We have been talking about Frege’s puzzles of cognitive value and attitude ascriptions. As it should be clear from Kripke’s numerous objections to Frege and Russell’s promising theories, it’s not clear how exactly the puzzles are to be solved. Given Kripke’s objections, Frege’s puzzles took a significant amount of attention in the last three decades. Numerous attempts to solve them sprung, but to this center, none of them has come to be widely accepted. Moreover, the solutions are often quite technical, and understanding them requires a significant amount of familiarity with formal tools that we won’t present in class.

So instead of introducing a new view, we’ll briefly discuss a similar problem, raised originally by Héctor Neri-Castaneda, and made prominent by John Perry. Perry calls it “the problem of the essential indexical”. When you read Perry’s paper and these notes, it will be convenient to keep this question in mind: is this the same problem as Frege’s puzzle of cognitive significance? If not, how is it different?

1 The problem of the essential indexical

Perry considers the following three cases:

Sugar:

Perry is walking around the supermarket, when he spots a trail of sugar. He says to himself ‘The shopper with a torn sack is making a mess’, and believes that the shopper with a torn sack is making a mess. Later on, he realizes that he is the shopper with a torn sack, and now he says to himself ‘I am the shopper with a torn sack, I am making a mess’. He now believes that he is making a mess, and since he is a responsible person, he fixes the sack of sugar in his cart, so that he stops making a mess.

Adventure:

An adventurer is in the forest, looking for the Mt. Tallac trail. He knows that the trail is next to Gilmore lake. If he were asked where the Mt. Tallac trail is, he would say ‘the Mt. Tallac trail is next to Gilmore lake’. Unbeknownst to our adventurer, he is standing right on the Mt. Tallac trail, and the lake next to him is Gilmore lake. After a while of looking at the map and his surroundings, he realizes this. He says to himself ‘This is the Mt. Tallac trail, and that lake next to me is Gilmore Lake’. Having acquired this new belief, he continues to walk on the trail, relieved not to be lost anymore.

Meeting:

A professor who works on indexicals knows that he has a meeting at noon. However, he has lost track of time while working on his research and, at noon, he hasn’t gone to the meeting yet. At noon, he still continues to remind himself that he has a meeting at noon. Suddenly, he realizes that he is late for his meeting. He tells himself ‘I have a meeting now’ or ‘now is noon!’ All along, he believed that he had a meeting at noon; what he suddenly realized and now believes is that he has a meeting now.

According to Perry, what is interesting about these cases is that, in each of them, the indexicals we use in the attribution of the second of their beliefs is essential to the attribution: replacing the indexical with a different word, even if it has the same referent, no longer seems to express the same thing. One piece of evidence for this is that once we substitute a different expression for the indexical, the belief attribution no longer seems to be explanatory.

For instance, Perry knew all along that the shopper with the torn bag was making a mess. What he didn’t know was that he was the one making a mess. He could have been repeating to himself ‘The shopper with the torn bag was making a mess’, but he hadn’t told himself ‘I am making a mess’. His belief that the shopper with the torn bag was making a mess didn’t make him stop and rearrange his sugar bag. It was only the belief that he was making a mess that explains why he stopped and rearranged his bag. But he was the shopper with the torn bag. So even though the two expressions denote the same thing in this case, one can’t be substituted for the other while retaining explanatory power, nor can they be substituted salva veritate in the context of a belief attribution.

As you may have noticed, indexicals are words like ‘I’, ‘he’, ‘now’, and ‘here’. What is interesting about these words is that, unlike proper names, they don’t denote the same thing independently of the context. Rather, they only denote some thing or other in context. If I say ‘I like apples’ ‘I’ refers to me, but if you say the same sentence, ‘I’ refers to you. Similarly, if I say ‘My computer is on now’, ‘now’ refers to a particular time: August 4 at noon. If I say that same sentence at a different time, ‘now’ will refer to another time.

In the cases above, it seems like the indexical can’t be replaced by a term with the same referent in a way that preserves the explanatory force of the original statement. This is why, in that sense, the use of an indexical seems to be essential to the explanatory force of the statements that include it (in the cases above). This is what Perry calls the problem of the essential indexical.

