From a quite general point of view, language is a means of connecting form and meaning. That is, a spoken language involves largely arbitrary strings of sounds that are associated, by the conventions of that language, with particular meanings.

Phonetics and phonology are the study of the properties of linguistic forms in this sense -- what sounds make up morphemes, words, phrases, sentences, whole utterances.

Semantics is the study of the meaning of these forms.

Morphology and syntax are concerned with the way pieces of form are combined, as well as how this interacts with their meanings.

Lexical semantics: the meanings of words

Semantics vs. Pragmatics

Semantics can be defined as "the study of the meaning of morphemes, words, phrases and sentences."

You will sometimes see definitions for semantics like "the analysis of meaning," To see why this is too broad, consider the following. Kim, returning home after a long day, discovers that the new puppy has crapped on the rug, and says "Oh, lovely."

We don't normally take this to mean that Kim believes that dog feces is inspiring of love or affection, has pleasing or attractive qualities, or is delightful. Someone who doesn't know English will search the dictionary in vain for what Kim means by saying "lovely":

	  (ADJECTIVE): [love-li-er, love-li-est].

	    1. Full of love; loving.
	    
	    2. Inspiring love or affection.
	    
	    3. Having pleasing or attractive qualities.
	    
	    4. Enjoyable; delightful.

	

Obviously this is because Kim is being ironic, in the sense of "using words to convey the opposite of their literal meaning". Kim might have said "great," or "wonderful," or "beautiful", or "how exquisite", and none of the dictionary entries for these words will help us understand that Kim means to express disgust and annoyance. That's because a word's meaning is one thing, and Kim's meaning -- what Kim means by using the word -- is something else.

There are lots of other ways besides irony to use words to mean something different from what you get by putting their dictionary entries together. Yogi Berra was famous for this: "if you can't imitate him, don't copy him;" and "you can observe a lot just by watching" and dozens of others.

In fact, even when we mean what we literally say, we often -- maybe always -- mean something more as well. The study of "speaker meaning" -- the meaning of language in its context of use -- is called pragmatics, which we'll talk about in the second part of today's lecture.

Philosophers have argued about "the meaning of meaning," and especially about whether this distinction between what words mean and what people mean is fundamentally sound, or is just a convenient way of talking. Still, most linguists find the distinction useful, and we will follow general practice in maintaining it, even if it is not always easy to draw the line.

Basic word meanings and relations between them

Shared forms and meanings

We need to distinguish homonymy ("same name") from polysemy ("many meanings"):

• two words are homonyms if they are (accidentally) pronounced the same:
  • too and two
  • lead (the metal) and led (the past tense)
  • pool table and swimming pool
• a single word is polysemous if it has several meanings, related in some way:
  • pig the animal and pig the sloppy person
  • pool of water on the ground and swimming pool

Homonyms are roughly the same thing as homophones, except that

• the term homophone is most often used when we're talking about things with different spelling (see, sea), while
• the term homonym focuses on two words with the same pronounciation but different meaning, regardless of spelling (or sometimes, explicitly with the same spelling, such as the two senses of pool).

It's not always easy to decide if two word-forms are actually two separate words, or just one word with two pronunciations. You can see what the creators of dictionaries think by the way they list words -- under one entry, or under two. These are from American Heritage.

POOL 1 1. A small body of still water. 2. An accumulation of standing liquid; a puddle: "a pool of blood." 3. A deep or still place in a stream. 4. A swimming pool. 5. An underground accumulation of petroleum or gas in porous sedimentary rock. POOL 2 1. a. A game of chance, resembling a lottery, in which the contestants put staked money into a common fund that is later paid to the winner. b. A fund containing all the money bet in a game of chance or on the outcome of an event. 2. A grouping of resources for the common advantage of the participants: "a pool of implements for the use of all the workers on the estate; forming a pool of our talents." 3. An available supply, the use of which is shared by a group. 4. A group of journalists who cover an event and then by agreement share their reports with participating news media: "the White House press pool." 5. a. A mutual fund established by a group of stockholders for speculating in or manipulating prices of securities. b. The persons or parties participating in such a fund. 6. An agreement between competing business concerns to establish controls over production, market, and prices for common profit. 7. Any of several games played on a six-pocket billiard table usually with 15 object balls and a cue ball.

