Literal vs. Non-literal Meaning

Literal vs. Non-literal Meaning Philippe Schlenker

(Institut Jean-Nicod & NYU)

Literal Meaning vs. Reasoning

1960’s-1990’s: the neo-Gricean synthesis a. Much information conveyed by sentences is not part of their meaning, but results from an analysis of the speaker’s intentions. b. In some cases, the use of certain words automatically evokes alternatives). The utterance of a sentence with those words is automatically compared to the utterance of a sentence with the competing words.

1990’s-now: the localism debate (Chierchia, Fox, Spector) Localism: implicatures are part of the semantics. a. Direct argument: truth conditions. b. Indirect argument: presence of local implicatures explains non-trivial phenomena.

Literal Meaning vs. Reasoning

A neo-Gricean treatment a. Utterance: I’ll invite John or Mary. b. Alternative: I’ll invite John and Mary. c. Inference: –the speaker couldn’t utter b.; –possibly because he knows it to be false.

A localist treatment a. Utterance: I’ll invite John or Mary [or both]. b. Representation: I’ll invite Exh[John or Mary] [or both] c. Meaning: I’ll invite only John OR Mary [or I’ll invite both].

a. There are very strong arguments on the localist side. b. But it raises non-trivial issues.

Literal Meaning vs. Iconicity

There are arguably cases in which inferences are drawn on the assumption that symbols resemble what they represent. a. John got depressed and he left his wife. vs. John left his wife and he got depressed. b. That was a long speech. vs. That was a loooong speech! (Liddell 2003)

But the problem is particularly salient in sign language: a. On the one hand, various sign language constructions – in particular pronouns – obey formal constraints familiar from contemporary linguistics; b. but they are also sensitive to iconic constraints.

Literal Meaning vs. Iconicity

Sign language anaphora a. The antecedent establishes a position in signing space. b. Anaphora is realized by pointing towards this position.

Formal properties a. Condition A, Condition B b. Ambiguities in ellipsis c. Strong and probably Weak Crossover effects

Iconic Meaning IX-a LITTLE BOY a-MEET-b GIANT. IX-a LIKE IX-b. ‘A little boy met a giant. He liked him.’ Here we find a combination of: –the standard realization of pronouns in ASL: loci; –a clear iconic component: IX-a signed low, IX-b high.

The New Debate on Scalar Implicatures

Structure of the Argument

The neo-Gricean analysis has some good properties: a. simple b. might account for acquisition and processing data.

It encounters two kinds of problems: A. It fails to predict the desired inferences. B. It fails to account for cases in which a constituent behaves as if it had a strengthened meaning.

These originally motivated a localist approach.

a. With a few exceptions, the problems in A. are not decisive, i.e. everybody needs an ‘upgraded’ Gricean procedure. b. The problems in B. are decisive – but less discussed.

These slides draw heavily on: –B. Spector ESSLLI 2010 handouts on implicatures; –Classes co-taught at Ecole Normale Supérieure in Paris with Emmanuel Chemla. –Chemla and Spector’s presentation of their experiment on embedded scalar implicatures.

The Neo-Gricean Account

Pragmatics

Dear Colleague, Mr. John Smith has asked me to write a letter on his behalf. Mr. Smith is unfailingly polite, is neatly dressed at all times, and is always on time for his classes. Sincerely yours, Harry H. Jones

Inference Smith is a bad student.

Pragmatics

Hypothesis 1: The inference is an entailment a. Problem 1 (S) Mr. Smith is unfailingly polite, is neatly dressed at all times, and is always on time for his classes. (T) But these are only his most apparently qualities. When one reads his work, one can only be struck by the extraordinary depth of his thinking. S implies: Smith is a bad student (S and T) doesn’t imply: Smith is a bad student b. Problem 2 (T’) He is also a student of great quality. (S and T’) isn’t contradictory

Pragmatics

Hypothesis 2: The inference stems from a reasoning on the speaker’s motives. (i) In a letter of recommendation, the professor is normally supposed to mention the most positive features of the student. (ii) The professor only mentioned that Smith is polite, neatly dressed and always on time. (iii) Therefore these are probably his most positive qualities, and therefore he is probably a bad student.

Entailments vs. Implicatures

Entailments follow from what is linguistically encoded. Implicatures do not (... because additional assumptions about the speaker’s motivations are needed).

Entailments satisfy the following test. Implicatures generally don't. In every conceivable situation in which it is true that p, it is true that q.

Entailments cannot be cancelled. Implicatures can be. (... because some of the assumptions needed to derive them might turn out to be false).

Conversational Implicatures

Utterance: Can you pass the salt? Implicature: I want you to pass the salt.

A's utterance: Smith doesn't seem to have a girlfriend these days. B's utterance: He has been paying a lot of visits to New York lately. B's implicature: Smith has a girlfriend in New York.

The Gricean Picture

Cooperative Principle Make your conversational contribution such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged. (Grice 1975/1989: 26)

The Gricean Picture (Geurts 2011)

Quantity 1. Make your contribution as informative as is required 2. Don’t make your contribution more informative than nec

Quality: 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: Be relevant.

Manner: Be perspicuous: 1. Avoid obscurity of expression. 2. Avoid ambiguity. 3. Be brief (avoid unnecessary prolixity). 4. Be orderly.

Scalar Implicatures

a. inclusive or : (p or q) is true iff p is true, or q is true, or both are true. b. exclusive or : (p ou q) is true iff p is true and q is false, or p is false and q is true.

Examples that suggest that or is exclusive a. I will invite Ann or Mary b. Sam is a poet or he is a musician

Examples that are irrelevant a. Sam is in Paris or in Rome b. Peter will become a lawyer or a doctor c. It will rain or it will snow

Hypothesis 1. Or is exclusive

Problem 1: sometimes or seems to be inclusive a. At John’s party, there was pizza or ice cream => odd if both were available b. At John’s party, there’ll be pizza or ice cream => ok if both are available b’. I’ll bet you 5$ that John will invite Ann or Mary => I win if John invites both

Problem 2: it is no contradiction to say: a. Sam is a poet or a musician - in fact he is both! b. I’ll invite Ann or Mary - in fact I’ll invite them both

Hypothesis 1. Or is exclusive

Problem 3: wrong predictions a. Every Italian who is a philosopher or a poet is a socialist. b. Whenever I invite a philosopher or a poet to a party, it ends up being a success.

Situation i1, is a philosopher but not a poet, and he is a socialist. i2, is a poet but not a philosopher, and he is a socialist. i3, is both a philosopher and a poet, but he is not a socialist.

Predictions a. If or is exclusive, the sentence should be true b. If or is inclusive, the sentence should be false

Hypothesis 2. Or is ambiguous

Problem 1: sometimes or seems to be inclusive: Ok

Problem 2: it is not contradiction to say: Ok a. Sam is a poet or a musician - in fact he is both! b. I’ll invite Ann or Mary - in fact I’ll invite them both

Problem 3: wrong predictions Every Italian who is a philosopher or a poet is a socialist. Still a problem

Hypothesis 2. Or is ambiguous

Problem 4: wrong predictions In order to have an A, you should turn in perfect problem sets or write a good term paper. a. NOT an inference: You should [turn in perfect problem sets or write a good term paper BUT NOT BOTH] b. Inference not [you should turn in perfect problem sets AND write a good term paper]

The inference in b. is not predicted by the ambiguity account.

Hypothesis 3. Scalar Implicatures

Implicature a. Semantics: or is inclusive b. Pragmatics (i) The speaker said: p or q (ii) He could have said: p and q, which is more informative. (iii) a. If the speaker did not choose the more informative option, it’s probably because he was not in a position to assert it ... b. ... possibly because he thinks it is false. (= Epistemic Step) Conclusion: (p or q) and not (p and q)

The Neo-Gricean Account: <or, and>

Step 1. Definition of Alternatives Alt(S) = {S': S' is a sentence obtained from S by replacing simultaneously any number of occurrences of or by and and any number of occurrences of and by or}.

Step 2. Ordering Let S be a sentence and let S' be a member of Alt(S). S' is better than S if: a. S' entails S and S does not entail S' [terminology: we say in this case that S' asymmetrically entails S] b. The speaker believes that S'

Step 3. Cooperation If the speaker is cooperative and he utters S, then there is no S’ in Alt(S) which is better than S.

