Knowledge of syntax If Jon or Leo shows up, we’ll have fun TP CPTP C TP NP T’ NP T’ N T VP if NP co NP show up we ’ll Jon or Leo have fun * Jon if or Leo.

Knowledge of syntax

If Jon or Leo shows up, we’ll have fun

TP

CP TP

C TP NP T’

NP T’ N T VP

if NP co NP show up we ’ll

Jon or Leo have fun

* Jon if or Leo shows up we’ll have fun

What is knowledge of meaning?

Intuitions about entailment

• The door in this room is opened

• The door in this room isn’t closed

• Some door in this building is open

• Not every door in this building is closed

….

A entails B

Intuitions about presuppositions

• The door in this room is open

• The door in this room is closed

• To use the door in this room, there must be one and only one window in this room

• The X Vs presupposes:

There is just one X (around)

A presupposes B

• A presupposes B = B must be true for A to be asserted or denied felicitously

* The door is open; but there is no door

* The door isn’t open; but there is no door

How to tell the difference

a. John had lunch

b. Someone (here) had lunch

c. John didn’t have lunch

d. It was John who had lunch

e. It wasn’t John who had lunchBoth (a) and (d) entail (b); in addition, (d) also presupposes (b).

That’s because the negation of (d), namely (e), still requires the

truth of (b) to be felicitous. The negation of (a), namely (c),

doesn’t.

What presuppositions associate with

• It is XP that [IP…GAP…] Cleft sentences

• It is John that [IP Bill saw __ in the garden]

Focus has a similar semantics:

(a) I saw [JOHN] in the garden

(b) I didn’t see [JOHN] in the garden

(c) I saw someone in the garden (a) and (b) presuppose (c)

Presuppositions may associate with:

- lexical items (the)

- syntactic structures (cleft sentences)

- intonational contours (focus)

Intuitions about implicatures

The door is open

I am cold

I want to get in and steal everything

I want to run away with you

Can you pass me the salt?

- are you able to?

- pass me the salt!

What are implicatures?

• A implicates B: A suggests/conveys B; but it can be called off:

• Brrr. The door is open…

But leave it that way.

Can you pass me the salt?

I have the ability; but I will choose not to exercise it.

More implicatures

(a) John fell down and broke his leg

(b) John fell down and then broke his leg

(c) It is true that John fell down and broke his leg. But not in that order; in fact it turns out that he fell down because he broke his leg

(d) * It is true that John fell down and then broke his leg. But not in that order; in fact it turns out that he fell down because he broke his leg

A then-component is systematically associated with and; but it is NOT an entailment of and. It must be an implicature.

Semantic competence: summary

For any sentence S of our language, we know:

1. What the world would have to be like for it to be true (truth conditions)

2. What it entails

3. What it presupposes

4. What it implicates

These are the semantic counterparts of intuitions about well

formedness; they constitute our primary semantic data.

Knowledge of word meaning: How words channel (1)-(4)

Why these four?• Why not something else? E.g. what about synonymy…

• But what is synonymy?

• Try: A and B are synonymous iff they can always be used interchangeably.

(a) Sherlock Holmes found all of the five clues but one

(b) Sherlock Holmes found four of the five clues

(c) …which, however, is the crucial one

Nothing is ALWAYS intercheangable with something else

The semantic relations you pick must have a clear enough characterization for us to go after them in a computationally tractable manner

Productivity of semantic competence

And of course,• The number of sentences is infinite; hence their truth

conditions are also infinite• For each single sentence, the entailments,

presuppositions, implicatures it gives rise to are infinite

• We productively recognize entailments, etc. we have never encountered

I own a pink whale I own a whale

A daunting task…

Semantics: a computational theory of- Truth conditions- Entailment - Presuppositions- Implicatures…just like syntax is a theory of what

constitutes a well formed sentence

Non symmetry and transitivity of entailment

a. Every Italian passed the test

b. Gennaro passed the testc. No Italian failed the test

(a) entails (b)(b) does not entail (a)(a) and (c) entail each otherIf A entails B, it may or may not be that B entails C

a’. Gennaro had pasta for lunch

b’. Some Italian had pasta for lunch

c’. Some Italian had lunch

(a’) entails (b’)

and (b’) entails (c’)

(a’) entails (c’)

If A entails B and B entails

C, then A entails C

Structure sensitivity of entailment

a. Leo owns three (or more) carsb. Leo owns two (or more) cars [three two]c. If Leo got rich, he now will own three (or more) carsd. If Leo got rich, he now will own two (or more) cars

[three two]e. If Leo owns two (or more) cars, he is richf. If Leo owns three (or more) cars, he is rich

[two three]

