Friday, May 23, 2008

Unit 8

1. Explain the following terms and concepts:
*extension *fuzzy set * extension of a one-place predicate *ostensive definition *prototype *denotation
2. Is the difference between reference and sense clear-cut or not? Explain and illustrate.
Not with respect to the two notions being completely separate from each other. Because sense fixes extension, i.e. because we have to know a predicate's sense in order to know what it can refer to, there is a relationship between the two notions.
3. Explain the notion of potential referents in connection with the phrase the book.
The potential referents of the book is the set of all individual books to which the predicate book can be truthfully applied.
4. What term introduced in this unit describes the set of potential referents of a referring expression such as the noun phrase the book in #3 above?
Extension of the predicate.
5. Distinguish between referent and extension.
The referent of a referring expression is an individual entity referred to by that expression that is dependent on a particular occasion of use. The extension of a referring expression is the set of individual entities to which the referring expression could potentially refer. The extension is independent of any occasion of use.
6. Make sure you understand the chart in which the differences and similarities between sense, extension, and reference are described. In what way are sense and extension alike, and unlike reference? In what way are extension and reference alike, and unlike sense?
Sense and extension are alike (and unlike reference) in that they are independent of any occasion of use.
Extension and reference are alike (and unlike sense) in that they share the property of connecting linguistic expressions to the world.
7. In this unit we said that "A speaker's knowledge of the sense of a predicate provides...an idea of its extension". In other words, we noted that sense fixes (determines) extension. Explain as best you can in your own words.
Your answer may vary, but it should contain the idea that we have to know something about the stable, context-free meaning of a predicate (sense) in order to know what entities in the world (or possibly some imaginary world) can be referred to by that predicate.
8. Do you think it would be possible for the extension of a predicate to fix (determine) the sense of that predicate? Why or why not?
No, because as we have defined sense and extension we would have no way to figure out for sure the full context-free meaning of a predicate (its sense) just by knowing one or more of the entities that the predicate can refer to. Knowing that an entity is a referent of a predicate gives little insight into what the other members of the extension might be, which would be necessary in order to fully determine the predicate's sense.
9. Describe briefly the extension of car.
The set of all entities to which the predicate car can be truthfully applied.
10. What is meant by the statement that "extensions are relative to all times, past, present and future"? How can we restrict the extension of a predicate?
The extensions of most common predicates don't generally change much over time. For example, the extension of tree is probably much the same as it was 1000 years ago, since the concept has not appreciably changed in that time, nor has the number and type of entities to which the predicate can be applied. An exception might be if the sense of a predicate changed in some way so as to alter the kinds of entities in the predicate's extension. An example might be the sense of building, which has arguably broadened to include additional kinds of structures over the years.
One way to restrict the extension of a predicate is to restrict the tense of the verb in the sentence in which the predicate is used. Another is by using modifiers, such as adjectives, to narrow down the range of noun predicates, as in old book, which restricts the extension of book to the subset of books that are old.
11. In this unit we noted that extension and meaning cannot be equated (cf. featherless biped and rational animal). Why not?
Extension and meaning are not the same thing, because more than one expression can have the same set of potential referents (extension) and yet differ in meaning. Featherless biped and rational animal both have the same extension (i.e. the set of human beings), and yet they don't mean the same thing, because they have different senses that pick out different aspects of what it means to be a human.
12. What is the basic flaw in the idea of extensions? What are fuzzy sets and how is this notion supposed to resolve the problem? Give your own example.
The basic flaw in the idea of extensions is that the boundaries of the sets characterized by the extensions of most predicates is often fuzzy and indeterminant. Speakers often aren't sure whether an entity is in the extension of a predicate, or not, because there are gradations in set membership. Fuzzy sets are sets whose boundaries are flexible, i.e. not rigidly defined with respect to whether an entity is in the set or not. An example is the difference between a table and a desk: speakers may not be sure whether a particular entity belongs to the extension of table or desk if the entity has characteristics that are indeterminant between the two things.
13. What does the notion of natural kind play with respect to the notion of extension? What originally motivated the notion of an extension?
Natural kinds are entities occurring in the real world, such as particular kinds of animals and plants, etc. whose extensions have relatively clear-cut boundaries. The notion of an extension was originally motivated to explain speakers' ability to refer to objects in the world, among other things. A fuller account of this is given in the unit.
14. Briefly describe prototypical examples of the following entities, along with one or two non-prototypical examples that could also be referred to by each predicate. Explain why the non-prototypical examples diverge from the prototype.
a. bird d. dog b. book e. flower c. furniture f. chair
Your answers will vary considerably, and so I do not provided any here.
15. What does the concept prototype have to do with meaning? How is it related to the learning of the meanings of certain expressions?
A prototype is a typical, most central example of a predicate. Often the meanings of expressions will be learned by ostensive definition involving a prototype. A learner will be shown a typical example of a predicate ostensively (by pointing), and this will enable the learner to gradually extend her knowledge of the extension of the predicate.
16. In this unit we gave several examples in which cultural differences can lead to different prototypes. Think of some more examples not mentioned in the book.
Possible examples: building, shoe, car, bus, dog, etc., all of which might have different prototypes in different cultures.
17. Give some examples not in the book which would likely be learned via ostensive definition and some which are not likely learned that way.
Your answers will vary. Typically, predicates learned ostensively tend to be those referring to concrete entites in the real world, such as dog, cat, mountain, etc. Less likely to be learned in this way are such abstractions as love, hate, beauty, etc.