1. 8a. Sense, reference, intension, extension, modality 5.1-2,3-4;7
CAS LX 502 Semantics
8a. Sense, reference, intension, extension, modality
5.1-2,3-4;7

2. The topic of the class
We’ve spent a fair amount of time talking about how we can build up an understanding of the meanings of sentence (or at least the truth conditions) by assembling meanings of pieces.
We could say the topic of the class is formal semantics.
Tuesdays at 11am in Fall 2006, we discuss formal semantics.
Tuesdays at 11am in Fall 2006, we discuss the topic of the class.

3. Possible worlds
It is uncontroversially true that things might have been otherwise than they are. I believe, and so do you, that things could have been different in countless ways. But what does this mean? Ordinary language permits the paraphrase: there are many ways things could have been besides the way they actually are. On the face of it, this sentence is an existential quantification. It says that there exist many entities of a certain description, to wit, “ways things could have been.” I believe permissible paraphrases of what I believe, taking the paraphrase at its face value, I therefore believe in the existence of entities which might be called “ways things could have been.” I prefer to call them “possible worlds.” (Lewis 1973)

4. Things could have been otherwise
For example, it was possible that LX522 might have been scheduled at this time. If that were the case, we would say:
Tuesdays at 11am in Fall 2006, we (at least some of us) discuss Merge and feature checking.
But we would still say:
Tuesdays at 11am in Fall 2006, we discuss the topic of the class.

5. There is a sense…
The topic of the class refers to formal semantics insofar as we limit ourselves to the facts as they are (the actual world).
But there’s kind of a “concept” that this expresses as well, that would describe (or refer to) whatever the topic of the class actually turns out to be.
We’ve been focusing mainly on the first kind of reference as we combine things compositionally to arrive at meanings.

6. Definite descriptions
Definite descriptions have several complex properties. For one thing, the individuals they denote may vary with the context of utterance:
The President of the United States
The man in the corner
And two different definite descriptions can sometimes refer to the same individual.
My neighbor drives an SUV
The coach of the hockey team drives an SUV

7. Venus = Venus
In fact, I can know that my neighbor drives an SUV without knowing that the coach of the hockey team drives an SUV, even if they are the same person.
In that case, the knowledge I lack is that my neighbor is the coach of the hockey team.

8. Venus = Venus This kind of example brings up an interesting conundrum.
My neighbor is the coach of the hockey team.
This kind of example brings up an interesting conundrum.
My neighbor denotes the individual that is my neighbor. Let’s call him Mike.
The coach of the hockey team denotes the individual that is the coach of the hockey team. That happens also to be Mike.
So, is the meaning of this sentence ‘Mike is self-identical’? Clearly not.

9. Frege and the stars
Gottlieb Frege, a central figure in the formalization of semantics, observed this in relation to the morning star and the evening star, definite descriptions that both—as it turns out—refer to the planet Venus. But it is not self-evident that both are in fact the same—it’s a discovery. We’ve learned something when we discover that the morning star is the evening star.

10. Sense and reference
The bottom line is that meaning and reference (denotation) can’t be exactly the same thing—there’s more to meaning than reference.
If the morning star and the evening star mean the same thing, then we should be able to substitute one in for the other and then The morning star is the evening star should mean the same thing as The morning star is the morning star.

11. Sense and reference
Frege divided meaning into sense (intension) (Sinn) and reference (extension) (Bedeutung).
The reference of an expression is what it stands for on a given occasion of use.
The sense of an expression is the way in which the reference is presented. The reference can vary depending on the situation.

12. Extension and intension
The extension of The PotUS (as uttered now) is the same as the extension of George W. Bush (as uttered whenever).
The intension is the “sense” of an expression. The intension of The PotUS remains constant across utterance contexts.
We’ll formalize this later, but the idea is that the intension of The PotUS is whichever individual meets the description when the NP is evaluated. It’s GWB in 2003, it’s WJC in 1999, it’s GHWB in 1991, etc.

13. Names and reference
Names refer to individuals. And that seems to be basically all they do.
What’s in a name?
Can a name be like a definite description?
Confucius is the most famous Chinese philosopher.
Confucius seems to be a rigid designator, at least intuitively.
Even the guy we call Confucius seems to fail.

14. Names and reference
Wading into philosophy… How does a name attach to a referent? (Given that a name is pure extension, reference and nothing else.)
Causal chain (Kripke)? Parents named Confucius and shared this designation with others, who gained the ability to refer to the individual by Confucius.
Complications with mistakes (Madagascar), and spontaneously generated names (7th Ave, 14B), but the problems don’t seem so bad.
Names can evolve, multiply. I don’t think there’s any particular problem with having several names refer to the same individual, but a thought.

