Pragmatics in natural logic

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Abstract
I would like to discuss two aspects of pragmatics that in recent years have been treated very differently: indexicals and conversational implicatures. Montague and Scott proposed to handle indexicals by adding to points of reference (sometimes called ‘indices’) extra coordinates for speaker, hearer, time and place of utterance. This proposal places indexicals among those phenomena to be dealt with by formal logic, and such systems have in recent years been articulated by Lewis and Kamp, among others. Implicatures on the other hand, were taken by Grice to be by nature informal inferences of a fundamentally different kind than logical inferences, and hence not to be dealt with by the apparatus of formal logic. In other papers I have dropped hints to the effect that indexicals and implicatures should be treated somewhat differently than they are in the Montague-Scott and Grice proposals. I would like to elaborate a bit on those hints. The basic suggestion is this: (I) If the goals of what I have called natural logic are adopted, then it should in time be possible to handle indexicals without any extra coordinates for speaker, hearer, and time and place of utterance, and it should also be possible to handle implicatures without any kinds of extralogical inference. The basic ingredients of the suggestion are as follows: (A) The so-called performative analysis for imperatives, questions, statements, promises, etc. (B) The limitation of points of reference to assignment coordinates for variables and atomic predicates. […]

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