Presuppositions

LIN 141: Semantics

Masoud Jasbi

Types of Meaning

Implications

Entailments

Ordinary

(At-issue)

Presupposition

(non-deductive) Inferences

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Conventional Implicatures

New

Old

Gricean

Conversational Implicature

Other?

Other (social?)

Meaning

Pointing Game!

(Type the number for the Picture)

Point to a dog!

1

2

3

4

5

Point to a running dog!

1

2

3

4

5

Point to a sitting dog!

1

2

3

4

5

Point to the dog!

1

2

3

4

5

Point to the running dog!

1

2

3

4

5

Point to the sitting dog!

1

2

3

4

5

Discussion

Point to:

• a/the dog!
• a/the running dog!
• a/the sitting dog!

What is happening?

What is the role of a/the?

What is the role of the adjectival modifiers?

In this picture, there is a dog!

In this picture, there is a dog too!

In this picture, there is a dog too!

In this picture, there is a dog!

Discussion

In this picture:

• there is a dog!
• there is a dog too!

What is happening?

What is the role of too?

Know vs. Think

Are they flat-earthers?

Oh! Of course!

Bob thinks that the Earth is flat.

Are they flat-earthers?

Oh! Of course!

Bob believes that the Earth is flat.

Pragmatic Presuppositions

Pragmatic Presuppositions

The presuppositions of an utterance are the pieces of information that the speaker assumes (or acts as if they assumes) in order for their utterance to be meaningful in the current context.

This general definition does not limit the source of information. The source can be:

The physical context

World knowledge

Knowledge about conversational participants

Discourse/linguistic Information

Representing Knowledge

Suppose that “it is raining”.

p = “it is raining.”

Amanda looks outside and sees that it is raining.

p ⋀ K_A [p]

Bob also looks outside and sees that it is raining.

p ⋀ K_A [p] ⋀ K_B [p]

Amanda and Bob know that it is raining.

p

p

Introspection

Amanda knows that she knows that it is raining!

p ⋀ K_A [p] ⋀ K_B [p] ⋀ K_A [K_A [p]]

If Amanda thinks about it, she knows that she knows that she knows!

The same is true of Bob.

Bob also knows that he know that it is raining!

p ⋀ K_A [p] ⋀ K_B [p] ⋀ K_A [K_A [p]] ⋀ K_B [K_B [p]]

p

p

Amanda sees Bob in the hallway.

She says: “it is raining.”

Did she tell Bob something he did not know?

Did Bob learn anything new?

Now Bob knows that Amanda knows that it’s raining!

p ⋀ K_A [p] ⋀ K_B [p] ⋀ K_A [K_A [p]] ⋀ K_B [K_B [p]] ...

⋀ K_B [K_A [p]]

p

p

p

It’s raining!

But now Amanda also knows that Bob knows.

p ⋀ K_A [p] ⋀ K_B [p] ⋀ K_A [K_A [p]] ⋀ K_B [K_B [p]] ...

⋀ K_B [K_A [p]] ⋀ K_A [K_B [p]]

Does Bob know that Amanda knows he knows?

p ⋀ K_A [p] ⋀ K_B [p] ⋀ K_A [K_A [p]] ⋀ K_B [K_B [p]] ...

⋀ K_B [K_A [p]] ⋀ K_A [K_B [p]] ⋀ K_B [K_A [K_B [p]]]

Does Amanda know that Bob knows she knows?

p

p

p

It’s raining!

p ⋀ K_A [p] ⋀ K_B [p] ⋀

K_A [K_A [p]] ⋀ K_B [K_B [p]] …

⋀ K_B [K_A [p]] ⋀ K_A [K_B [p]] ⋀

K_B [K_A [K_B [p]]] ⋀ K_A [K_B [K_A [p]]] …

K_A [K_B [K_A [K_B [p]]]] ⋀ K_B [K_A [K_B [K_A [p]]]] …

...

p

p

p

It’s raining!

Common Ground

We say proposition p is common ground for members of community C iff:

1. members of C have information that p.
2. members of C have information that I.
3. members of C have information that II.
4. So on ad infinitum

Uttering a sentence like “it’s raining” makes its meaning i.e. proposition p part of the common ground between discourse participants.

​

p ⋀ K_A [p] ⋀ K_B [p] ⋀

K_A [K_A [p]] ⋀ K_B [K_B [p]] …

⋀ K_B [K_A [p]] ⋀ K_A [K_B [p]] ⋀

K_B [K_A [K_B [p]]] ⋀ K_A [K_B [K_A [p]]] …

K_A [K_B [K_A [K_B [p]]]] ⋀ K_B [K_A [K_B [K_A [p]]]] …

...

p

It’s raining!

