Griceans claim that SIs are a type of pragmatic inference called implicature that involves scales, e.g. ⟨or, and⟩, ⟨some, (most,) all⟩, ⟨possible, certain⟩
Some neo-Griceans (e.g., Geurts 2010) use the term quantity implicature
For grammaticalists (e.g., Chierchia, Fox & Spector 2011), SIs are not 'implicatures', but they still use the term 'scalar implicature'
2.1 Primary vs. secondary implicatures
2.2 The Symmetry Problem
2.3 Embedded scalar implicatures
Not all meaning is encoded in linguisitc expressions
One naturally concludes from (1A) that the speaker does not speak Korean (and more)
But this inference is arguably not part of the meaning of the linguistic expressions used
Paul Grice pioneered the study of pragmatic inferences
Idea: With the assumption that the speaker is cooperative, one draws inferences based on their (linguistic or non-linguistic) behaviour
Grice called such pragmatic inferences implicatures
It's reasonable to assume that conversational agents are generally cooperative
Pragmatic inferences arise in non-linguistic communication as well
They can be analysed as implicatures too.
What does it mean to be cooperative?
Grice's (tentative) answer: To be a cooperative agent is to follow:
The Maxim of Quantity is about informativity
(Neo-)Griceans claim that SIs are implicatures, a type of pragmatic inference generated on the cooperativity assumptions
Recipe for SI:
According to this theory, an SI arises via counterfactual reasoning about a hypothetical utterance of a more informative alternative
According to the Gricean approach:
But the preceived SI is typically stronger than this: The speaker has enough evidence for the falsity of ψ (secondary implicature)
Neo-Gricean (Spector 2003, Sauerland 2004, etc.) assume that a primary implicature gets strengthened to a secondary implicature via an auxiliary assumption, Opinionatedness (alt. Experthood, Competence)
1. + 3.
But some experimental evidence that secondary SIs are drawn even if Opinionatedness does not hold (i.e., the speaker is known to be uncertain)
Classical Gricean theories are naive about alternatives
The crucial alternative is formed with "all", but one could think of another alternative formed with "some but not all" or "only some"
These alternatives are called symmetric alternatives
Symmetric alternatives cannot be both negated consistently, while maintaining the truth of the prejacent
One might think that the symmetry between "all" and "some but not all" can be broken by the difference in structural complexity (see Katzir 2007)
But not all symmetry problems can be explained by structural complexity (Romoli 2013, Trinh & Haida 2015, Breheny et al. 2018)
Gricean derivations of SIs only apply at the utterance level
But SIs seem to be able to take scope under logical operators (Chierchia 2004, Chierchia, Fox & Spector 2011, etc.)
Geurts & Pouscoulous 2009 failed to observe evidence for embedded SIs
Chemla & Spector 2011 found some evidence
More work: Geurts & Van Tiel 2013, Cummins 2014, Van Tiel 2014, Potts, Lassiter, Levy & Frank 2014, Franke, Schlotterbeck & Augurzky 2017, Noveck & Kissine 2018
Difficulties
E.g., the global reading is true and the local reading false, when 3 students flunked some but not all, 1 flunked all
Note that these sentences might lack the global reading altogether
NB: The global and local readings amount to the same thing for 'exactly one'
The grammatical approach to SI was developed mainly to deal with embedded SIs
SIs are triggered by a phonologically null operator called 'Exh' (Groenendijk & Stokhof 1984, Chierchia 2004, Van Rooij & Schulz 2004, Chierchia, Fox & Spector 2011)
The disjunct-alts are used to derive the ignorance inference (= primary implicatures)
They sometimes give rise to SIs
The disjunctive-alts are stronger (and hence non-weaker) than the prejacent, but negating them independently will contradict the prejacent
Fox 2007 puts forward innocent exclusion: Negate as many alternatives as possible, while maintaining consistency with the prejacent
E.g.
In most theories of SI, generation of a scalar implicature involves:
Theories mostly differ with respect to the negation mechanism
Two experimental topics
A) Implicature priming
B) Scalar diversity