1. CAS LX 502 Semantics 5a. Plurals, mass, and measurement 5.5

2. Singular individuals The Last Juror is a book. The Last Juror is a book. Cat’s Cradle is a book. Cat’s Cradle is a book. What is Meaning? is a book. What is Meaning? is a book. [book] M = x [ x  F(book) ] [book] M = x [ x  F(book) ] F(book) = {The Last Juror, Cat’s Cradle, What is Meaning?} F(book) = {The Last Juror, Cat’s Cradle, What is Meaning?} F(The Last Juror)  F(book) F(The Last Juror)  F(book) F(Cat’s Cradle)  F(book) F(Cat’s Cradle)  F(book) F(What is Meaning?)  F(book) F(What is Meaning?)  F(book)

3. Plurals The Last Juror and Cat’s Cradle are books. The Last Juror and Cat’s Cradle are books. The Last Juror and What is Meaning? are books. The Last Juror and What is Meaning? are books. Cat’s Cradle and What is Meaning? are books. Cat’s Cradle and What is Meaning? are books. The Last Juror, Cat’s Cradle, and What is Meaning? are books. The Last Juror, Cat’s Cradle, and What is Meaning? are books. So, something  F(books). So, something  F(books). The question is: what is in F(books)? ‘What is the denotation of books?’ The question is: what is in F(books)? ‘What is the denotation of books?’

4. Collections Intuitively, The Last Juror and What is Meaning? is something like a collection of individuals (each a book). Intuitively, The Last Juror and What is Meaning? is something like a collection of individuals (each a book). A natural thing to suppose is that F(books) contains collections of individuals—all of those collections such that each member is in F(book). A natural thing to suppose is that F(books) contains collections of individuals—all of those collections such that each member is in F(book). F(books) = { {The Last Juror, Cat’s Cradle}, {The Last Juror, What is Meaning?}, {Cat’s Cradle, What is Meaning?}, {The Last Juror, Cat’s Cradle, What is Meaning?} } F(books) = { {The Last Juror, Cat’s Cradle}, {The Last Juror, What is Meaning?}, {Cat’s Cradle, What is Meaning?}, {The Last Juror, Cat’s Cradle, What is Meaning?} } NP 1 and NP 2 creates a collection {[NP 1 ] M, [NP 2 ] M } NP 1 and NP 2 creates a collection {[NP 1 ] M, [NP 2 ] M }

5. The structure of plurals A, B, C are the atoms; all sums (collections) of atoms are in the plural. (The atoms aren’t: The Last Juror isn’t books) A, B, C are the atoms; all sums (collections) of atoms are in the plural. (The atoms aren’t: The Last Juror isn’t books) A+B+C A+B A+CB+C (A)(B)(C)F(book) F(books)

6. Distributivity Great. So, The Last Juror and Cat’s Cradle comes out as denoting the collection {The Last Juror, Cat’s Cradle}. Great. So, The Last Juror and Cat’s Cradle comes out as denoting the collection {The Last Juror, Cat’s Cradle}. The Last Juror and Cat’s Cradle are boring. The Last Juror and Cat’s Cradle are boring. Notice that agreement registers whether we’re looking at a plural or singular noun phrase here. Notice that agreement registers whether we’re looking at a plural or singular noun phrase here. Under what conditions is this true? Under what conditions is this true?

7. Distributivity Notice that the way we’ve been thinking of the definition of boring from the formal fragment of English, we do not predict this: Notice that the way we’ve been thinking of the definition of boring from the formal fragment of English, we do not predict this: [boring] M = x [ x  F(boring) ] [boring] M = x [ x  F(boring) ] So while it may (hypothetically) be the case that The Last Juror  F(boring) and that Cat’s Cradle  F(boring), we hadn’t considered the possibility that {The Last Juror, Cat’s Cradle}  F(boring). So while it may (hypothetically) be the case that The Last Juror  F(boring) and that Cat’s Cradle  F(boring), we hadn’t considered the possibility that {The Last Juror, Cat’s Cradle}  F(boring). Moreover, we probably don’t want that. Moreover, we probably don’t want that.

8. Distributivity It’s very predictable that a collection C like these is only boring if, for each member x in the collection, x is boring. It’s very predictable that a collection C like these is only boring if, for each member x in the collection, x is boring. The predicate distributes through the collection, applying to each member. The predicate distributes through the collection, applying to each member. Predictable things should be in the grammar. Predictable things should be in the grammar.