With our existing machinery, we predict inferences of the form: It is not the case that the speaker believes that S’ written not K S’ (also: not K S’) where S’ is a stronger alternative than S.

We often obtain a stronger inference: The speaker believes that it is not the case that S’ written K not S’ (also: K not S’)

Step 4. Epistemic Step Either the speaker believes that S’, or the speaker believes that not S’. not K S’ [K S’] or [K not S’] ____________________ K not S’

Scalar Implicatures

Informativity is crucial -To obtain the not [... and ...] inference, it was crucial that ... and... is more informative than ... or ... -If ... and ... is less informative than ... or ..., we predict that or should lose its ‘exclusive reading’

a. I will never have lunch with a linguist or a psychologist! b. Every Italian who is a poet or a musician is a socialist. c. None of the pirates found the jewel or the necklace.

Predictions This explains why in negative environments ‘standard’ implicatures disappear... and new ones appear.

Downward-Entailing Environments

Situations in which I invite John and Mary

Situations in which I invite John or Mary

I will invite John and Mary

I will invite John or Mary

It’s not the case that I will invite John or Mary

It’s not the case that I will invite John and Mary

New Implicatures

New Implicatures I S = I won’t (both) invite John and Mary S’ = I won’t invite John or Mary -S’ is more informative than S. S’ triggers no implicature! -We predict an implicature: (not S’) Conclusion: It’s not the case that I won’t invite John or Mary - i.e. I will invite John or Mary

Situations in which I invite John and Mary

Situations in which I invite John or Mary

New Implicatures

New Implicatures II S = I will never have lunch with a linguist and a psychologist! S’ = I will never have lunch with a linguist or a psychologist! -S’ is more informative than S. S’ triggers no implicature! -We predict an implicature: (not S’) Conclusion: It’s not the case that I will never have lunch with a linguist or a psychologist i.e. I will sometimes have lunch with a psychologist or a linguist

New Implicatures

News Implicatures III S = No student studies psychology and linguistics S’ = No student studies psychology or linguistics -S’ is more informative than S. S’ triggers no implicature! -We predict an implicature: (not S’) Conclusion: It’s not the case that no student studies psychology or linguistics i.e. some student studies psychology or linguistics

New Implicatures

News Implicatures IV S = Every Italian who is a philosopher and a poet is a socialist S’ = Every Italian who is a philosopher or a poet is a socialist -S’ is more informative than S. S’ triggers no implicature! -We predict an implicature: (not S’)

Italians who are philosophers and poets

Italians who are philosophers or poets

Some, Most, Every

a. Some of my friends are clever => Not all of my friends are clever. => A minority of my friends are clever. b. Some of my friends are clever. In fact, all of them are.

a. Most of my friends are clever => Not all of my friends are clever. b. Most of my friends are clever. In fact, all of them are.

a. Whenever most of the students come to class, there is a pleasant atmosphere. b. Every student who read most of the articles on the reading list will get an A.

Extensions

<and, or>

<all, most, some>

<certain, {probable/likely}, possible>

<..., 6, 5, 4, 3, 2, 1>

<boiling, hot, warm>

<adore, love, like>

<excellent, good, okay>

More on Scales V: Minimal Assumptions

To get the Gricean account going, we need the assumption that: in the context of the conversation, the utterance of S evokes the utterance of some competitor S’.

If we could find some independent criterion of what ‘evokes’ means (e.g. priming), we could make do without lexical scales. We would simply make predictions that correlate: a. which sentences are ‘evoked’, with b. what inferences are triggered.

But this is not something that is currently available.

Against Scales?

Geurts 2011 a. I saw an animal on the lawn this morning. => not K I saw a dog on the lawn this morning. b. I saw a dog on the lawn this morning. ≠>not K I saw a poodle/schnauzer on the lawn this morning.

“if an individual x is introduced as an “animal”, the hearer is likely to wonder what species of animal x is, whereas if x is introduced as a “dog”, the question whether x is a schnauzer will not in general present itself with equal force. Of course, such expectations may be dependent on the context to a greater or lesser degree...[Horn scales] are partial representations of contextual relevance.” (Geurts 2011)

Primary vs. Secondary Implicatures I

Primary implicatures If S evokes S’ and S’ is more informative than S, Gricean reasoning leads to: not K S’ where B is what the speaker believes.

Secondary implicatures Often this gets strengthened to: K not S’ Do we need a special mechanism, or is contextual knowledge enough?

Primary vs. Secondary Implicatures II

At the beginning of the semester: Every student who is hard-working and competent will get an A. => not K Every student who is hard-working or competent will get an A. ≠> K not [Every student who is hard-working or competent will get an A].

At the end of the semester: Every student who was hard-working and competent got an A. => not K Every student who was hard-working or competent got an A. => K not [Every student who was hard-working or competent got an A]

Crimmins and Katsos

10 acceptances, 57 rejection

Crimmins and Katsos

64 acceptances, 0 rejection

Crimmins and Katsos

Acquisition of Scalar Implicatures

The Truth Value Judgment Task (Crain and colleagues)

How can we determine how children understand a sentence? a. We can’t ask them directly about truth conditions b. We don’t want to force them to correct adults c. The task should be fun

Crain’s Description

[Credits: Crain & co-workers, U. Maryland]

Acquisition of Scalar Implicatures

a. Children appear not to compute scalar implicatures obtained by adults. b. They access ‘pure’ logical meanings.

Possible explanations a. Problem with inferences? Unlikely: children make fine-grained inferences on the basis of the logical meaning of words. b. Lack of a pragmatic principle? c. Processing difficulty, e.g. connected to the comparison of alternatives?

Processing Scalar Implicatures

Scalar Implicatures Take Time

Noveck and Posada 2003

Possible Explanations

Computing a scalar implicature requires reasoning.

Computing a strengthened meaning requires reference to alternatives – and this might take time. (This is compatible with an operator-based analysis!)

When a strong meaning is computed, it is non-monotonic: p or q = at least one of {p, q} p orS q = exactly one of {p, q} Non-monotonic readings might be harder in general. (This is compatible with virtually any view!)

Properties of Scalar Implicatures

Unlike entailments, they can be cancelled.

They ‘disappear’ in certain environments (and ‘appear’ in others).

They are acquired relatively late by children.

They take time to compute.

Problems for the Standard Neo-Gricean Account

Problem 1: Predictions that are too strong

Multiple Disjunctions ((p or q) or r) John is a philosopher or he is a poet or he is musician.

Negation of stronger alternatives a. not K (p and q) or r b. K not ((p and q) or r) hence K not r! Inference: John isn’t a musician!!!

Directions a. Need for a different procedure to compute implicatures. b. Revisit primary vs. secondary implicatures.

Problem 1: Predictions that are too strong The problem is general

[... weak scalar term...] or r yields the implicature a. not K ([... stronger scalar term...] or r) b. K not([... stronger scalar term...] or r) hence K not r

a. Kai had the broccoli or some of the peas (Sauerland) b. Kai had the broccoli or most of the peas => !! Kai didn’t have the broccoli

[Problem 1: Predictions that are too strong ?]

a. How did students satisfy the course requirement? Some made a presentation or wrote a paper. Some took the final test. (Chierchia 2002)

b. Predicted implicature not (some made a presentation and wrote a paper) hence none did both.

a. Who will get a good grade in that class? Some students who read some Salinger stories will get a good grade.

b. Predicted implicature not (some student who read every Salinger story got a good grade) i.e. no student who read every Salinger story did.

Problem 2: Predictions that are too weak

Believe a. John: “Some students are waiting for me” (Chierchia) b. John believes that some students are waiting for him. c. Predicted implicature: It’s not the case that John believes that every student is waiting for him. d. Actual implicature (according to Chierchia): John believes that not every student is waiting for him

Directions a. The implicature we compute is too weak => need for a different procedure. b. There is a hidden assumption: John is opinionated, i.e. either he believes that p or he believes that not p.

