Toward a new taxonomy for pragmatic inference: Q-based & R-based implicature Laurence R. Horn (1984)

“Force of Unification” or “Speaker’s Economy” George Kingsley Zipf and the Principle of Least Effort (and the Principle of Sufficient Effort) “Force of Unification” or “Speaker’s Economy” “Force of Diversification” or “Auditor’s Economy” The two forces are “in extreme conflict”

Speaker’s Economy Zipf’s speaker’s economy is a direct least effort correlate, a drive toward simplification which, operating unchecked, would result in the evolution of exactly one totally unmarked infinitely ambiguous vocable (presumably uhhh; cf. Beavis and Butthead)

Auditor’s Economy Auditor’s Economy, or “The Force of Diversification” is an anti-ambiguity principle leading toward the establishment of as many different expressions as there are messages to communicate. The hearer’s economy will tend toward “a vocabulary of m different words with one distinct meaning for each word”

The kicker The thing is, as Zipf (1949:21) puts it, “The two opposing economies are in extreme conflict”

Martinet (1962) - these sort of antinomies drive language change “In order to understand how and why a language changes, the linguist must keep in mind two ever-present and antinomic factors: first, the requirements of communication, the need for the speaker to convey his message, and second, the principle of least effort, which makes him restrict his output of energy, both mental and physical, to the minimum compatible with achieving his ends”

What Horn is up to Horn seeks to “demonstrate that these same two antinomic forces - and the interaction between them - are largely responsible for generating Grice’s conversational maxims and the schema for pragmatic inference derived therefrom.

Grice’s Maxims of Conversation Quantity 1. Make your contribution as informative as is required (for the current purposes of the exchange). 2. Do not make your contribution more informative than is required. Quality Super Maxim - Try to make your contribution one that is true. 1. Do not say what you believe to be false. 2. Do not say that for which you lack adequate evidence. Relation 1. Be relevant. Manner Super Maxim - Be perspicuous [L. persicuus “transparent”] 1. Avoid obscurity of expression. 2. Avoid ambiguity. 3. Be brief. 4. Be orderly.

Horn’s reduction of Grice The Q Principle (hearer-based): Make you contribution sufficient (cf. Quantity1) & Say as much as you can (given R). The R Principle (speaker-based): Make your contribution necessary (cf. Relation, Quantity2, Manner) and Say no more than you must (given Q)

Notions from information structure The Q-Principle is a lower-bounding principle, inducing upper-bounding implicata. The R-Principle is an upper-bounding principle, inducing lower-bounding implicata.

What this means (I think) “Lower-bounding” - this seems to be the “at least (or given quantifier) if not all “ reading. “Upper-bounding” - this is the “at most [quantifier]” reading.

What “bounding” looks like in terms of the Q-principle In regard to Q-based scalar implicature, the following sentences (next slide) assert (or entail) a lower bound and they implicate an upper bound. The assertion + implicate combination yields the “two-sided” reading. (So I do not show the implication in the following diagrams):

1-sided (entailment): “at least 3” He ate three carrots Q-implic ?: “at most 3” 2-sided (combo): “exactly 3”

1-sided (entailment): “some if not all” You ate some of the cookies Q-implic ?: “at most some” 2-sided (combo): “some but not all”

1-sided (entailment): “possible if not certain” It’s possible she’ll win. Q-implic ?: “at most possible” 2-sided (combo): “possible but not certain”

1-sided (entailment): “[inclusive or]” Maggie is patriotic or quixotic Q-implic ?: “at most one of them(?)” 2-sided (combo): “[exclusive or]”

1-sided (entailment): “happy if not ecstatic” I’m happy. Q-implic ?: “at most happy” 2-sided (combo): “happy but not ecstatic”