9. Plural predicates The standard way to think about this is to suppose that for every predicate like boring there is a plural predicate, notated  boring, that holds of collections: The standard way to think about this is to suppose that for every predicate like boring there is a plural predicate, notated  boring, that holds of collections:  can be viewed as a function from singular predicates to plural predicates:  can be viewed as a function from singular predicates to plural predicates: [  ] M = P [ C [  x[ x  C  P(x) ] ] ] [  ] M = P [ C [  x[ x  C  P(x) ] ] ] The idea is that the word boring can either correspond to boring or  boring; the one you choose is based on whether it is an individual or a collection that it applies to. The idea is that the word boring can either correspond to boring or  boring; the one you choose is based on whether it is an individual or a collection that it applies to.

10. This works fabulously. Loren and Bond are tall. Loren and Bond are tall. Nemo and Dory are fish. Nemo and Dory are fish. It is not the case that Loren and Nemo are fish. It is not the case that Loren and Nemo are fish. The books are boring. The fish are hungry. The books are boring. The fish are hungry. (what are the collections here?) (what are the collections here?)

11. Er… Loren and Bond bought a house. Loren and Bond bought a house. Pavarotti and Bond lifted a piano. Pavarotti and Bond lifted a piano. The men gathered. The men gathered. Loren and Pavarotti are similar. Loren and Pavarotti are similar. The meaning here is does not seem to be distributive. The meaning here is does not seem to be distributive.

12. Groups A collection of individuals can be viewed either distributively (as individuals) or collectively (as a group). A collection of individuals can be viewed either distributively (as individuals) or collectively (as a group). The students gathered. The students gathered. The students have blue eyes. The students have blue eyes. We even have names for some groups: committee, jury, senate, … We even have names for some groups: committee, jury, senate, … The jury gathered. The jury gathered. Note that these are morphologically singular even though they are semantically plural in some sense. Note that these are morphologically singular even though they are semantically plural in some sense.

13. Collections of groups The animals filled the barn to capacity. The animals filled the barn to capacity. The pigs and the cows filled the barn to capacity. The pigs and the cows filled the barn to capacity. The pigs and the cows argue. The pigs and the cows argue. The boys and the girls touched the ceiling. The boys and the girls touched the ceiling. …There are many complex issues left to address with plurals and groups, but this gives you a taste… …There are many complex issues left to address with plurals and groups, but this gives you a taste…

14. Plurals and part-whole structure One of the main things to take away here is that plurals are structured. One of the main things to take away here is that plurals are structured. Additivity: Additivity: If C 1  F(books), C 2  F(books), then C 1 and C 2  F(books) If C 1  F(books), C 2  F(books), then C 1 and C 2  F(books) Books and books are books. Books and books are books.

15. Mass nouns Certain kinds of nouns, mass nouns, also show this kind of part structure (unlike count nouns) Certain kinds of nouns, mass nouns, also show this kind of part structure (unlike count nouns) Soup and soup is soup. Soup and soup is soup. Parts of soup are soup. Parts of soup are soup. A chair and a chair is not a chair. A chair and a chair is not a chair. Parts of a chair are not a chair. Parts of a chair are not a chair.

16. Distinguishing mass and count John bought four books. John bought four books. *Mary bought four barley(s). *Mary bought four barley(s). Each chair is brown. Each chair is brown. *Each furniture is brown. *Each furniture is brown. *John doesn’t have much chair(s). *John doesn’t have much chair(s). Mary doesn’t have much furniture. Mary doesn’t have much furniture.

17. Coercions It is possible to interpret nouns that are “naturally” mass as count, or interpret nouns that are “naturally” count as mass. Although you can do these coercions, you can feel that they are coercions. It is possible to interpret nouns that are “naturally” mass as count, or interpret nouns that are “naturally” count as mass. Although you can do these coercions, you can feel that they are coercions. John bought three coffees. John bought three coffees. There is chair all over the room. There is chair all over the room.

18. Making mass nouns countable: How do you count soup? I have two gallons of soup. I have two gallons of soup. I have two pounds of soap. I have two pounds of soap. I have three pieces of furniture. I have three pieces of furniture. By providing a measure, we can begin to count the number of those measurements. These measurements can in some sense be natural or imposed. By providing a measure, we can begin to count the number of those measurements. These measurements can in some sense be natural or imposed. I found three grains of rice in my pocket. I found three grains of rice in my pocket. I found three pocketfuls of rice in my closet. I found three pocketfuls of rice in my closet.

19. Measurement Measurement can come in a couple of different kinds. Let’s explore two of them for a while: Measurement can come in a couple of different kinds. Let’s explore two of them for a while: Pseudopartitive: One quarter inch of wire Pseudopartitive: One quarter inch of wire Compound: One quarter inch wire Compound: One quarter inch wire What do these refer to? What do these refer to? How do we know that? How do we know that?

