CAS LX 502CAS LX 502SemanticsSemantics

8a. Sense, reference, 8a. Sense, reference, intension, extension, intension, extension,

modalitymodality

5.1-2,3-4;75.1-2,3-4;7

The topic of the classThe topic of the class We’ve spent a fair amount of time talking We’ve spent a fair amount of time talking about how we can build up an understanding of about how we can build up an understanding of the meanings of sentence (or at least the the meanings of sentence (or at least the truth conditions) by assembling meanings of truth conditions) by assembling meanings of pieces.pieces.

We could say the topic of the class is formal We could say the topic of the class is formal semantics.semantics.

Tuesdays at 11am in Fall 2006, we discuss formal Tuesdays at 11am in Fall 2006, we discuss formal semantics.semantics.

Tuesdays at 11am in Fall 2006, we discuss the topic Tuesdays at 11am in Fall 2006, we discuss the topic of the class.of the class.

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

Things could have been Things could have been otherwiseotherwise

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

But we would still say:But we would still say: Tuesdays at 11am in Fall 2006, we Tuesdays at 11am in Fall 2006, we discuss the topic of the class.discuss the topic of the class.

There is a sense…There is a sense… The topic of the class The topic of the class refers to formal refers to formal semantics insofar as we limit ourselves semantics insofar as we limit ourselves to the facts as they are (the actual to the facts as they are (the actual world).world).

But there’s kind of a “concept” that But there’s kind of a “concept” that this expresses as well, that would this expresses as well, that would describe (or refer to) whatever the describe (or refer to) whatever the topic of the class actually turns out topic of the class actually turns out to be.to be.

We’ve been focusing mainly on the first We’ve been focusing mainly on the first kind of reference as we combine things kind of reference as we combine things compositionally to arrive at meanings. compositionally to arrive at meanings.

Definite descriptionsDefinite descriptions

Definite descriptions have several Definite descriptions have several complex properties. For one thing, the complex properties. For one thing, the individuals they denote may vary with individuals they denote may vary with the context of utterance:the context of utterance: The President of the United StatesThe President of the United States The man in the cornerThe man in the corner

And two different definite And two different definite descriptions can sometimes refer to descriptions can sometimes refer to the same individual.the same individual. My neighbor drives an SUVMy neighbor drives an SUV The coach of the hockey team drives an SUVThe coach of the hockey team drives an SUV

Venus = VenusVenus = Venus

In fact, I can know that In fact, I can know that my my neighbor drives an SUV neighbor drives an SUV without without knowing that knowing that the coach of the the coach of the hockey team drives an SUVhockey team drives an SUV, even , even if they are the same person.if they are the same person.

In that case, the knowledge I In that case, the knowledge I lack is that lack is that my neighbor is the my neighbor is the coach of the hockey teamcoach of the hockey team..

Venus = VenusVenus = Venus My neighbor is the coach of the hockey My neighbor is the coach of the hockey team.team.

This kind of example brings up an This kind of example brings up an interesting conundrum.interesting conundrum.

My neighbor My neighbor denotes the individual that denotes the individual that is my neighbor. Let’s call him Mike.is my neighbor. Let’s call him Mike.

The coach of the hockey team The coach of the hockey team denotes denotes the individual that is the coach of the the individual that is the coach of the hockey team. That happens also to be hockey team. That happens also to be Mike.Mike.

So, is the meaning of this sentence So, is the meaning of this sentence ‘Mike is self-identical’? Clearly not.‘Mike is self-identical’? Clearly not.

Frege and the starsFrege and the stars

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

Sense and referenceSense and reference

The bottom line is that meaning and The bottom line is that meaning and reference (denotation) can’t be reference (denotation) can’t be exactly the same thing—there’s more exactly the same thing—there’s more to meaning than reference.to meaning than reference.

If If the morning starthe morning star and and the evening starthe evening star mean the same thing, then we should be mean the same thing, then we should be able to substitute one in for the other able to substitute one in for the other and then and then The morning star is the evening The morning star is the evening starstar should mean the same thing as should mean the same thing as The The morning star is the morning starmorning star is the morning star..

Sense and referenceSense and reference

Frege divided meaning into Frege divided meaning into sensesense ((intensionintension) () (SinnSinn) ) and and reference reference ((extensionextension) () (BedeutungBedeutung)).. The The reference reference of an expression is what it of an expression is what it stands for on a given occasion of use.stands for on a given occasion of use.

The The sense sense of an expression is the way in of an expression is the way in which the reference is presented. The which the reference is presented. The reference can vary depending on the reference can vary depending on the situation.situation.

Extension and intensionExtension and intension The The extensionextension of of The PotUSThe PotUS (as uttered now) (as uttered now) is the same as the extension of is the same as the extension of George W. George W. BushBush (as uttered whenever). (as uttered whenever).

The The intension intension is the “sense” of an is the “sense” of an expression. The intension of expression. The intension of The PotUSThe PotUS remains constant across utterance contexts.remains constant across utterance contexts. We’ll formalize this later, but the idea is that We’ll formalize this later, but the idea is that the intension of the intension of The PotUS The PotUS is whichever is whichever individual meets the description when the NP is individual meets the description when the NP is evaluated. It’s GWB in 2003, it’s WJC in 1999, evaluated. It’s GWB in 2003, it’s WJC in 1999, it’s GHWB in 1991, etc.it’s GHWB in 1991, etc.