We won't focus excessively on this distinction, but the terms will come up. For example, significant lexical ambiguity most often involves cases of homonyms.

I put five dollars in the pool.

1. "placed a bet in the amount of $5"
2. "dropped some money into the water"

The polysemy relationship is often so close that no significant ambiguity arises, just shades of meaning.

I threw a stone into the pool.

1. "into the swimming pool"
2. "into the pool of water that had collected after the rain"

The slight uncertainty in the interpretation of I threw a stone into the pool is best thought of as a kind of vagueness, rather than two mutually inconsistent interpretations, as in I put five dollars in the pool (each of which may also be more or less vague).

Sometimes homonyms are pronounced the same due to historical accident, as in the case of pool:

POOL of water is from Old English pól of the same meaning. It's related in somewhat obscure ways to Dutch poel and Swedish pól, and to Celtic words such as Irish poll meaning "hole, bog, pond."

POOL in gambling is a 17th century borrowing from French poule "chicken", seemingly based on a slang term for "booty, spoils, plunder."

In other cases, homonyms may have started out as the same word (i.e. as polysemous), but may have diverged so much over time that speakers without specialized knowledge no longer recognize them as the same word.

BANK of a river is found in Middle English and is probably borrowed from Old Norse banke meaning "ridge, eminence, bank of clouds, of a river, chasm, etc."

BANK as a financial institution comes to us more recently through Italian banca, a bench or moneychanger's table. But this word itself was borrowed from a Germanic language, from the same root found in Scandinavian, and probably originally meant "shelf" of some kind -- a natural shelf of earth or sand, or an artificial shelf (table) of wood.

What matters in describing a speaker's understanding of their language is how they interpret the words, not where they came from.

Inclusion and exclusion

Hyponymy (literally "under-name") is the relation between a more general and more specific word, a relation of inclusion.

If you can say	then this means
all X's are also Y's	X is a hyponym of Y

The opposite relation is that Y is a superordinate of X (also called hypernym "above-name").

	Hyponym	Superordinate
Nouns	mouse car thief	rodent vehicle criminal
Verbs	punch look	hit see
Adjectives	scarlet alert	red awake

The reference of the hyponym -- the set of things that it can point to -- is wholly contained by the reference of the superordinate. In other words, every X is a Y, to use the same convention as above.

Here are some typical contexts in which it's natural to find hyponyms (X) and superordinates (Y) :

dogs and other animals

there's no flower more beautiful than a rose

he likes all fruit except bananas

she reads books all the time, especially novels

But not all such contexts involve pure hyponymy, since instances of overlap can also occur:

dogs and other pets
(not all dogs are pets)

snakes and other poisonous creatures
(not all snakes are poisonous)

there's no weapon more versatile than a knife
(not all knifes are weapons, e.g. a butter knife)

In this case, the pairs of words are compatible, but not hyponymous.

Their reference overlaps, but one does not wholly contain the other.

For compatible words, we can say things like the following:

This is a snake but it's not poisonous.

This is a knife but it's not a weapon.

Such statements are absurd for hyponyms, assuming the ordinary meanings of the words:

?? This is a rose but it's not a flower.

?? I punched him but I didn't hit him.

One might, for example, mean something like "This has the appearance of a rose but it's not an actual flower, it's just silk." But in this case, rose and flower are used inconsistently -- one is used in an extended sense ("real" and "artificial" roses), the other in a narrow sense ("real" flowers only).

Of course, it's also possible for there to be no overlap at all in the reference of two words -- that is, the words might be incompatible. In such cases, we know that

if X then not Y, and

if Y then not X

Diagrammatically, there's no overlap between the sets.

