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A Theory of Truth and Semantic Representation

A Theory of Truth and Semantic Representation - A Theory of...

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A Theory of Truth and Semantic Representation Hans Kamp 1 Introduction Two conceptions of meaning have dominated formal semantics of natural language. The first of these sees meaning principally as that which determines conditions of truth. This notion, whose advocates are found mostly among philosophers and logi- cians, has inspired the disciplines of truth-theoretic and model-theoretic semantics. According to the second conception meaning is, first and foremost, that which a language user grasps when he understands the words he hears or reads. This second conception is implicit in many studies by computer scientists (especially those involved with artificial intelligence), psychologists and linguists - studies which have been concerned to articulate the structure of the representations which speakers construct in response to verbal inputs. It appears that these two conceptions, and with them the theoretical concerns that derive from them, have remained largel!- separated for a considerable period of time. This separation has become an obstacle to the development of semantic theory, imped- ing progress on either side of the line of division it has created. The theory presented here is an attempt to remove this obstacle. It combines a definition of truth with a systematic account of semantic representations. These two components are linked in the following manner. The representations postulated here are (like those proposed by others; cf. e.g. Hendrix (1975) or Karttunen (1976)) similar in structure to the models familiar from model-theoretic semantics. In fact, formally they are nothing other than partial models, typically with small finite domains. Such similarity should not surprise; for the representation of, say, an indicative sentence ought to embody those conditions which the world must satisfy in order that the sentence be true; and a particularly natural representation of those conditions is provided by a partial model with which the (model describing the) real world will be compatible just in case the conditions are fulfilled. Interpreting the truth-conditional significance of representations in this nay we are led to the following characterization of truth: A sentence S, or discourse D, with representation m is true in a modcl M if and only if M is compatible with m; and
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190 Hans Kamp compatibility of M with m, we shall see, can be defined as the existence of a proper embedding of m into M, where a proper embedding is a map from the universe of m into that of M which, roughly speaking, preserves all the properties and relations which m specifies of the elements of its domain. -4 theory of this form differs fundamentally from those familiar from the truth- theoretical and model-theoretical literature, and thus a substantial argument will be wanted that such a radical departure from existing frameworks is really necessary. The particular analysis carried out in the main part of this paper should be seen as a first attempt to provide such an argument. The analysis deals with onl!- a small number of linguistic problems, but careful reflection upon just those problems alread!- reveals,
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