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Fregean Description Theory in Proof-Theoretical Setting

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EN
We present a proof-theoretical analysis of the theory of definite descriptions which emerges from Frege’s approach and was formally developed by Kalish and Montague. This theory of definite descriptions is based on the assumption that all descriptions are treated as genuine terms. In particular, a special object is chosen as a designatum for all descriptions which fail to designate a unique object. Kalish and Montague provided a semantical treatment of such theory as well as complete axiomatic and natural deduction formalization. In the paper we provide a sequent calculus formalization of this logic and prove cut elimination theorem in the constructive manner.
EN
In this paper I argue that the notions of speaker’s reference and semantic reference-used by Kripke in order to counter the contentious consequences of Donnellan’s distinction between the referential use and the attributive use of definite descriptions-do not have any application in the interpretive interaction between speaker and hearer. Hearers are always concerned with speaker’s reference. Either, in cases of cooperation, as presented as such by the speaker or, in cases of conflict, as perceived as such by the hearer. Any claim as to semantic reference is irrelevant for the purposes of communication and conversation. To the extent that the purpose of semantic theory is to account for linguistic communication, there is no reason to take definite descriptions to have semantic reference.
Lodz Papers in Pragmatics
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2011
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vol. 7
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issue 2
291-307
EN
Very few philosophers and linguists doubt that definite descriptions have attributive uses and referential uses. The point of disagreement concerns whether the difference in uses is grounded on a difference in meaning. The Ambiguity Theory holds while the Implicature Theory denies that definite descriptions are ambiguous expressions, having an attributive meaning and a referential meaning. Contextualists have attempted to steer between the Ambiguity Theory and the Implicature Theory. I claim that the early contextualist account provided by Recanati and Bezuidehnout based on the idea that definite descriptions are semantically underdetermined and in need of a completion from the contextually available information through an optional top-down pragmatic process suffers from an explanatory gap.
EN
In the paper I discuss the legacy of Donnellan’s famous theory of definite descriptions in which he distinguishes between attributive and referential uses of these expressions. On the one hand I sketch the philosophical context within which Donnellan developed his theory. I put emphasis on the innovatory aspect of the theory by comparing it to a slightly older account proposed by Strawson. On the other hand, I discuss one of the main debates that have their source in Donnellan’s work. Namely, the debate between so called semanticists, who claim that the distinction between two uses of descriptions is of semantic nature, and so called pragmaticists, who believe that two ways of using descriptions is a pragmatic phenomenon while the semantic properties of descriptions have been analysed correctly in Russsell’s theory of descriptions.
EN
From the logical point of view, the most interesting among the pronouns are demonstrative pronouns (especially: this/that), indefinite pronouns (a/an), definite pronoun (the) and quantifying pronouns (every, all, some). Unlike personal pronouns (e.g. I/you/he) they are in fact functors (of the n/n category). The differentiation between personal pronouns (n) and functor pronouns (n/n) is vital here. This differentiation does not exist in traditional grammar. The study is limited to determining functor pronouns with the use of logical properties of quantifying expressions, which are functor pronouns themselves – all (n) and some (cr) – formally expressed in the quantifier-less calculus of names (BRN). The calculus is properly enriched with demonstrative pronouns (demonstrativa), in connection to certain studies by Toshiharu Waragai (LID). An attempt to employ this system (BRND) in the analysis of some fragments of Ockham’s Summa Logicae is shown here. The work is concluded with the analysis of a functor pronoun the only (t), being a special case of a definite pronoun, which is characterised here by means of rules. The work reveals the connection between this pronoun and the operator of definite descriptions (marked in the same way) in relation to a certain Ludwik Borkowski’s conception.
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