We can't form the sorts of sentences we did for hyponyms and compatible words.

?? dogs and other cats

?? bananas and other apples

It's quite common, however, to conjoin (with and, but not other) words that are hyponyms of the same superordinate word.

dogs and cats

bananas and apples

At the same time, it's odd to conjoin a hyponym with its superordinate unless some acknowledgment is made of their relationship (such as "other").

?? dogs and animals

?? bananas and fruit

It should be clear that our knowledge of the interrelationships of words has a significant impact on our knowledge of how reasonable sentences can be constructed.

Much of this seems obvious, because it's so automatic for a native speaker of a language, but if we want to understand what linguistic knowledge consists of -- to study the organization of the mind, or to teach computers to speak like people -- this is the kind of knowledge that has to be discovered and stated clearly.

Synonymy

"A word having the same or nearly the same meaning as another word or other words in a language."

American Heritage Dictionary

One important distinction to recall when discussing synonymy is that between denotation and connotation.

denotation: The most specific or direct meaning of a word, in contrast to its figurative or associated meanings.

connotation: The set of associations implied by a word in addition to its literal meaning.

Even when words can be called true synonyms -- in which case they can be interchanged with no difference in the meaning of a sentence -- it's a matter of having the same denotation, leaving room for slightly or even radically different connotations.

A simple example is found with scientific terminology, where the scientist's term for, say, a chemical compound might have an everyday equivalent, referring to the same compound but appropriate to rather different circumstances.

Person to friend at dinner table:

Please pass me the salt.

Chemist to assistant in lab:

Please pass me the sodium chloride.

In these two circumstances, the substance is the same (the denotation), but is likely to be in a rather different sort of container and intended for different uses (the connotation). But since the denotation is the same, we can consider them to be synonyms.

The term salt used scientifically for a certain class of compounds reflects the polysemy of this word; only one meaning of salt is synonymous with sodium chloride.

True synonyms, then, are typically differentiated by style of speech or appropriate context of use. Some more examples of a scientific or technical sort:

water = H₂O

lion = Panthera leo

Some non-technical words also seem to be essentially equivalent, i.e. true synonyms, with relatively minor differences in the contexts of use. The choice can depend on dialect differences or just individual preference.

fall = autumn

bag = sack

soda = pop

sofa = couch

car = automobile

There can still, of course, be some connotational differences; for example, the term sofa seems to become more common as the price of the item increases.

Truth conditions

A more formal way of determining whether two words or sentences mean the "same" thing is to ask whether their truth conditions are the same.

This term refers to the conditions in the world necessary to determine whether a proposition is true or false, i.e. what its truth value is.

That is, if we make a claim about the world using one word, and then substitute another word, is the result always equally true of the world (or indeed, of any possible world in which the two words could apply)? If so, the words are synonyms.

The bottle contains water.
The bottle contains H₂O.

The gazelle was killed by a lion.
The gazelle was killed by a Panthera leo.

Chris just bought a new car.
Chris just bought a new automobile.

We cannot imagine a world (i.e. a set of circumstances) in which just one of each pair is true: the synonymy of the words prevents this. (It doesn't count if you imagine a world where the words have different meanings!)

If two words are not true synonyms, we should be able to find some sentences that permit substitution with the same truth value, but others that don't. This is certainly the case with hyponyms.

My neighbor has a dog.
My neighbor has a border collie.

Since we can easily imagine a case in which one of these is true (dog) at the same time that the other isn't (border collie), they aren't synonyms.

Trade names often become generalized to describe a particular product, whether it's produced by the original company or not.

kleenex = facial tissue

to xerox = to photocopy

If you say I xeroxed the page, it doesn't normally imply that you used a machine manufactured by Xerox Corporation. In these cases, the words xerox and photocopy are true synonyms.

Other trade names haven't been entirely "bleached" of their specific meaning, though they can be used in a generic way (leading to polysemy).

