A Discussion on Kaplan s and Frege s Theories of Demonstratives

Volume III (2016) A Discussion on Kaplan s and Frege s Theories of Demonstratives Ronald Heisser Massachusetts Institute of Technology Abstract In this paper I claim that Kaplan s argument of the Fregean theory of demonstratives rests on a faulty assumption, namely that its analytical powers go farther than the scope of the theory. There are two parts to my discussion: In the first part I will summarize Kaplan s discussion of Frege s and his own theory of demonstratives, and in the second part I will provide my own argument to challenge the strength of Kaplan s theory as a whole. I have provided some paragraph headers to guide my discussion. Context: In order to have a complete understanding of Kaplan s theory of demonstratives, one needs to have many more terms defined than are in this paper. However, I feel that they are not truly relevant to this discussion, so I will only make use of context. Let context be a possible occasion of use, where use means an expression is used to make a speech act. 1 A speech act is just an assertion with an accompanying demonstration. Fregean Theory of Demonstrations: I will first recapitulate Frege s theory of sense and reference to show an analogical relationship with his theory of demonstrations. For Frege, the meaning of an expression is a definite description, which uniquely picks out an associated individual, the referent, and carries with it a sense, a way in which the referent is presented. Because demonstrations seem to work in a sufficiently approximate way analogous to expressions, demonstrations can be said to have a sort of meaning. The referent of a demonstration is the demonstratum, or the unique individual picked out by a demonstration. The sense of a demonstration is the mode of presentation, or how the demonstration is carried out. Kaplan points out, however, that this mapping onto demonstrations is still an approximation. That demonstrations do not have syntax or structure like expressions do and that an individual s 1 David Kaplan, Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals. A Symposium on Demonstratives. Pacific Division of American Philosophical Association, (2013), 507. 9

unique viewpoint of a demonstration may give it a different sense (whereas an expression is in most cases uniformly experienced by all hearers/readers) do make the analogy relatively imperfect. 2 Fregean Theory of Demonstratives: Demonstratives, non-pure indexicals like there or him or that, are troublesome when used in making a proposition unless a demonstration clarifies what the meaning of the demonstrative is at the demonstration s context. For Frege, the meaning of a demonstrative is the sense of the demonstration. From this, the propositional content added by the demonstrative is the sense presentation of the demonstratum. This explanation of the demonstrative is particularly useful for the Fregean; it explains why that man is Sam Clemens is equivalent with that man is Mark Twain contains extra information. Those two expressions contain different senses, which are supplied by that. Frege s demonstrative, which can solve problems such as the one answered above, is contentious for Kaplan; in fact, he disagrees with it completely. Kaplan s Argument against Frege s Demonstratives: Kaplan believes that using the sense as the meaning of a demonstrative is bound to create a problem, namely that a sense-presentation of a demonstration will not in all cases match to the demonstratum which renders the demonstrative inadequate. To bring out the importance of this objection, he gives an illustrating example. The example is as follows: Consider a speaker A, a demonstration PL [pointing to the left], and two persons Paul and Charles. Say Paul lives in X and Charles lives in Y. Paul is to the left of A and Charles is to the right of A. This all takes place in a context C. Now consider a statement N uttered by A: He [PL] now lives in X. On Frege s account, he would mean Paul and N would be true, as Paul is presented to the left, as shown in the top picture of Figure 1. This seems to be the correct prediction. 2 Kaplan, Demonstratives: An Essay on the Semantics, Logic, Metaphysics, and Epistemology of Demonstratives and Other Indexicals, 517. 10

Context C Context C Figure 1 Now consider a context C where Paul and Charles change appearances and switch sides, so that Paul is really to the right of A. According to Frege s theory, the presentation of Paul is still from the left of A, so an utterance of N would still yield that he means Paul. If this is the case, then Frege s theory still predicts that N is true. However, N is false because Charles does not live in X. N cannot be true and false; Frege s theory must have made the wrong prediction, as shown in the bottom picture of Figure 1. Note here that if one meant he to just mean the person standing to the left, then one might consider the prediction still intact. Let us assume this is not the case, though. Kaplan s Alternative Theory of Demonstratives: To resolve this bad prediction, Kaplan provides a different scheme of the demonstrative. The meaning of a demonstrative, in Kaplan s mind, is only the demonstratum, or its referent. Sense is completely eliminated from the equation. By correcting the meaning of demonstrative, Kaplan believes he is able to correctly predict the truth values of N expressed by A at C and C. When A utters N at C, he means Paul, which makes N true at C. At C, he refers to the actual person who is dressed up as Paul: Charles. And the proposition that Charles lives in X is actually false. So Kaplan s theory would predict that N is false at C. Furthermore, Kaplan believes his theory is more consistent than Frege s because the meaning cannot be interpreted for anything else than the referent itself. A Note on Kaplan s Argument: I think Kaplan is right about two things. He is right that 11

