Scalar implicatures are a special variety of quantity implicatures. Not only are they popular in the conversational pragmatics and philosophy of language literature, but crucially, they entertain deductive and abductive reasoning patterns in a distinctively computational way. This rigor is indeed no surprise, as symmetries are quite part of how human mind functions; yet, languages also display a vastness of asymmetries. In the case of scalar implicatures, asymmetries seem to be higher in the presence of a negation. That is, scales change in property but do not necessarily behave in a precisely predictable way when negated, as one might anticipate. The main point of this essay is to shed light on this cross-borders phenomenon, in a way to expand on our in-class discussions, from its conceptual positionality to its specificities.

As a pragmatic truth, it is not the speaker’s intent but the intent’s interpretation by the hearer that conversation substantially runs on. Together with the utterances themselves, that interpretation is more or less the product of mutual beliefs and plan deductions (Green, 1996). These conversational dynamics, unconscious but conventional, realize upon the Cooperative Principle, by which we assume the interlocutor to be expressly goal-directed (Grice, 1975). As the four maxims state, it follows that the agents act perspicuously and efficiently (Manner), say what they believe to be true and evident (Quality), speak relevantly and relatively to the intention (Relation), and do strictly as much as is necessary (Quantity). When a maxim is seemingly violated, the agent infers the interlocutor’s true message — that is, the implicature — by conducting some additional reasoning through the context of the conversation in order to link the peculiar utterance to the Cooperative Principle.

The reasoning behind implicatures goes across two logical paths: deduction and abduction (Peirce, 1931), respectively. On the one hand, the deductive process is a forward, sentential assessment that infers daughter premises (that is, entailments) from a parent premise. Consider (1) “Martha used to live in Argentina” and (2) “Martha doesn’t currently live in Argentina.” Given the grammatical and lexical connotations that describe (1), we infer (2). On the other hand, the abductive process is a backward, contextual assessment that rather than inferring daughter premises, generates parent premises from which the one under inspection could possibly follow and selects the most likely (Geurts, 2010). To illustrate abductive reasoning, let us imagine that I go to my kitchen and find the plate where I had laid my chocolate bars empty. I infer that someone (probably either of my parents) ate them, but if this had happened in a different context, for instance, in my grandmother’s kitchen, I might think she put them in the refrigerator. Now, let us assume that (1) was given as an answer to (3) “Where does Martha live?” Since (1) entails (2), (1) seems to violate the Relation Maxim — it isn’t relevant to the question which is on where Martha lives currently. One of the possible reasons, the best to my understanding, is that the utterer of (1) doesn’t know where Martha currently lives; therefore, it follows that the implicature is “I don’t know.” Overall, deductions follow precise instructions stipulating axioms (improvable suppositions that render more complex premises provable) and inference rules (Goldfarb, 2003) whereas abductions are far more flexible as they simply depend on the experiences of the interlocutor and on the context, which is to say that there is no single, absolute method of assessing implicatures.

The author of one of my readings, Geurts, proposes a specific demonstration they call the “Standard Recipe” for the analysis of quantity implicatures, which we now narrow our focus to. The demonstration goes as the following: (i) Why didn’t the agent make a stronger (more informative) statement X’ rather than the weaker X? (ii) The agent most likely doesn’t believe X’ to be true. (iii) In addition to ¬BELIEVEagent(X’), it’s most likely that either BELIEVEagent(X’) or BELIEVEagent(¬X’). (iv) Therefore, BELIEVEagent(¬X’). Now let us consider the following dialogue: (4) “Does Martha live in Buenos Aires?” (5) “She lives in Argentina.” Why didn’t the answerer say (5′) “She lives in Buenos Aires” (“Yes”) rather than (5) which is weaker? They most probably don’t believe (5′) to be true. Still, it is also probable that they believe either that (5′) is true or that it is false. Therefore, the implication is that Martha doesn’t live in Buenos Aires. Importantly, the Standard Recipe doesn’t apply to any quantity implicature, the ones where too much information is given for instance, but it achieves to explain non-negated scalar implicatures entirely.

