Read chapter one carefully. Except for Section 1.2.1. Read Section 1.2.1 carelessly. Try not to remember any of the terminology introduced there.

Do the exercises introduced in this lecture with Exercise heading.

An expression like the president uttered last week denoted a particular individual in the world, George Bush.

Uttered today, it denotes Barak Obama.

Uttered in 1993 it denoted Bill Clinton.

Nevertheless the meaning or sense of the expression the president hasn't changed. Modulo the elimination of a few voters in a few Florida and Ohio counties, the way of determining what the expression the president denotes is the same.

Important terms:

1. Sense: a particular linguistic meaning of an expression. The word orange has at least 2 (color, fruit);
2. Denotation: What the expression picks out in the world (? on a particular occoasion of use)

Now if we say the Republican Senator from Arizona who was a candidate for president in the election of 2008, that has a different sense and a different denotation. It has a different denotation because it has a different sense. Expressions with different meanings can pick out out different things in the world.

We say the sense determines the denotation. (though we'll modify this slightly below).

Sense determines denotation.

Although in the previous discussion we focused on the expression the president, we can narrow our attention to the lexical item president. What exactly the word the does we're not ready to discuss yet, but clearly the word president bears primary responsibility for the fact that the expression the president picks out Barak Obama.

Since we're interested in meaning, let's talk about how the meaning of a word like president is defined:

1. Ostensive (pointing) definition. An act of ostension is an act of pointing. A definition by ostension is one performed by pointing at the denotation or part of the denotation of a word.
   Pointing at Barak Obama to define the word president
   Of course if we are really explaining the word to someone who has no idea what the word president means, looking at barak Obama may not be enough to give her the idea. So we may need a list of examples:
   Washington, Adams, Jefferson, Monroe, Madison, ... , Clinton, George Bush, Barak Obama
   There is often something a little unsatisfying about ostensive definitions. We are left a little unsure as to whether someone who knows all the list members could still recognize something or someone not on the list who falls under the definition. This despite the fact that the list may be factually complete.

   For example someone looking at this list might well conclude that being male was part of the definition of being president, but this should definitely not be part of the definition. More on this later...

2. Definition by paraphrase Giving another word or phrase that has the same sense.
   president: the executive head of an organization or a state, usually elected.
   Of course this raises other issues, such as what exactly is an "executive" head? Also have we really identified all the necessary and sufficient conditions of being a president?

Note: A word may have many senses, even when we control for syntactic category. The verb bank has several senses:

1. We bank at the Savings and Loan.
2. We're banking on Philip Rivers playing well.
3. The plane banked hard left.

Both kinds of definition have their problems and won't really play a role in our theory.

However they are useful in identifying some of the intuitions that go with sense and denotation. Ostensive definitions try to pick out parts of the denotation of a word; definitions by paraphrase try to pick out the sense.

Also we saw that in some sense definitions, of either kind, aren't complete. But it's not clear that complete definitions are the business of semantics. This is the subject of exercise one:

Exercise one:

Consider the following principle of Generative linguistics.

Goal of theoretical linguistics: Characterize what speakers know when they speak and understand a language.

Part A: Are speakers are able to speak and understand without knowing complete definitions of the words they use? Give 3 plausible examples of successful communications in which speakers aren't able to produce complete definitions of the words they use. Hint: There are lots of ways to do this but use at least one simple example using what are called natural kind terms. A natural kind term denotes some natural kind of thing in the real world. Examples are dog, cat, tree, dolphin, Border Collie. You might also consider using some non-natural kinds in your discussion. Non-natural kinds are kinds that are human-made.Chair, telephone, computer are examples. Don't use any of these exact words as your examples. Also, don't use technical language. In other words, I don't know the definition of the term chondromalacia (something bad that can happen to a knee) but it's also pretty clear that me trying to communicate with this word is fraught with peril. So what we're interested in is cases where you don't know the exact definition of a common word but you can still communicate with it effectively.

Part B: Address the following issue in your discussion. When we do syntax we concede that speakers are not able to articulate what a subject or a constituent is, but we argue that they have tacit knowledge of these things on the basis of the evidence of their grammaticality intuitions. Thus we argue that speakers know that the book about Lincoln is a constituent in

John lost the book about Lincoln.

It was the book about Lincoln John lost.

John put the book on the table

* It was the book on the table John put.

Can we argue the same about complete definitions? That is, can we argue that speakers DO have complete definitions in their heads but that the knowledge is tacit and they are unable to articulate these definitions?

Finally, one way of answering this question is to take the position that people can know the meaning of a word without having a complete definition in their heads. But if you take that position you need to say what it is that a competent speaker knows when he knows the meaning of a word. You don't have to come up with a precise definition of what they know. Take a stab at an operational definition. An operational definition is one that works most of the time in practice without settling all questions about all logical possibilities. Operational definitions can be tremendously useful, but they are tricky. An operational definition of an eclair is what they bring you when you order an eclair. You can get pretty far with this operational definition, identifying lots of eclair instances, but remember, with this definition you are in no position to complain when they bring you a Napoleon.

