1. Kaplan’s Theory of Indexicals
Introduction to Pragmatics
Elizabeth Coppock
HHU, Summer 2012

2. Indexicals
Indexical: A word whose referent is dependent on the context of use, which provides a rule which determines the referent in terms of certain aspects of the context. (Kaplan 1977, Demonstratives, p. 490) Examples: I, my, you, that, this, here, now, tomorrow, yesterday, actual, present

3. Demonstratives
Demonstrative: An indexical that requires an associated demonstration. Examples: this, that Cf. Fillmore’s gestural uses of deictic terms.

4. Pure Indexical
Pure indexical: An indexical for which no demonstration is required. Example: I, now, here, tomorrow. (Although here has a demonstrative use: “In two weeks, I will be here [pointing]”)

5. Two obvious principles
The referent of a pure indexical depends on the context, and the referent of a demonstrative depends on the associated demonstration.
Indexicals, pure and demonstrative alike, are directly referential.

6. Directly referential
An expression is directly referential if its referent, once determined, is taken as fixed for all possible circumstances.
(Like Kripke’s rigid designators)
Proper names (John) are directly referential
Definite descriptions (the man) are not

7. Alternative World 2
Said by me today (in the US):
“The president is a Democrat”
The actual world
false
Alternative World 1
true
true

8. Alternative World 5
Said by me today:
“The president is a Democrat”
Alternative World 3
true
Alternative World 4
true
false

9. Alternative World 2
Said by me today:
“Barack Obama is a Democrat”
The actual world
true
Alternative World 1
true
true

10. Alternative World 5
Said by me today:
“Barack Obama is a Democrat”
Alternative World 3
true
Alternative World 4
true
true

11. Alternative World 2
Said by Barack Obama today:
“I am a Democrat”
The actual world
true
Alternative World 1
true
true

12. Alternative World 5
Said by Barack Obama today:
“I am a Democrat”
Alternative World 3
true
Alternative World 4
true
true

13. Conclusion
“Barack Obama” designates the same individual in every possible world; it is directly referential.
“The president” can designate different individuals in different possible worlds.
When Barack Obama says “I”, he means “Barack Obama”. “I” is directly referential too.

14. (Complication)
There are so-called descriptive uses of indexicals. Says a prisoner on death row (Nunberg): I am traditionally allowed a last meal. [“I” – a person on death row.] But nevermind that. Ignore this slide.

15. Recall: Directly referential
An expression is directly referential if its referent, once determined, is taken as fixed for all possible circumstances. Kaplan continues: This does not mean it could not have been used to designate a different object; in a different context, it might have. But regardless of the circumstance of evaluation, it picks out the same object.

16. Alternative World 5
“I am a Democrat”
Actual World
Context:
Speaker=Obama: true
Speaker=McCain: true
Context:
Speaker=Obama: true
Speaker=McCain: false

17. Context vs. Circumstance
Context of utterance: Who is speaking to whom, where, when, what they’re gesturing to, etc. Circumstance of evaluation: A possible world at which the truth of the utterance might be evaluated.

18. Direct Reference
The word “I”, uttered by Barack Obama (or whoever), picks out the same individual in every possible world / circumstance of evaluation.
You don’t have to look to see what properties the object has in the possible world in order to decide what it refers to.
Unlike definite descriptions, whose referent depends on who is, for example, the president.
The only thing that can affect what “I” refers to is who the speaker is (the context).

19. Fixed/Variable Meaning
The meaning of an indexical like "I" is:
Fixed across all circumstances of evaluation
Variable across contexts of use
The meaning of a definite description is:
Variable across circumstances of evaluation
(Arguably variable across contexts of use as well.)

20. Same or different meaning?
May 11, 2010:
May 12, 2010:
I am turning 30 today.
I am turning 30 today.

21. Same or different meaning?
May 11, 2010:
May 12, 2010:
I am turning 30 today.
I turned 30 yesterday.

22. Frege's answer
If somebody wants to say the same today as he expressed yesterday using the word today, he must replace this word with yesterday. Although the thought is the same its verbal expression must be different so that the sense, which would otherwise be affected by the differing times of utterance, is readjusted. G. Frege, in "The thought: A Logical Inquiry"

23. Content vs. Character
Character: The aspect of meaning that two utterances of the same sentence share across different contexts of utterance. Content: The proposition expressed by an utterance, with the referents of all of the indexicals resolved.