Before proceeding to his discussion of some possible solutions, let’s introduce a bit of useful terminology. In our discussion of Russell’s theory of definite descriptions, we introduced a distinction between two kinds of attributions of beliefs or other attitudes: de re (about the thing) and de dicto (about what is said). We might as well introduce a new term for the kind of attributions that essentially involve indexicals. Let’s call such attributions de se (of oneself). Perry’s discussion then has to do with the right analysis of de se belief attributions.

The reports that essentially involved indexicals in the cases we called Sugar, Adventure, and Meeting above are all De Se. Perry calls the beliefs that are reported by de se reports locating beliefs.

According to Perry, de se belief reports and locating beliefs are problematic for a certain kind of view about propositions usually associated with Frege. Call it the Fregean view of propositions.¹ The Fregean view of propositions has the following commitments:

(i)

“Belief is a relation between a subject and an object, the latter being the object denoted, in a canonical belief report, by a that-clause” (p. 6) The objects denoted by that-clauses are what we call propositions.

(ii)

“[Propositions] have a truth-value in an absolute sense, as opposed to merely being true for a person or at a time.” (p. 6)

(iii)

In order for the propositions that S and that S’ to be the same, they must:

(a)

Have the same truth value.

(b)

Have the same truth condition, i.e. attribute to the same objects the same property.

(c)

Involve the same concepts (in Fregean terms, have the same sense).

2 The problem for the Fregean view

Is there a proposition that the people in our cases above come to believe and satisfies the identity conditions of the Fregean theory of propositions? Perry doesn’t think so. To some extent, his argument seems to rely on a certain way of understanding the way in which indexicals work. He says:

What he means is that the word ‘I’, unlike the word ‘Martín’ or the description ‘the teacher of Central Problems’, doesn’t seem to determine a referent just by itself. This is why, in some occasions, it can refer to me, but in some others to you or someone else, depending on who the speaker is.

Even if Perry is right that the sentence ‘I am making a mess’, say, doesn’t by itself determine a proposition, this fact is hardly remarkable. For even if we had used a description, the sentence may have failed to determine a proposition just by itself. When we use quantifiers or definite descriptions, we often assume that some domain of quantification is in place. But nothing in the sentence says anything about the domain of quantification.

More or less around the time Perry published his paper, another paper by David Kaplan had undergone unofficial circulation. That paper (“Demonstratives”) laid the foundations for a theory of indexical and other context-sensitive expressions. We won’t examine Kaplan’s view in all detail. Suffice it to say that, on his view, an indexical term like ‘I’ has a denotation only relative to a context. In particular ‘I’ denotes the person who speaks in the context in which the word is used.

Kaplan’s view is widely accepted. So even if Perry is right that the ‘I am making a mess’ by itself doesn’t determine a proposition, a defender of the Fregean theory of propositions can offer an easy reply: perhaps the sentence doesn’t determine a proposition by itself, but in any context in which it is used, that sentence does determine a referent.

However, this doesn’t help to solve the real problem for the Fregean view of propositions. Recall Frege’s solution to the puzzle about attitude ascriptions: he thought that the sentence embedded in a that-clause referred to its customary sense. So in the sentence ‘I believe that I am making a mess’, ‘that I am making a mess’ should refer to such customary sense (the proposition expressed by ‘I am making a mess’). Perry thinks that this Fregean view won’t be enough to explain the difference in content between ‘I believe that the shopper with a torn bag is making a mess’ and ‘I believe that I am making a mess’ when the user of these sentences is Perry, and absent a belief that Perry would express by means of the sentence ‘I am the shopper with a torn bag’.

The reason is this. Suppose, for the sake of the argument, that on any given use of the sentence, there is a concept associated with the word ‘I’. In particular, when Perry is in the supermarket and says to himself ‘I am making a mess’, he associates some sense or mode of presentation with the word ‘I’. Now, either this sense is a description involving an indexical, or it is not. If it involves an indexical, then we are just in the starting position again, so this option just takes us back in a circle. If the description does not involve an indexical, then there should be a concept d such that when Perry says ‘I am making a mess’, he means the thing that is d is making a mess. Now there are two problems: first, in order for a belief in that proposition to explain why Perry fixed his bag, Perry must also believe that he is the person that is d—which seems to take us back to our starting point. Second, it must be that Perry is indeed the person that is d, but we don’t always have a reason to think that this is so. Suppose, for instance, that Perry self-identifies as the smartest person in the room. Unbeknownst to him, Kit Fine is also in the room, so as it happens, Perry is not the smartest person in the room. But then the second condition fails, and so, the difference between the indexical and the non-indexical description has been left unexplained.