CG_A,B [p]

CG_A,B [p ⋀ q]

CG_A,B [p ⋀ q ⋀ r]

CG_A,B [p ⋀ q ⋀ r ⋀ s]

...

p

It’s raining!

I’m happy.

I don’t like rain.

I love rain.

CG and Presuppositions

The information in common ground, is presupposed (old information).

The information that is not already in common ground is new information.

Every act of utterance updates the common ground.

But not all of the information in an utterance is new.

We can divide the information in an utterance into:

New vs. Old

Asserted vs. Presupposed

CG_A,B [Rain]

CG_A,B [Rain ⋀ love(Bob, Rain)]

“I love rain too” carries two propositions:

Assertion: love(Amanda, Rain)

Presupposition: ∃x[x≠Amanda ⋀ love(x, Rain)]

The assertion here provides new information.

The presuppositional content is already entailed by the common ground.

p

It’s raining!

I love rain!

I love rain too!

While the assertion updates the common ground, the presupposition acts like a check, or a requirement.

CG_A,B [Rain ⋀ love(Bob, Rain) ⋀ love(Amanda, Rain)]

Check: ∃x[x≠Amanda ⋀ love(x, Rain)]

When common ground is compatible with the signaled presupposition, the utterance is acceptable.

“I love rain too” carries two propositions:

Assertion: love(Amanda, Rain)

Presupposition: ∃x[x≠Amanda ⋀ love(x, Rain)]

p

It’s raining!

I love rain!

I love rain too!

But sometimes what is presupposed by the utterance and what is (presupposed) in common ground can clash:

CG_A,B [Rain ⋀ hate(Bob, Rain) ⋀ love(Amanda, Rain)]

Check: ∃x[x≠Amanda ⋀ love(x, Rain)]

“I love rain too” carries two propositions:

Assertion: love(Amanda, Rain)

Presupposition: ∃x[x≠Amanda ⋀ love(x, Rain)]

p

It’s raining!

I hate rain!

I love rain too!

​

Notice that there will be no clash if “too” is dropped.

CG_A,B [Rain ⋀ hate(Bob, Rain) ⋀ love(Amanda, Rain)]

​

This suggest that the source of the presupposition was really the word “too”.

So presuppositional information can be encoded in some words and constructions.

p

It’s raining!

I hate rain!

I love rain!

Uncertainty about CG

The picture of CG depicted so far is very simplistic.

There is a shared body of knowledge.

Each utterance adds information to the CG.

But we are not always certain about what is in CG.

We are constantly checking/updating our representations of common ground!

There is NO central CG database to access and check!

CG + p + q

p

q

Uncertainty about CG

We each have a version of CG.

A representation of what we believe is common ground.

These versions can differ from each other.

We may be more or less certain about some info being CG.

Therefore, communication happens in two dimensions:

1. At-issue: communicate what we believe to be new
2. Presuppositional: communicate what we believe to be old and part of CG.

​

CG_B + p + q

p

q

CG_A + p + q

Syncing CGs

Suppose Bob loves rain but he does not know (or forgot) that Amanda knows that.

But Amanda thinks Bob knows she knows.

​

Suppose Amanda says: “I love rain too!”

Now Bob can both sync his CG as well as add the new information that Amanda loves rain!

​

CG_B

At-Issue: I love rain!

-------------------------

Presup:

Bob loves rain.

CG_A + love(Bob, Rain)

Accommodation

This process of syncing is called presupposition “accommodation”.

Accommodation is a way of dealing with mismatch in the versions of the CG.

As well as a way of forcing information into the common ground.

Example: Abe knows he should not cross the line!

CG_A +

love(Bob, Rain) + love(Amanda, Rain)

CG_B +

love(Bob, Rain) + love(Amanda, Rain)

Accommodation

Successful accommodation depends on many factors:

Consistency with the common ground

“Bob knows the Earth is flat.”

Speaker authority or knowledge

Trust

Plausibility/surprise

“Oh I forgot to feed my cat/giraffe this morning!”

Semantic Presuppositions

Semantic Presupposition

Semantic (conventional, lexical) presuppositions are part of the encoded meanings of specific words and constructions called presupposition triggers.

​

Example: “I love rain too”

Assertion: I love rain love(Amanda, Rain)

Presupposition: Someone else loves rain. ∃x[x≠Amanda ⋀ love(x, Rain)]

Presupposition Triggers

• The king of France is bald.
1. Presupposition: there is a unique entity d which is “king of France”
2. Assertion: d is bald.
• Abe realized that the king of France is bald.
• Presupposition: the the king of France is bald.
• Assertion: Abe realized it.
• Why is the king of France bald?
• Presupposition: the king of France is bald.
• Query: what is the reason?

