A small semantics quiz

2

Guess the determiner...

1. PQx(P(x)&Q(x))

2. PQx(Plural(x)&P(x)&Q(x))

3. PQx(P(x)Q(x))

4. PQx(P(x)&y(P(y)y=x)&Q(x))

5. PQx(y(P(y)y=x)&Q(x))

6. PQx(P(x)&Q(x))

a

some

every

the

the

no

3

Guess the truth conditions...4. PQx(P(x)&y(P(y)y=x)&Q(x))

5. PQx(y(P(y)y=x)&Q(x))

the

the

P Q

P Q

P Q

P Q

TRUE FALSE

FALSE FALSE

4

Another way of representing definites5. PQx(y(P(y)y=x)&Q(x))

7. Px(P(x))

> Takes a set and picks out the unique individual in that set. If such a unique individual is not available, the result is undefined.

P P P

UNDEFINED UNDEFINED

5

Guess the truth conditions...

P Q

P Q

P Q

P Q

TRUE FALSE

FALSE FALSE

The P is Q

TRUE FALSE

UNDEFINED UNDEFINED

Carlson (1977)

7

Background> semanticist (works at Rochester)

> American

8

Overview

> BP is not the plural counterpart of a> BP is not even a normal indefinite

> the generic and the existential reading of BPs are two sides of the same coin

> how to connect the sides of the coin?

9

Overview

> BP is not the plural counterpart of a> BP is not even a normal indefinite

10

Anticipated semantics

If the bare plural were the plural of the singular indefinite...

... we would expect it to behave semantically in the same way except for an extra condition of plurality.

11

Opacity phenomena: a

Minnie wishes to talk to a young psychiatrist.

> Minnie’s wish is to talk to a young psychiatrist.

> There is a young psychiatrist who is such that it is Minnie’s wish to talk to him.

ok

ok

12

Opacity phenomena:

Minnie wishes to talk to young psychiatrists.

> Minnie’s wish is to talk to young psychiatrists.

> There are young psychiatrists that are such that it is Minnie’s wish to talk to them.

ok

#

13

Opacity phenomena: a few

Minnie wishes to talk to a few young psychiatrists.

> Minnie’s wish is to talk to a few young psychiatrists.

> There are a few young psychiatrists such that it is Minnie’s wish to talk to them.

ok

ok

14

Opacity phenomena: conclusion

> opacity phenomena = scope with respect to intensional verbs (such as believe, wish)

> whereas bare plurals can only take scope below the intensional verb, regular indefinites can take scope below and above it

15

Narrow scope phenomena: a

Everyone read a book on caterpillars.

> For everyone there is a book on caterpillars that is such that he/she read it.

> There is a book on caterpillars that is such that everyone read it.

ok

ok

16

Narrow scope phenomena:

Everyone read books on caterpillars.

> For everyone there are books on caterpillars that are such that he/she read them.

> There are books on caterpillars that are such that everyone read them.

ok

#

17

Narrow scope phenomena: a few

Everyone read a few books on caterpillars.

> For everyone there are a few books on caterpillars that are such that he/she read them.

> There are a few books on caterpillars that are such that everyone read them.

ok

ok

18

Narrow scope phenomena: conclusion

whereas bare plurals can only take scope below other operators, regular indefinites can take scope below and above them

19

Overview

Bare plurals behave differently from singular indefinite a and indefinites in general in that they can only take narrow scope.

20

Differentiated scope: a

A dog was everywhere.

> There is a dog such that it was everywhere.> All places were such that they had a dog in

them.

ok

#

21

Differentiated scope:

Dogs were everywhere.

> There are dogs that are such that they were everywhere.

> All places were such that they had dogs in them.

#

ok

22

Differentiated scope: a again

A flag was hanging in front of every building.

> There is a flag such that it was hanging in front of every building.

> All buildings were such that they had a flag in front of them.

ok

ok

23

Differentiated scope: conclusion

> According to Carlson BPs can sometimes take scope below operators indefinites cannot take scope under.

> This might however be due to his choice of examples.

> What does seem to hold is that bare plurals can only take narrow scope.

24

Anaphora: a

Harriet caught a rabbit yesterday, and Ozzie caught it today.

> a rabbit = it> a rabbit it

ok

#

25

Anaphora:

Harriet caught rabbits yesterday, and Ozzie caught them today.

> rabbits = them> rabbits them

ok

ok

26

Anaphora: plural them

I bought a potato because they contain vitamin C.

27

Anaphora: plural them

I bought a potato because they contain vitamin C.

> Carlson’s anaphora argument is based on the assumption that it and them are different only in number.

> This assumption turns out to be ill-guided. Them but not it seems to be able to pick up the descriptive content of the noun.

> The contrast between it and them makes any argument that is based on a comparison between singular and plural anaphora flawed.

28

Anaphora: conclusion

> According to Carlson BPs sometimes allow for anaphora indefinites don’t allow for.

> This might however be due to his choice of pronoun.

29

Overview

> BP is not the plural counterpart of a> BP is not even a normal indefinite> Argumentation hinges on scope facts.

30

Overview

> the generic and the existential reading of BPs are two sides of the same coin

31

Bare plurals and kindsStrong claim

“A unified analysis is not only desirable, but necessary, if we are to have a complete account of this construction.”

32

Bare plurals and kindsTwo sides of the same coin...

Argument #1

they are in complementary distributionPotatoes rolled out of the bag.Potatoes contain vitamin C.

Why is this not a very strong argument?

33

Bare plurals and kindsTwo sides of the same coin...

Argument #2

kind-referring DPs behave in the same way:This kind of vegetable rolled out of the bag. This kind of vegetable contains vitamin C.

Why is this still not a very strong argument?

34

Bare plurals and kindsStrongest point

Unambiguously kind-referring DPs behave scopally in the same way!

> If we assume that BPs are kind-referring we get the funny scope behaviour for free!

35

Bare plurals and kinds

Max believes this kind of animal to have eaten his pet sponge.

> No specific instantiation of this kind of animal can be intended.

36

Bare plurals and kinds

Everyone saw this kind of animal.

> A reading according to which there is a particular instantiation of this kind of animal that everyone saw is not available.

37

Overview

> BPs refer to kinds and the context decides whether you get the kind or an existential reading.> Scope facts form the knock-down argument

38

Overview

> how to connect the sides of the coin?

39

Kinds and their instantiationsCarlson doesn’t give an explicit semantics

for the kind and generic readings.

For the existential readings he proposes that there are predicates that select kinds and existentially quantify over their instantiations (the realization operation):

yx[R(x,y)&P(x)]

Baking the existential quantifier into predicates guarantees narrow scope.

40

Kinds and their instantiations

yx[R(x,y)&here(x)] = to be herey-x[R(x,y)&here(x)] = not to be here-x[R(x,catk)&here(x)] = catsk not to be here

41

Overview

> BPs refer to kinds and the context decides whether you get the kind or an existential reading.

> BP is not the plural counterpart of a> BP is not even a normal indefinite

> existential readings are obtained through a realization operation baked into predicates

> the whole story hinges on scope facts