Examples

Scalar implicatures (SIs) are inferences like (1)–(3)

"Or" doesn't entail "not both"

This inference is not part of the lexical meaning of "or"

1. Adding "not both" is not redundant

"Or" doesn't entail "not both"

This inference is not part of the lexical meaning of "or"

2. The inference disappears in certain grammatical contexts

"Or" doesn't entail "not both"

This inference is not part of the lexical meaning of "or"

3. The inference interacts with certain operators in an unexpected way

• Obligation: Go to only one of It and Fr!
• Obligation: Go to at least one of It and Fr (and the other one is optional)!

"Some" doesn't entail "not all"

This inference is not part of the lexical meaning of "some"

"ほとんど" doesn't entail "すべて"

This inference is not part of the lexical meaning of "ほとんど"

Research questions

Expressions that give rise to SIs are called scalar expressions (alt: scalars)

If SIs are not part of the lexically encoded meanings of scalar expressions, where do they come from?

Terminological note

• Griceans claim that SIs are a type of pragmatic inferences called implicatures that involve scales, e.g. ⟨or, and⟩, ⟨some, (most,) all⟩, ⟨possible, certain⟩

• Some neo-Griceans (e.g., Geurts 2010) use the term quantity implicature

  • The Gricean derivation of a SI refers to the Maxim of Quantity
  • Quantitiy implicatures are a broader concept, subsuming those cases not involving 'lexical scales', e.g., ad hoc implicatures

• For grammaticalists (e.g., Chierchia, Fox & Spector 2012), SIs are technically not 'implicatures', but they still nevertheless use the term 'scalar implicature'

Roadmap

1   Gricean approach

2   Some theoretical issues

2.1   Primary vs. secondary implicatures
2.2   The Symmetry Problem
2.3   Embedded scalar implicatures

3   Grammatical approach

Pragmatic inferences

Not all meaning is encoded in linguisitc expressions

One naturally concludes from (1A) that the speaker does not speak Korean.

Gricean implicature

Paul Grice pioneered the study of pragmatic inferences

• Idea: With the assumption that the speaker is cooperative, one may draw extra inferences based on their (linguistic or non-linguistic) behaviour

• Grice called such pragmatic inferences implicatures

Cooperativity

It's reasonable to assume that conversational agents are generally cooperative

Implicatures arise in non-linguistic communication as well

Gricean Maxims

What does it mean to be a cooperative conversational agent?

Maxim of Quantity

In the Gricean approach to SIs, the Maxim of Quantity plays a crucial role

The Maxim of Quantity is about informativity

• Sub-maxim 1: Don't be underinformative
• Sub-maxim 2: Don't be overinformative

Gricean derivation of SI: Or

1. Utterance: "I speak Korean or Japanese"
2. Why didn't the speaker say "I speak Korean and Japanese"?, which would have been more informative?
   • "I speak K and J" asymmetrically entails "I speak K or J"
   • Therefore the Maxim of Quantity favours this alternative
3. It must be because asserting the alternative would have been uncooperative
   • The Maxims of Relation and Manner would have been respected
   • It must have violated the Maxim of Quality
   • Therefore, the speaker doesn't believe the alterantive to be true

Gricean derivation of SI: Some

1. Utterance: "Some of the cats are asleep"
2. Why didn't the speaker say "All of the cats are asleep"?
   • That would have been more informative
   • Therefore the Maxim of Quantity favours this alternative
3. It must be because asserting the alternative would have been uncooperative
   • The Maxims of Relation and Manner would have been respected
   • It must have flouted the Maxim of Quality
   • Therefore, the speaker doesn't believe the alterantive to be true

Summary

(Neo-)Griceans claim that SIs are implicatures, a type of pragmatic inference generated via reasoning based on cooperativity

Recipe for SI:

1. Identify a more informative (stronger) alternative (e.g., "and" for "or", "all" for "some")
2. Gricean reasoning about Quantity and Quality leads to the negation of the alternative

Exercise: More SIs

Controversial cases

Experimental research on SIs

Since the early 2000s, SIs have been investigated experimentally, as well as theoretically (see Chemla & Singh 2014a,b, Noveck 2018 for overviews)

Some relevant findings

• Interpretations with SIs often require extra cognitive resources/processing time (Bott & Noveck 2004, De Neys & Schaeken 2007, a.o.)
• Children often fail to draw SIs (Noveck 2001, Papafragou & Musolino 2003, a.o.)