Advil = ibuprofen

Coke = cola soft drink

If you ask for an Advil, and someone gives you ibuprofen manufactured by another company, you're unlikely to feel betrayed. And you might ask for a Coke when you really don't care whether it's a Pepsi, but your host is likely to ask you if Pepsi is okay, realizing that they're not entirely equivalent.

Some people use Coke to mean "any soft drink," as when someone say It's really hot, let's get a Coke and then goes to the store and buys a 7-Up. This reflects another potential polysemy of that word.

Antonymy

An antonym, in vague terms, has the opposite meaning of some other word. But there's far more to it than this definition implies.

Generally speaking, some adjectives are gradable while others are not. This means that properties can be said to exist to a degree (=gradable) rather than being an either/or proposition (=nongradable, or complementary).

The simplest test for gradable adjectives is whether you can modify the word with very.

Gradable:

very large / very small

very sad / very happy

very wet / very dry

Nongradable

*very first / *very last

*very alive / *very dead

*very single / *very married

So, schematically:

large

small

s i n g l e	m a r r i e d

There are, of course, special uses of nongradable adjectives with very that treat the quality as a matter of degree, but not in the literal meaning.

They're very married

"they act very much the way you expect married couples to act"

She's very pregnant

"it's very obvious that she's pregnant; her belly is very large due to pregnancy"

These special cases need to be distinguished from ordinary gradable adjectives, where it's the core meaning of the adjective that's evoked.

They're very large

"they're large to a great degree"

She's very happy

"she's happy to a great degree"

Nongradable opposites can belong to other parts of speech, in addition to the adjectives discussed so far.

nouns

man / woman
stalactite / stalagmite

verbs

hit / miss (a target)
pass / fail (an exam)

Claiming that these are nongradable opposites means that (within the right semantic domain) some thing or action has to be one or the other.

• among adult humans, any individual is either a man or a woman
• if one aims and shoots a gun, one either hits or misses the target

In some cases, there may be difficulties of definition: what if the target is merely nicked by the bullet? Is that hit or miss? The usual analysis is that this is a problem of defining or applyng the words, rather than a problem of their relationship.

For example, the contrast alive / dead is not always easy to define -- does it depend on, say, heart function, or brain function? What if these can be sustained only with the help of medical equipment? But this is a medical or philosophical question, not a linguistic one. Whatever definition of "life" is accepted, it is complementary with "death" and no true gradability exists between the two.

In addition, everyday linguistic restrictions are based on a folk understanding of the world, which may not stand up to modern scientific findings. For example, the categories "man" and "woman" are inappropriate for people with more complex sexual identities, such as hermaphrodites. But in everyday use, these two categories are all that is acknowledged, and the language reflects that fact.

Converse terms

In this special case of complementarity, each member of the pair implies the existence of the other in a single relationship.

Prepositions

over / under
before / after
in front of / behind

Verbs

follow / precede
buy / sell
borrow / lend
bequeath / inherit

Nouns

parent / child
ancestor / descendant
guest / host

Thus:

if A is over B, then B is under A; and

if A is the parent of B, then B is the child of A.

if A sells something to B, then B buys something from A.

Sometimes one of these terms may have a dual function: as a member of a pairing, and also as an inherent quality. In the following examples, the first term can exist without the second, as a basic property of a person or animal.

doctor / patient
predator / prey
teacher / pupil

One can be a doctor (i.e. hold an M.D.) even without patients, but a patient can't exist without a doctor (or other healthcare provider). Similarly, a young eagle is a predator (by nature) even before the first prey is taken. Another view is that these "inherent qualities" are just examples of a potential converse relationship.

Polar opposites

A special case of gradable adjectives is found in polar pairs such as the following, in which one member is privileged.

old / young
long / short
heavy / light
fast / slow
high / low
deep / shallow
wide / narrow
thick / thin
difficult / easy

Why do we say that one member is priviledged? When you want to ask about the age, or length, or weight of something, it's normal to use the first word in each pair.