At this point, Perry stops considering the Fregean view of propositions and examines some other explanations.

3 De Re beliefs

Recall Russell’s distinction between de dicto and de re occurrences of a quantifier. When we introduced the distinction, we used something like the locution “believing of x” to signal that we were making an attribution de re. Let’s continue to speak that way. Let someone S believe of x that she has such and such property just in case there is a definite description such that x in fact is the unique satisfier of that description and S believes that the satisfier of the description is so and so.

For instance, since Aristotle is in fact the center of the Nicomachean Ethics, Tim can believe of Aristotle that he was smart as long as he believes that the center of the Nicomachean Ethics is smart. How can this definition help solve Perry’s problem? We can readily see that it won’t. For suppose that Perry believes of Perry that he is making a mess. The attribution of such belief won’t do the explanatory work that we would expect. For there is no difference between the de re attribution of the beliefs that the shopper with the torn sack is making a mess and that I am making a mess. The De Re readings of these two attributions are exactly the same. So we still lack an explanation of how one of them can move Perry to rearrange his bag of sugar, but the other doesn’t.

4 Relativized propositions

It’s time for a bit more of terminology. Many traditions have stemmed from the writings of Frege, Russell, and Kripke, together with other prominent philosophers. In particular, during the 60s and 70s many linguists started using the technical resources developed by philosophers at the time. One very prominent such resource was Kripke’s possible worlds semantics for modal logic.

Kripke developed a way of formally determining the truth conditions for statements involving operators such as ‘necessarily’ and ‘possibly’. In particular, he assimilated these operators to quantifiers whose domain was a set of possible worlds (formally, a set of points). There are many different interpretations of Kripke’s formal apparatus, but the one he preferred was the following: a possible world is something like a story about how things could have been. Presumably, there are infinitely many ways that things could have been: cats could have been blue, there could have been only one object in the universe, people could have never existed, etc. For each of those ways that things could have been, there is a possible world.

In Kripke’s semantics, to say that something is necessarily true is to say that it is true in all possible worlds, and to say that something is possibly true is to say that it is true in at least one possible world.² Philosophers were very impressed with possible world semantics. So impressed, in fact, that they and some linguists started using it to study ordinary language.

From the work on possible world semantics stemmed a new way of thinking about propositions. Russell thought of them as structured entities, in which objects and properties could figure as parts; the Fregean theory of propositions sees them as things made of concepts. The new view of propositions, inspired by Kripke’s treatment, sees propositions as sets of possible worlds, namely, the set of possible worlds in which the proposition is true.

On that new conception (call it the possible world conception of propositions), a proposition is never true or false simpliciter. Instead, it is only true or false relative to a certain world with respect to which it is evaluated. However, we pointed out that sentences involving indexicals only had definite truth values relative to a context. This can mean either of two things: that the proposition expressed by the sentence is determined by a context, but once the sentence is determined, it is true or false only relative to a possible world; or it could mean that the very truth or falsity is relative to a context. The latter captures the view that Perry is now considering.

On this view, a sentence like ‘I am making a mess’ is true only relative to a pair consisting of a possible world and a person. The latter will be the value of ‘I’. The considerations involving this kind of view are many and subtle, and a proper evaluation of this view could require an entire seminar by itself, so for the time being let’s rest content with stating Perry’s objection.

His objection is something like this. In order for a belief in this relativized proposition (that I am making a mess) to explain Perry’s behavior of rearranging the sugar bag in his cart, Perry must not only have the belief in the relativized proposition, but he also must believe that he is the person relative to which the proposition is being evaluated. Moreover, he must believe it in a special way that involves Perry’s telling to himself something like ‘I am the person to which ‘I’ refers’, or something like that. If he merely believed that ‘I am making a mess’ is true relative to Perry, that wouldn’t help unless he knew that he was Perry. But then again, such belief seems to contain an indexical element. So it seems that the new strategy doesn’t quite help.³

So what’s the right view, then? Well, what indeed. Perry thinks that we should reject the idea that our belief states should be classified by the proposition one believes. But of course, this is just a picture for how a good theory might look. It is not a theory by itself.

All contents by martin.abreu@nyu.edu