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CAS LX 502
Semantics
8a. Sense, reference, intension,
extension, modality
5.1-2,3-4;7
The topic of the class
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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.
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Tuesdays at 11am in Fall 2006, we discuss formal semantics.
Tuesdays at 11am in Fall 2006, we discuss the topic of the class.
Possible worlds
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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)
Things could have been
otherwise
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For example, it was possible that LX522
might have been scheduled at this
time. If that were the case, we would
say:
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Tuesdays at 11am in Fall 2006, we (at least
some of us) discuss Merge and feature
checking.
But we would still say:
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Tuesdays at 11am in Fall 2006, we discuss the
topic of the class.
There is a sense…
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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.
Definite descriptions
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Definite descriptions have several complex
properties. For one thing, the individuals they
denote may vary with the context of
utterance:
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The President of the United States
The man in the corner
And two different definite descriptions can
sometimes refer to the same individual.
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My neighbor drives an SUV
The coach of the hockey team drives an SUV
Venus = Venus
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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.
Venus = Venus
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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.
Frege and the stars
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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.
Sense and reference
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The bottom line is that meaning and
reference (denotation) can’t be exactly the
same thing—there’s more to meaning than
reference.
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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.
Sense and reference
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Frege divided meaning into sense (intension)
(Sinn) and reference (extension) (Bedeutung).
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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.
Extension and intension
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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.
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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.
Names and reference
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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.
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Even the guy we call Confucius seems to fail.
Names and reference
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Wading into philosophy… How does a name
attach to a referent? (Given that a name is
pure extension, reference and nothing else.)
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Causal chain (Kripke)? Parents named Confucius and
shared this designation with others, who gained the
ability to refer to the individual by Confucius.
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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.
Back to sense
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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.
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E.g., counterfactuals: If it were raining, I’d be wet.
Modal auxiliaries
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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.
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How can we paraphrase Pat might
have eaten the sandwich?
Pat might have eaten the sandwich
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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
Epistemic modals
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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.
Pat hasn’t
eaten t.s.
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.
Epistemic modals
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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 has
eaten t.s.
What I believe
is false.
Pat hasn’t
eaten t.s.
The modal base
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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.
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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.
Other modal bases
You must stay attentive.
 You should clean your office.
 You may leave.
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How can we paraphrase these? Same
sort of thing, but a different modal
base (in the likely interpretation).
Other modal bases
Pat can leave.
 Pat can write software.
 Pat can juggle.
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Yet a different modal base.
Notice that these are somewhat
ambiguous, although different modals
have different preferences for the
modal base they use.
Modal bases
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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.
Modal bases vs. accessibility
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In the textbook, the modal bases are
discussed in terms of being worlds in an
“accessibility relation” to one another.
Same thing.
Subjective/objective
deontic modals
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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)
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May vs. might, Can vs. could
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Different modals can communicate
different forms of likelihood, and have
tendencies toward different modal bases.
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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.
Can vs. could
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Certain pairs of modal look as if they’re tense variants:
can/could, may/might, will/would, shall/should.
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QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.
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).
Connection with conditionals
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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.
Marking modality
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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.
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Wanting and hoping
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The verbs want, hope, etc. are also
interpreted in a way similar to modals.
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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.
Accessible worlds
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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.
De re vs. de dicto
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When we talk about propositional
attitude verbs (think, believe, doubt,
say, …), there’s a detectible
ambiguity:
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Pat thinks that the brightest student is a spy.
De dicto belief: belief about
description.
De re belief: belief about individual(s).
De re vs. de dicto
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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.
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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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QuickTime™ and a
TIFF (LZW) decompressor
are needed to see this picture.