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Next: Conditional truth conditions Up: Indexicals and Indexical Previous: Can an adequate

Can an adequate truth-theory incorporate indexical theorems?

If we allow Evans the use of a semantic mechanism which Hector-Neri Castañeda has claimed to exist in natural language, we can devise specific T-theorems which state something that (i) can be known by different speakers and (ii) interprets the relevant utterance. First I will introduce Castañeda's basic concepts.

Castañeda has argued in a series of papersgif that in certain contexts expressions like ``he'' or ``then'' do not function as indexicals. Let me illustrate this with an example. I can report a belief Dr. Lauben has about Dr. Lauben in the following way:

(S5)
Dr. Lauben believed that he was wounded.

Let us stipulate that ``Dr. Lauben'' and ``he'' are co-referential in (S5). The expression ``he'' functions in this sentence not as a demonstrative or an anaphorical pronoun. Its semantical role is similar to an anaphorical expression in that its reference is dependent on the grammatical antecedent ``Dr. Lauben''. But unlike an anaphor the grammatical antecedent cannot be substituted salva veritate for the expression in its scope. Dr. Lauben can forget his name and still believe himself to be wounded. Therefore the sentence
(S6)
Dr. Lauben believed that Dr. Lauben was wounded.

and (S5) can have different truth-values in the same situation.

Because of considerations like these Castañeda holds that in English there are two different words with the same spelling:

is only a linguistic freak that ``he'' in the sense of ``he*'' looks exactly like the third person pronoun ``he'', which occurs, for instance in ``Arthur came, but he knew nobody he saw; he left early.''gif
Castañeda distinguishs the non-deictic ``he'' from the deictic one either by indexing it with ``*'' or by adding in parentheses ``himself''. Castañeda names expressions which function like ``he*'' quasi-indicators.

Quasi-indicators and indicators in belief-ascriptions in oratio recta are differentiated by a an interesting property. Compare:

(S7)
John believes that I am wounded.

with (S4). In (S7) the indicator ``I'' is in the mouth of the speaker who attributes a belief to John. The indicator is used to refer to the speaker and this way of refering to the speaker is surely not one that is available to John to whom the belief is ascribed. This gives rise to general characteristic of indicators in oratio obliqua which Castañeda described in the following way:
indexical reference R in oratio obliqua, [(1)] that is not part of an attribution of self-knowledge (self-belief, self-conjecture, etc.) leaves it by itself wholly unspecified how the person to whom knowledge (belief, etc.) is attributed refers to the person or object to whom R is made.''gif
The saving clause (1) is well motivated. My utterance of
(S8)
I believe that I am wounded

specifies in the most precise manner how the person to whom the belief is ascribed refers to the item he believes something about. Castañeda's apt term for this characteristic is propositional opacity, which should not be confused with referential opacity. In (S7) ``I'' is propositionally opaque but referentially transparent.

In contrast to indexicals quasi-indicators are according to Castañeda propositionally transparent: a construction like ``S believes that he* is wounded'' reveals the proposition S which is the content of S' belief. It is the proposition S would express with the words ``I am wounded''.

This characteristic of quasi-indicators seems to be what is needed for Evans' account. In order to show this I rewrite the above criticized statement with quasi-indicators:

order to understand the utterance of ``I am having a good time today'', made by a on d, one must have on d, the thought one might express in words by `What the speaker said is true if he* is having a good time on that day*' ''.
This seems to give the right results. I understand an utterance of ``I am F'' in the strong sense if and only if I come to know that it is true if what the speaker said is true if and only if he* is F. This suggests a modification of Evans' strategy. The general rule should not be ``Include indicators in the meta-language of the truth-theory'' but ``Include quasi-indicators in the meta-language of the truth-theory''.

This rule takes for granted that there are quasi-indicators. But are there any in a natural language like English. Castañeda's homonymy-thesis is surely not very plausible. A good methodological rule is ``Do not posit homonyms, if it is not necessary''. And in the cases to which Castañeda calls our attention it seems not to be necessary. We can account for Castañeda's data by pragmatic explanations. Therefore it is not necessary to assume that there are words like ``he*'' which have a distinct semantic role.gif

If ``he'' in constructions like ``S believes that he is F'', where ``S'' and ``he'' are co-referential, had the distinctive semantic role Castañeda assigns to this word, then this construction should imply the truth of the following sentence:

(I)
S is willing to utter ``I am F'' under appropriate circumstances.