20. Measurement It seems that the pseudopartitive and compound forms of measurement have certain restrictions on how they measure: It seems that the pseudopartitive and compound forms of measurement have certain restrictions on how they measure: 80° water. 80° water. *80° of water. *80° of water. *Two mile highway. *Two mile highway. Two miles of highway. Two miles of highway. What’s the difference here? What’s the difference here?

21. Kinds of measurement Consider measuring the wire. Say we measured a wire and found it to be 10 inches. If we cut it in half, what’s the measurement of each bit? Consider measuring the wire. Say we measured a wire and found it to be 10 inches. If we cut it in half, what’s the measurement of each bit? *5 inch wire. 5 inches of wire. *5 inch wire. 5 inches of wire. *5 pound sugar. 5 pounds of sugar. *5 pound sugar. 5 pounds of sugar. Consider measuring the water. Say we measured the water and found it to be 80°. If we split it in two, what is the measurement of each part? Consider measuring the water. Say we measured the water and found it to be 80°. If we split it in two, what is the measurement of each part? 80° water. *80° of water. 80° water. *80° of water. 25 mph wind. *25 mph of wind. 25 mph wind. *25 mph of wind.

22. Metrics Some metrics are monotonic. Some metrics are monotonic. Monotonic: For a a part of b, where a measures m, and b measures n, m < n. Monotonic: For a a part of b, where a measures m, and b measures n, m < n. Length, volume, weight, depth are like this. Length, volume, weight, depth are like this. Temperature is not. Temperature is not. Three miles of highway. Three inches of dirt. Three pounds of sugar. *80° of water. *25 mph of wind. Three miles of highway. Three inches of dirt. Three pounds of sugar. *80° of water. *25 mph of wind.

23. Hypothesis Pseudopartitive (measure of stuff) is possible only when the measure is monotonic. Pseudopartitive (measure of stuff) is possible only when the measure is monotonic. 2 pounds of sugar. *30° of water. 2 pounds of sugar. *30° of water. Compound (measure stuff) is possible only when the measure is not monotonic. Compound (measure stuff) is possible only when the measure is not monotonic. 30° water. *2 pound sugar. 30° water. *2 pound sugar.

24. Monotonicity and parts Pseudopartitive—monotonic. Pseudopartitive—monotonic. Twenty pounds of sugar. Twenty pounds of sugar. Twenty pounds of apples. Twenty pounds of apples. So, weight is monotonic. The pseudopartitive is allowed… So, weight is monotonic. The pseudopartitive is allowed… Twenty pounds of turtle. Twenty pounds of turtle. So why does this lead to an unpleasant reading? So why does this lead to an unpleasant reading?

25. Parts and unpleasantness It seems that the requirement on the pseudopartitive (monotonicity) not only requires that parts measure less than wholes, but that there are parts. It seems that the requirement on the pseudopartitive (monotonicity) not only requires that parts measure less than wholes, but that there are parts. 20 pound turtle 20 pound turtle 20 pounds of turtle 20 pounds of turtle

26. Compounds Compounds are used when the requirement (monotonicity) is not met… Compounds are used when the requirement (monotonicity) is not met… …either because the measure is not monotonic …either because the measure is not monotonic Some 80° water(*80° of water) Some 80° water(*80° of water) A 20 mph wind(*20 mph of wind) A 20 mph wind(*20 mph of wind) …or because the noun doesn’t have parts …or because the noun doesn’t have parts A two-hour job(*2 hours of job) A two-hour job(*2 hours of job) A twenty-pound dog(  20 pounds of dog) A twenty-pound dog(  20 pounds of dog)

27. 8 inches of snow What does 8 inches of snow mean? What is being measured? Is it monotonic? What does 8 inches of snow mean? What is being measured? Is it monotonic? Delaware got more 2 inches more rain than Texas. Delaware got more 2 inches more rain than Texas. What is 1/4 inch wire? What is being measured? Is it monotonic? What is 1/4 inch wire? What is being measured? Is it monotonic? What is 1/4 inch of wire? What is being measured? Is it monotonic? What is 1/4 inch of wire? What is being measured? Is it monotonic?

28. So Moving beyond the simple conception of individuals, we find complex individuals. Moving beyond the simple conception of individuals, we find complex individuals. Mass nouns Mass nouns Plural nouns Plural nouns Language is sensitive to the abstract property of having parts (divisibility, additivity), e.g., in choosing between the pseudopartitive and compound measure forms. Language is sensitive to the abstract property of having parts (divisibility, additivity), e.g., in choosing between the pseudopartitive and compound measure forms.

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