Frege s theory does in these cases fail to pick out the actual demonstratum. He is also right that his theory does give the correct prediction for the actual demonstratum. I do, however, disagree with Kaplan with the idea that Frege s has the goal of achieving what Kaplan does in his theory. In fact, I think that the Fregean makes his theory of demonstratives to characterize something that Kaplan cannot. This will be discussed in the next section. A Key Distinction: To properly introduce my analysis, to note the distinction between what a speaker believes is true at some context C and what is actually true at C. We can imagine that there are sets of propositions at C can be constructed for speaker beliefs and the actual state. Call them B-Propositions (B-sets) and A-Propositions (A-sets), respectively. There are two assumptions I make for B-sets: the first assumption is that I might say something I think is true. The second assumption strengthens the first; I might say something I think is true because I think it is true. In other words, I will not say something false simply because I think it is false. All propositions in a B-set, then, are and must be consistent with my beliefs. There may be cases where this does not apply, but let this serve as a good first approximation. The only assumption that needs to be made for A-sets is that the propositions it contains are true at C. Thus, if a proposition at C is not in the A-set, then it is false. It may also be true that both sets of propositions will change over time, but this does not have any effect on the discussion as long as we consider the sets at the same time. Lastly, when A-sets are discussed, they are to be unique to a certain context. Likewise, B-sets are also unique to a context and to one speaker. For this discussion, let B-sets contain only propositions that apply to their respective contexts. When all parameters are met, we can imagine them to serve as functions that take in a proposition and output a truth value given the properties described above. An example will show what this looks like. If I see a red ball and think it is red, then that [pointing at the ball] ball is red is in both the B-set and A-set. If the ball is blue but I truly believe it is red, then that same utterance is in the B-set but not the A-set. If we look at a proposition and it is in the B-set for C, then we get at the belief state of the individual from the expressed proposition. 12

Application to Fregean and Kaplanian theories of Demonstratives: This distinction can be applied to both conflicting theories of demonstratives considered in this paper. To do this, I will show how the differences in deciding what the meaning of a demonstrative is for a particular situation carries over exactly to determination of truth values. Let us reconsider A s utterance of N at the two contexts C and C discussed above, but this time add in A s belief of what he refers to. I have made a table to illustrate the different cases. Belief refers to what A believes he means, Actual is what he actually means, and Frege and Kaplan are what Frege s and Kaplan s theories would predict he means, respectively. Context Belief Actual Frege Kaplan C Paul Paul Paul Paul C Paul Charles Paul Charles From this table it is easily discernable that the Fregean will predict what A believes he refers to and that the Kaplanian will predict what he actually ends up referring to. For example: in C, A believes the person to the left is Paul and thus says N. He, to the Fregean also means Paul at C. It is important to remember that in most cases, B-sets and A-sets do contain the same elements (otherwise our beliefs would not be useful in helping us make propositions), but in cases such as these, Frege s theory cannot predict what is in the A-set nor can Kaplan s theory predict that of the B-set. They are independent of each other. How does this carry over into the truth determinations of A s utterance of N at C and C? We can make a table to show a similar result, except with truth values (remember, if a proposition is not in an A-set, it is false): Context B-set A-set Frege Kaplan C T T T T C T F T F 13

Here, the meaning of he at C/C changes to the truth of N at C/C. Similar to the first table, Kaplan s results are aligned with those of the A-set, likewise with Frege s results and the B-set. From this, it seems clear that the Fregean predicts is not what he actually refers to, as Kaplan would like to think, but what A believes it to be. I reiterate: Kaplan does show that the Fregean will make the wrong prediction about the actual context, but this is not to say that the Fregean demonstrative is any worse than Kaplan s theory, for the Kaplanian demonstrative will make the wrong prediction about A s belief state in these same cases. In this way, Frege s theory is shielded from Kaplan s argument. Context C Context C Figure 2 Why Speaker Belief States Should Be Taken into Account: Now, even after this distinction has been made, one still might Kaplan s theory is better than Frege s; do we not want to know what propositions at C are actually true? And while I do believe that we usually want to know the actual truth of a situation, there are some situations where the Fregean demonstrative can actually be more helpful than the Kaplanian demonstrative. To show why this is the case, I do not need to change the example at hand; I will add another initial observer B of both contexts C and C. Refer to Figure 2 for a visual representation. Imagine that B sees C change to C, while A does not (we can say that A makes a false proposition because of this). This means that B sees A utter N in C, Paul and Charles change appearances, and A utters N in C. B hears N both times and can form beliefs about the meaning of he and the truth of N at both contexts. We can thus form the same type of table for B as we did A. For the meaning of he : 14

