Hyperbolic readings in embedded environments - Inference Task
Creators: name: Sossidi, Eirini
name: Spector, Benjamin
Publisher: name: OSF Registries
Year: 2024
Subjects: subject: Linguistics
subject: FOS: Languages and literature
subject: Semantics and Pragmatics
subject: Social and Behavioral Sciences

description: Background, motivation and hypotheses

A number of works within the RSA model and related frameworks have focused on non-literal readings such as hyperbolic readings, as illustrated in (1) (see, e.g., Kao et al. 2014).

(1) This shirt costs one thousand euros =&gt; This shirt is extremely expensive

The gist of the proposals on the market consists in assuming that the interpretation of a sentence can be relativized to a salient (though sometimes implicit) question under discussion (QUD).

If the speaker is understood to answer the question ‘Is the shirt too expensive?’, then the sentence in (1), though literally false (if the shirt did in fact cost 126 euros), can be used when it entails a true answer to the question that the speaker believes (e.g. that the shirt costs more than the speaker can afford).

We take inspiration from this kind of analysis and aim to empirically explore what happens when the relevant expressions appear in more complex structures. Our goal will be to have a clear view of how hyperbolic sentences behave and what readings they licence when embedded in complex environments. Our starting point is an observation that the following two sentences do not lend themselves equally to a hyperbolic reading. (first observed by Diego Fienmann) 

(2) a. If the coffee costs a million pounds, I won’t get one.
 [Potential hyperbolic reading less accessible (‘If the coffee is extremely expensive, I won’t get one’)]
 b. If the coffee doesn't cost a million pounds, I will get one. 
[Potential hyperbolic reading more accessible (‘If the coffee is not extremely expensive, I will get one’)]

At the theoretical level, we can start from two different plausible hypotheses :

One plausible hypothesis is that hyperbolic readings arise only when the literal reading expresses a proposition that is highly unlikely to be the speaker’s intended meaning. A proposition can be unlikely to be the speaker’s intended meaning if it describes an unlikely event, where more specifically the speaker is unlikely to believe it, as in (2b) under its literal meaning (which entails for instance that I might buy a coffee that costs 999 euros), or if it describes a very likely event, so that it is not very informative and a rational speaker would not bother to express it, given the tradeoff between informativity and cost, as in (2a) under its literal meaning (where it’s somewhat obvious that I would not buy a coffee that expensive). 

This hypothesis predicts that hyperbolic readings should arise equally, depending solely on whether the literal meaning is unlikely to be the speaker’s intended meaning. On this reading, hyperbolic readings should arise in both (2a) and (2b).

Our scientific hypothesis is that hyperbolic readings should be more accessible when the literal reading expresses a proposition that describes a highly unlikely event. In some specific implementations of the RSA model proposed by Kao et al., we find that the hyperbolic, non-literal reading arises at lower recursion levels in the case of sentences whose literal meaning expresses near-impossible events than for those whose literal meaning expresses an obvious truth. This would predict that the hyperbolic meaning should not be as accessible when the triggering expression occurs in the immediate scope of an operator that reverses informativity strength such as if, since in this case, the literal reading becomes an obvious truth.

This hypothesis predicts the contrast reported in the minimal pair, since under the
literal meaning, the prior probability of (2a) but not (2b) is very high (if conditionals are viewed as material or strict conditionals).

Our goal is therefore to investigate in detail the fine-grained phenomenology of hyperbolic readings, and how they behave in embedded environments. In order to pursue this question, we create an experimental design whose first goal is to test the first hypothesis and disprove it. To do so, we are designing an experiment whose goal is to assess to what degree a hyperbolic reading is available in various syntactic contexts. We outline an experimental design as follows. We will have two target conditions (with a high price in the triggering expression, with or without negation in the phrase) and four control conditions (each instantiated several times with sentences based on different lexical items). Participants will be asked how likely the conclusion is after two premises: 

Target Condition 1
Premise 1: If the shirt costs a million pounds, Dan will not buy it. Otherwise, he will.
Premise 2: The shirt costs 280 pounds.
Conclusion: Dan will buy the shirt.

Target Condition 2
Premise 1: If the shirt does not cost a million pounds, Dan will buy it. Otherwise, he will not.
Premise 2: The shirt costs 280 pounds.
Conclusion: Dan will buy the shirt.

On a literal reading for Premise 1, the conclusion does follow in both conditions. On a hyperbolic reading, where the first sentence of Premise 1 is understood to mean ‘If the shirt [is/is not] extremely expensive, Dan [will not/will] buy it’, the conclusion does not follow. The degree of rejection for the conclusion will thus give us the rate of hyperbolic readings.



In order to control for the possibility that whatever effect we will find is not due to a difference in relevance between the two readings, or an independent influence of sentence structure (including the presence or absence of negation) on participants’ choices, we create two types of controls, a normal price control and a paraphrase. In the normal price control, both the price of the triggering expression and the context price are normal, while in the paraphrase, the triggering expression is a paraphrase of the hyperbolic meanings of the target conditions, while the context price remains the same as in the target conditions. Both types of controls have the same syntactic structure as the target conditions and are presented in the same contexts. Inferential judgments will be collected using a sliding scale (cursor), rather than by asking for binary responses.