Above we used the term denotation to pick out what a noun phrase referred to. In the special case of a noun phrase this is also called its reference. We use the term denotation for more than just noun phrases. For all kinds of expressions, the part of reality the expression picks out is its denotation.

Expression	Type	Denotation
the cat	Noun Phrase	a particular feline entity, say, Garfield, the one referred to on this occasion of utterance
cat	Common Noun	a set of animals, all of them felines
dog	Common Noun	a set of animals, all of them canines
walk	Verb	a set of actions, entailing movement and use of the legs
pass the salt	Verb Phrase	a set of actions, not greatly more or less complicated than walking as actions go, but requiring more linguistic parts to identify

We said above sense determines denotation.

This can't be quite right.

First of all the expression the president denotes different persons on different occasions of use.

So it's at least the case that sense + time of utterance determines the denotation. In other words, at least one other thing besides the sense is required to determine the denotation.

But also we have the following, which is perfectly fine even I utter it right now:

In the summer of 1862 the war was going badly. The president knew...

So context can fill in the time of the presidency we are talking about.

Of course context has been filling more stuff than time in all the examples we've been talking about:

1. the president of the United States of America.
2. the president of General Motors

3. the president of the United States of America in 1862
4. the president of General Motors in 1960
5. the president of the United States of America in 1860

So we have the following:

Sense + Discourse Context + Linguistic Context Determines Denotation

Expressions with very different senses can have the same denotations and this is largely unpredictable linguistically, because it has to do with the weird and wonderful way the world turned out.

Some expressions with different senses and identical denotations:

The Boston Red Sox	the winner of the 2004 World Series
George Bush	the president of the U.S. in 2005
the United States	the U.S.
the president of the United States in 2005	the president of the U.S. in 2005
the morning star	Venus
Venus	the evening star
the morning star	the evening star
Mr. Universe 1970	the governor of California 2005
1970	the year of the great tsunami
the governor of California 1970	the governor of California the year of the great tsunami

Speculation: Substitutivity of Identicals (Leibniz's Law)

Replacing an expression E with denotation D with another expression E' with the same denotation D does not change the denotation of the larger expression in which E occurred.

Substitution of Identicals again:

x = 14 x + 9 = y 14 + 9 = y 23 = y

Mathematical expressions have denotations too. The numeral "9" denotes the number 9. Different expressions can have the same denotation This is why equations can be informative: n ∑ i=1 2n -1 = n2   ! Superman is Clark Kent!

The preceding examples should pretty much have convinced you that what's important for the theory of semantics is sense, not denotation. Denotations vary at the whim of the electorate and the Gods of baseball. What matters linguistically is senses!

The trouble with this conclusion is that there's lots wrong with senses as well.

1. Senses pick out classes of things in the world that may have vague or poorly defined boundaries. (bald, young, smart), so there is no paraphrase that captures a sense.
2. Family resemblances: Sometimes senses don't come with clear set of defining conditions; instead they come with a variety of sets of conditions, each set similar to, but not identical with, the last. Wittgenstein's example of the word game: soccer, chess, ring-around-the-rosie, pretend games, solitaire
3. The family resemblance problem is a special case of a general problem with senses: Determining how many senses a word has isn't always easy, as any lexicographer (dictionary writer) knows.

Denotations, despite their limits, are clearer, For example, the principle of substitutivity gives us a very powerful handle on denotations. We have clearer intuitions about what they are, how they change.

Still there is the problem of the evanescence of denotations.

Consider dog again. We said its denotation is:

a set of animals, all of them canines

We are in search of an object of study for semantics

We want a substitute for meanings, because we don't know what they are.

Two criteria

1. Something we can characterize precisely enough to be useful for scientific purposes (something that isn't hopelessly fuzzy, so I can mark you wrong when I ask for one on an exam).
2. Something that has a shot at being what it is speakers know when they know the meaning of a word.

Results thus far:

1. Denotations did splendidly on the first criterion; they are very precise. They do pretty lousy on the second.
2. Senses do pretty badly on the first criterion, but pretty well on the second, kind of by definition. They're what dictionary writers try to identify when they write a dictionary entry for words like hard, easy, soft.

Solution: We're going to extend the way we use the term denotation by means of a theoretical construct.

Consider dog. At any instant of time there is a certain set of individuals that is the set of dogs. If the world were only slightly different than it is, there would be a slightly different set of dogs.

Thus the denotation depends not only on the sense but also on the way the world is, or as we shall say, on what world we are in.