But this implication does not hold. Boër and Lycan remark:
[S] may not be willing to assert anything, having been handsomely bribed by Boër and Lycan (who will stop at nothing to gain their philosophical ends) never to assert anything again.''gif
Boër and Lycan concede that this remark only shows that the potential implicatum has not been described in the right way. They think that the potential implicatum could be:
(I)
S tokens a mental sentence which says the same as S' utterance of the public language sentence ``I am F''.gif

But this is no real option for someone who is not willing to accept the language of thought hypothesis.

Yet there is still a third alternative. Peter Geach and Wilfried Sellars have pointed out that oratio recta constructions can be used metaphorically to report thoughts. So it is quite usual to say ``S said in his heart `The weather is fine today' '' in order to ascribe a thought to S. Using this way of speaking we can reformulate the alleged implicatum:

(I)
S says in his heart ``I am F''.

This belief-ascription is metaphorical. Its literal content could be spelled out along the following lines: S has a belief such that: if S would express it, he would express it with an utterance of ``I am F''.

Does a construction like ``S believes that he is F'' imply the truth of a sentence like (I')? We must distinguish between implication and implicature. If p implies q, it is not possible that q is false and p true. But if p implicates q, it is possible that q is false and p true. Implicature is best understood as a (in some cases conventionalized) form of suggestion. The sentence ``John doesn't make much money but he is happy,'' implicates (suggests) the truth of the sentence ``If someone doesn't make much money, he tends to be unhappy.'' But of course this utterance doesn't imply the truth of the second sentence.

We have a good reason to suppose that p implicates q, but doesn't imply it, if we can cancel q without contradicting our original statement. Such a cancelation seems possible in the case of constructions with quasi-indicators. Imagine the following story: The new editor of Noûs has been appointed. Yet his identity has been revealed only to certain privileged persons. John becomes curious who the new editor is and starts gathering information about him. John asks his informants, draws conclusions etc. Soon he has a rich body of information about the new editor. But all his informants have given him only information about this person with sentences like: ``The new editor of Noûs is F''. Suppose now that in fact John is the editor of Noûs. In this situation it would be true to say:

John believes that he is the editor of Noûs, but his friends have deceived him so cleverly that he hasn't realized it yet. They want it to be a birthday surprise.

Given the additional information we no longer suppose that the statement ``John believes that he is clever'' commits us to the truth of ``John says in his heart ``I am the editor of Noûs''. This is a good reason to suppose that the alleged implication is just an implicature.

Castañeda often uses ``himself'' in place of ``*'' to distinguish the non-deictic ``he'' from the ordinary third person pronoun. Does the construction ``S believes that he himself is F'' imply and not implicate ``S says in his heart `I am F' ''? One of Perry's examples constitutes a good reason that the alleged implication is just an implicature, since it is cancellable:

dean has been complaining that professors who publish less than ten articles per year on the average are overpaid. He has particular ones in mind, Professors A, B, Q, and Z in the blind sample he has been studying. Thn one day he counts the articles he has written and finds only ninety-three articles over the past teen years, agreeing exactly with the figure for Professor Z, which could not be a coincidence.
We say,
The dean was surprised to find that he believed himself to be overpaid.''gif

I think we have now reason to say that Castañeda has misdescribed his own findings: There are no semantically special expressions, quasi-indicators, in natural language. But there is the phenomenon of quasi-indication, which can be explained by pragmatic mechanisms. Which are the consequences of this view for our investigations?

A semanticist who is attracted to a truth-theory whose meta-language contains expressions like ``he himself'' won't be over-impressed by this finding. He can simply stipulate that certain expressions function exactly like Castañeda's quasi-indicators and introduce them into the meta-language of his truth-theory. This manouver is possible, but a truth-theory of this kind will have lost much of the intuitive plausibility which was at first sight connected with the concept of a quasi-indicator. In the next paragraphes I will delineate a truth-theory that introduces quasi-indicators as technical devices of the semanticist and investigate which insights we can gain in this way.

In his unpublished paper ``Fregean indexicals'' Mark Sainsbury has developed a truth-theory whose meta-language contains expressions which play in effect the same role as quasi-indicators. He also takes up an aspect I have up to now neglected: In the context of a truth-theory we think of the T-sentences as derived from general principles. Sainsbury introduces like Davidson universally quantified T-sentences. But unlike Davidson's T-sentence Sainsbury's truth-theory entails conditional T-sentences of the following sort:gif

T
(x) (y) (x is an utterance of ``I am hungry'' y utters x, then:
x is true that person is hungry.)