How old is it?
How long is it?
How heavy is it?
How fast is it?

In doing so, you're not presupposing that the thing is old, or long, or heavy. Such a use is called impartial, since you're not taking a position about the applicability of the adjective in its normal use.

How old is your baby?
= What is its age?

How long was that subliminal message on the screen?
= What was the length of time?

How heavy is that feather?
= What does that feather weigh?

If you ask the question using the other term, however, you do presuppose something about the thing. Such a use is called committed, since this form of phrasing implies a commitment to the claim that the basic meaning of the adjective applies.

How young is your baby?
= The baby is young, but to what degree?

How short was that message?
= The message was short, but to what degree?

How light is that feather?
= The feather is light, but to what degree?

Notice that these sentences are odd, because the presupposition is odd.

? How young is your great-grandmother?

? How short is this highway?

? How light is that piano?

It would require quite specific circumstances to make these sentences appropriate -- in particular, a preceding assertion that my great-grandmother is young (relatively speaking); the highway is short or the piano is light (considering how long or heavy most of them are).

The same asymmetry holds for stating measurements. These terms are impartial:

The book is only 30 pages long.
= Its length is 30 pages, but it's not necessarily long.

The baby is just 1 month old.
= Its age is 1 month, but it's not necessarily old.

While these are committed:

This laptop is 1" thin.
= Its thickness is 1", and it's thin.

My grandmother is 80 years young.
= Her age is 80 years, and she's young (at heart, in outlook...).

Compare the implications of these two sentences, where old is impartial and consistent with either context, while young is committed and not so flexible. (Note that "and" implies consistency, while "but" implies a contrast.)

My grandmother is 80 years old, and in poor health.

My grandmother is 80 years old, but she still acts like a teenager.

?? My grandmother is 80 years young, and in poor health.

?? My grandmother is 80 years young, but she still acts like a teenager.

My grandmother is 80 years young -- she still acts like a teenager.

Thus, one of the things we learn when we acquire a language is not just what these adjectives mean, but also how they relate to each other.

Symmetrical opposites

In this type of gradable adjective, neither member of the pair is privileged, and both are committed. Thus, there's no impartial member, as with long / short. These are less common, and the most interesting example is hot / cold.

A question can be formed with either word.

How hot is it today?
= It's hot, but to what degree?

How cold is it today?
= It's cold, but to what degree?

If you don't actually know whether it's hot or cold out (i.e. you're not presupposing either one), you need to use another formulation, such as What's the temperature today?

In a polar opposition, either adjective can be used in a comparison without implying the basic quality of the term, just relative location on the scale.

My great-grandfather is younger than my great-grandmother.
(but neither is "young")

My nephew, at 12 months, is older than my niece, at 10 months.
(but neither is "old")

This leaf is heavier than that feather.
(but neither is "heavy")

An elephant is lighter than a whale.
(but neither is "light")

These symmetrical adjectives aren't like that: they do imply the quality that they describe.

A blue flame is hotter than a yellow flame.
(and it's true that a blue flame is "hot")

?? A yellow flame is colder than a blue flame.
(but it's not true that a yellow flame is "cold," so this sentence is odd)

Winters are colder in Yellowknife than in Philadelphia.
(and it's true that winters are "cold" in Yellowknife)

?? Winters are hotter in Philadelphia than in Yellowknife.
(but it's not true that winters are "hot" in Philadelphia, so this sentence is odd)

Due to the nature of these adjectives, we sometimes have to choose other phrasings or other terms. In particular, warm / cool are not committed; nor are the negations of hot and cold.

A yellow flame is cooler than a blue flame.
(does not imply that a yellow flame is "cool," so this sentence is fine)

Winters are warmer in Philadelphia than in Yellowknife.
(does not imply that winters are "warm" in Philadelphia, so this sentence is fine)

A yellow flame is not as hot as a blue flame.
(does not imply that a yellow flame is "not hot," so this sentence is fine)

Winters are not as cold in Philadelphia as in Yellowknife.
(does not imply that winters are "not cold" in Philadelphia, so this sentence is fine)

The pairs warm / cool and hot / cold have a special and fairly complex relationship. For example, while cooler doesn't imply cool, it does imply not cold!