Problem 2: Predictions that are too weak

Know (Chierchia 2002) a. John knows that some students are waiting for him b. Presupposition: Some but not all students are waiting for John

Every (debated!) a. All my students have read some book by Chomsky b. Ok: not (all my students have every book by Chomsky) c. ? all my students have read some but not every book by Chomsky

For reasons we’ll see later, new globalist accounts do predict a reading like c. Negation of non-weaker alternatives: not [Some of my students have read every book by C.]

Chierchia’s Localist Solution (related ideas by Schwarz and Landman)

Outline

Implicatures are part of the recursive semantics This is a radical departure from Gricean assumptions: implicatures are not the result of reasoning on the speaker’s intentions (why did s/he utter S rather than S’ ?)

Basic Architecture a. When a positive (or non-negative) operator is encountered, one obtains a ‘strong meaning’ by applying the meaning of the operator to the strong meaning of its argument, and adding a (well-chosen) implicature.

b. When a negative operator is encountered: -the strong meaning of the operator is applied to the normal meaning of its argument (otherwise... weaker result!); -new implicatures are added (= ‘scale reversal’)

A Simplified Version of Chierchia’s System: Disjunctions

a. If F is an elementary clause, its strong meaning FS is the conjunction of the meaning of F together with the implicature predicted by the neo-Gricean analysis. b. If F = (A or B), Fs = (AS or Bs) and not (A and B)

Example 1: F = A or B, where A and B are non-scalar. Rule a. immediately yields the result that the strong meaning of (A or B) is: (A or B) and not (A and B) [= exclusive or] We henceforth write this as A v B. So Fs = A v B

Multiple Disjunctions

b. If F = (A or B), Fs = (AS or Bs) and not (A and B)

Example 2: G = A or (B or C) Step 1: Compute the strong meaning of (B or C) By the preceding reasoning, it is just (B or C)S = (B v C) Step 2: Compute the strong meaning of A or (B or C) By b., it is (As or (B or C)S) and not (A and (B or C)) So Gs = (A or (B v C)) and not (A and (B or C))

Gs = (A or (B v C)) and not (A and (B or C)) Step 1. If Gs is true, exactly one of {A, B, C} is true. a. Clearly, it must be that one of {A, B, C} must be true.

b. It couldn’t be that A and B are true, because this would make the second conjunct false.

c. Same reasoning: it couldn’t be that A and C are true.

d. It couldn’t be that B and C are true, because if so A would have to be true to make the first conjunct true... and the second conjunct would be false. Step 2. If exactly one of {A, B, C} is true, Gs is true,

Prediction: Exactly one of {A, B, C} is true.

A Subtlety

Choosing the Right Rule

a. Actual Rule: If F = (A or B), Fs = (AS or Bs) and not (A and B)

b. Hypothetical Rule: If F = (A or B), Fs = (AS or Bs) and not (AS and BS)

Effect of the Hypothetical Rule in Step 2:

Gs = (A or (B v C)) and not (A and (B v C))

In other words: Gs = (A v (B v C))

Why this is disastrous Gs is now predicted to be true if A, B and C are all true!

Embedded Scalar Terms

b. If F = (A or B), Fs = (AS or Bs) and not (A and B)

Example 3: H = A or [some P] H

Kai had the broccoli or some of the peas

Step 1: Compute the strong meaning of [some P] H By Rule a., this is just: [some P] H and not [every P] H = ‘Kai had some but not all of the peas’

Step 2: Compute the strong meaning of A or [some P] H Hs= (A or ([some P] H and not [every P]H)) and not (A and [some P] H)

Results

Special rules must be added for negative environments

The problem of predictions that are too strong is sometimes solved - as seen in the example of disjunction (because we do not have to negate the stronger global alternatives).

The problem of predictions that are too weak is solved a. John believes that some students are waiting for him b. John knows that some students are waiting for him c. All my students have read some book by Chomsky. => The right result is obtained by applying believe / know to the strong meaning of the embedded clause.

Some Problems

a. This analysis fails to derive the ‘ignorance implicatures’ of (A or B or C), namely: not K A; not K B ; not K C b. The problem already arises for: (A or B).

a. We get: K (A or (B v C)) and not (A and (B or C)) b. But this is satisfied if K A, K (not B and not C)

a. So we need to add alternatives to (A or B or C), namely: {…, A, B, C}. By symmetry: (A or B), (B or C), (A or C) b. But then we run into the earlier problem: not K A; K not A; disaster. c. but: K not A, leads to: K (B or C) which contradicts: not K (B or C)

Neo-Gricean Responses (Sauerland, Spector, van Rooij & Schulz)

Main Ingredients

Ingredient 1: Enriching the Set of Alternatives Example: p or q will have as alternatives {p or q, p and q, p, q}

Ingredient 2: Distinguishing between 2 Stages Stage 1: Primary Implicatures are computed: not K S’ for various S’ Stage 2: Secondary Implicatures are computed: if compatible with Stage 1, strengthen to K not S’ for various S’

Ingredient 3: Negating non-weaker alternatives

Ingredient 1: More Alternatives I: Ignorance Inferences

Ignorance implicatures a. I’ll invite John or Mary b. Predicted implicature: I won’t invite them both c. Additional implicature: I don’t know whether I’ll invite John I don’t know whether I’ll invite Mary

Enriched Set of Alternatives: Alt(p or q) = {p, q, p or q, p and q}

Ingredient 1: More Alternatives II: Distributivity Inferences (e.g. Spector 2010)

Every student either solved Problem 1 or Problem 2 a. not K Every student solved Problem 1 not K Every student solved Problem 1 not K Every student solved Problem 1 and Problem 2. b. K not Every student solved Problem 1. K not Every student solved Problem 2.

Every student either solved Problem 1 or Problem 2 a. No! No student solved Problem 1 b. No! Every student solved Problem 1. (Spector 2010)

Enriched Set of Alternatives: Alt([Every P](Q or R)) = {[Every P] Q, [Every P] R, [Every P](Q or R), [Every P](Q and R)}

Ingredient 2: Two Steps

Step 1: not (Speaker believes that …) a. I’ll invite John or Mary = p or q K (p or q) b. not K p, not K q, not K (p and q)

Step 2: Epistemic Step: Speaker believes that not … If compatible with Step 1, strengthen not K F to K not F • Can we get K not (p and q)? Yes: coherent • Can we get K not p? No: if K (p or q) and K not p, it must be that K q - which contradicts Step 1. • Can we get K not q? No: Same reason.

Fox’s Presentation (2006)

Ingredient 2: Two Steps

Step 1: not (Speaker believes that …) a. Every student solved Problem 1 or Problem 2 = = [Every S](P1 or P2) K [Every S](P1 or P2) b. not K [Every S] P1, not K [Every S] P2, not K [Every S] (P1 and P2)

Step 2: Epistemic Step: Speaker believes that not … If compatible with Step 1, strengthen not K F to K not F • Can we get K not [Every S](P1 and P2)? Yes. • Can we get K not [Every S]P1? Yes! • Can we get K not [Every S]P2? Yes!

Effects of Ingredient 1 and Ingredient 2

Ingredient 1: Enriching the Set of Alternatives => This has the effect of strengthening the primary implicatures that one gets => Together with Ingredient 2: • More primary implicatures than before • Less secondary implicatures than before when they contradict the primary implicatures • More secondary implicatures than before when they don’t contradict the primary implicatures

Ingredient 2: Distinguishing between 2 Stages => This will prevent some ‘absurd’ implicatures from arising [because primary implicatures are ‘stronger’]

A Problem of Implementation

If (i) p is an alternative of (p or q) and (ii) the relation ‘x is an alternative of y’ is symmetric and transitive, then (iii) for every p’, p and p’ are alternatives.

p is an alternative of (p or p’) p’ is an alternative of (p or p’) hence (p or p’) is an alternative of p’ [Symmetry] p is an alternative of p’ [Transitivity]

Sauerland’s Technical Solution Add as alternatives to or and and two unpronounced connectives L and R: ||p L q|| = ||p|| ||p R q|| = ||q||

No more inferences that are too strong

Primary Implicatures of (F or G) (where F and G can themselves contain scalar terms) not K F, not K G, not K (F and G) + K (F or G) [since this was asserted!]

