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Albert GattLIN3021 Formal SemanticsLecture 6In this lectureWe focus on referring expressionsHow do definite descriptions work?What is the relationship between names (Lucienne) and definite descriptions (the woman who lives next door)?Do pronouns have meaning?Sense and referencethe woman next doorSuppose that theres a woman called Lucienne who lives next door.The above description would then refer to her.But its quite easy to imagine situations (worlds) in which a different woman (say, Paula) lives next door. Assume such a case. Then:The woman next door would refer to Paula.Lucienne wouldnt it would still refer to Lucienne.Sense and referenceIt seems as if the woman next door has a meaning which allows us to pick out different entities in different situations.So we need Freges distinction:The sense of the expression is what enables us to determine which individual is intended in different situations.The reference of the expression is the actual individual.

Note:The reference is an individualThe sense isnt.

Were going to see that from the point of view of compositionality, its the reference that counts.What is a sense?the old woman

Weve sometimes glossed the sense of an expression as its descriptive meaning.

More precisely, we might say that the sense of a referring expression is an instruction. In the above case, the individual we need to identify:must be a womanmust be old

Part 1Definites and individualsPredication revisitedThe old woman is tall.Lucienne is tall.(Assume that Lucienne is indeed the old woman in question).

If the old woman and Lucienne refer to the same individual, then the above sentences would seem to be synonymous (have the same truth conditions).

Predication revisitedThe old woman is tall.Lucienne is tall.Observe that in both cases we have an example of predication.TRUEFALSE[[tall]]It looks like both referring expressions can fit into the individual-shaped slot of tall.Predication revisitedThe old woman is tall.Lucienne is tall.Remember Lewiss and Cresswells advice:For two sentences and , if in some situation is true and is false, then and must have different meanings (Cresswell)In order to say what a meaning is, we may first find what a meaning does, and then find something that does that. (Lewis)Since our two sentences are true in the same situation (by assumption), then the two NPs must be playing the same role in the sentence consisting of ___is tall.Predication revisitedThe old woman is tall.Lucienne is tall.TRUEFALSE[[tall]]The problem is that these two expressions are qualitatively different!Lucienne denotes an individual its just a name.Type eBut the old woman consists of:A modifier (old)A predicate (woman)Under our analysis of modifier + predicate constructions, the phrase old woman is of type

The role of the definite articleWe can think of the as a procedure which, given a particular context anda property (such as old woman)Finds the unique individual in that context that satisfies that property.Returns that individual.

In other words:old woman is a predicate ()the old woman refers to the individual (type e) satisfying that predicate

Once this is done, definites can be slotted into the individual-shaped slot of predicates, to saturate them and return propositions, just like names.

So, given that the old woman refers to an individual, and that individual is the same one called Lucienne, the two sentences are indeed synonymous in the given context.This is also why we suggested that its the reference that is most relevant to compositionality for our purposes.

Salience and context[Context: there are three old women]A: The old woman is my grandmother.B: Which one do you mean?A: The middle one.B: Oh.[... 15 minutes later ...]B: By the way, the old womans gone. The other two are still around though.Ambiguous: all three women are equally salient. Unique identification fails, and no individual is picked out.No longer ambiguous. After the first disambiguation, there is now one old woman who is more salient or familiar.The connection between sense and referenceThis analysis is very much in line with Freges.Under this analysis, there is an intimate connection between sense and reference, for it is the sense that helps us determine what the intended reference is.

Context is obviously playing an important role in singling out the unique, intended referent.

