs are several and a few. Here one may, following Keenan and Stavi, stipulate that several = three, a few = some. 2. Context-dependent DETs. The DETs many and few are not only vague but also context-dependent in the sense that the 'standard of comparison' may vary with the context. For example, in (8) Many boys in the class are right-handed, (9) Lisa is dating many boys in the class, some 'normal' standard for the least number considered to be many is used, but probably different standards in the two cases.
Case I: X; and ~ are both finite. Then the partition sets in ViM are finite and thus have the same cardinality as the corresponding partition sets in U;M', since M ~ n M' for all n. X; differs from ViM' only by certain of the aI' ... , an-I, and 1'; differs in the same way from U;M'. Therefore, IX; I = I 1'; I and I~ I = Ilj I, and the conclusion follows. Case 2: X; and ~ are both infinite. Then IX; I is the max of the cardinalities of the partition sets making up ViM; say, IX;I = Ip,MI, and similarly I~I = IPtMI.