Presupposition Triggers

• Bob quit smoking.
• Presupposition: Bob smoked in the past.
• Assertion: Bob does not smoke now.
• Bob continued smoking.
• Presupposition: Bob smoked in the past.
• Assertion: Bob smokes now.
• Consider both options.
• Presupposition: there are two options.
• Directive: consider them!

Presupposition Triggers

• Cleo ran very quickly!
• Presupposition: Cleo ran.
• Assertion: the running was very quick.
• Bob regrets that Abe cheated on the exam.
• Presupposition: Abe cheated on the exam.
• Assertion: Bob regrets it.
• Abe acknowledged that he cheated on the exam.
• Presupposition: Abe cheated on the exam.
• Assertion: Abe acknowledged it.

Presuppositions as Entailments

We can treat presuppositions as a type of entailment.

Remember that we tested entailments using explicit cancellability.

We can do the same with presuppositional entailments..

At-issue: Barbara met a wizard ⇒ There is a wizard.

Test(S₁⋀¬S₂): # Barbara met a wizard and there is no wizard.

Presuppositional: Barbara met the wizard ⇒ There is a wizard.

Test(S₁⋀¬S₂): # Barbara met the wizard and there is no wizard.

Presuppositions as Entailments

Presuppositional: Cabe realized that the Earth is flat ⇒ The earth is flat

Test(S₁⋀¬S₂): # Abe realized that the Earth is flat and the Earth is not flat.

Non-presuppositional: Cabe thinks that the Earth is flat ⇏ The earth is flat

Test(S₁⋀¬S₂): Abe thinks that the Earth is flat and the Earth is not flat.

Presuppositional: Cleo quit smoking. ⇒ Cleo smoked before.

Test(S₁⋀¬S₂): # Cleo quit smoking and she had not smoked before.

# My tripod legs are both broken.

# With the big bang, the universe continued to exist.

Detecting Triggers

But how do we know what is a trigger and what is not a trigger?

How do we know what counts as presuppositional content?

We need diagnostics!

Presupposition Diagnostics

Two common properties shared by presuppositions.

1. Projection
2. Common Ground Constraints (Strong contextual felicity)

Projection

Entailment Canceling

Ordinary (at-issue) entailment is often cancelled by these operators:

1. Negation
2. Questions
3. Conditional antecedents
4. Possibility modals

Negation:

Barbara met a wizard. ⇒ there is a wizard.

Barbara did not meet a wizard ⇏ there is a wizard.

Entailment Canceling

Question:

Barbara met a wizard. ⇒ there is a wizard.

Did Barbara meet a wizard? ⇏ there is a wizard.

Conditional antecedent:

Barbara met a wizard. ⇒ there is a wizard.

If Barbara met a wizard, then she learned some magic. ⇏ there is a wizard.

Possibility modal:

Barbara met a wizard. ⇒ there is a wizard.

Barbara might have met a wizard. ⇏ there is a wizard.

Projection

Presuppositional content is typically not cancelled by these operators.

At-issue content is trapped, but presuppositional content escapes (i.e. projects).

Negation:

Barbara met a wizard. ⇒ there is a wizard.

Barbara did not meet a wizard ⇏ there is a wizard.

Barbara met the wizard. ⇒ there is a wizard.

Barbara did not meet the wizard ⇒ there is a wizard.

Barbara met the wizard. ⇒ there is a wizard.

Question:

Did Barbara meet the wizard? ⇒ there is a wizard.

Conditional antecedent:

If Barbara met the wizard, then she saw some magic. ⇒ there is a wizard.

Possibility modal:

Barbara might have met the wizard. ⇒ there is a wizard.

Family of Sentences Diagnostic

One way to diagnose a presupposition is to see if it projects when it is embedded under these operators.

The family-of-sentences for sentence S are its variants under: negation, question, antecedent of conditionals, and possibility modals.

S = “Barbara met the wizard.”

FOS(S) =

1. Negation: “Barbara didn’t meet the wizard.”
2. Question: “Did Barbara meet the wizard?”
3. Conditional Antecedent: “If Barbara met the wizard, then she saw some magic.”
4. Possibility modal: “Barbara might meet the wizard.”

FOS Diagnostic (Formal Definition)

Let S be a sentence that contains trigger t and gives rise to implication m.

Let FOS(S) be the family-of-sentences variants of S.

If implication m is also implied by FOS(S) then we say that m is projective.