Another possibility, analysed by Bertrand Russell, is that definite descriptions arent referential in this sense. Russells analysisThe old woman is tall.Bertrand Russell interpreted the definite description along the following lines:there is an x such that:x is an old woman; andfor any y, if y is an old woman, then y = x; andx is tallx[(old-woman(x) & y(old-woman(y) y=x)) & tall(x)]Asserts uniqueness: if anything is an old woman, its the x were talking about. Alternatively: nothing other than x is an old woman.Russells analysis: things to noteThis is a purely descriptive analysis.The definite description is analysed as a quantified expression (there is...).In a sense, the meaning of a description the N is incomplete. It needs to combine with a predicate before it is fully meaningful:

the old womanPx[(old-woman(x) & y(old-woman(y) y=x)) & P(x)]the old woman is tall:x[(old-woman(x) & y(old-woman(y) y=x)) & tall(x)]Russells problemThe old woman is tall.

x[(old-woman(x) & y(old-woman(y) y=x)) & tall(x)]If theres no such thing as an old woman (or more than one), the sentence the old woman is tall simply comes out false.The problem is even greater when we use definites that have sense, but no reference. Russells examples:the present king of Francethe round squareWe are also apparently quite capable of referring to the old woman in a context where theres more than one, so long as the intended woman is the most prominent.Russells problemThe old woman is tall.

Under the Fregean analysis of descriptions as referential:If there is more than one old woman, the assumption is that the old woman intended is the most prominent or salient one.If there is no such woman, then the sentence is infelicitous, its truth value undefined.So which analysis is correct?Russells analysis emphasises the descriptive aspect of definite descriptions. The alternative analysis seems to emphasise the referential aspect.

Maybe both are required?

Donnellan (1966) argued that both indeed are.Donnellans distinction - IImagine that somebody called Smith has just been murdered. Jones has been charged with the murder and hes on trial. He behaves oddly. Afterwards, you tell a friend: The man who murdered Smith is insane.

Your description suggests a referential use. You intend it to refer to Jones.But what if Jones were innocent? The description the man who murdered Smith wouldnt apply to Jones. Yet your act of reference would still be to Jones.This suggests that theres a cleavage between the descriptive aspect (sense) and the referential aspect.This case is compatible with the purely referential analysis of definites.But note: Donnellan used this case to argue that in fact, definites can refer even independently of their descriptive content, as long as the hearer can understand what the intended referent is.Donnellans distinction - IIImagine that somebody called Smith has just been murdered. You come across the murdered body of Smith. Youve no idea who did it. You turn to your friend and say: The man who murdered Smith is insane.

Here, apparently, the man who murdered Smith isnt really referring to someone identifiable (youve no idea who murdered Smith). Your description here has an attributive use, equivalent to Whoever murdered Smith.This seems more compatible with the Russellian view. It seems to require a descriptive meaning along the lines of: there is an x, x murdered Smith and x is insane.Speakers reference vs Semantic referenceIt seems we have a problem:We analysed the N as referring to the most salient unique individual satisfying NBut Donnellans Scenario 1 suggests that we can have a referential use even when the referent doesnt literally satisfy N.

Heres another example, from Numberg:(Waitress to colleague): the ham sandwich wants his billClearly, the client referred to doesnt literally satisfy the description the ham sandwich.

We could conclude that the definite article is ambiguous between the referential and attributive meanings.(But then, why isnt there a language with two different definite articles, one for each meaning?)

Kripkes argumentKripke suggested that in fact, Donnellans point is better understood as about the use of definite NPs:They can be used referentially or attributivelyThey have a single core meaning (Kripke favoured Russells analysis) that is evinced in their attributive use.The referential use where uniqueness and identifiability play a role is more of a pragmatic phenomenon, i.e. Speakers meaning

Part 2Names vs definite descriptionsPredication revisitedThe old woman is tall.Lucienne is tall.Having established that both expressions can identify an individual (in a certain context, assuming salience/familiarity), there still remains a question:

Under our Fregean analysis, definite descriptions can refer because they express a property which, combined with the forms an instruction to pick out an individual.

So they are a bit like names. But is reference all there is to names?Theory 1 about namesNames are actually hidden descriptions, with a descriptive meaning. We identify the referent by virtue of this hidden, descriptive meaning.(So, rather than say that the tall woman works a bit like the name Lucienne, its more correct to say its the other way round.)

Example: Plato = the most famous Greek philosopherProblems with Theory 1Under this theory, if we replace Plato with the most famous Greek philosopher, we should have a synonymous sentence.NB: this means that the name Plato and the phrase the most famous Greek philosopher are playing exactly the same role in a given sentence.So they have the same sense and the same reference.