In the widest sense, scales are sets of grading values or gradable items; though, not all scales correspond to scalar implicatures. The most popular and logically approachable among them are Horn (1972) Scales, which have some criteria on their content. The elements of a Horn Scale are ordered from the weakest to the strongest, where the stronger entails the weaker elements. In <nice, sympathetic, charming>, “sympathetic” entails “nice” and “charming” entails “sympathetic” (and thus “nice”) but not vice versa. In the light of the Standard Recipe, it follows that weaker values implicate (but don’t entail) the negation of the stronger values. “She is nice” implicates “she is not sympathetic” (and thus “she is not charming”). These entailment and implication chains are not interchangeable; that is, “charming” may not implicate “sympathetic” or “nice” since this is an entailment relation, and “nice” may not entail “sympathetic” or “charming.” Crucially, a Horn Scale involves elements with the same negation state and same connotations; that is, *<not nice, nice, sympathetic, charming> isn’t possible, nor is *<nice, sympathetic, talented, charming>. An error that may rise therefrom is to include opposites in the same scale, as in *<tedious, bad, nice, sympathetic, charming>. This array may give rise to quantity implicatures but not scalar implicatures. “He is not bad” implicating “He is not charming (either)” may be a quantity implicature by principle, the latter being relatively weaker than the former, but it isn’t a scalar implicature. As an aside, “non-entailment” scales like <dating, engagement, marriage> also do give rise to scalar implicatures (Hirschberg 1985), but they are rare in the literature and have lower applicability since the relationships between their elements are subject to substantial variation from culture to culture. Interestingly, scalar implicatures have a distinctive precision in computing alternatives. For “He is sympathetic” with <nice, sympathetic, charming>, we immediately intuit the other options (“He is nice” and “He is charming”) and eliminate the unlikely “He is nice” since it wouldn’t be an implicature (but an entailment). However, the way negated scalar implicatures behave isn’t ¬WEAK⎟→ ¬(¬STRONG) as one might intuit, since the negation of the weaker in fact cancels the stronger.

When a scale is negated, the strength of the values and the direction of entailment get inverted. Consider <some, many, all>, the negative correspondents are *<none, not many, not all>: “None” is stronger than “not many (few)” and “not many” is stronger than “not all” (whereas this was the opposite case with the non-negative counterparts), and “none” entails “not many” and so on — though, by convention, this scale would be modified as <not all, not many, none>. As for negated scalar implicatures, it turns out that they still behave such that WEAK⎟→ ¬STRONG, as in the following example: (A and B go out of the house in a relatively mild winter day) (A) “It’s not cold.” As speakers of English who therefore presuppose the connotations of “not cold,” we compute the alternatives and obtain the Horn Scale: <not freezing, not cold, not chilly>. “Not cold” is weaker than “not chilly,” so it follows that the implicature is “not not chilly,” which is to say “(simply) chilly.” Now let us imagine that A and B had left the house in an extremely cold winter day and that A made the statement “It’s not cold.” Do they implicate that the weather is chilly (“not not chilly”)? The implication here seems to be rather “It’s freezing” or potentially “It’s freezing!” This is named as the meta-linguistic negation: The negation here does not modify the value “cold,” it points out that the signifier “cold” isn’t the most informative way of describing the current reality (which “freezing” is). Although it may be true that they feel the same weather, their qualifications can vary; that is, for the one it may be “freezing” while for the other, simply “chilly.” Moreover, one wouldn’t necessarily use intonation (“!”) as an additional indicator — the ways intonation patterns are shaped vary anyway from language to language. In fact, though one scenario might look more or less likely, there is no precise algorithm that predicts whether a negated scalar implicature follows the WEAK⎟→ ¬STRONG or not. Therefore, the implication, in both cases, might be either of “It’s chilly” and “It’s freezing.”

If the effect of the negation were “symmetrical,” we would be able to “compute” the output of any negated scalar implicature, just like holding an object against a mirror to obtain its reflection; however, that’s not the case as we have seen. A further investigation might be on whether negations have a symmetry-breaking effect on not only scalar implicatures, but also on other phenomena within and beyond implicatures, and if yes, on whether negation asymmetry is a cross-linguistic phenomenon. At the end, the non-geometrical behavior of the negation, the “asymmetry,” turns out to be a way language multiplies the many subtle ways it conveys information.

References

• • Geurts, Bart (2010). Scalar Implicatures. In Quantity Implicatures (pp. 49-66). Cambridge: Cambridge University Press. doi:10.1017/CBO9780511975158.005
• Goldfarb, Warren (2003). Deductive Logic. Indianapolis: Hackett Publishing Company, Inc.
• Green, Georgia M. (1996). Pragmatics and Natural Language Understanding. Psychology Press. • Lee, Chungmin (2008). Scalar Implicatures: Pragmatic Inferences or Grammar? In 22nd Pacific Asia Conference on Language, Information and Computation, (pp. 30-45).
• Matsumoto, Yo (1995). The Conversational Condition on Horn Scales. Linguistics and Philosophy 18, no. 1 (pp. 21-60). http://www.jstor.org/stable/25001577.

December 2020, Istanbul