No secondary implicature can yield: K not F because if so: K (F or G) K not F Hence K G ... which contradicts the primary implicature not K G.

a. John is a philosopher or he is a poet or he is musician. b. Kai had the broccoli or some of the peas.

Disjunctions with Scalar Terms: Sauerland

r v sh a. Kai had the broccoli or some of the peas b. John did the reading or some of the homework.

Alternatives All possible replacements of R L & a (r v s h)

... resulting in 8 (- 1 - 1) alternatives

Fox’s Presentation

Sauerland’s secondary implicature: = (r or sh) and not (ah) and not (r and sh)

Chierchia’s Prediction

r v sh a. Kai had the broccoli or some of the peas b. John did the reading or some of the homework.

Reminder: Chierchia’s Rule If F = (A or B), Fs = (AS or Bs) and not (A and B)

Chierchia’s strengthened meaning (r or sh)s = (rS or (sh)s) and not (r and sh) = [r or (sh and not ah)] and not (r and sh)

Sauerland’s secondary implicature: = (r or sh) and (not ah) and not (r and sh)

Comparing Predictions

The differences in terms of primary implicatures are obvious (since Chierchia predicts none).

I. Chierchia’s strengthened meaning [r or (sh and not ah)] and not (r and sh)

II. Sauerland’s secondary implicature: [(r or sh) and not ah] and not (r and sh)) [(r and not ah) or (sh and not ah)] and not (r and sh))

a. Clearly, II => I. b. Assume I. –If r = 1, sh = 0 (2nd conjunct), ah = 0, (r and not ah) = 1. –If r = 0, (sh and not ah) = 1 and II is true.

A or (B or C)

Alternatives All possible replacements of R R L L and and A or (B or C)

Primary Implicatures [not K p, not K q, not K r] not K (p or q), not K (q or r), not K (p or r)

Secondary Implicatures Exactly one of A, B, C is true (see homework).

Sauerland’s Presentation

Attitude Verbs

a. John believes that some students are waiting for him. b. John knows that some students are waiting for him.

Chierchia John believes that only some students are waiting for him.

Sauerland a. not K John believes that every student is waiting for him. b. K not John believes that every student is waiting for him.

Opinionated agent (John believes p) or (John believes not p)

Chierchia vs Sauerland: some differences

Modular Organization a. Chierchia abandons the standard division of labor: the computation of scalar implicatures (i) has some pragmatic features (e.g. preference for stronger readings) (ii) but it is computed by a recursive procedure. Chierchia doesn’t get primary impl.: [p or q] => not K p

b. Sauerland preserves the standard division of labor between semantics and pragmatics - but he must introduce some new (counterintuitive?) alternatives.

Predictions a. They predict different primary implicatures for (p or q). b. They predict different implicatures under every /believe

Ingredient 3: Negating Non-Weaker Alternatives I (Spector, Fox, van Rooij and Schulz)

a. Every letter is connected with some of its circles. b. Alt(a) = {Every letter is connected with all of its circles, Some letter is connected with all of its circles, Some letter is connected with some of its circles}

The negation of the underlined alternative gives rise to the ‘local reading’ = Every letter is connected to some but not all of its circles.

Ingredient 3: Negating Non-Weaker Alternatives II

a. Exactly one student solved some of the problems. b. Exactly one letter is connected with some of its circles.

Alternatives Exactly one student solved all of the problems but it’s not stronger than the original.

Negating Non-Weaker Alternatives Exactly one student solved some of the problems and not [exactly one student solved all of the problems] => Exactly one student solved at least one of the problems, and that student didn’t solve all of the problems.

a. Exactly one student solved some of the problems. b. Exactly one letter is connected with some of its circles.

Now this is different from the reading we would have with an embedded implicature, i.e. Exactly one student solved solve but not all of the problems. (note that the ‘local’ reading doesn’t entail the literal reading; whereas the global reading with negation of non-weaker alternatives does entail the literal reading).

Chemla and Spector 2011 argue that both readings exist.

From a Gricean perspective, it’s rather surprising that non-weaker rather than just stronger alternatives should yield implicatures: if S has been uttered and S’ fails to entail S, in what sense is S’ better than S?

But one could still rationalize this result by comparing S to (S and S’). If so, it is the case that (S and S’) is strictly more informative than S.

Interim Conclusion

a. Chierchia’s original localist analysis fails to derive the primary implicatures of disjunctions. b. In order to derive those, the space of alternatives must be enriched.

If we draw a natural distinction between primary and secondary implicatures, several of the original problems of the globalist approach can be addressed (Sauerland).

a. If in addition we allow non-weaker (rather than just stronger) alternatives to be negated, we derive some local readings in a globalist fashion (= Every some) b. But some differences do remain (= Exactly one some).

Operator-Based Treatments

Two Ways to Look at Operators

a. If operators are given widest scope only, operator-based approaches can be seen as a convenient shorthand to represent patterns of reasoning about utterances. b. This raises the question of how the procedures can be derived from a theory of rationality (recent work by van Rooij and Schulz, Franke, Rothschild).

a. If they are given non-widest scope, operators must be seen as a component of the syntactic or semantic component. b. This yields a departures from Gricean assumptions.

Sauerland-style Operator

Observation Only often behaves as an operator that turns an implicature into the asserted content. a. I’ll invite John or Mary. (In fact, I’ll invite them both) b. I’ll only invite John OR Mary. (#In fact, I’ll invite them both).

Suggestion (Fox, Chierchia, Spector) a. Maybe implicatures result can be viewed in terms of exhaustivity operators (covert counterparts of only), which are syntactically realized. b. ... but Exh, unlike only, is not presuppositional.

Reformulation of Sauerland’s Analysis (Fox)

a. NW(p, A) = {q ∈ A: p does not entail q} = set of alternatives that are not weaker than p [... if they were, negating them would be inconsistent with p!] b. q is innocently excludable given p and A if ¬∃q’ ∈ NW(p, A) [(p and ¬q) ⇒ q’] = given p, q can be negated without thereby entailing the truth of any member of NW(p, A)

a. [ExhA p](w) = 1 iff p(w) = 1 and every member q of NW(p, A) which is innocently excludable given A and p is false in w. b. Same for [ONLYA p] – with a presupposition that p!

a. NW(p, A) = {q ∈ A: p does not entail q} = set of alternatives that are not weaker than p [... if they were, negating them would be inconsistent with p!] b. q is innocently excludable given p and A if for every K, ¬∃q’ ∈ NW(p, A) K (p and ¬q) ⇒ K q’, i.e. = given p, q can be negated without thereby entailing the truth of any member of NW(p, A)

for every K, K (p and ¬q) ⇒ K q’ iff for every K, K [(p and ¬q) ⇒ q’] iff |= (p and ¬q) ⇒ q’ (Note: for ‘only if’, take K = |= )

Step a. corresponds to the statements that would be obtained with primary implicatures: I1 = {not K q: q ∈ NW(p, A)}

a. NW(p, A) = {q ∈ A: p does not entail q} = set of alternatives that are not weaker than p [... if they were, negating them would be inconsistent with p!] b. q is innocently excludable given p and A if for every K, ¬∃q’ ∈ NW(p, A) K (p and ¬q) ⇒ K q’, i.e. = given p, q can be negated without thereby entailing the truth of any member of NW(p, A)

Step b. roughly corresponds to secondary implicatures: I2 = {K not q: q isn’t entailed by p and for no q’ such that (not K q’) ∈ I1, K(p and not q) => Kq’} ‘Strengthen a primary implicature if doing so is consistent with each primary implicature.’ [Sauerland had: ‘Strengthen a primary implicature if this is consistent with the CONJUNCTION of the p. impls.]

Let S be a sentence and Alt be its set of alternatives (sometimes we’ll write Alt as Alt(S)).

ExhSauerland(S, Alt) = {w: S is true in w and for every S’∈ Alt, if (i) S does not entail S’ [i.e. S’ is non-weaker than S], and (ii) ¬∃S” ∈ Alt s.t. (a) S doesn’t entail S” and (b) (S and not S’) entails S” [i.e. S’ is innocently excludable] then S’ is false in w}

‘Negate as many non-entailed alternatives, as long as this doesn’t contradict any primary implicature.’