Context Belief Actual Frege Kaplan C Paul Paul Paul Paul C Charles Charles Charles Charles One might wonder why the B-state and Fregean prediction line up exactly with the belief column. After all, the man to the left of A does still look like Paul. Because B sees Paul and Charles switch appearances, we can say that to B, their senses swap as well. Thus, the person who looks like Charles becomes Paul etc. Thus, B can form beliefs about N that lie in the A-set at both contexts. As a note: since belief states pertain to speakers, we can imagine that B takes A s place or utters N in his mind. We can make a similar table for the truth values as well: Context B-set A-set Frege Kaplan C T T T T C F F F F Now that we have truth values for B, we can gain more insight into Fregean and Kaplanian analysis. At first glance, it looks just as if there is a coincidence of A/B-set truth values with their respective predictions. However, if one were to recall the second intuitive assumption made for B- sets, one could reliably claim using Frege s theory that person B, if she did not want to contradict her own beliefs, would not state N in C. If B knows Charles lives in Y, then she would know that N is false. Perhaps this second assumption, since it is not explicitly part of Frege s theory, would not even be needed. It seems to me that by intuition, B would not want to say N at C if she knows it would be wrong at C, unless she wanted to go along with this thought experiment. Kaplan s theory unfortunately cannot make any claims as to what B would do in a given context. Kaplan s theory can only predict what the meaning of he is and what truth value N 15

yields if B were to utter N at C and C. And this limitation occurs because Kaplan restricts his demonstrative only to mean the demonstratum. One might say that B could state N at C and just be wrong, but that would still violate our second assumption. How to Deal with This Discrepancy: At this point, it seems as if both Kaplan and Frege have good selling points for their theories, putting them in a sort of tie. On the one hand, Kaplan s theory provides information about contexts C and C as they actually are. This is always of the utmost importance. Yet Frege s theory provides information about speaker belief states and functions when non-sense presentation knowledge of a context is not available. And with this, it seems that the two are completely independent theories and should be left at that. However, I would like to make one more comment on the nature of Kaplan s theory which might provoke some more thought about the relationship between Frege s and Kaplan s theories. The Epistemological Problem for Kaplan: Let us examine once more our speakers A and B. B has the correct beliefs about N at C because B sees the context shift from C to C, while A does not. But would one say that B gained this information in a manner unbeknownst to A? No: we can say that if A stood right next to B after the first utterance of N, A too would gain the same information and develop the same beliefs. That B was able to form the correct belief is just to say B was presented with the best possible information. This presentation of information seems to me nothing more than the sense Frege rests his theory of demonstratives on. In other words, both A s and B s utterances in N only reflect that of the belief domain, while B s beliefs happen to coincide with the actual domain. The only reason we, the readers, can get outside of the belief domain is because we have defined the parameters of the example. Our knowledge of what actually happens is trivial. From this, it seems that Kaplan can really make his demonstrative effective only in cases where he can know the contents of A-sets at a context, without needing any information from sensepresentation. For cases where he cannot look at a predefined situation (i.e. he himself is an observer or a hearer of a situation) it looks like the sense is all he has. A Last Look at Kaplan: To take this idea further within our thought experiment, we can 16

make B s knowledge of the actual context arbitrarily close to its A-set. For proposition N, we know that B s beliefs correspond to the actual context, so we can imagine that B is able to form correct beliefs about other aspects of context C. If we let B somehow have complete equivalence of his B-set with the A-set, thus endowing her with some divine insight, then B maintains an equal footing in stating beliefs as well as stating actual propositions about C and C. This extension of B s insight, while still within Fregeian boundaries, thus also wholly captures Kaplan s theory. Kaplan s theory, being more limited than Frege s, cannot do the same. This is because the relevant A-set and B-set in this case are equal. We can conclude, then, that the A-sets that come out of Kaplan s theory all make up a subset of Frege s possible B-sets. In other words, if one can predict the actual truth value of N for an omniscient B in context C using Frege s theory (which would also give insight to belief states), why would one need to use Kaplan s theory? In this case, it would be redundant and limited. 17