MANFRED BIERWISCH The Semantics of Gradation 1 Introduction The term 'gradation' is meant to cover a range of phenomena which for the time being I shall call quantitative evaluations regarding dimensions or features. I shall actually be looking into the principles governing the way gradation is expressed in language. The quantitative aspect of the adjectives of dimension occupies a key position which can be systematically explained and this aspect will be the crucial point of the discussion. I shall focus on the various grammatical forms of comparison: comparative, equative, superlative and some related constructions, and indications of measurement and adverbial indications of degree. A substantial number of the relevant facts have been researched in a series of analyses and theoretical proposals on the semantics of comparison." There are two main reasons why the present essay, while building on the insights gained 50 far, attempts to formulate a new theory concerning the same facts. Firstly, there remain many relevant and revealing facts that have not been taken into account in previous analyses and could in fact not be incorporated without radical changes.' " Secondly, while the facts dealt with so far have been systematically analysed and explicitly described, they have not been traced back to the general conditions and principles underlying the interactions of the phenomena observed; A fresh approach also seems called for if we are to bring together system­ atically the explanations and insights provided by existing analyses, because of their sometimes widely differing orientation regarding (a) the way they treat the central facts, (b) their aims in doing 50 and (c) the methods they use. Regarding the first point, the theory I propose extends the domain of 'relevant and revealing facts' in an attempt to achieve greater descriptive adequacy. How­ ever, it is important that this aim is not achieved only by enriching descriptive statements and generalizations but - and this is where the second point comes in - by tracing the facts back to underlying principles, thus attempting to achieve greater explanatory adequacy. Important ideas and findings are taken over from existing analyses and theories; they are modified, mostly slightly, and extended. But the total picture that emerges is a radically different one, regarding both the semantic structure of the elements and constructions concerned and, more Manfred Bierwiech & Ewald Lang (Eds.): Dimensional Adjectives: Grammatical Structure and Conceptual Interpretation. © Springer-Verlag Berlin Heidelberg 1989 72 Manfred Bierwisch The Semantics of Gradation 73 importantly, the overall theory in which the assumptions underlying them are the present theory of gradation can be related to other syntactic theories. The placed. framework I shall use for the semantics of gradation can be summarized thus: The picture which emerges results from an attempt to bring together,and (1) (PF ... LF SF) =- (es ...) generalize upon, the various relatively independent but interacting mechanisms • v ' --....-... which underly the phenomena of gradation. Although this was not part of the G C original intention, one point of view which has been crucial to developments in the The phonetic form PF is related to the logical form LF by a well defined sys­ theory of syntax over the past ten years has had a particularly important bearing tem of intermediate representations, and regarding this relation I shall take for on the elaboration of the present theory: the discovery of general conditions granted the notions and concepts developed in GB. Let me make some prepara­ and principles which allow us to disentangle special properties of particular rules tory remarks though on the nature of the semantic form SF and its relation to LF. and of structures, in order to arrive at generalizations in the way most forcefully The whole representational system ranging from PF to SF is determined by the demonstrated by CHOMSKY (1981 and later works). In particnlar it will be shown elements, rules and principles subsumed under the grammar G, which contains that, while the comparative and constructions related to it playa crucial part the lexical system 1S as a component. The symbol '===}' stands for the map­ in the range of facts relevant to gradation, their characteristic features follow ping of linguistic structures onto conceptual representations, in other words the largely from more general principles whose domain covers more than the syntax interpretation of SF on the level of conceptual structures es. This mapping, and of comparison.? Hence the title 'The semantics of gradation'. the structure of es, on which only fragmentary ideas are available in comparison By the very nature of things I cannot pursue all the relationships into which to the levels of linguistic structures, will be the subject of some explanatory re. the systems involved in gradation enter. Nor can I elaborate systematically upon marks in Section 4. These will be restricted to the subject of gradation. Generally all the components which are involved in the facts I shall be dealing with. For speaking, es is determined by elements, rules and principles of the conceptual example, I shall confine myself to just a few remarks here and there on the role knowledge subsumed under C. SF, by way of technical metaphor, can be re­ of sentence stress, although the general principles for the semantic interpretation garded as the interface between linguistic and conceptual knowledge, just as PF of sentence stress playa central role in comparison. Similarly, little attention is the interface between linguistic patterns on the one hand and articulatory and can be given to the interrelation between comparison and quantifiers. But in the perceptual patterns on the other.. course of developing and explaining the theoretical framework I shall indicate as Concerning the structure of SF·] shall take for granted the basic concepts I far as possible how these problems might usefully be pursued further. have developed elsewhere (e.g. BIERWISCH (1982, 1983, 1986); d. also ZIMMER­ The theory proposed here, as I said above, has resulted partly from sifting MANN (this volume)), confining myself here to a few stipulations which I shall through the facts previously left aside and partly from following up, modifying add in the course of the analysis. and rejecting ideas put forward in the various existing analyses of the syntax and The format of the representation of SF is fixed by a categoriallanguage which semantics of comparison. In the present framework I shall refer to these analyses contains constants and variables as basic units. The units and the complex ex­ only where this serves to clarify and explain the issues taken up. pressions formed from these are categorized. There are two basic categories: S, The form in which the theory is presented here has come about via a number which contains expressions that representations of states-of-affairs are assigned to of steps and not without modifications on the way.3 While I believe that the in es; and N, which contains expressions identifying referential instances ('things' main threads which emerge lead in the right general direction, there is no doubt in a sufficiently abstract sense) in es. S andN are used to form complex cate­ that there will have to be more additions and modifications regarding both the gories: SjN for one-place predicates, (SjN)N for two-place predicates, etc. The questions left open here and the theoretical framework as a whole. categorization of the basic units at the same time determines the combinatorial structure of SF: a predicate of the category SiN together with an expression' of the category N forms an expression of the category S etc. The details of this 2 Technical Preliminaries combinatory mechanism will become clear as we proceed. 2.1 The Nature of SF Of the constants in SF we are primarily interested in those connected with gradation. They will be introduced systematically below. For purposes of il­ The theory must be based on a certain framework of conditions within which the lustration I shall also invoke provisional units whose status is a non-committal various interrelated systems and the principles on which they are organized have one: constants like TABLE or HANS, appropriately categorized, will stand for SF their own place. structures not analysed further here. The theory of syntax which forms the background of the analysis is the Gov­ Besides the specific constants relevant to gradation,'SF will contain the usual ernment and Binding Theory (GB) of generative grammar as developed in CHOM­ connectors /\, V, - and "', for which the standard logical axioms and definitions SKY (1981) and in subsequent work. I shall not take up the question of how far are valid. SF also contains the two quantifiers 'r;f and 3, which together with a Manfred Bierwisch 74 The Semantics of Gradation 75 variable of any category form a functor expression of the category SIS. The way i[P x] means: 'x with the property P' or,more simply, 'the property P of a". the two quantifiers are used differs somewhat from the standard interpretation. That is why the so-called lambda conversion defined in (4b) holds. They are to be understood thus: The five operators specified in (2) to (4) bind all instances of their respective (2)( a) :3x is interpreted in CS by the nearest instance which satisfies the category variable which occur (freely) in their scope. The scope is their operand, i.e. the expression with which they form the next higher complex expression. Operators of e. can be interlocking, i.e. one operator can occur within the scope of another. (b) \Ix is interpreted in CS by any instance in a given domain which satisfies The effect of the general stipulations I have made will become clear through the category of e. the use I shall be making of them.