T
(x) (y) (x is an utterance of ``Today is fine'' on y, then:
x is true that day is fine.)

I will supplement this T-sentences with a third one in Sainsbury's style for second person utterances:
T
(x) (y) (z) (x is an utterance of ``You are a fool'' y addresses z in uttering x, then:
x is true that person is fool.)

Phrases like ``that person'' and ``that day'' function, we might say, as sortally restricted quasi-indicators. The subscript indicates which phrase of the whole T-sentence functions as their grammatical antecedent. Although these expressions are explicitly introduced by the semanticist as technical terms, I will refer to them simply as ``quasi-indicators''.

Do conditional T-sentences like these interpret individual utterances, i.e. do they specify what is said by the utterance? Of course not. For instance an conditional assertion like T doesn't assert something about an individual utterance of mine. But given such a conditional assertion we should be able to infer an unconditional assertion that interprets an utterance. Sainsbury's rule is: `` instantiate, detach, and finally use what is to the right of the biconditional to interpret u, or to report what was said by u.'' ( FI, p. 5.)

Let us see, if it works. I utter on March 26th 12 o'clock the sentence ``I am hungry''. Let us call this utterance u. From (1)

(1)
u is an utterance of ``I am hungry'' and Mark Textor utters u.

and T we should now be able to infer a sentence that interprets my utterance. But on Sainsbury's account we can't do that. From (1) and T we get:
(2)
u is true that person is hungry.

This is not the conclusion we want and need. We need a sentence that expresses a complete proposition to interpret u and (2) doesn't express a complete proposition, because the quasi-indicator has lost his grammatical antecedent.

Compare:

(3)
Bertrand knows that 2 + 2 = 4.
(4)
2 + 2 = 4.

And:
(5)
Jeff knows that he* is the new editor of Noûs.
(6)
He* is the new editor of Noûs.

We need an inference like the one from (3) to (4), but we only have got one like the one from (5) to (6).

Perhaps there is way to fix this problem, if we are generous in the interpretation of the quasi-indicators: we can think of the reference of the quasi-indicator ``that person'' in the conclusion still anaphorically dependent on the grammatical antecedent ``Mark Textor'' in the premises. This idea gains support from the fact that analogous referential chains seem to exist in natural language discourse:

John was convinced that he* is the editor of Noûs. But then he realized that he* wasn't.

If the derived T-sentence stays in ``anaphorical contact'' with the premises, Sainsbury's idea seems to work. It just requires - so to say - semi-detachability. Let us see, if this really works.

The central question for our purposes is: Is someone who knows a truth-theory like the one Sainsbury favours placed thereby in a position to understand indexical utterances in the strong sense we are interested in? We would not say that S had understood an indexical utterance, if S did not identify the referents of indexicals in a specific way. Does Sainsbury's account capture this dimension of our intuitive concept of understanding?

The answer seems to be No. Suppose I hear an utterance of ``You are a fool''. Call this utterance u. I know that this is an utterance of an English sentence and I know that it is made by P.T. and addressed to M.T. Now I use Sainsbury's machinery to interpret and derive a T-sentence. If everything works out allright and the quasi-indicators pick up the right references, I should finally know that the following is true of u:

(T( u))
P.T.'s utterance u addressed to M.T. is true that person is a fool.

According to Sainsbury's theory this knowledge enables me to interpret the relevant utterance. But I think it does not. I think it is uncontroversial to say: in the strong sense I understand u only if I realize that I am the one addressed, i.e. only if I think the thought I would express with the words: ``I am a fool, that's what this guy is saying''. But I could come to know what was said by (T( u)) without realizing that I am M.T. and consequently without realizing that I am addressed. So this knowledge does not enable me to interpret the relevant utterance. I could know all the truth-theoretic facts about u without thereby grasping the thought required for understanding it.

If I am right about this, the introduction of quasi-indicators in the meta-language doesn't yield a truth-theory that enables us to interpret indexical utterances in the sense our linguistic intuitions seem to require. An explanation of this failure is easily given: Our linguistic ability is a systematic and general competence. A theoretical representation of this competence must conceive of the T-sentences which shall interpret individual utterances as derived from a finite set of universally quantified principles. But such principles will license the derivation of T-sentence which are not apt for the interpretation of individual utterances. The truth-theory itself cannot discriminate between ``right'' and ``wrong'' T-sentences.



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