So our theoretical construct is this: there is a set of worlds we call the set all possible worlds, and the denotation of dog varies from world to world:

w1	Fido, Bowser, Argus, Rex
w2	Bowser, Argus, Rex
w3	Fido, Argus, Rex
w4	Ashes, Bowser, Argus, Rex

So denotations are double-layered. A denotation is an intension that picks out an extension at each possible world.

These examples are incomplete. The set of all possible worlds really needs to cover all possible ways the world might differ from the way it is. With respect to the word dog the set of possible worlds needs to provide with all possible individuals that might be a dog, and at least one world for each distinct possible set of dogs. That's a lot of worlds....

Intension of "Arnold Schwarzenegger"	Intension of "the governor of CA 2005"	Intension of "Mr. Universe 1970"
w1 Arnold w2 Arnold w3 Arnold w4 Arnold	w1 Arnold w2 Gray w3 Cruz w4 Arnold	w1 Arnold w2 Brett w3 Steve w4 Arnold

And suppose that this is the way it is with grinning in our 4 worlds:

Intension of "grin"

w1	{Arnold, Cruz, Gray, Steve, Brett}
w2	{Arnold, Cruz, Gray, Steve}
w3	{Arnold, Gray, Brett, Steve}
w4	{Cruz, Gray, Steve, Brett}

And consistent with these we have the following intension:

Arnold Schwarzenegger grins	The governor of CA 2005 grins	Mr. Universe 1970 grins
w1 true w2 true w3 true w4 false	w1 true w2 true w3 false w4 false	w1 true w2 false w3 true w4 false

Note: I differ slightly from the text in saying that intension of a sentence is a table giving the truth value at each world. The text just says the intension of a sentence is the set of possible worlds at which the sentence is true. These ideas are equivalent: You can construct the table from the set, and vice versa. More on this later.

The wrong theory: the meanings of the words determine the meaning of a sentence.

Problem:

The A that Xed the B Yed the C

Pick from among the following nouns for A,B,C:

dog, cat, rat

Pick from among the following transitive verbs for X,Y.

chased, bit

Many sentences with MANY different meanings:

1. The dog that chased the cat bit the rat
2. The rat that chased the cat bit the dog
3. The cat that chased dog bit the rat.

Sentence Meaning = Lexical Meaning + Structural Meaning

Determine structural meaning!

That's what it's for. That's why there IS such a thing as syntax!

You finally know.

A compositional semantics for a (fragment of a) language is a formal account of how the meaning of the whole is composed of the meaning of the parts.

Given what we just noted about structural meaning, this means that a compositional semantics combines lexical meaning and structural meaning to compute the meaning of sentences. It does this by providing rules for interpreting strcutures.

More technically, we have just committed to a denotational theory, where denotation means intension. Thus our theory needs to account for how the intension of the whole is composed out of the intension of the parts.

But in working out the details, it quickly becomes clear that not every word has a natural intension:

1. and
2. or
3. every be

A syncategorematic expression is one that does not have a denotation of its own but which has a special interpretive RULE associated with it. Thus syncategorematic meaning can be thought of part of structural meaning.

For example, the extensional rule for and (discussed in Section 1.3.4, (38), (39)) is:

'A and B' is true if and only if 'A' is true and 'B' is true.

Thus, all the rule has to do is tell us under what circumstances the sentences is true or false (in terms of the truth values of the sentence's parts). A similar rule for or:

'A or B' is true if and only if 'A' or true or 'B' is true.

The intensional treatment of and has to define an intension; that is, for every world, it has to tell us under what circumstances the conjoined sentence is true in that world, and under what circumstances it is false:

'A and B' is true at a world w if and only if 'A' is true at w and 'B' is true at w.

A small compositional semantics.

The exercise is in the section labeled "Exercise".

1. Sense vs denotation
   1. Sense: a meaning or definition.
   2. Denotation: The part of the world a word picks out
2. Problems with both:
   1. Senses are hard to define or even count
   2. Denotations change as the world changes
3. Solution: Model meaning with an abstraction (called an intension) that tracks changes in denotation across changes in the world.
4. The role of Structural Meaning: Combine with lexical meaning to give meaning.
5. The role of Syntax: In this course Syntax is the handmaiden of semantics. The role of syntax is to determine structural meaning.
6. Compositional Semantics: A formal theoretical account of how structural meaning combines with lexical meaning to give the meaning. It consists of rules that assigns denotations to structures.
7. For us meaning is always denotational. Denotations are intensions; denotations at a possible world are extensions.
8. Conclusions
   1. In some sense Chapter 1 of our text proposes an answer to the question "What is meaning?", but it doesn't go about trying to answer the question as if it was an empirical question.
   2. It's a not a common sense question with an answer drawn out of experience
   3. Meaning is a theoretical concept.
   4. The criterion we'll use for whether we've given the question a good answer is whether it helps us give account of what speakers of a language know when they speak and understand utterances of that language in contexts of real communication.