Bott & Noveck 2004: Experiment 3

Bott & Noveck 2004: Experiment 4

Short = 900 ms; Long = 3000 ms

De Neys & Schaeken 2007: Dual-task experiment

Memory task sandwitching sentence verification (à la Bott & Noveck 2004):

• Memorise dots ➤ Sentence verification ➤ Reproduce dots
• Load (≈difficulty) manipulated within-subjects

2.1   Primary vs. sencodary implicature

Epistemic Step

1. Primary implicature:
2. Secondary implicature:

Dieuleveut, Chemla & Spector 2014: Experiment 2

Conditions

• False: All visible, no hearts
• Literal: All visible, all hearts
• Primary: Only some visible, all visible cards are hearts (as in pic)
• Seconday: Only some visible, only some visible cards are hearts

Scalars: some, almost, two, PLURAL

Dieuleveut, Chemla & Spector 2014: Results

2.2   The Symmetry Problem

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

Structural complexity

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)

2.3   Embedded SIs

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 2012, etc.)

Experimental research on embedded SIs

• Geurts & Pouscoulous 2009 failed to observe evidence for embedded SIs

• Chemla & Spector 2011 found some evidence

• Debate: Geurts & Van Tiel 2013, Cummins 2014, Van Tiel 2014, Potts, Lassiter, Levy & Frank 2014, Franke, Schlotterbeck & Augurzky 2017, Van Tiel, Noveck & Kissine 2018

Difficulties

• By assumption SIs don't arise under negative operators (e.g., negation, "no"), positive or 'non-monotonic' operators must be used
• With a positive operator (e.g., "every"), the local SI reading would asymmetrically entail the global SI reading, so we can't have direct evidence for it

Chemla & Spector 2011: Items

"Every letter is connected with some of its circles" (in French)

• Literal reading (true in L, W, S):
  ∀x(Lx → ∃y(●y ∧ Cxy))

• Global reading (true in W, S):
  (∀x(Lx → ∃y(●y ∧ Cxy)) ∧ ¬∀x(Lx → ∀z(●z → Cxz))

• Local reading (true in S):
  ∀x(Lx → (∃y(●y ∧ Cxy) ∧ ¬∀z(●y → Cxz)))

Chemla & Spector 2011: Results

Chemla & Spector 2011 claim the difference between Weak and Strong as suggesting that there is a local SI reaidng ('the more readings are true, the truer the sentence sounds')

Non-monotonic contexts

• 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'

Exh

The grammatical approach to SI was developed mainly to deal with embedded SIs

SIs are triggered by a phonologically null operator Exh (alt: ) (Groenendijk & Stokhof 1984, Chierchia 2004, Van Rooij & Schulz 2004, Chierchia, Fox & Spector 2012)

• is called the prejacent
• is the set of (relevant) alternatives to
• is some condition on given ; some options:
  • is stronger than (i.e. entails but doesn't entail )
  • is non-weaker than (i.e., doesn't entail )
  • is 'innocently excludable' given

Example

"Every linguist met some of the philosophers"

• Exh(Every linguist met some of the philosophers)

  • Every linguist met at least one of the philosophers; and
  • ¬(Every linguist met all of the philosophers)

• Every linguist λx Exh(x met some of the philosophers)
  Every linguist is such that

  • they met at least one of the philosophers
  • ¬(they met all of the philosophers)

Disjunctive alternatives

The disjunct-alts are used to derive ignorance inferences (= primary implicatures)

Too many stronger alternatives

The disjunctive-alts are stronger (and hence non-weaker) than the prejacent, but negating both of them independently will contradict the prejacent

Innocently excludable alternatives

Fox 2007 puts forward innocent exclusion: Negate as many alternatives as possible, while maintaining consistency with the prejacent

E.g. ;

Remarks

• When Exh appears under an opeartor, the SI takes scope below the operator
• Exh is, by assumption, anti-licensed under negation. There might be other distributional constraints (Fox & Spector 2018)
• Exh is similar to only, but not Strawson-DE so does not license weak NPIs
• The grammatical approach is compatible with Gricean Pragmatics, including certain pragmatic inferences (e.g., ignorance implicatures as primary implicatures)
• The burden of proof is on the grammaticalist
  • Embedded SIs (Chierchia 2004, Chierchia, Fox & Spector 2012)
  • Obligatory SIs (Chierchia 2004, 2013, etc.)
  • Multiple SIs (Franke & Bergen 2020)

Summary

• In most theories of SI, generation of a scalar implicature involves:

  1. Reference to an alternative
  2. Negate the alternative

• Theories mostly differ with respect to the negation mechanism

  • Gricean approach: Reasoning about Quantity and Quality
  • Grammatical approach: Exh

• Every theory needs a recipe for determining alternatives

Next time?

Experimental topics
A) Implicature priming
B) Scalar diversity
C) "Ya" in Japanese

Theoretical topics
D) Free choice as SI (or not)
E) SIs and presuppositions
F) SIs and anaphora

References

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References

References

References