Graduate studies at Western
Linguistics and Philosophy 24 (5):531-595 (2001)
|Abstract||The prime purpose of this paper is, first, to restore to discourse-bound occasion sentences their rightful central place in semantics and secondly, taking these as the basic propositional elements in the logical analysis of language, to contribute to the development of an adequate logic of occasion sentences and a mathematical (Boolean) foundation for such a logic, thus preparing the ground for more adequate semantic, logical and mathematical foundations of the study of natural language. Some of the insights elaborated in this paper have appeared in the literature over the past thirty years, and a number of new developments have resulted from them. The present paper aims atproviding an integrated conceptual basis for this new development in semantics. In Section 1 it is argued that the reduction by translation of occasion sentences to eternal sentences, as proposed by Russell and Quine, is semantically and thus logically inadequate. Natural language is a system of occasion sentences, eternal sentences being merely boundary cases. The logic hasfewer tasks than is standardly assumed, as it excludes semantic calculi, which depend crucially on information supplied by cognition and context and thus belong to cognitive psychology rather than to logic. For sentences to express a proposition and thus be interpretable and informative, they must first be properly anchored in context. A proposition has a truth value when it is, moreover, properly keyed in the world, i.e. is about a situation in the world. Section 2 deals with the logical properties of natural language. It argues that presuppositional phenomena require trivalence and presents the trivalent logic PPC3, with two kinds of falsity and two negations. It introduces the notion of -space for a sentence A (or A/A, the set of situations in which A is true) as the basis of logical model theory, and the notion of P A / (the -space of the presuppositions of A), functioning as a `private' subuniverse for A/A. The trivalent Kleene calculus is reinterpreted as a logical account of vagueness, rather than of presupposition. PPC3 and the Kleene calculus are refinements of standard bivalent logic and can be combined into one logical system. In Section 3 the adequacy of PPC3 as a truth-functional model of presupposition is considered more closely and given a Boolean foundation. In a noncompositional extended Boolean algebra, three operators are defined: 1a for the conjoined presuppositions of a, ã for the complement of a within 1a, and â for the complement of 1a within Boolean 1. The logical properties of this extended Boolean algebra are axiomatically defined and proved for all possible models. Proofs are provided of the consistency and the completeness of the system. Section 4 is a provisional exploration of the possibility of using the results obtained for a new discourse-dependent account of the logic of modalities in natural language. The overall result is a modified and refined logical and model-theoretic machinery, which takes into account both the discourse-dependency of natural language sentences and the necessity of selecting a key in the world before a truth value can be assigned.|
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
|Through your library||Configure|
Similar books and articles
Prof em Dr Hans-Ulrich Hoche (forthcoming). In Search of an Integrated Logic of Conviction and Intention. .
Dirk Greimann (2008). Does Frege Use a Truth-Predicate in His ‘Justification’ of the Laws of Logic? A Comment on Weiner. Mind 117 (466):403-425.
Philip Hugly & Charles Sayward (1992). Classical Logic and Truth-Value Gaps. Philosophical Papers 21 (2):141-150.
Hirohiko Kushida (2010). The Modal Logic of Gödel Sentences. Journal of Philosophical Logic 39 (5):577 - 590.
Kevin C. Klement, Propositional Logic. Internet Encyclopedia of Philosophy.
M. McKeon (2005). A Defense of the Kripkean Account of Logical Truth in First-Order Modal Logic. Journal of Philosophical Logic 34 (3):305 - 326.
Christopher Menzel (1998). Logical Form. In Edward Craig (ed.), Routledge Encyclopedia of Philosophy. Routledge.
George Lakoff (1970). Linguistics and Natural Logic. Synthese 22 (1-2):151 - 271.
Sorry, there are not enough data points to plot this chart.
Added to index2009-01-28
Recent downloads (6 months)0
How can I increase my downloads?