%0 Journal Article
%T Superlative Quantifiers as Modifiers of Meta-Speech Acts
%A Ariel Cohen
%A Manfred Krifka
%J The Baltic International Yearbook of Cognition, Logic and Communication
%D 2010
%I New Prairie Press
%R 10.4148/biyclc.v6i0.1578
%X The superlative quantifiers, at least and  at most, are commonly assumed  to have the same truth-conditions as the comparative quantifiers  more than and  fewer than. However, as Geurts & Nouwen (2007)  have demonstrated, this is wrong, and several theories have been proposed to account for them. In this paper we propose that superlative quantifiers are illocutionary operators; specifically, they modify meta-speech acts. Meta speech-acts are operators that do not express a speech act, but a willingness to make or refrain from making a certain speech  act. The classic example is speech act denegation, e.g. I don't promise to come, where the speaker is explicitly refraining from performing the speech act of promising What denegations do is to delimit the future development of conversation, that is, they delimit future admissible speech acts. Hence we call them meta-speech acts. They are not moves in a game, but rather commitments to behave in certain ways in the future. We formalize the notion of meta speech acts as commitment development spaces, which are rooted graphs: The root of the graph describes the commitment development up to the current point in conversation; the continuations from the  root describe the admissible future directions. We define and formalize the meta-speech act GRANT, which indicates that the speaker, while not necessarily subscribing to a proposition, refrains from asserting its negation. We propose that superlative quantifiers are quantifiers over GRANTs. Thus, Mary petted at least three rabbits means that the minimal number n such that the speaker GRANTs that Mary petted  n rabbits is n = 3. In other words, the speaker denies that Mary petted two, one, or no rabbits, but GRANTs that she petted more. We formalize this interpretation of superlative quantifiers in terms of commitment development spaces, and show how the truth conditions that are derived from it are partly entailed and partly conversationally implicated. We demonstrates how the theory accounts for a wide variety of phenomena regarding the interpretation of superlative quantifiers, their distribution, and the contexts in which they can be embedded. References Bolinger, D. 1978. ¡®Yes-No Questions are not Alternative Questions¡¯. In H. Hiz (ed.) ¡®Questions¡¯, Dordrecht: Reidel. Borkin, A. 1971. ¡®Polarity Items in Questions¡¯. In ¡®Papers from the 7th Regional Meeting of the Chicago Linguistic Society¡¯, 53¨C62. Bott, L. & Noveck, I. A. 2004. ¡®Some Utterances are Underinformative: The Onset and Time Course of Scalar Inferences¡¯. Journal of Memory and Language 51, no. 3: 437¨C
%U http://dx.doi.org/10.4148/biyclc.v6i0.1578