Can an Operator-Based analysis fully replace a Gricean Analysis?

Problem The operator-based only derives secondary implicatures. Example: (p or q) a. Primary implicature: not K p, not K q b. Secondary implicature: K not (p and q) c. Exh(p or q) = (p or q) and not (p and q)

Assertion operators Adding an assertion operator is probably a bad idea. a. It would allow one to have: Exh Assert(p or q) b. But what could be the semantics of Assert? w |= Assert p iff for each world w’ compatible with what the speaker believes in w, w’ |= p. Bad idea.

Can an Operator-Based analysis fully replace a Gricean Analysis?

(p or q): Option 1: no secondary implicature – no Exh a. Literal meaning: (p or q) b. Primary implicatures only: not K p, not K q, not K (p and q)

(p or q): Option 2: Exh (p or q) a. Literal meaning: Exh(p or q) hence in Sauerland’s system ((p or q) and not (p and q)) b. Primary implicatures not K Exh q, not K Exh, not K (p and q)

Operators and Motivations

ExhSauerland a. derives Sauerland’s secondary implicatures; b. encounters problems with Fred talked to some girl (all the strengthenings together might be contradictory). c. iterated, accounts for ‘free choice readings’: may(p or q)

Exhminimal-models a. is based on ‘minimal models’; b. has no problem with Fred talked to some girl; c. cannot account for ‘free choice readings’.

ExhFox a. is a refinement of ExhSauerland b. has no problem with Fred talked to some girl; c. iterated, accounts for ‘free choice readings’:may(p or q)

A Problem: Someone VP

–Who did Fred talk to? –Some GIRL. (Fox 2008)

Assume that there are three girls in the domain of discourse, and that the alternatives we have are: {Fred talked to some girl, Fred talked to g1, Fred talked to g2, Fred talked to g3}, abbreviated as: {p, g1, g2, g3}.

Sauerland’s predictions a. Primary implicatures: not K g1, not K g2, not K g3 b. Secondary implicatures: K not g1, K not g2, K not g3

Diagnosis a. Each secondary imp is compatible with all primary imp; b. but taken together they yield a contradiction.

Minimal model operators

a. [ExhA p](w) = 1 iff p(w) = 1 and Minimal(w)(A)(p) b. [ONLYA p](w) = 1 iff p(w) = 1 and Minimal(w)(A)(p) (… but p(w) =1 is a presupposition!)

Minimal(w)(A)(p) iff for no world w’ s. t. p(w’) =1, Aw’ ⊂ Aw where Aw is the set of members of A that are true at w, i.e. Aw = {p ∈ A: p(w) = 1}

A = {p, g1, g2, g3} Note: same result if the set A contains all conjunctions from {g1, g2, g3}

ExhA p = λw. p(w) = 1 and Minimal(w)(A)(p) = λw. p(w) = 1 and for no world w’ s. t. p(w’) =1, Aw’ ⊂ Aw = λw. p(w) = 1 and only one of {g1, g2, g3} is true at w.

Exhminimal models(S, Alt) = {w: S is true in w and ¬∃w’: S is true in w’ and w’ <Alt w} where for all worlds w’, w, w’ <Alt w iff {S’: S’ ∈ Alt and S’ is true in w’} ⊂ {S’: S’ ∈ Alt and S’ is true in w} (where ⊂ is strict inclusion)

‘Be in an S-world that makes false as many as possible of the alternatives’ (note that you couldn’t be in a world in which the negated propositions are inconsistent!’)

Operators and Motivations

ExhSauerland a. derives Sauerland’s secondary implicatures; b. encounters problems with Fred talked to some girl (all the strengthenings together might be contradictory). c. iterated, can account for ‘free choice readings’.

Exhminimal-models a. is based on ‘mimimal models’; b. has no problem with Fred talked to some girl; c. cannot account for ‘free choice readings’.

ExhFox a. is a refinement of ExhSauerland b. has no problem with Fred talked to some girl; c. b. has no problem with Fred talked to some girl.

The Free Choice Problem

a. You may have tea or coffee. b. => you may have tea and you may have coffee.

a. may (p or q) b. may p, may q

Sauerland’s primary implicatures rule out a solution a. may (p or q) b. not K may p, not K may q

Minimal model operators rule out a solution a. S = may (p or q) b. Alt = {may p, may q, may (p and q)} b. {w: S is true in w and w is a minimal S-world wrt <Alt} = {w: exactly one of {may p, may q} is true in w}

Fox’s Operator

IE(p, A) = {q ∈ A: for all maximal A’ ⊆ A such that A’¬ is consistent with p}, where A’¬ = {¬p’: p’ ∈ A’} = ∩{A’: A’ is a maximal set in A s.t. A’¬ is consistent with p}

a. [ExhA p](w) = 1 iff p(w) = 1 and every member q of IE(p, A) is false in w. b. Same for [ONLYA p] – with a presupposition that p!

a. We don’t just require that every negated alternative on its own should be consistent with the assertion + primary implicatures; we wish to ensure that all negated alternatives taken together be so compatible. b. We also bar ‘arbitrary’ choices in the set.

Fox’s Operator

IE(p, A) = {q ∈ A: for all maximal A’ ⊆ A such that A’¬ is consistent with p}, where A’¬ = {¬p’: p’ ∈ A’} = ∩{A’: A’ is a maximal set in A s.t. A’¬ is consistent with p}

a. (p or q) b. A = {p, q, p or q, p and q}

IE(a, A) = {p and q} Note that {p and q, p} IS a maximal set in A such that {¬(p and q), ¬p} is consistent with (p or q). But this subset is not contained in {(p and q), q}

ExhA(a) = λw. (p or q)(w) = 1 and (p and q)(w) = 0.

Fox’s Operator

ExhFox(S, Alt) = = {w: S is true in w and for all S’ ∈ IE(S, Alt), S’ is false in w} IE(S, Alt) = ∩{A ⊆ Alt: A is a maximal subset of Alt such that A¬ ∪ {S} is consistent where A¬ = {¬p: p ∈ A}

‘Negate all the non-entailed alternatives that can be negated together (i) consistently, and (ii) non-arbitrarily.’

a. Exh(may (p or q)) is compatible with {may p, may q}; Reason: can’t both have not may p, not may q. b. Exh Exh(may (p or q)) entails ((may p) and (may q)).

Fox’s Operator 1st try

IE(p, A) = {q ∈ A: for all maximal A’ ⊆ A such that A’¬ is consistent with {p}, q ∈ A’} = ∩{A’: A’ is a maximal set in A s.t. A’¬ is cons with p}

a. p = [Some G] Q b. A = {p, g1, g2, g3}

IE(a, A) = Ø • {g1, g2, g3} is NOT a set in A such that {¬g1, ¬g2, ¬g3} is consistent with p. • {g1, g2} IS a maximal set in A such that {¬g1, ¬g2} is consistent with p. But it is NOT contained in {g1, g3}

ExhA(a) = a

Fox’s Operator 2nd try

IE(p, A) = {q ∈ A: for all maximal A’ ⊆ A such that A’¬ is consistent with {p}, q ∈ A’}, where A’¬ = {¬p’: p’ ∈ A’}

a. p = [Some G] Q b. A = {p, g1, g2, g3, (g1 ∧ g2), (g1 ∧ g3), (g2 ∧ g2), (g1 ∧ g2 ∧ g3)}

IE(a, A) = {(g1 ∧ g2), (g1 ∧ g3), (g2 ∧ g2), (g1 ∧ g2 ∧ g3)}

ExhA(a) = λw. (p(w) = 1 and (g1 ∧ g2)(w) = 0 and (g1 ∧ g3)(w) = 0 and (g2 ∧ g3)(w) = 0}

Fox’s Operator

A Footnote

As pointed out to me by Angelika Kratzer and Fred Landman, the proposed mechanism for exhaustification is reminiscent of what is needed for counterfactuals in the premise semantics developed by Veltman (1977) and Kratzer (1981). In particular, the set of propositions that can be added as premises to acounter factual antecedent p is ∩{A⊆C: A is a maximal set in C, s.t., A ∪ {p} is consistent} where Cis the set of all true propositions. (Fox 2006)

See van Rooij and Schulz’s work for an explicit connection with non-monotonic reasoning.

