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Lectures on Interpreted Languages and Compositionality Lectures on Interpreted Languages and Compositionality Marcus Kracht Fakult¨atLiLi Universit¨atBielefeld Postfach 10 01 31 33501 Bielefeld [email protected] June 1, 2010 Introduction This manuscript presents an outline of something which I like to call metatheory of linguistics. It is not the attempt to replace any existing framework by a new one; it is rather the attempt to provide some result that show us the interconnection between certain requirements on theories. The word “metatheory” emphasises that we do not try to establish a new framework or discover concrete properties of languages but that we want to find methods of establishing the properties that a given language has. The aim is to find out in what way our initial assumptions about the structure of language or linguistic theory can actually yield an insight into languages and what this insight consists in. We shall isolate a few principles and investigate their empirical potential in this way. One such principle is the Principle of Compositionality. It will emerge, for example, that the Principle of Compositionality has no empirical impact whatsoever unless we fix the input to be signs consisting of form and meaning; additionally, when defining form and meaning for natural languages we must make sure that there are restrictions on syntactic and semantic representations and functions. If this is guaranteed, however, we shall show that there can be concrete results about the structure of natural languages. This book owes much to [Keenan and Stabler, 2001]. However, here the em- phasis is quite different. Rather than assuming a particular grammar for a language at the outset, it is our aim to establish to what extent a language determines the grammar that generates it. In contrast to a lot of work in linguistics we do not take syntax as the exclusive source of evidence for structure, but both syntax and semantics together. Certainly, structural properties determine in which way ex- pressions can be formed, but it has often been assumed in the linguistic literature that this is effectively all there is to be said about structure. This prejudice is the rather unfortunate heritage of a view promoted mainly—but not exclusively— within generative grammar. That linguistics is neither just about form (syntax) nor just about content (semantics) has been emphasised also by [Manaster-Ramer and Michalove, 2001] in the context of historical linguistics. A reconstruction solely based on either sound or meaning is useless. It must obviously involve both. Although the style of the book is ostensively neutral, the motivation for this research is the belief that ultimately the Principle of Compositionality is correct. However the methodology is not to try and verify it (this is impossible) but to see what consequences there are to the belief that it is true. For it turns out to be 4 Introduction possible to show that there are noncompositional languages. This means that it is an empirical question whether natural languages are compositional. It should be clear though that no definitive answer can be given for any natural language. The reason for this is a—in my view unavoidable—peculiarity of the whole theory; namely that for a finite language no grammar is needed. A simple enumeration of all items is enough. Hence, we can only fruitfully apply the theory to infinite lan- guages. Thus, when we apply the present theory to a particular language we have to make assumptions about its global nature; and these assumptions are always tentative. One of the biggest problem areas that I have identified in the course of study- ing compositionality is the nature of semantics. While the prevailing attitude used to be that meanings are hopelessly unclear, many semanticists nowadays feel that there is not much to discuss either: meanings are objects of the typed universe. Both groups will feel that the present book got it wrong; the first because I include semantics as primitive data, the second because I reject most semantic approaches to compositionality on the grounds that their semantics encodes semantically con- tingent syntactic structure. My response to the first group is this: if it is possible that humans understand each other, and if we do agree that there is such a thing as meaning, which can be preserved—among other—in translation, we must con- clude that something of substance can be said about meanings, both concrete and abstract. The response to the second group is more complex. On the one hand, Montague Grammar has enjoyed a success, and it popularised the notion of com- positionality. Nevertheless, I feel that there is a sort of complacency in most research conducted within type logical grammar as a whole. Most questions of actual meaning are not really solved, they are only relegated (for example to lexi- cology). Instead, much formal semantics is just offering technology without much proof that this is what we really wanted. It is much like saying that technologi- cal advances have made it possible for man to fly. That is only half true because originally the dream was to fly like a bird. It will take large parts of this book (especially Chapter 4) to work out exactly what is at fault with type theoretical semantics for natural language. The Principle of Compositionality can be seen as an abstract requirement on the grammar of a language (and therefore, albeit indirectly, on the language it- self). The rationale for adopting it, however, comes from an assumption on the architecture of language that is not universally shared. A particularly blatant case of this sort is generative grammar, where interpretation is done after the structure Introduction 5 building has taken place. It will be seen, though, that even if we grant this as- sumption, there is still so much to take care of that it becomes unclear just why a level such as LF is at all needed and how it can help us. In addition, it turns out that many more frameworks or theories are not compositional. This may be surprising since linguists commonly judge theories on the basis of whether they are compositional or not. Thus, if we value compositionality so highly we ought to know what exactly makes a theory compositional. This is what this book is about. Part of my claims may be contentious. For example, I claim below that indices are not part of a syntactic representation. This militates against a num- ber of well-established theories, among them generative grammar and Montague Grammar (!). It may therefore be thought that this diminishes the usefulness of the present approach. On the other hand, it is not my task to agree with a the- ory simply because it is popular. What is at stake is rather the very foundation on which the current theories are built. And in this respect it seems to me that linguistic theory on the whole suffers from a lack of understanding of how solid the ground is on which it rests. The actual syntactic structure, for example, has become highly theory internal in generative grammar. The independent evidence of Kayne’s Antisymmetry Thesis, for example, was originally quite thin. And it is simply not true that it has been proved to be correct thereafter. Rather, the factual approach has been to adopt it and explore its consequences (just as I adopt here the Principle of Compositionality and explore its consequences). It is therefore not surprising that a careful review of the syntactic structure of German (within the generative framework) undertaken in [Sternefeld, 2006] has yielded a far less articulated structure than standardly assumed. This book has basically two parts. The first consists in the Chapters 2 and 3, the second in Chapters 4 and 5. The first part develops a mathematical theory of interpreted languages; Chapter 2 provides the background of string languages, using grammars that generate the languages from the lexicon, known from Mon- tague Grammar. Chapter 3 then turns to interpreted languages. In the second part, starting with Chapter 4 we zoom in on natural languages. We ask what the meanings of natural language constituents are and how they can be manipulated. Then, in Chapter 5 we apply the theory. We shall show that the notion of a con- cept defined in Chapter 4 changes the outlook on predicate logic: finite variable fragments are compositional, while with infinite variables the languages have no compositional context free grammar. Then we show how we can argue for struc- ture from a purely semantic point of view. 6 Introduction The current text is a development of ideas found in [Kracht, 2003]. Since then I have spent considerable energy in getting a clearer idea on the central notion of this book, namely compositionality. In the meantime, new articles and books have appeared (for example [Barker and Jacobson, 2007]) showing that the topic is still a lively issue. I have had the benefit of extended discussions with Damir Cavar,´ Lawrence Cheung, Herbert Enderton, Kit Fine, Hans-Martin Gartner,¨ Ben George, Fritz Hamm, Laszl´ o´ Kalm´ an,´ Ed Keenan, Ben Keil, Istvan´ Kenesei, Udo Klein, Greg Kobele, Andras´ Kornai, Uwe Monnich,¨ Yannis Moschovakis, Chris Pinon,˜ Nathaniel Porter, Richard Schroder¨ and Ed Stabler. Special thanks also to Istvan´ Kenesei for his support and to Damir for organising the summer school in Zadar, which got me started on this manuscript. All of them have influenced my views on the subject in numerous ways. The responsibility for any occurring errors in this text remains entirely with me. A Note on Notation. This text contains lots of examples and occasional “inter- missions”. The end of an example or an intermission is marked by o.
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