?? Winters are cooler in Yellowknife than in Philadelphia.
(odd because winters are actually "cold," not just "cool," in Yellowknife)

The same is true also for warmer and not hot. Since these pairs describe the same basic dimension of temperature, it shouldn't be surprising that they interact in this fashion.

Extending word meaning

Word meanings are somewhat like game trails. Some can easily be mapped because they are used enough that a clear path has been worn. Unused trails may become overgrown and disappear. And one is always free to strike out across virgin territory; if enough other animals follow, a new trail is gradually created.

Since word meanings are not useful unless they are shared, how does this creation of new meanings work? There are a variety of common processes by which existing conventional word meanings are creatively extended or modified. When one of these processes is applied commonly enough in a particular case, a new convention is created; a new "path" is worn.

Metaphor

Consider the difference in meaning between "He's a leech" and. "he's a louse." Both leech and louse are parasites that suck blood through the skin of their host, and we -- being among their hosts -- dislike them for it. Both words have developed extended meanings in application to humans who are portrayed as like a leech or like a louse -- but the extensions are quite different.

According to the American Heritage Dictionary, a leech is "one who preys on or clings to another", whereas a louse is "a mean or despicable person." These extended meanings have an element of arbitrariness. Most of us regard leeches as "despicable," and lice certainly "prey on" and "cling to" their hosts. Nevertheless, a human "leech" must be needy or exploitative, whereas a human "louse" is just an object of distaste.

Therefore it's appropriate for the dictionary to include these extended meanings as part of the meaning of the word. All the same, we can see that these words originally acquired their extended meanings by the completely general process of metaphor. A metaphor is "a figure of speech in which a term is transferred from the object it ordinarily designates to an object it may designate only by implicit comparison or analogy." For instance, if we speak of "the evening of her life", we're making an analogy between the time span of a day and the time span of a life, and naming part of life by reference to a part of the day.

In calling someone a leech, we're making an implicit analogy between interpersonal relationships and a particular kind of parasite/host relationship.

This kind of naming -- and thinking -- by analogy is ubiquitous. Sometimes the metaphoric relationship is a completely new one, and then the process is arguably part of pragmatics -- the way speakers use language to express themselves. However, these metaphors often become fossilized or frozen, and new word senses are created. Consider what it means to call someone a chicken, or a goose, or a cow, or a dog, or a cat, or a crab, or a bitch. For many common animal names, English usage a conventionalized metaphor for application to humans. Some more exotic animals also have conventional use as epithets ("you baboon!" "what a hyena!") No such commonplace metaphors exist for some common or barnyard animals ("what a duck she is"?), or for most rarer or more exotic animals, such as wildebeest or emus. Therefore, these are available for more creative use. The infamous 'water buffalo incident' at Penn a few years ago was apparently a case where what was began as a fossilized metaphor coming from a language other than English was interpreted as a much more offensive novel usage.

Sometimes the metaphoric sense is retained and the original meaning disappears, as in the case of muscle, which comes from Latin musculus "small mouse".

Metonymy and synecdoche

Metonymy is "a figure of speech in which an attribute or commonly associated feature is used to name or designate something."

Synecdoche is a special kind of metonymy, "a figure of speech by which a more inclusive term is used for a less inclusive one, or vice versa." A short definition is "part for whole." or "whole for part."

Whole for part	Basis
"The river is too deep to cross"	this part of the river (it might be fine upstream)
"Would you like more chicken?"	a piece of a chicken

Like metaphors, many examples of metonymy and synecdoche become fossilized: gumshoe for detective, hand as in "all hands on deck". However, the processes can be applied in a creative way: "the amputation in room 23".