Experimental Approaches

Skepticism towards Localism: Geurts and Pouscoulous 2009

The primary goal of this paper is to argue, on the basis of experimental evidence, that mainstream conventionalism is wrong. One way of saving conventionalism (if one is so inclined) is by leaving the mainstream and contenting oneself with the position that sentences containing scalar expressions are systematically ambiguous, without claiming a preference for any particular type of reading. We believe that even such a minimal version of conventionalism can be refuted, and will back up this claim with experimental evidence as well

Geurts and Pouscoulous 2009: Inferential Task

Geurts and Pouscoulous 2009 Inferential Task

Results “ While in both experiments SIs were endorsed over 90% of the time in the simple Ø-conditions, in the complex conditions these rates were considerably lower.”

Geurts and Pouscoulous 2009 Verification and Inferential Task

Geurts and Pouscoulous 2009 Ambiguity Detection

(discussion from Chemla and Spector’s slides)

Geurts and Pouscoulous 2009 Ambiguity Detection

Chemla and Spector 2011 (Chemla and Spector’s slides)

Chemla and Spector 2011

Interim Conclusion

On the basis of experimental data, the argument for localism (as opposed to reformed globalism) is real but slim.

It hinges on the availability of the ‘some but not all’ reading under exactly one.

The main arguments for localism will turn out to be indirect.

Arguments for Localism

Types of Arguments

Direct Argument: truth conditions a. Sometimes, one obtains inferences that are compatible with the existence of implicatures that are computed in the scope of other operators. b. Two directions –Refine the neo-Gricean, globalist account. –Adopt a system in which implicatures are locally computed.

Indirect Argument: intervention a. Find a semantic property P which constrains constituents, not sentences. b. Argue that constituent X must have a locally computed implicature to satisfy property P.

Two Indirect Arguments

The Argument from Hurford’s Constraint (Spector, Fox and Chierchia 2008) a. Base A disjunction (F or G) is deviant if, say, G entails F. * ... F or G ... if G entails F. b. Argument These structures can be ‘saved’ if the meaning of F can be strengthened by a locally computed implicature.

Two Indirect Arguments

The Argument from NPI Licensing (Chierchia 2002) a. Base Negative Polarity Items (e.g. any, ever, at all) are licensed if one can find a constituent C of propositional type such that the NPI is in a ‘downward-entailing environment’ in C. Ok ... [C ... any ... ] ... if in C any is in a DE position b. Argument In the computation of downward-entailingness in C, one must take into account scalar implicatures. Specifically, NPP licensing can be disrupted by locally computed implicatures... *... [C ... Exh ... any ... ] ...

Hurford’s Constraint: Spector, Fox and Chierchia 2008)

Hurford’s Constraint A sentence that contains a constituent [F or G] is infelicitous if F entails G, or G entails F .

a. #John lives in France or in Paris. b. ??John lives in Paris or in France.

a. #Mary saw a dog or an animal. b. #Mary saw an animal or a dog. c. #Every girl who saw an animal or a dog talked to Jack.

Hurford’s Constraint: Apparent Exceptions

a. Mary solved [the first problem or the second problem] or both problems. b. Mary read some or she read all the books. c. Either the first year students came or all of the students came.

Hypothesis (Fox, Spector) Locally computed implicatures are taken into account in the computation of Hurford’s Constraint.

a. Exh [Mary solved the first problem or the second problem] or both problems. b. Exh[Mary read some books] or she read all the books

Two Types of Consequences

Direct truth-conditional effect (on the literal meaning) In general, if G entails F, F or G is equivalent to F Exh(F) or G need not be equivalent to F

Indirect truth-conditional effect (on implicatures) In a special case, Exh(p or q) or (p and q) IS equivalent to (p or q) or (p and q) ... but an effect via implicatures can still be detected because the two sentences have different alternatives.

Direct Effect: Truth Conditions

Either the first year students came, or all of the students came.

Hurford’s Constraint An exhaustivity operator must be present in the first disjunct - otherwise it would be entailed by the second.

a. Either Exh [the first year students came] or all the students came b. ≈ Either ONLY the first year students came or all the students came

Prediction One of two situations must hold: first year students and no other students came, or all the students came.

Indirect Effect: Alternatives

a. (p or q) or (p and q) b. Exh(p or q) or (p and q) c. (p or q)

a. and b. are equivalent – but have different alternatives Alt(b) = {(p or q), (p and q), (p or q) and (p and q)} Alt(a) = {Exh(p or q), (p and q), Exh(p or q) and (p and q)}

When we add a further exhaustivity operator, a truth-conditional effect can be detected.

a. Every student [is a syntactician or a semanticist]. b. Every student [is a syntactician or a semanticist or both].

Observation –b. gives rise to the inference that at least one student is both a syntactician and a semanticist. –No such inference is obtained in a.

Intuitive explanation a. ∀x [Px or Qx] b. ∀x [Exh(Px or Qx) or both] => implicature that: not ∀x [Exh(Px or Qx)] hence with a/b: ∃x [(Px and Qx)]

a. ∀x (Px or Qx) b. ∀x [Exh(Px or Qx) or (Px and Qx)]

a. implicates: not ∀x Px, not ∀x Qx, not ∀x (Px and Qx)

b. implicates: not ∀x Exh(Px or Qx), not ∀x(Px and Qx), not ∀x(Exh(Px or Qx) and (Px or Qx))

Further Examples

The professor demanded that we read Ulysses or Madame Bovary. a. No ! We have to read both. b. #No ! We are not allowed to read both.

The professor demanded that we read Ulysses or Madame Bovary or both. a. No ! we have to read both. b. No ! we are not allowed to read both.

Further Examples

a. Every boy did some of the homework. b. #No! No boy did all of the homework.

a. Every boy either did some or all of the homework. b. No! No boy did all of the homework

Is a Lexical Alternative Plausible? (Fox, Spector, Sauerland)

a. Alternative: in these cases or in general, the relevant scalar terms are ambiguous between a weak a strong meaning. b. Prediction: it should not be possible to replicate these effects with intermediate exhaustivity operator.

What will have to do to pass my orals? You’ll have to have an A in syntax or semantics. a. Plausible: Exh should [A in syntax or A in semantics] b. Implausible: should Exh [A in syntax or A in semantics]

Replicating the argument’s from Hurford’s constraint with exhaustivity operators with intermediate scope.

What will have to do to pass my orals? Depending on the school, Exh[you’ll have to have an A in syntax or semantics] or you’ll have to have an A in both.

Note In this case no truth-conditional effect is detectable, because all Exh does is exclude the alternative that appears on the right-hand side.

Detecting a truth-conditional effect –What will I have to do to pass my orals? –Depending on the school, Exh[you’ll have to have an A in some field] or you’ll have to have an A in all fields

a. Intuitively, this excludes the possibility that the condition should be: have an A in at least two fields. b. ... but this does not raise the possibility that you’ll have to have an A in some but not all fields.

Detecting a truth-conditional effect –What will I have to do to pass my orals? –Depending on the school, Exh[it’s required that you have an A in half the fields] or you’ll have to have an A in all fields.

a. Intuitively, this excludes the possibility that the condition should be: have an A in two thirds of the fields. b. ... but this does not raise the possibility that you’ll have to have an A in half but not all fields.

Another Example (Spector, p.c.)

Either we must solve more than 3 problems, or we must solve more than 7 problems (I don't remember)

Reading either we must solve more than 3 and do not have to solve more than 4, or we must solve more than 7 and do not have to solve more than 8.

Argument -The truth-conditional argument is the same as before. -But in addition, more than 3 cannot be given an ambiguous lexical entry (= more than 3 but not more than 4, i.e. exactly 3!)

[Can we force the insertion of exhaustivity operators be inserted in DE environments?]

Every student who got an A in some field came from a state school. => probably makes predictions about students who got an A in multiple fields.

Every student who got an A Exh [in some field] or in all fields came from a state school. => does this exclude from consideration students who got an A in two fields only?

