Semantics in generative grammar, A Kratzer, I Heim

Tags: indirect evidence, indirect access, truth conditions, independent clauses, verb, red rubber ball, Donald Davidson, lexical items, compositional aspects, introductory book, verbs, denotation
Content: 1 Semantics in Generative Grammar Angelika Kratzer September 14, 2007 1. The denotation of verbs: Stripping off inflectional elements. What's left? In many languages, verbs are inflected. In all languages, verbs bring along at least some inflectional heads, lexical items bearing inflectional meanings: e.g. agreement, voice, aspect, tense, negation, mood, question markers, and evidentials. Whether inflectional heads are literally attached to a verb or not is an issue that is of interest for morphology or phonology, but it is not likely to be relevant at all for syntax or semantics. In semantics, we are interested in the compositional aspects of meaning. The inflectional items we care about, then, are those that make a compositional meaning contribution. In our introductory book, Irene and I only talk about the meanings of bare verbs. We neglect all contributions of inflectional items. In LING 620, you will look at the semantics of at least tense and mood, and possibly also at the semantics of aspect and questions. The guiding idea about verb denotations we fleshed out in our book is one that we inherited from logic: the meaning of a (bare, inflectionless) intransitive verb like dance determines who the actual dancers are. The denotation of dance, then, is the set of individuals who dance. Adapting this kind of denotation to the demands of Frege's Conjecture, we construed the denotation of dance as the characteristic function of the set of individuals who dance. But wait. Who are the individuals who dance? Those who are dancing right now? Those who have just finished dancing? Those who have danced in the past? Those who dance habitually? The professional dancers? Or those who are able to dance? It's much easier to swallow that the common noun goat might pick out the set of actual goats, or that the adjective plastic might pick out the set of actual things that are plastic. But how can anybody who wants to be taken seriously tell us that dance picks out the set of actual dancers, and leave it at that? How come verbs do, but nouns and adjectives do not bring along inflectional heads related to aspect, tense, and mood? Wouldn't we expect there to be
2 something about the meaning of verbs that could explain that crucial difference? Shouldn't verb meanings be different in kind from the meanings of common nouns and adjectives?
2. Bringing in events
Davidson In his famous paper "The Logical Form of Action Sentences", Donald Davidson has argued that verbs have an additional argument, the event argument. The evidence he gave came from adverbial modification.
(1) Jones buttered the toast in the bathroom with a knife at midnight.
(2) a. b. c. d. e. f. g.
Jones buttered the toast. Jones buttered the toast in the bathrooM. Jones buttered the toast with a knife. Jones buttered the toast at midnight. Jones buttered the toast in the bathroom with a knife. Jones buttered the toast in the bathroom at midnight. Jones buttered the toast with a knife at midnight.
How can we account for the fact that (1) logically implies each of 2(a) to (g)? Davidson's answer is that (1) is interpreted as stating that there was an event satisfying a conjunction of event descriptions:
(3) There was a past event e, e was a buttering of the toast by Jones, e was in the bathroom, e was with a knife, and e took place at midnight.
If (3) is the way (1) is interpreted, the inference from (1) to 2(a) to (g) is licensed by the same logical principles as the inference from 4(b) to 5(a) to (g):
(4) a. b.
What was there in his pocket? There was a tiny red rubber ball.
(5) a. b. c. d. e. f. g.
There was a ball. There was a tiny ball. There was a red ball. There was a rubber ball. There was a tiny red ball. There was a tiny rubber ball. There was a red rubber ball.
"In general, what kind of predicates do have event-places? Without pursuing the question very far, I think it is evident that if action predicates do, many predicates that have little relation to action do. Indeed the problems we have been mainly concerned with are not at all unique to talk of actions: they are common to talk of events of any kind. An action of flying to the Morning Star is identical with an action of flying to the Evening Star; but equally, an eclipse of the Morning Star is an eclipse of the Evening Star. Our ordinary talk of events, of causes and effects, requires constant use of the idea of different descriptions of the same event." (Davidson, op. cit., quoted from Ludlow (ed.), p. 230).
Adjusting verb meanings In a Davidsonian event semantics the denotations of verbs characterize events in addition to telling us something about who the participants in those events are. The verbs dance and cross, for example, characterize dancing and crossing events respectively. In a Davidsonian event semantics, the verb dance doesn't denote a set of individuals any longer (using set talk), but a relation between individuals and events. The relation holds between an individual a and an event e just in case e is an event of dancing by a. The verb cross denotes a three-place relation that holds between two individuals a and b and an event e just in case e is an event of a's crossing b. Here is how we would flesh out this idea formally:
In addition to the basic domains De and Dt, we have a domain Ds, the domain of (actual) events. We adjust Definition 5 on p. 28 of Heim & Kratzer accordingly:
4 Semantic Types (a) e, t, and s are semantic types. (b) If and are semantic types, then <> is a semantic type. (c) Nothing else is a semantic type. Semantic denotation domains (a) De = D = the set of individuals. (b) Dt = {0,1} = the set of truth-values. (c) Ds = the set of events. (d) For any semantic types and , D<,> is the set of all functions from D to D. Examples of lexical meaning assignments: [[dance]] D>. For all a D and e Ds, [[dance]](a)(e) = 1 iff e is an event of dancing by a. [[cross]] D>>. For all a and b D and e Ds, [[cross]](b)(a)(e) = 1 iff e is an event of crossing b by a. Consequence Small clauses like Mary dance or Mary cross Main Street might now be taken to denote (the characteristic functions of) sets of events. (1) I saw Mary dance. (2) I saw Mary cross Main Street. (3) We made Mary dance. (4) We made Mary cross Main Street. Next question Shouldn't Mary cross Main Street pick out the set of completed events of Mary crossing Main Street? If I saw Mary cross Main Street, it follows that she crossed Main Street. I couldn't have seen her cross Main Street if she started crossing Main Street, for example, but never
5 made it to the other side because she was hit by a truck. This might mean that cross should have the following denotation: For all a and b D and e Ds, [[cross]](b)(a)(e) = 1 iff e is a completed event of a crossing b. There is another possibility that we might have to face, however. The cross we see in I saw Mary cross Main Street might not be the bare (inflectionless) verb cross that we are looking for. There might still be some `invisible' piece of inflection lurking in the vicinity. How can we ever find out the meaning of a bare verb, then? How can we ever find out what verbs mean all by themselves? How can we ever abstract away from all contributions of pieces of inflection? 3. The question of inDirect Access to verb meanings "..... in analyzing the meaning of temporal and aspectual features, we make assumptions about the truth conditions of uninflected clauses like `Carnap fly to the moon', `Terry build a house' and `Terry be at home'. However, we have only indirect evidence of how these sentences are interpreted by native speakers, since they do not occur as independent clauses in English. I'll refer to the problem of determining the truth conditions of the base sentences that are the input to tense and aspect markers as the problem of indirect access in the semantics of tense and aspect. Making hypotheses based on indirect evidence is common practice in the Natural Sciences and I have no intention of arguing that the task of providing a truth-conditional analysis of temporal and aspectual features is hopeless or misconceived because of the problem of indirect access. I'm interested instead in the relevance of this problem for the analysis of the progressive. I'll argue that the choice between different approaches to the semantics of the progressive that are currently available in the literature involves choosing between different analyses of the meaning of base predicates: to decide which approach to the semantics of the progressive is empirically more adequate, we have to find evidence, even if indirect, that allows us to establish what event types these predicates denote." Sandro Zucchi: Incomplete Events, Intensionality and Imperfective Aspect. natural language Semantics 7, 1999, p. 179-215. Quote from p. 180.

A Kratzer, I Heim

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