It often requires some creativity to figure out what level of specificity, or what associated object or attribute, is designated by a particular expression. "I bought the Inquirer" (a copy); "Knight-Ridder bought the Inquirer" (the company). "Lee is parked on 33rd St." (i.e. Lee's car).

Connotation/denotation

The word "sea" denotes a large body of water, but its connotative meaning includes the sense of overwhelming space, danger, instability; whereas "earth" connotes safety, fertility and stability. Of many potential connotations, the particular ones evoked depend upon the context in which words are used. Specific kinds of language (such as archaisms) also have special connotations, carrying a sense of the context in which those words are usually found.

Over time, connotation can become denotation. Thus trivial subjects were originally the subjects in the trivium, consisting of grammar, rhetoric and logic. These were the first subjects taught to younger students; therefore the connotation arises that the trivium is relatively easy, since it is taught to mere kiddies; therefore something easy is trivial.

Compositional semantics and literal sentence meaning

When we talked about syntax, we were concerned with putting together the spoken form of language out of its component parts. How is a sentence built out of words?

We face the same issues in semantics. How do we determine the meanings of complex phrases and sentences from the meanings of simpler ones?

Kim admires Sandy.
Kim hates Sandy.

But also on the way they are combined together:

Kim admires Sandy.
Sandy admires Kim.

There have been many systematic efforts to address this problem, and the central insight of most work on it is usually associated with Gottlob Frege. His idea is called compositionality, and it basically amounts to saying that the meaning of any sentence is derived from the meanings of its parts and the rules that are associated with putting them together.

This may seem sort of obvious, but it's an extremely powerful idea. It says that if you know what the words in a sentence mean and you know how they were put together, you can figure out exactly what the sentence means in deterministic fashion.

Obviously, this compositionality can only hold of the semantic meaning of the sentence, not its pragmatic meaning.

Here is a simple sketch of one approach to compositional semantics:

Suppose we take the meaning of "brown" to be associated with the set of brown things, and the meaning of "cow" to be associated with the set of things that are cows. Then the meaning of "brown cow" is the intersection of the first set (the set of brown things) with the second set (the set of things that are cows). Proceeding along these lines, we can reconstruct in terms of set theory an account of the meaning of predicates ("eat"), quantifiers ("all"), and so forth, and eventually give a set-theoretic account of "all cows eat grass" analogous to the account we might give for "((3 + 4) * 6)".

This sort of analysis -- which can become very complex and sophisticated -- does not tell us anything about the meanings of the words involved, but only about how to calculate the denotation (technical meaning) of complex expressions from the denotation of simple ones. The denotation of the primitive elements -- the lexemes -- is simply stipulated (as in "the set of all brown things").

Since this account of meaning expressed denotations in terms of sets of things in the word -- known as "extensions" -- it is called "extensional".

The notion of Entailment

Sentence A entails sentence B just in case the set of truth conditions for A includes the set of truth conditions for B.

Let us see some examples of entailment:

1. A: John has two legs.
   B: John has one leg.
   Here, A entails B, since in every situation in which John has two legs, he also has one.
   
   
2. A: If John has two legs then I'm the king of France - and I'm not the king of France!
   B: John doesn't have two legs.
   Here again, A entails B - in fact, the type of information expressed in B is the usual message of constructions like A.
   
   
3. A: Lisa ate an apple.
   B: Apple was eaten by Lisa.
   Here, both A entails B and B entails A, since both describe exactly the same set of conditions.
   
   
4. A: If it doesn't rain, I'll be fine.
   B: I'm fine.
   Here, there is no relation of entailment between the two sentences, since the set of conditions in which I'm fine may or may not necessarily exclude raining! (this one usually takes a little bit of thinking).