The Argument from Intervention on NPI Licensing

Embedded Implicatures and NPI Licensing (Chierchia 2002)

Negative Polarity Items must be contained in a propositional constituent in which they are in a downward-entailing (=negative) environment. Ok ... [C ... any ... ] ... if in C any is in a DE position

Hypothesis (Chierchia) Locally computed implicatures can disrupt NPI licensing. *... [C ... Exh ... any ... ] ...

NPI Licensing in Propositional Constituents

Negative Polarity Items only require that they be contained in a subpart of the sentence which is downward entailing.

a. *There is any wine. b. It isn't true that there isn't any wine.

Negative Polarity Items must be contained in a propositional constituent in which they are in a downward-entailing (=negative) environment. Ok ... [C ... any ... ] ... if in C any is in a DE position

Intervention Effects on NPI Licensing (Chierchia 2002)

a. I doubt that Theo drank the leftover wine or any coffee. b. *I doubt that Theo drank the leftover wine and any coffee.

a. John didn’t talk to Mary or to any other girl. b. *John didn’t talk to Mary and to any other girl.

a. I didn’t meet a person who read any of my poetry. b. *I didn’t meet ten people who read any of my poetry.

a. John didn’t introduce Mary to anyone she knows. b. *John didn’t introduce every woman to anyone she knows.

Intervention Effects on NPI Licensing (Chierchia 2002)

So far, we only have an argument that the notion of meaning which matters to the computation of DEness for NPIs incorporates scalar implicatures.

Let us embed all these examples under: Peter claims that ___

On a globalist view of implicatures, it should be possible to find a constituent with the right DE properties, namely: _

On a localist view of implicatures, this need not be so... ... if these implicatures are obligatorily local! (Why?)

Structure of Localist Accounts

A Gricean-style pragmatic mechanism is needed to derive primary implicatures, of the form: the utterance of S leads to the inference that not K S’

a. A different mechanism, the insertion of an exaustivity operators, is needed to get local implicatures. b. The exhaustivity operator must be powerful enough to get several cases of apparently local implicatures, e.g. with (p or q or r), or even: [Every P](Q or R) ≈> not [Some P](Q and R), hence [Every P](Q orS R)

The insertion mechanism must be constrained by monotonicity consideations (normally, inserting it should not weaken the meaning of the sentence).

From O to E: Charnavel 2011

Argument for E

An expression, son propre (= ‘his own’), is preferably with a meaning that can be analyzed with a covert even. Personne n’a défendu Paul. Sa propre mère a gardé le silence. ‘Nobody defended Paul. His own mother remained silent.’ ≈ Even Paul’s mother remained silent.

An analysis of the truth conditions in complex examples suggests that E can be inserted at a variety of scope sites.

E intervenes between focused elements and operators.

This suggests that even has a covert counterpart E, just like only has a covert counterpart O (= Exh).

Two Readings of ‘son propre’

Possessor ‘propre’ (irrelevant here!) Julie compare sa PROPRE vie à celle de Louise. ‘Julie compares her own life to Louise’s.’ a. No need for a covert even to derive the meaning. b. Alternatives are generated by focus on ‘own’.

Possessum ‘propre’ Personne n' a défendu Paul. Sa propre MERE a gardé le silence. Nobody took P.'s defense. His own mother remained silent. a. The sentence is understood as: Even [his mother] did. b. Alternatives are generated by focus on the entire DP (i.e. the contrasting elements need not be anybody’s mother).

Against ‘Wide Scope Only’

E can have scope under other operators Ann’s parents don’t want her E [to betray her own children]

Against ‘Wide Scope Only’

E can have scope under other operators Both individuals who E [betrayed their own parents] arrived.

Against ‘Narrow Scope Only’

E can have scope outside of islands Luc is never happy: E [he is not happy when his own children are there].

E can have scope above quantifiers E The new law prohibits [a victim from denouncing her own aggressor]!

E can have scope above operators E The police refuse that [a victim denounce her own aggressor]!

Intervention Effects

E can intervenes between focused elements and too For his 30th birthday, Jean invited his family and friends.

<??> (E) He also (E) invited his own enemies.

Intervention Effects

E can intervenes between focused elements and only ??This year, E2 Jean only1 visited his [own parents]2 [for Christmas]1.

Possessor vs. possessum 'propre'

a. 'Propre' always has a property/proximity meaning. b. In many cases, it is redundant with the possessive pronoun. c. When it is focused (possessor 'propre'), it thereby acquires a semantic/pragmatic function. d. When it is not focused (possessum 'propre' – something larger is focused), it has no semantic function... [because alternatives only consider [[his own NP]] = [[his NP]]) ... unless its 'property/proximity' meaning plays a role in specifying a scale... e. This happens when association with E occurs: unexpected because of proximity.

Propre can have a property/proximity reading [Context: Claire owns two cars: a professional car and a personal car] Claire a pris sa propre voiture. Claire has taken her own car 'Claire took her own car.' [i.e. her personal car]

Propre never loses its property/proximity reading [Context: Jeanne and Lucie Dupont are two sisters going to a clinic; Jeanne has an appointment with the dentist and Lucie with the ophtalmologist.]

Propre explaining unexpectedness

Other redundant restrictors explaining unexpectedness

Propre justifying other scales

Katzir’s Structurally-Defined Alternatives Katzir 2007, Katzir and Fox 2011

Defining Alternatives

Katzir and Fox 2011 S’ is an alternative of S if S’ ′ can be derived from S by successive replacements of sub-constituents of S with elements of the substitution source for S in C, SS(S,C)

SS (X, C), the substitution source for X in context C, is the union of the following sets: a. the lexicon b. the sub-constituents of X c. the set of salient constituents in C

Defining Alternatives

Katzir 2007 Let S, S' be parse trees. If we can transform S into S' by a finite series of deletions, contractions and replacements of constituents in S with constituents of the same category taken from L(S), the substitution source of S, we will write: S' ≤ S

a. Deletion = removing edges and nodes b. Contraction = removing an edge and identifying its end nodes. c. Replacement = substitution of a constituent in S with a constituent of the same category taken from L(S).

[Some F] G

Desirable alternative: [All F] G

Undesirable alternative: [Some but not all F] G

The desirable alternative is derived: a. Replace Some b. with All, which is in the lexicon.

The undesirable alternative cannot be obtained.

[F or G]

[F and G] is an alternative because: a. or is a subconstituent of [F or G]; b. it can be replaced with and, which is in the lexicon.

F is an alternative because: a. F is a subconstituent of [F or G]; b. the entire sentence can be replaced with it

Same argument for G.

Hence no need for Sauerland’s operators L and R.

Better Sentences

F is at least as good as G, F ≤ G, if (i) F is an alternative of G, (ii) F entails G.

F is better than G if F < G, i.e. if F ≤ G but not G ≤ F, i.e. if F ≤ G and (G is not an alternative of F, i.e. F is more complex than G) or (G is not entailed by F, i.e. F is more informative than G)

Conversational principle Do not assert F is there is a better G which could have been asserted.

Manner

a. Every candidate who sang was elected. b. Every candidate was elected.

(b) is an alternative to (a) but (a) isn’t an alternative to (b).

(b) is better than (a): –it is simpler –it is more informative

Hence we infer that (b) wasn’t assertable.

Manner

a. The President gave a good speech. b. ?The President from Chicago gave a good speech.

(b) is an alternative to (a) but (a) isn’t an alternative to (b).

(b) is better than (a): –it is simpler –though relative to common knowledge it is not more informative.

Hence we infer that (b) shouldn’t be asserted.

Conclusion

a. There is direct but subtle truth-conditional evidence for embedded implicatures ([exactly one P](Q or R)) b. There is relatively strong indirect evidence for embedded implicatures: –Hurford's constraint + induced effects; –Intervention on NPI licensing.

a. It is unclear whether strengthened meanings are obtained from a syntactic, semantic or pragmatic procedure. b. But it doesn't seem that standard Gricean reasoning can explain local implicatures.