Structure sensitivity of Entailment

Leo owns two (or more) cars

if______, ______

2 3 3 2

Structure sensitivity of Entailment

L met M or S L met M

If L went to school, he met M or S

If L went to school, he met M

If L met M or S, he will be depressed

If L met M, he will be depressed

if______, ______

a or b a a or b a

Structure sensitivity of entailment

a. At least three students smoke

b. At least two students smoke

At least: 3 2

a. At most three students smoke

b. At most two students smoke

At most: 2 3

Context sensitivity of entailment

a. John tried to become a writer

b. John’s mother tried that (when she was in college)

c. John’s mother tried to become a writer

a. John wanted to become a writer

b. John’s mother wanted that too

c. John’s mother wanted to become a writer

d. John’s mother wanted for John to become a writer

Pervasiveness of entailment: Connectives

a. I will see Eva and Leo

b. I will see Leo

a. I will see Eva or Leo

b. I will see Leo

This entailment pattern differentiates the meaning of and from that of or

Pervasiveness of entailment: Types of verbs

a. Yesterday Leo was swimming

b. Yesterday Leo swam

a. Yesterday Leo was drowning

b. Yesterday Leo drowned

Pervasiveness of entailment:Types of adjectives

a. This is a piece of chalk

b. This is white

c. This is a white piece of chalk

a. This is a hamster

b. This is small

c. This is a small hamster

Why a theory of entailment is challenging:

a. Non symmetric

b. Transitive

c. Structure dependent

d. Context dependent

e. Pervasive and diversified

f. Productive (we are able to compute it on novel sentences)

And similarly for the rest of our semantic relations…

Getting started

Gennaro swims Gennaro is a linguist This is red

Interpretation:- A mapping of expressions into meanings- Meanings: ways of getting from situations of

use/times/contexts to informational values

Gennaro swims Gennaro is a linguist This is red

Lexicon:

||Gennaro||t = GC

||this||t = a, where a is what the speaker at t is pointing at

||runs||t = r, where for any u, r(u) = 1 iff …

u does whatever constitutes running at t

||linguist||t = l, where for any u, l(u) = 1 iff

u belongs to the class of linguists at t

||red||t = r, where for any u, r(u) = 1 iff

u reflects light in the red range at t

Gennaro swims Gennaro is a linguist This is red

Composition rules:

i. || [TPNP T’]||t = ||T’||(||NP||)

ii. ||[XPX]||t = ||X||t

||Gennaro runs||t = ||runs||t (||Gennaro||t),

which is 1 iff GC runs at t

Truth conditions: a specification of how a

sentence leads us from times/contexts t to

whether that sentence holds in t

Meaning is compositional

TP

NP T’

N T AP

This is A

red||this is red||t = ||is red||t (||this||t) = ||is||t (||red||t)(||this||t) =

what the speaker is pointing at at t is red

||is||t (At) = At

||was||t (At) = At’, where t’ is some t that precedes t

Variations on the semantics of predicates and theories of concepts

The Classical strategy (‘the good’):

||red||t (u) = 1 iff the necessary and sufficient conditions for

being red are met by u. Under this view, the function ||red||t

corresponds to/determines a set { x: ||red||t(x) = 1}

The Fuzzy strategy (‘the bad’):

||red||t (u) = n, where n [1,0] depending how close u is to

focal red

The Supervaluation strategy (‘the ugly’)

||red||t(u) = 1, if u is certainly red, ||red||t(u) = 0, if u is

certainly not red; if u is neither, then ||red||t(u) lacks a value

Comparatives:this is more red than that

• The Fuzzy strategy/ (the bad):

r(u) > r(u’)

• The Supervaluation strategy (the ugly):

It is impossible to extend r to r+ so as to make

r+(u’) = 1, without also making r+(u) = 1

• The Classical strategy (the good)

This is red = rd (u) = u is red to degree d

• This is more red than that = the degree d such that rd(u) = 1 is higher than the degree d’ such that rd’(u’) = 1

Where we stand

The beginning of a theory of Truth Conditions, in which they depend on the denotation of predicates and nouns.

• Our current model of model of the semantics of predicates:

Functions from times and individuals into truth values (in three variants – the good, the bad, and the ugly)

Three questions that we are led to:

i. Which predicate is associated with which function?

ii. How does one determine whether ||red||t(u) = 1 (what makes something red/a cat, etc.?)

iii. What does a normally competent speaker know about the red-function?

Our three questions

Referential DPs: t individuals

Predicates: t characteristic functions from

individuals into truth values

i. Which predicate is associated with which function?

This is determined by some historically established link between a phonological form and a particular function, sustained and transmitted by a spontaneous social convention

• This first question is relatively uncontroversial

Two more controversial questions

ii. How do you determine whether ||cat||t(u) = 1?

= What makes something a cat?

To be addressed in terms of the best theory of what cats are (a certain genetic template?); but also a matter of social practices/ecology (when are people willing to call a cat-embryo a cat? When does a dead cat cease to be a cat?)

iii. What does a normally competent speaker know about the cat-function? What concept does the competent speaker associate with being a cat?

Some way of computing a cat-function causally linked to cats and reliable enough for successful communication/survival

Two positions• Externalism: only extra-mental cat-functions matter to language• Internalism: only mind-internal cat-functions matter to language

An internalist needs some story of how concepts are linked to their extra-mental manifestations. Not trivial.

• A classic externalist argument:

Let w be your water-function; applied to some quantity x of clear liquid it returns 1; we then discover that x is not H2O.

Do we still want to say that x is water?

Internalist prediction: yes (x fits with the procedure)

Externalist prediction: no (x is not a sample of what water is causally linked to)

In conclusion, what do we know about the meaning of content words?

• Something about:

- their ‘logical type’

- how to link them up with the appropriate data set in our

environment and/or to the corresponding cognitive

structures

Perhaps this isn’t all that much.• But wait until we get to function words…

(Which is what linguists have been doing anyhow):

- how content words contribute to entailment, presuppositions, etc. and viceversa

Good news: we don’t have to decide between exernalism and internalism to keep going