Names and referenceNames and reference

Names refer to individuals. And that Names refer to individuals. And that seems to be basically all they do.seems to be basically all they do. What’s in a name?What’s in a name? Can a name be like a definite Can a name be like a definite description?description?

Confucius is the most famous Chinese Confucius is the most famous Chinese philosopher.philosopher.

Confucius Confucius seems to be a rigid seems to be a rigid designator, at least intuitively.designator, at least intuitively.

Even Even the guy we call Confuciusthe guy we call Confucius seems to seems to fail.fail.

Names and referenceNames and reference

Wading into philosophy… How does a name Wading into philosophy… How does a name attach to a referent? (Given that a attach to a referent? (Given that a name is pure extension, reference and name is pure extension, reference and nothing else.)nothing else.) Causal chain (Kripke)? Parents named Causal chain (Kripke)? Parents named Confucius and shared this designation with Confucius and shared this designation with others, who gained the ability to refer to others, who gained the ability to refer to the individual by Confucius.the individual by Confucius.

Complications with mistakes (Madagascar), and Complications with mistakes (Madagascar), and spontaneously generated names (7th Ave, 14B), but spontaneously generated names (7th Ave, 14B), but the problems don’t seem so bad.the problems don’t seem so bad.

Names can evolve, multiply. I don’t think there’s Names can evolve, multiply. I don’t think there’s any particular problem with having several names any particular problem with having several names refer to the same individual, but a thought.refer to the same individual, but a thought.

Back to senseBack to sense The The sense sense of something like of something like PotUSPotUS kind kind of “takes into account” all of the of “takes into account” all of the possible worlds.possible worlds.

So far when determining meanings of So far when determining meanings of sentences like sentences like Bond is hungryBond is hungry, we , we haven’t needed to worry ourselves with haven’t needed to worry ourselves with this because the facts of the this because the facts of the situation were all given by the model.situation were all given by the model.

But there are bits of language that But there are bits of language that invite us explicitly to consider other invite us explicitly to consider other ways the world could be.ways the world could be. E.g., E.g., counterfactualscounterfactuals: If it were : If it were raining, I’d be wet.raining, I’d be wet.

Modal auxiliariesModal auxiliaries

There is a class of words, There is a class of words, modal modal auxiliariesauxiliaries, , that have this kind that have this kind of effect.of effect. Pat might have eaten the sandwich.Pat might have eaten the sandwich. Pat must have eaten the sandwich.Pat must have eaten the sandwich. Pat could have eaten the sandwich.Pat could have eaten the sandwich.

How can we paraphrase How can we paraphrase Pat might Pat might have eaten the sandwichhave eaten the sandwich??

Pat might have eaten the Pat might have eaten the sandwichsandwich

We know how to We know how to characterize characterize Pat Pat has eaten the has eaten the sandwichsandwich in terms in terms of possible of possible worlds.worlds.

By asserting that, By asserting that, we assert that the we assert that the actual world is actual world is one of the ones on one of the ones on the left here.the left here.

How does How does Pat might Pat might have eaten the have eaten the sandwichsandwich differ?differ?

Pat has eatenthe sandwich

Pat has not eatenthe sandwich

Epistemic modalsEpistemic modals

When is When is Pat Pat might have might have eaten the eaten the sandwichsandwich true? true?

When is When is Pat Pat must have must have eaten the eaten the sandwichsandwich truetrue??

Pat haseaten t.s.

Pat hasn’teaten t.s.

Pat hasn’teaten t.s.

What I believeis false.

Pat haseaten t.s.

What I believeis true.

What I believeis true.

What I believeis false.

Epistemic modalsEpistemic modals

When is When is Pat Pat might have might have eaten the eaten the sandwichsandwich true? true?

When is When is Pat Pat must have must have eaten the eaten the sandwichsandwich truetrue??

Pat haseaten t.s.

Pat hasn’teaten t.s.

What I believeis false.

Pat haseaten t.s.

What I believeis true.

What I believeis false.

The modal baseThe modal base Epistemic modalsEpistemic modals restrict the restrict the assertion to just the possible worlds assertion to just the possible worlds in which what I know/believe is true.in which what I know/believe is true.

This set of worlds is called the This set of worlds is called the modal basemodal base.. Pat might have eaten the sandwich.Pat might have eaten the sandwich.There’s a world in the modal base in There’s a world in the modal base in which Pat has eaten the sandwich.which Pat has eaten the sandwich.

Put must have eaten the sandwich.Put must have eaten the sandwich.Every world in the modal base is one in Every world in the modal base is one in which Pat has eaten the sandwich.which Pat has eaten the sandwich.

Other modal basesOther modal bases

You must stay attentive.You must stay attentive. You should clean your office.You should clean your office. You may leave.You may leave.

How can we paraphrase these? How can we paraphrase these? Same sort of thing, but a Same sort of thing, but a different modal base (in the different modal base (in the likely interpretation).likely interpretation).