Gricean reasoning is still needed to derive primary implicatures (e.g. (p or q) => not K p, not K q)

Structure of Localist Accounts

A Gricean-style pragmatic mechanism is needed to derive primary implicatures, of the form: the utterance of S leads to the inference that not K S’

a. A different mechanism, the insertion of an exaustivity operators, is needed to get local implicatures. b. The exhaustivity operator must be powerful enough to get several cases of apparently local implicatures, e.g. with (p or q or r), or even: [Every P](Q or R) ≈> not [Some P](Q and R), hence [Every P](Q orS R)

The insertion mechanism must be constrained by monotonicity consideations (normally, inserting it should not weaken the meaning of the sentence).

Magri’s Blind Implicatures

Motivations for Blind Implicatures

a. #Some Moldovans come from a warm country. b. ? All Moldovans come from a warm country. c. Moldovans come from a warm country.

#Only SOME Moldovans come from a warm country.

Let us write ‘F is common belief in the conversation’ as C F. C (some Moldovans come from a warm country => all Moldovans come from a warm country.)

a. (a) and (c) are contextually equivalent. b. But then why do we get an inference that (not c)?

Motivations for Blind Implicatures

Context: In Italy, children always inherit the last name of their father. a. #Some of the children of that couple have a funny last name. b. The children of that couple have a funny last name.

Context: Prof. Smith always assigns the same grade (possibly a different one every term) to all of his students. a. #This year, prof. Smith assigned an A to some of his students. b. This year, prof. Smith assigned an A to his students.

Magri’s Initial Assumptions

Exhaustivity operator a. Scalar implicatures are brought about by a covert operator akin to overt ‘only’: EXH. b. The domain of this exhaustivity operator is restricted by a contextually assigned relevance predicate R; the exhaustivity operator with its restriction is written EXHR. c. EXHR(F) = F ∧ ∧F’ ∈ R and F’ is stronger than F ¬F’ F is called the prejacent and the F’ that are negated are called the excludable alternative. d. EXH is present at all sites in which it can be inserted, but its semantic contribution may be trivialized due to R.

Magri’s Initial Assumptions

Strength Excludable alternatives are those alternatives that are logically stronger than the prejacent. Variant: exclude all the non-weaker alternatives.

Relevance The relevance predicate R is assigned by context. But its denotation must satisfy two requirements: a. The prejacent of the exhaustivity operator is relevant. b. If two propositions are contextually equivalent, then they pattern alike with respect to Relevance, namely they are either both relevant or else both irrelevant.

The Argument from Only

#Only someF Italians come from a beautiful country.

a. Some Italians come from a beautiful country. b. All Italian come from a beautiful country.

#Only every boy arrived.

John has an odd number of children. . . . . . #He has only twoF.

a. John has at least two. b. John has at least three. c. John has at least four.

[The Argument from DE-ness]

Every year, the dean has to decide: if the college has made enough profit that year, he gives a pay raise to every professor who has assigned an A to at least some of his students; if there is not enough money, then no one gets a pay raise. a. #This year, every professor who assigned an A to all of his students got a pay raise. b. This year, every professor who assigned an A to some of his students got a pay raise.

Context: In Italy, children always inherit the last name of their father. a. #Every father some of whose children have a funny last name must pay a fine. b. Every father whose children have a funny last name must pay a fine.

a. #Every student with a blue eye is German. b. Every student with blue eyes is German.

Context: Every year, the dean has to decide: if the college has made enough profit that year, he gives a pay raise to every professor who has taught a graduate or an undergraduate class; if there is not enough money, then no one gets a pay raise. a. This year, no professor who taught a graduate or an undergraduate class got a pay raise. b. #This year, no professor who taught a graduate and an undergraduate class got a pay raise.

Context: In this department, every professor teaches both a graduate and an undergraduate class in the same field of linguistics. a. #This year, no professor who taught graduate or undergraduate Semantics got a pay raise b. This year, no professor who taught graduate and undergraduate Semantics got a pay raise.

[Two Problems]

Problem 1: Why is this good? Every father whose children have a funny last name must pay a fine. i.e. why not: and not Every ... some ...

Problem 2: Why is this bad? #Every father some of whose children have a funny last name must pay a fine. i.e. why is a blind implicature obtained?

[Radical Operator-Based Analysis: obligatory embedded implicatures]

[Radical Operator-Based Analysis]

Problem 1: Why is this good? Every father whose children have a funny last name must pay a fine. i.e. why not: and not Every ... some ...

Exh [Every father Exh[whose children have a funny last name] must pay a fine.]

Exh does nothing here, but it makes the alternative with ‘some’ trivial, hence not contextually equivalent, hence one that need not be relevant. Exh [Every father Exh[some whose children have a funny last name] must pay a fine.] => a contradiction need not be obtained.

[Radical Operator-Based Analysis]

Problem 2: Why is this bad? #Every father some of whose children have a funny last name must pay a fine. i.e. why is a blind implicature obtained?

Exh[Every father Exh[some of whose children have a funny last name] must pay a fine.] • Since the underlined sentence is contextually equivalent to its alternative, the latter is relevant and hence excluded. • This is enough to derive the deviance of the sentence.

Problems

Primary vs. Secondary Implicatures I [Looking at a pile of homeworks] A: Did all students turn in their homeworks? B: Well, most did.

B utters 'Well, most did' after looking at the size of the pile; we get the primary implicature in a. but not the secondary implicature b: a. not Believe_B [all did] b. Believe_B not [all did]

Magri’s analysis yields: Exh [most students did].

Problems

Primary vs. Secondary Implicatures I [Looking at a pile of homeworks] A: Did all students turn in their homeworks? B: Most did.

Context: It’s early and only 4 of my 10 students are at the Department. I’ve just seen two of them drop by my mailbox. A. How many of your students turned in their homeworks? Did at least three do so this time? B: Well, two did. And maybe three. B'. Well, only two did. #And maybe three. (see Romoli 2011)

Could Exh be weakened so only the alternatives the speaker is competent about get excluded? (Magri, p.c.)

Problems

Primary vs. Secondary Implicatures II We will hire Leon or George. (And we might hire both – if the Dean gives us 2 positions.)

We obtain the inference in (a) but not that in (b): a. not K (L and G) b. K not (L and G)

Magri has: Exh_D (L or G) Notation: Exh_D is an exhaustivity operator whose alternatives are given by a variable D – whose value is provided by the context.

Problems

Primary vs. Secondary Implicatures II Exh_D (L or G)

Gricean alternatives Alt = {Exh_D S: S is a scalar alternative to 'L or G' and S is relevant}

g(D) cannot include (L and G), or else we would get a 'not both' entailment.

a. If Alt = {Exh_D(L), Exh_D(G), Exh_D(L and G)}, we get not K (L and not G), not K (G and not L), not K(L and G) – which is too weak (compatible with K L!). b. Solutions: Exh is absent when vacuous? (Magri) L, G not relevant?

Problems

The Role of Local Contexts a. #[Every professor who assigned the same grade to each of his students]i ti assigned the best possible grade to some of his students. b. [Every professor who assigned the same grade to each of his students]i ti assigned the best possible grade to all of his students.

Amendment to Magri’s theory Contextual equivalence in the definition of Relevance is computed relative to the local context of the prejacent.

Problems

Contextual scales a. In my company, everyone who has any degree at all has a Ph.D. #? Bill works in my company, and he has a high school degree. b. In my company, everyone who has any degree at all has a Ph.D. #Bill works in my company, and he only has a high school degree. c. In my company, everyone who has any degree at all has a Ph.D. Bill works in my company, and he has a Ph.D.

Problems

The some/every symmetry problem Context: A professor who is renowned for the difficulty of his tests announces to this students: a. I’ll give a bottle of Champagne to every student who gets a perfect score on the next test. b. I’ll give a bottle of Champagne to some/at least one student who gets a perfect score on the next test. => no presupposition of non-emptiness of the restrictor

Problems

The some/every symmetry problem a. Standard accounts: no problem – simply posit that contextual knowledge can be accessed when checking that the pair <[Some P] Q, [Every P] Q> stands in the appropriate relation of asymmetric entailment. b. Magri’s theory: in the absence of contextual knowledge, he cannot predict that some student is interpreted as some but not every student without also predicting that every student is interpreted as every but not some student; but the latter is equivalent to no student – and clearly this interpretation is not available in these cases.

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