This paper is devoted to the formulation and investigation of a dynamic semantic interpretation of the language of first-order predicate logic. The resulting system, which will be referred to as ‘dynamic predicate logic’, is intended as a first step towards a compositional, non-representational theory of discourse semantics. In the last decade, various theories of discourse semantics have emerged within the paradigm of model-theoretic semantics. A common feature of these theories is a tendency to do away with the principle of compositionality, (...) a principle which, implicitly or explicitly, has dominated semantics since the days of Frege. Therefore the question naturally arises whether non-compositionality is in any way a necessary feature of discourse semantics. Since we subscribe to the interpretation of compositionality as constituting primarily a methodological principle, we consider this to be a methodological rather than an empirical question. As a consequence, the emphasis in the present paper lies on developing an alternative compositional semantics of discourse, which is empirically equivalent to its non-compositional brethren, but which differs from them in a principled methodological way. Hence, no attempts are made to improve on existing theories empirically. Nevertheless, as we indicate in section 5, the development of a compositional alternative may in the end have empirical consequences, too. First of all, it can be argued that the dynamic view on interpretation developed in this paper suggests natural and relatively easy to formulate extensions which enable one to deal with a wider range of phenomena than can be dealt with in existing theories. Moreover, the various approaches to the model-theoretic semantics of discourse that have been developed during the last decade, have constituted a ‘fresh start’ in the sense that much of what had been accomplished before was ignored, at least for a start. Of course, this is a justified strategy if one feels one is trying to develop a radically different approach to recalcitrant problems. However, there comes a time when such new approaches have to be compared with the older one, and when an assessment of the pros and cons of each has to be made. One of the main problems in semantics today, we feel, is that a semantic theory such as Montague grammar, and an approach like Kamp’s discourse representation theory, are hard to compare, let alone that it is possible to unify their insights and results.. (shrink)

Die Leitgedanken meiner Untersuchungen über die Grundlagen der Mathematik, die ich - anknüpfend an frühere Ansätze - seit 1917 in Besprechungen mit P. BERNAYS wieder aufgenommen habe, sind von mir an verschiedenen Stellen eingehend dargelegt worden. Diesen Untersuchungen, an denen auch W. ACKERMANN beteiligt ist, haben sich seither noch verschiedene Mathematiker angeschlossen. Der hier in seinem ersten Teil vorliegende, von BERNAYS abgefaßte und noch fortzusetzende Lehrgang bezweckt eine Darstellung der Theorie nach ihren heutigen Ergebnissen. Dieser Ergebnisstand weist zugleich die Richtung (...) für die weitere Forschung in der Beweistheorie auf das Endziel hin, unsere üblichen Methoden der Mathematik samt und sonders als widerspruchsfrei zu erkennen. Im Hinblick auf dieses Ziel möchte ich hervorheben, daß die zeit weilig aufgekommene Meinung, aus gewissen neueren Ergebnissen von GÖDEL folge die Undurchführbarkeit meiner Beweistheorie, als irrtüm lich erwiesen ist. Jenes Ergebnis zeigt in der Tat auch nur, daß man für die weitergehenden Widerspruchsfreiheitsbeweise den finiten Stand punkt in einer schärferen Weise ausnutzen muß, als dieses bei der Be trachtung der elementaren Formallsmen erforderlich ist. Göttingen, im März 1934 HILBERT Vorwort zur ersten Auflage Eine Darstellung der Beweistheorie, welche aus dem HILBERTschen Ansatz zur Behandlung der mathematisch-logischen Grundlagenpro bleme erwachsen ist, wurde schon seit längerem von HILBERT ange kündigt. (shrink)