24. Same character, different content
May 11, 2010:
May 12, 2010:
I am turning 30 today.
I am turning 30 today.

25. Same content, different character
May 11, 2010:
May 12, 2010:
I am turning 30 today.
I turned 30 yesterday.

26. Strawson made a similar point about definite descriptions
During the reign of Louis XIV
During the reign of Louis XV
The king of France is wise.
The king of France is wise.

27. Strawson: Meaning as use
Obviously in the case of this sentence, and equally obviously in the case of many others, we cannot talk of the sentence being true or false, but only of its being used to make a true or false assertion, or (if this is preferred) to express a true or false proposition. And equally obviously we cannot talk of the sentence being about a particular person, for the same sentence may be used at different times to talk about quite different particular person, but only of use of the sentence to talk about a particular person.

28. Indexicals and Descriptive Content
“Indexicals have descriptive meaning, but this meaning is relevant only to determining a referent in a context of use and not to determining a relevant individual in a circumstance of evaluation.” I.e., the descriptive meaning is part of the character, but not the content.

29. Imagine if it were otherwise!
Suppose “I do not exist” is true in a circumstance of evaluation if and only if the speaker (assuming there is one) of the circumstance does not exist in the circumstance. Nonsense! If that were the correct analysis, what I said could not be true. From which it follows that: It is impossible that I do not exist.

30. Impossibility
Something that is possible is true in at least one possible world.
Something that is impossible is false at every possible world.
Something that is necessary is true at every possible world.

31. Alternative World 8
The actual world
Alternative World 7

32. “I am here now”
This is a logical truth, in the sense that whenever it is uttered, it is true.
But it is not a necessary truth, because the circumstances could be otherwise.

33. Indexicals are weird! Normally logical truths are necessary truths!
This is the principle of necessitation (or necessity generalization) in modal logic.
If p is a theorem, then ☐p is a theorem.
theorem: a provable statement
☐p = "necessarily p"
So indexicals produce "a distinctive and deviant pattern of logical consequence" (Kaplan, The Meaning of Ouch and Oops).

34. Solution
“Indexicals have descriptive meaning, but this meaning is relevant only to determining a referent in a context of use and not to determining a relevant individual in a circumstance of evaluation.”
In other words, the descriptive content of an indexical goes into determining the character, but not the content.

35. What is a content? The content of a sentence is a proposition.
A proposition is a set of possible worlds, or a mapping from possible worlds to truth values.
e.g. {w1, w3, w4}
Another way of saying it: a proposition determines the circumstances in which the sentence is true.
circumstances (of evaluation) = possible worlds.
Another way to think about propositions: Functions from circumstances to truth values.
e.g. f(w1) = 1, f(w2) = 0, f(w3) = 1, f(w4) = 1, etc.

36. Intension vs. Extension
The actual truth value of a sentence in a particular world is its extension.
The proposition that a sentence denotes can be thought of as a function from circumstances of evalution to extensions.
Such a function is an intension (Carnap).
Nouns like dog also have intensions and extensions.
Intension + Possible World => Extension
Content + Circumstance => Extension

37. What is a character?
The character of a sentence is something that, given a context of utterance, gives you a content.
Formally: A function from contexts to contents

38. { The Kaplanian Picture Character + Context => Content
Content + Circumstance => Extension
Character + Context + Circumstance => Extension {
Content

39. Strawson: Meaning as use
Meaning (in at least one important sense) is a function of the sentence or expression; mentioning and referring and truth or falsity, are functions of the use of the sentence or expression. To give the meaning of an expression (in the sense in which I am using the word) is to give general directions for its use to refer to or mention particular objects or persons; to give the meaning of a sentence is to give general directions for its use in making true or false assertions. Strawson (1950), On Referring

40. Kaplan's Reflections on Demonstratives
In [Demonstratives], I tried to show that by adding context as a parameter, Strawson's "conventions for referring" as he calls them, even if neglected by logicians, could be accommodated within the range of our methods. And at the time I regarded my work as extending current semantical methods just to the degree necessary to incorporate the indexicals. I regarded what I was doing as a sort of epicycle on Carnap's method of extension and intension and I didn't think of it as involving any different conception of semantics or what semantics was supposed to do.

41. Kaplan's Reflections on Demonstratives, cont'd
Some years ago, it occurred to me that the analysis of indexicals in Demonstratives could be seen as the scientific realization of a Strawsonian semantics of use. Ask not after other-worldly meanings, ask only after rules of use.
--David Kaplan, The Meaning of Ouch and Oops