Plato is the most famous Greek philosopher.Plato is PlatoThe most famous Greek philosopher is the most famous Greek philosopher.Are these sentences the same?Problems with theory 1Imagine a world, different from the actual one, where Plato was a usurper, who nicked a friends work and claimed it as his own.So Plato =/= the most famous Greek philosopher

It would seem that wed still use the name Plato for the same man, even though the description doesnt work for him anymore.

Salvaging Theory 1Perhaps we could try to salvage this theory:Names are rigid designators. They refer to the same referent in every possible world.They have an associated description, which however is not a rigid designator, unlike the name.In case the description fails in some possible world, the name still succeeds.

But then, why claim that names are descriptions at all?Theory 2: names are purely referentialTheory mainly due to Saul Kripke.Names do not describe, they simply refer.

Problem:Under Theory 1, we had a story about how we come to know that a name refers to what it refers (we know it via its hidden description).How does this work if names dont describe?

Theory 2: causal chainsKripke suggested that names acquire their reference due to a causal chain:Initial act of naming is passed down generations and communities, so that the name remains attached to the individual referred to.

Problem: Sometimes, the causal chain breaks down.E.g. Madagascar was originally not the name of an island, but the name of a stretch of African coast.It became the name of the island by mistake.So the original naming wasnt passed down.Theory 2: communityGareth Evanss solution to this problem:The causal chain theory is really just one special case of a more general tendency.Names refer not (just) by virtue of the original naming, but also by virtue of commonality of use in a specific community.

Madagascar refers to the island in spite of the original naming, because of convention within the speech community.(So its not just an original name that can be passed down, but also naming mistakes that can establish conventions)Part 3A bit about pronounsPronouns are variablesPronouns like she and her seem to contain very little descriptive information (beyond the fact that x is female...).

How do we determine what a pronoun refers to in contexts like these?

Denise went shopping. She bought a sword.Denise met Sally. She chatted with her.Types of pronominal use Referential:Its really ugly [spoken by someone looking at a painting]Denise met Sally. She chatted with her.Pronoun depends on context for interpretation. The antecedent for the pronoun is not completely specified grammatically.

Bound:Only John loves his mother.Pronoun depends on an antecedent in the linguistic context (its binder).

E-type:Few politicians admire Kennedy and they are very junior.Pronoun doesnt seem to be bound by few politicians: this sentences doesnt mean few politicians admire Kennedy and few politicians are junior.(Compare: Jenny admires Kennedy and she is very junior)

Pronouns as variablesIn different contexts, she can refer to lots of different things.Logically, we can think of the way they are interpreted in terms of an assignment function. Very roughly, lets think of the above asmeet(d,s)chat(x, y)Denise met Sally. She chatted with her.If we assume an assignment function g, then in this context:g(x) = Denise.g(y) = SallyBut how does the assignment function know which is which?Pronouns and contextNote that alternative (2) seems possible (though less likely).Clearly, one way in which variable assignments work with pronouns is through salience:Denise is the most salient antecedent for she.Sally is the most salient antecedent for her.Context interacts with grammatical role information (subject/object) to let us come to the most likely conclusion.1. Denise met Sally. She chatted with her.2. Denise met Sally. She chatted with her.Bound pronounsOnly John likes his mother.

This sentence seems to allow two interpretations:John is the only person who likes his mother (nobody else likes their mother)the reference of his shifts depending on who we assign his toa bound pronounJohns mother is only liked by John (nobody else likes her)his = John Note further that the two interpretations are mutually exclusive:We cant have an interpretation where John likes his mother, Steve likes Johns mother (=2) and Frank doesnt like his own mother (=1)

Pronouns and grammarOnly John likes his mother.This sentence also has particular truth conditions, where only is playing a role.Johns mother is only liked by John (nobody else likes her)his = JohnSentence is true iff John likes Johns mother and for all x different from John, x doesnt like Johns mother.Pronoun his here seems to exhibit a referential use.John is the only person who likes his mother (nobody else likes their mother)the reference of his shifts depending on who we assign his toSentence is true iff John likes Johns mother and for all x different from John, x doesnt like xs mother.How do we obtain interpretation (2)?Digression: relative clauses (reminder)In a sentence such as John is who Mary killedthe phrase who Mary killed is also a predicate(i.e. an unsaturated proposition, that yields a complete proposition when combining with John)