Sense and Reference

One trouble with this line of inquiry was raised more than 100 years ago by Frege. There is a difference between the reference (or extension) of a concept -- what it corresponds to in the world -- and the sense (or intension) of a concept -- what we know about its meaning, whether or not we know anything about its extension, and indeed whether or not it has an extension. We know something about the meaning of the word "dog" that is not captured by making a big pile of all the dogs in the world. There were other dogs in the past, there will be other dogs in the future, there are dogs in fiction, etc. One technique that has been used to generalize "extensional" accounts of meaning is known as possible worlds semantics. In this approach, we imagine that there are indefinitely many possible worlds in addition to the actual one, and now a concept -- such as dog -- is no longer just a set, but rather is a function from worlds to sets. This function says, "Give me a possible world, and I'll give you the set of dogs in that world." Like many mathematical constructs, this is not a very practical arrangement, but it permits interesting and general mathematics to continue to be used in modeling natural language meaning in a wider variety of cases, including counterfactual sentences ("If you had paid me yesterday, I would not be broke today") or non-existant things ("All unicorns are beautiful").

Syntax-semantics interface

Compositional semantics of this kind can be related very closely to syntax, so that the way that we put together the meanings of the elements corresponds to the way they are put together by the syntax. Take the following sentence as an example:

Brown cows eat grass.

          S  
        /  \   
       /    \   
     NP      VP
    / \     /  \
   A   N    V   NP
  /    |    |   |
brown cows eat grass 
 

The idea is that the meaning of each node in the tree is determined by putting together the meanings of the parts of the tree they dominate. So we get the meaning of the VP by combining that of the V and that of its NP object, in this case a statement about something eating grass.

In the same way, the meaning of the subject NP is determined by combining the meanings of the A and N it dominates, in this case the set of all things that are brown and that are also cows.

To get the meaning of the sentence we then combine the NP and the VP.

Given that we can assign interpretations to novel utterances, something like the principle of compositionality must be true, but there are many problems that semanticists have to deal with.

idioms:

kick the bucket (=die)

anaphora:

Sam and Kim came in. They sat down.

uses of language that depend on context:

He did it there, like that, yesterday.

mismatches of syntactic and semantic structure:

Every man loves a woman.
b. [ For All x man(x) [ Some y woman(y) [ loves(x,y) ] ]]
c. [ Some y woman(y) [ For All x man(x) [ loves(x,y) ] ]]

The problems of anaphora and context-dependence will be discussed in detail in the next lecture. The problems that lie at the interface of syntax and semantics involve an interesting choice for linguists, who must complicate their description of grammar to deal with these problems. The choice is where to put the complication: make syntax stranger, make the semantics stranger, or relax the compositionality by making the transition from syntax to semantics more complicated?

Pinker has some discussion of interpreting meaning at the sentence level, where an important issue is figuring out the roles of various phrases in a sentence. This interpretation is complicated when a phrase has moved from its usual location, where a gap remains in sentence structure. The listener has to figure out how to relate the phrase and the gap; a trace establishes a link between the gap and the constituent elsewhere in the sentence.

A beautiful demonstration for the reality of traces comes from the phenomenon called wanna-contraction: want+to --> wanna.
For example, compare the affirmative sentence below, and a related question, in which the word who was moved to the beginning:

You want to invite John and Mary to the party.
Who do you want to invite ___ to the party? --> Who do you wanna invite to the party?

Now, look at the sentences below, and notice the location of the gap/trace! It comes in between the word want and the word to, making the contraction impossible:

You want John to come to the party.
Who do you want ___ to come to the party? -/-> * Who do you wanna come to the party?

Here are some examples from a movie review in Entertainment Weekly. These first two sentences contain three gaps.

Rollerball is a remake of the 1975 Norman Jewison thriller that no one I know ____ was clamoring to see a remake of ____ . cf. I know no one (who was clamoring to see a remake). cf. They were clamoring to see a remake of the 1975 Norman Jewison thriller.   The original is best remembered ____ for its future-shock vision of extreme sports. cf. People best remember the original for its future-shock vision of extreme sports.

As Pinker notes, the real-time parsing of such sentences imposes particular demands on memory, as the status of a phrase is uncertain until the gap is found.

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