S = “Barbara met the wizard.” ⇒ m = there is a wizard (t = “the”)

FOS(S) =

1. Negation: “Barbara didn’t meet the wizard.” ⇒ m = there is a wizard
2. Question: “Did Barbara meet the wizard?” ⇒ m = there is a wizard
3. Conditionals: “If Barbara met the wizard, then she saw some magic.” ⇒ m = there is a wizard
4. Possibility modal: “Barbara might meet the wizard.” ⇒ m = there is a wizard

​

Tonhauser, Beaver, Robers, Simons (2013). Language

Problems with the FOS diagnostic

It is not always possible to have all the FOS variants of a sentence.

Sometimes different parts of the test give variable results.

So we should not be just following the diagnostic.

We should carefully examine what is going on when we apply it.

Exercise

Test if the following implications are projective using the FOS diagnostic.

1. Bob quit smoking.
1. Implication 1: Bob smoked in the past.
2. Implication 2: Bob does not smoke now.
2. Barbara ate her favorite dish, namely Shahi Paneer.
• Implication 1: Barbara ate.
• Implication 2: Barbara’s favorite dish is Shahi Paneer.

Common Ground

Constraints

Constraints on the Common Ground

Presuppositional content as information entailed by the common ground.

Presupposition triggers are overt devices in a language that signal what the speakers have presuposed in the conversation.

We should be able to detect presupposed content by manipulating the CG.

But CG is highly abstract and malleable so manipulating it is going to be hard and careful work.

Manipulating the CG

Suppose we suspect that trigger t gives rise to implication m.

Does m stem from constraints on the CG?

We can construct two example CGs or contexts:

1. m-positive: implication m is part of CG
2. m-neutral: implication m is not part of CG

We can then see how the utterance with t sounds in each of these contexts.

If t requires a CG with m, then it should sound bad in a CG without it (m-neutral), and sound good in a CG with it (m-positive).

CG Diagnostic

✓

#

✓

Assume trigger t presupposes m.

CG Diagnostic: Example

✓

#

✓

U = “There is a cup too!”

t = too

m = there is something else.

There is a cup too!

There is a cup too!

CG Diagnostic: Example

✓

#

✓

U = I read the book!

t = the

m = there is a unique book.

I read the book!

I read the book!

Exercise

Use the CG diagnostic to see if the following projective content is presuppositional (the result of constraints on the common ground).

• Bob quit smoking.
• Implication: Bob smoked in the past.
• Barbara ate her favorite dish, namely Shahi Paneer.
• Implication: Barbara’s favorite dish is Shahi Paneer.

Translation into L_λ

Presuppositions in L_λ

How can we represent presuppositions in our semantic theory?

Presuppositions provide definedness conditions.

A statement can be true or false when its presuppositions are satisfied.

Otherwise, it is neither true nor false. It is just undefined.

Falsehood vs. Undefinedness

Bertrand Russell: a statement like “the king of France is bald” is false, because there is no king of France.

Strawson: It does not make sense to talk about truth or falsehood in such cases.

“The king of France is bald” is neither true, nor false. It is undefined.

What do you think?

Strawson’s treatment requires a whole new logic!

P. F. Strawson

Philosopher

1919-2006

Bertrand Russell

Mathematician

1872-1970

A Trivalent Logic

Now we need to expand our truth values to include a third option: undefined.

We will show undefined as #.

In our new logical system, a sentence can be true T, false F, or undefined #.

Partial Functions

A partial function from A to B is a function f: A′ → B, for some subset A′ of A.

It does not map all elements of the domain to the co-domain.

It generalizes the concept of a function f : A → B by not forcing f to map every element of A to an element of B.

If A′ = A, then f is called a total function.

The meaning of “the”

Define “the” as a function that takes a set as its input.

If the set has only one member, it returns that member.

If the set has no member, or more than one member, it returns #.

The definite article “the”

{ }→

{ }→

{ , } → #

{} → #

{ , , } → #

...

I(the) =

Syntax and Semantics of Iota

We define a new operator to enforce uniqueness called iota.

L_λ syntax rule for iota:

If 𝜑 is an expression of type t, and x is a variable of type 𝜎, then ꙇx.𝜑 is an expression of type 𝜎.

L_λ semantic rule for iota:

​

The Meaning of “the”

[ → 1, → 0, → 0, ... ] →

[ → 0, → 1, → 0, ... ] →

[ → 1, → 1, → 0, ... ] → #

[ → 0, → 0, → 0, ...] → #

...

​

[λP.ꙇx.P(x)] =

What is the type of this function?

<<e,t>, e>

Example Translation

“The president”

Exercise

Provide a translation for “The president ran” in L_λ.

Definedness Conditions

Let’s define an operator that imposes definedness conditions generally.

Syntax of definedness conditions:

If 𝜑 is an expression of type t, then ∂(𝜑) is an expression of type t.

Semantics of definedness conditions:

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