15. Back to sense
The sense of something like PotUS kind of “takes into account” all of the possible worlds.
So far when determining meanings of sentences like Bond is hungry, we haven’t needed to worry ourselves with this because the facts of the situation were all given by the model.
But there are bits of language that invite us explicitly to consider other ways the world could be.
E.g., counterfactuals: If it were raining, I’d be wet.

16. Modal auxiliaries
There is a class of words, modal auxiliaries, that have this kind of effect.
Pat might have eaten the sandwich.
Pat must have eaten the sandwich.
Pat could have eaten the sandwich.
How can we paraphrase Pat might have eaten the sandwich?

17. Pat might have eaten the sandwich
We know how to characterize Pat has eaten the sandwich in terms of possible worlds.
By asserting that, we assert that the actual world is one of the ones on the left here.
How does Pat might have eaten the sandwich differ?
Pat has eaten the sandwich
Pat has not eaten the sandwich

18. Epistemic modals When is Pat might have eaten the sandwich true?
When is Pat must have eaten the sandwich true?
Pat has eaten t.s.
Pat hasn’t eaten t.s.
What I believe is true.
What I believe is true.
What I believe is false.
What I believe is false.
Pat has eaten t.s.
Pat hasn’t eaten t.s.

19. Epistemic modals When is Pat might have eaten the sandwich true?
When is Pat must have eaten the sandwich true?
Pat has eaten t.s.
What I believe is true.
What I believe is false.
Pat hasn’t eaten t.s.
What I believe is false.
Pat has eaten t.s.

20. The modal base
Epistemic modals restrict the assertion to just the possible worlds in which what I know/believe is true.
This set of worlds is called the modal base.
Pat might have eaten the sandwich. There’s a world in the modal base in which Pat has eaten the sandwich.
Put must have eaten the sandwich. Every world in the modal base is one in which Pat has eaten the sandwich.

21. Other modal bases
You must stay attentive.
You should clean your office.
You may leave.
How can we paraphrase these? Same sort of thing, but a different modal base (in the likely interpretation).

22. Other modal bases Yet a different modal base.
Pat can leave.
Pat can write software.
Pat can juggle.
Yet a different modal base.
Notice that these are somewhat ambiguous, although different modals have different preferences for the modal base they use.

23. Modal bases Epistemic Worlds in which what I know/believe is true.
Deontic Worlds in which a certain standard of propriety is met.
Root Worlds that are consistent with the facts.

24. Modal bases vs. accessibility
In the textbook, the modal bases are discussed in terms of being worlds in an “accessibility relation” to one another. Same thing.

25. Subjective/objective deontic modals
The deontic modal base can be interpreted in a number of different ways.
I should work faster.
Objective: according to the rules
Subjective: according to my own standards
You may leave.
Objective: according to the rules/law
Subjective: according to me (permission)

26. May vs. might, Can vs. could
Different modals can communicate different forms of likelihood, and have tendencies toward different modal bases.
Pat may come.
Pat might come.
Pat can bend a spoon.
Pat could bend a spoon.
Pat must fix the spoon.
Pat should fix the spoon.

27. Can vs. could
Certain pairs of modal look as if they’re tense variants: can/could, may/might, will/would, shall/should.
Pat can’t move his arm.
Pat couldn’t move his arm.
Tracy can’t stay out past midnight.
Tracy couldn’t stay out past midnight.
John’s wife can’t be very rich.
John’s wife couldn’t be very rich.
The “future tense marker” will can also be considered to be a modal (rather than tense proper).

28. Connection with conditionals
If there is a blizzard, classes are canceled.
Restricting attention to worlds in which there is a blizzard, all of those worlds are also worlds in which classes are canceled.
Classes can/may be canceled.
Restricting attention to the modal base, there is at least one world in which classes are canceled.

29. Marking modality
In general, marking modality means raising a hypothetical situation and commenting on it.
We can do this with adverbs as well:
Probably, John ate the sandwich.
John might have eaten the sandwich.
Certainly, John ate the sandwich.
John definitely ate the sandwich.

30. Wanting and hoping
The verbs want, hope, etc. are also interpreted in a way similar to modals.
I want to buy a pony.
Restricting attention to worlds that are those in which my desires are satisfied, I buy a pony is true in those worlds.

31. Accessible worlds
I want to teach Tuesdays and Thursdays next semester.
In those worlds in which my desires are satisfied, I teach on Tuesdays and Thursdays?
There seems to be a secondary relativization on worlds that are “accessible” from the actual world.

32. De re vs. de dicto
When we talk about propositional attitude verbs (think, believe, doubt, say, …), there’s a detectible ambiguity:
Pat thinks that the brightest student is a spy.
De dicto belief: belief about description.
De re belief: belief about individual(s).

33. De re vs. de dicto
Mary believes that a movie star was caught shoplifting last week.
Mary claimed that an astronaut stole her homework.
John thinks that Mary claimed that an astronaut stole her homework.
De dicto for claim, de dicto for think.
De re for claim, de dicto for think.
De re for claim, de re for think.

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