Recent results of Partee, Rooth, Krifka and other formal semanticians confirm that topic-focus articulation (TFA) of sentence is relevant for its semantics. The essential import of TFA, which is more apparent in case of a language with relatively free word order such as Czech than in case of English, has been traditionally intensively studied by Czech linguists. In this paper we would like to indicate the possibility of the account for TFA in terms of the theory of generalized quantifiers, drawing (...) on the results of both these groups of theoreticians. The basic intuition which we accept as our point of departure is the intuition of topic as the “semantic subject” and focus as the “semantic predicate”; we point out that the role of topic is to specify the entity the sentence is “about” (thereby triggering a presupposition), while that of the focus is to reveal a characterization of this entity, and usually a characterization that is in some sense exhaustive. Then we show that it may be plausible to consider topic and focus as arguments to an implicit generalized quantifier, which may get overridden by an explicit focalizer. (shrink)

When philosophers talk about descriptions, usually they have in mind singular definite descriptions such as ‘the finest Greek poet’ or ‘the positive square root of nine’, phrases formed with the definite article ‘the’. English also contains indefinite descriptions such as ‘a fine Greek poet’ or ‘a square root of nine’, phrases formed with the indefinite article ‘a’ (or ‘an’); and demonstrative descriptions (also known as complex demonstratives) such as ‘this Greek poet’ and ‘that tall woman’, formed with the demonstrative articles (...) ‘this’ and ‘that’. Following the custom in philosophy, in this chapter often we use ‘description’ as short for ‘definite description’; and following the custom in linguistics, often we use ‘definite’, ‘indefinite’, and ‘demonstrative’ as shorthand nouns. For the most part we focus on definite and indefinites, although a few words about demonstratives are called for. At the centre of debates about descriptions is the matter of whether they are devices of reference or of predication (simple or higher-order), and much discussion focuses on how various proposals are to be incorporated into broader theories of the semantics of natural language. But philosophical interest goes beyond the confines of linguistics, logic, and the philosophy of language because choices made about the semantics of descriptions have repercussions elsewhere, particularly in epistemology and metaphysics. A simple match of form and meaning appears to fail.1 First, many occurrences of expressions of both forms ‘the φ’ and ‘a φ’ appear to be used to talk about particular individuals. Consider (1). (shrink)

The paper investigates the scope properties of indefinites.

Some philosophers, notably Professors Quine and Geach, have stressed the analogies they see between pronouns of the vernacular and the bound variables of quantification theory. Geach, indeed, once maintained that ‘for a philosophical theory of reference, then, it is all one whether we consider bound variables or pronouns of the vernacular'. This slightly overstates Geach's positition since he recognizes that some pronouns of ordinary language do function differently from bound variables; he calls such pronouns ‘pronouns of laziness'. Geach's characterisation of (...) pronouns of laziness has varied from time to time, but the general idea should be clear from a paradigm example: A man who sometimes beats his wife has more sense than one who always gives in to her.The pronouns ‘one’ and ‘her’ go proxy for a noun or a noun phrase in the sense that the pronoun is replaceable in paraphrase by simple repetition of its antecedent. (shrink)

Speaking of Professor Geach's belief that pronouns in natural language function like the bound variables in quantification theory, Gareth Evans, in ‘Pronouns, Quantifiers, and Relative Clauses - I’ says :I want to try to show that there are pronouns with quantifier antecedents that function in a quite different way. Such pronouns typically stand in a different grammatical relation to their antecedents, and; in contrast with bound pronouns, must be assigned a reference, so that their most immediate sentential contexts can always (...) be assigned a truth value. The relevant grammatical relation appears to be Klima's relation of ‘in construction with’. When the pronoun is in construction with its antecedent, as in [‘Some man loves his mother’] and [‘No man is happy when he is in love’] the result is a bound pronoun. (shrink)

The paper addresses foundational questions concerning the dynamic semantics of natural language based on dynamic logic of the Groenendijko-Stokhofian kind. Discussing a series of model calculi of increasing complexity, it shows in detail how the usual semantics of dynamic logic can be seen as emerging from the account for certain inferential patterns of natural language, namely those governing anaphora. In this way, the current ‘dynamic turn’ of logic is argued to be reasonably seen not as the product of changing the (...) focus of logic from the relation of entailment to „a structure of human cognitive action“ (van Benthem), but rather as merely another step in our long-term effort to master more and more inferential patterns. (shrink)