Weve dealt with the internal structure of this complex predicate by thinking of it as a property in the underlying logical form.Relative clauses: a rough estimationAssume who has moved to the front of the sentence.The underlying proposition is Mary killed e.[[who Mary killed]] = the proposition that Mary killed someoneunderlined part represents whatevers missing and needs to saturate the proposition.

We start with Mary killed e: the placeholder ei temporarily saturates killWe add whowho indicates that the logical object of kill is no longer in placethis can be interpreted as an instruction to (re-)unsaturate kill, before combining it with an NP to saturate it.whoMarykilledeiTowards an analysisOnly John loves his mother.In this example, Only John is binding the variable his.The variable assignment cant always depend on context. Sometimes, its down to grammar and semantics.We can think of Only John loves his mother along these lines:Only John1 likes his1 mother.=Only John1 [e1 likes his1 mother]Surface formUnderlying logical formA property, which we predicate of only JohnThe semanticsIf the bracketed part is a property, then its an unsaturated proposition: something like love-his-mother(x).The variable x plays a dual role as shown in the diagram:the one who loves (the subject e1 in the open proposition)the person whose mother were talking about (his)Only John1 likes his1 mother.=Only John1 [e1 likes his1 mother]Surface formUnderlying logical formA propertyThe semanticsWhen we combine the property with Only John we get a proposition which:Is true if John saturates the property loves-his-motherFalse otherwise.This corresponds to our desired interpretation:John likes his mother. For every other x, x doesnt like xs mother.Notice that here, the bound variable isnt getting its meaning from a context outside of the sentence. Theres a semantic restriction on the interpretation of his.Only John1 likes his1 mother.=Only John1 [e1 likes his1 mother]Surface formUnderlying logical formA propertyTwo analyses?So we seem to have two ways in which the assignment function for pronouns is determined:Through context (She likes him)Semantically, via grammar (only John likes his mother)

It seems we need both:Sometimes pronouns obviously depend on context, when they dont have linguistic antecedents:Its really ugly. [Spoken by someone looking at a painting]Binding also doesnt seem to work across sentences:Only John loves his mother. His fathers bad.The second his takes John as antecedent. It doesnt mean Only John loves his mother and has a bad father.

A note about e-type pronounsFew politicians admire Kennedy and they are very junior.The politicians who admire Kennedy are few and they are junior. (And there are no other politicians who admire Kennedy)#There are few junior politicians who admire Kennedy (but there may be senior ones who do).

Here, they cant be a bound variable. Interpretation (2) is excluded.It seems as if this is a case where the pronoun has some descriptive content:they = the politicians who admire KennedySo maybe this pronoun is unlike the others? I.e. Maybe we dont have variable binding here?A note about e-type pronounsFew politicians admire Kennedy and they are very juniorWe can account for this in two ways:Treat they on a par with purely referential uses (Its really ugly), where we have an assignment function that assigns the variable they to those politicians who admire Kennedy.This turns the pronoun interpretation into a pragmatic issue. It leaves open the question of how the function actually determines that this is the right interpretation.Assume that they is (semantically) interpreted as the politicians who admire KennedyThis is the position known as the E-type theory.Under this theory, these kinds of pronouns arent just variables.E-type pronouns: other examplesThe E-Type theory has been used to explain examples like these:Every girl who deserved it won the prize she wanted.Here it seems to mean the prize she wanted.Its not referring to a particular prize the specific prize changes depending on who the girl is were talking about.So theres no specific prize that the assignment function can bind the pronoun to.But notice:if it = the prize she wantedThen we have a pronoun (she) inside the meaning of the pronoun it.This pronoun would be bound by every girl in our example.So even if the pronoun it isnt just a variable, its meaning must itself contain a variable!