Online research in philosophy

It seems that the theories of language of the present century can be classified into two basic groups. The approaches of the first group perceive language as a mathematical structure and understand any theory of language as a kind of application of mathematics or logic. Their ideological background is furnished by logical positivism and analytical philosophy (esp. by Russell, Carnap, Wittgenstein and their followers); and their practical output is Chomskian formal syntax and subsequent formal semantics. The approaches of the other group do not approve of formalization and consider a theory of language closer to psychology than to mathematics. The specific position within this group is occupied by the so-called structuralists (de Saussure, Hjelmslev, Derrida).

• languages as sets of strings and early transformational grammar • interpreted languages as sets of string-meaning pairs • Montague in ‘Universal Grammar’: There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed I consider it possible to comprehend the syntax and semantics of both kinds of languages within a single natural and mathematically precise theory.

Tarskian model theory is almost universally understood as a formal counterpart of the preformal notion of semantics, of the “linkage between words and things”. The wide-spread opinion is that to account for the semantics of natural language is to furnish its settheoretic interpretation in a suitable model structure; as exemplified by Montague 1974.

This book provides a systematic study of three foundational issues in the semantics of natural language that have been relatively neglected in the past few decades. focuses on the formal characterization of intensions, the nature of an adequate type system for natural language semantics, and the formal power of the semantic representation language proposes a theory that offers a promising framework for developing a computational semantic system sufficiently expressive to capture the properties of natural language meaning while remaining computationally tractable written by two leading researchers and of interest to students and researchers in formal semantics, computational linguistics, logic, artificial intelligence, and the philosophy of language.

With a few notable exceptions formal semantics, as it originated from the seminal work of Richard Montague, Donald Davidson, Max Cresswell, David Lewis and others, in the late sixties and early seventies of the previous century, does not consider Wittgenstein as one of its ancestors. That honour is bestowed on Frege, Tarski, Carnap. And so it has been in later developments. Most introductions to the subject will refer to Frege and Tarski (Carnap less frequently) —in addition to the pioneers just mentioned, of course— , and discuss the main elements of their work that helped shape formal semantics in some detail. But Wittgenstein is conspicuously absent whenever the history of the subject is mentioned (usually briefly, if at all). Of course, if one thinks of Wittgenstein’s later work, this is obvious: nothing, it seems, could be more antithetic to what formal semantics aims for and to how it pursues those aims than the views on meaning and language that Wittgenstein expounds in, e.g., Philosophical Investigations, with its insistence on particularity and diversity, and its rejection of explanation and formal modelling. But what about his earlier work, the Tractatus (henceforth )? At first sight, that seems much more congenial, as it develops a conception of language and meaning that is both general and uniform, explanatory..

Almost forty years ago Richard Montague proposed to analyse natural language with the same tools as formal languages. In particular, he gave formal semantic analyses of several interesting fragments of English in terms of typed logic. This led to the development of Montague grammar as a particular style of formal analysis of natural language.

Formal semantics is an approach to SEMANTICS1, the study of meaning, with roots in logic, the philosophy of language, and linguistics, and since the 1980’s a core area of linguistic theory. Characteristics of formal semantics to be treated in this article include the following: Formal semanticists treat meaning as mind-independent (though abstract), contrasting with the view of meanings as concepts “in the head” (see I-LANGUAGE AND E-LANGUAGE and MEANING EXTERNALISM AND INTERNALISM); formal semanticists distinguish semantics from knowledge of semantics (Lewis 1975, Cresswell 1978), which has consequences for the notion of semantic COMPETENCE. A central part of the meaning of a sentence on this approach is its TRUTH CONDITIONS, and most although not all formal semantics is model-theoretic, relating linguistic expressions to model-theoretically constructed semantic values cast in terms of truth, REFERENCE, and possible worlds. This sets formal semantics apart from approaches which view semantics as relating a sentence just to a representation on another linguistic “level” (LOGICAL FORM) or a representation in an innate LANGUAGE OF THOUGHT. The formal semanticist could accept such representations as an aspect of semantics but would insist on asking what the model-theoretic semantic interpretation of the given representationlanguage is (Lewis 1970). Formal semantics is centrally concerned with COMPOSITIONALITY at the SYNTAX-SEMANTICS INTERFACE, how the meanings of larger constituents are built up from the meanings of their parts on the basis of their syntactic structure, and with the relation between compositional SENTENCE MEANING and meaning in discourse.

This paper aims to argue for two related statements: first, that formal semantics should not be conceived of as interpreting natural language expressions in a single model (a very large one representing the world as a whole, or something like that) but as interpreting them in many different models (formal counterparts, say, of little fragments of reality); second, that accepting such a conception of formal semantics yields a better comprehension of the relation between semantics and pragmatics and of the role to be played by formal semantics in the general enterprise of understanding meaning. For this purpose, three kinds of arguments are given: firstly, empirical arguments showing that the many models approach is the most straightforward and natural way of giving a formal counterpart to natural language sentences. Secondly, logical arguments proving the logical impossibility of a single universal model. And thirdly, theoretical arguments to the effect that such a conception of formal semantics fits in a natural and fruitful way with pragmatic theories and facts. In passing, this conception will be shown to cast some new light on the old problems raised by liar and sorites paradoxes.

One way of describing the enterprise of natural language semantics is by analogy with interpreted formal languages, e.g. the language of arithmetic interpreted on the natural numbers. English is then the formal language consisting of the well-formed sentences of English interpreted on the structure we happen to nd around us. The business of the natural language semanticist is to describe the correlation of the formal expressions with that structure. This paper is directed against this particular interpretation 1 of the enterprise of logical natural language semantics.

The relationships between logic and natural language are multiverse. On the one hand, logic is a theory of argumentation, proving and giving reasons, and such activities are primarily carried out in natural language. This means that logic is, in a certain loose sense, about natural language. On the other hand, logic has found it useful to develop its own linguistic means which sometimes in a sense compete with those of natural language. This has led to the situation where the systems of logic can be taken as interesting "models" of various aspects of natural language. Â Â Â Â Â Â Â The alliance of logic and linguistics has flowered especially from the beginning of the seventies, when scholars like Montague, Lewis, Cresswell, Partee and others showed how semantics of natural language can be explicated with the help certain suitable logical calculi and the corresponding model theory. (Montague went so far as to claim that in view of this, there is no principal difference between natural and formal languages - but this is, as far as I can see, rather misguiding.) Since that time, the interdisciplinary movement of formal semantics (associating not only linguists and logicians, but also philosophers, computer scientists, cognitive psychologists and others) has yielded a rich repertoire of formal theories of natural language, some of them (like Hintikka's game-theoretical semantics or the dynamic logic of Groenendijk and Stokhof) being based directly on logic, others (like the situation semantics of Barwise and Perry or DRT of Kamp) exploiting different formal strategies. Â Â Â Â Â Â Â Moreover, although the enterprise of formal semantics (i.e. of modeling natural language semantics by means of certain formal structures) seems to be the principal point of contact between linguistics and logic, there are also other cooperative enterprises. One of the most fruitful ones seems to be the logical analysis of syntax, which has resulted from elaboration of what was originally called categorial grammar. (However, even this enterprise can be seen as importantly stimulated by Montague.) Â Â Â Â Â Â Â All in all, the region in which logic and theoretical linguistics overlap has grown both in size and fertility..