Other modal basesOther modal bases Pat can leave.Pat can leave. Pat can write software.Pat can write software. Pat can juggle.Pat can juggle.

Yet a different modal base.Yet a different modal base. Notice that these are somewhat Notice that these are somewhat ambiguous, although different ambiguous, although different modals have different modals have different preferences for the modal base preferences for the modal base they use.they use.

Modal basesModal bases

EpistemicEpistemicWorlds in which what I know/believe is Worlds in which what I know/believe is true.true.

DeonticDeonticWorlds in which a certain standard of Worlds in which a certain standard of propriety is met.propriety is met.

RootRootWorlds that are consistent with the Worlds that are consistent with the facts.facts.

Modal bases vs. Modal bases vs. accessibilityaccessibility

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

Subjective/objectiveSubjective/objectivedeontic modalsdeontic modals

The deontic modal base can be The deontic modal base can be interpreted in a number of interpreted in a number of different ways.different ways. I should work faster.I should work faster. Objective: according to the rulesObjective: according to the rules Subjective: according to my own Subjective: according to my own standardsstandards

You may leave.You may leave. Objective: according to the rules/lawObjective: according to the rules/law Subjective: according to me Subjective: according to me (permission)(permission)

May vs. might, Can vs. May vs. might, Can vs. couldcould

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

Can vs. Can vs. couldcould

Certain pairs of modal look as if they’re tense Certain pairs of modal look as if they’re tense variants: variants: cancan//couldcould, , maymay//mightmight, , willwill//wouldwould, , shallshall//shouldshould.. Pat can’t move his arm.Pat can’t move his arm. Pat couldn’t move his arm.Pat couldn’t move his arm. Tracy can’t stay out past midnight.Tracy can’t stay out past midnight. Tracy couldn’t stay out past midnight.Tracy couldn’t stay out past midnight. John’s wife can’t be very rich.John’s wife can’t be very rich. John’s wife couldn’t be very rich.John’s wife couldn’t be very rich.

The “future tense marker” The “future tense marker” willwill can also be can also be considered to be a modal (rather than tense considered to be a modal (rather than tense proper).proper).

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Connection with Connection with conditionalsconditionals

If there is a blizzard, classes are If there is a blizzard, classes are canceled.canceled.

Restricting attention to worlds in which Restricting attention to worlds in which there is a blizzard, all of those worlds there is a blizzard, all of those worlds are also worlds in which classes are are also worlds in which classes are canceled.canceled.

Classes can/may be canceled.Classes can/may be canceled. Restricting attention to the modal base, Restricting attention to the modal base, there is at least one world in which there is at least one world in which classes are canceled.classes are canceled.

Marking modalityMarking modality

In general, marking modality In general, marking modality means raising a hypothetical means raising a hypothetical situation and commenting on it.situation and commenting on it.

We can do this with adverbs as We can do this with adverbs as well:well: Probably, John ate the sandwich.Probably, John ate the sandwich. John might have eaten the sandwich.John might have eaten the sandwich. Certainly, John ate the sandwich.Certainly, John ate the sandwich. John definitely ate the sandwich.John definitely ate the sandwich.

Wanting and hopingWanting and hoping

The verbs The verbs wantwant, , hopehope, etc. are , etc. are also interpreted in a way also interpreted in a way similar to modals.similar to modals. I want to buy a pony.I want to buy a pony.

Restricting attention to worlds Restricting attention to worlds that are those in which my that are those in which my desires are satisfied, desires are satisfied, I buy a I buy a pony pony is true in those worlds.is true in those worlds.

Accessible worldsAccessible worlds I want to teach Tuesdays and I want to teach Tuesdays and Thursdays next semester.Thursdays next semester.

In those worlds in which my desires In those worlds in which my desires are satisfied, I teach on Tuesdays are satisfied, I teach on Tuesdays and Thursdays?and Thursdays?

There seems to be a secondary There seems to be a secondary relativization on worlds that are relativization on worlds that are “accessible” from the actual world.“accessible” from the actual world.

De reDe re vs. vs. de dictode dicto When we talk about propositional When we talk about propositional attitude verbs (attitude verbs (thinkthink, , believebelieve, , doubtdoubt, , saysay, …), there’s a , …), there’s a detectible ambiguity:detectible ambiguity: Pat thinks that the brightest student Pat thinks that the brightest student is a spy.is a spy.

De dicto De dicto belief: belief: belief about belief about description.description.

De re De re belief:belief: belief about belief about individual(s). individual(s).

De re De re vs. vs. de dictode dicto

Mary believes that a movie star was Mary believes that a movie star was caught shoplifting last week.caught shoplifting last week.

Mary claimed that an astronaut stole her Mary claimed that an astronaut stole her homework.homework.

John thinks that Mary claimed that an John thinks that Mary claimed that an astronaut stole her homework.astronaut stole her homework. De dicto De dicto for claim, for claim, de dicto de dicto for for thinkthink.. De re De re for for claimclaim, , de dicto de dicto for for thinkthink.. De re De re for for claimclaim, , de re de re for for thinkthink..

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