NYU paper

Reasoning about thought Draft February 2004

Jane Heal

1. Introduction

Davidson proposed in ‘On Saying That’ an account of indirect discourse in which the idea that it involved indexicality played a central role. (Davidson 1968) He took seriously the idea that the ‘that’ of indirect discourse might be indexical and took it to be a referring demonstrative, picking out the token sentence or utterance which followed. His proposal provoked much discussion and many objections. In its original form I suspect that it would have few defenders today. But the idea that there is some kind of indexicality in indirect discourse, seems attractive. And if the indexicality is not referential, then the sensible thing seems to be the try the idea that it might be predicatival. Can we make sense of the idea that there are indexical predicates? I suggest that we can. (Heal 1997) And if this is right, can we apply the idea to illuminate what is going on in reports of speech and thought? Again I suggest that the answer is yes. Calling on the idea of indexical predication we can articulate an account of indirect discourse which has the advantages of Davidson’s but escapes many of the objections to his theory. (Heal 2001, 2003)

But there are loose ends. The reformulated account has not been shown to escape all the objections levelled at Davidson’s theory. One such objection provides the focus of this paper. It is due to Burge (1986) and it concerns the formal validity of inferences like this:

(A) Galileo said that the Earth moves


Galileo said that the Earth moves.

Davidson’s approach, says Burge, cannot make sense of the fact that this inference is formally valid, and we shall see that Burge is right. But, given this, a plausible line of argument suggests that a reformulated indexical account, calling on the idea of indexical predication, might also be vulnerable to the same charge, or rather to a suitably modified version of it. I hope to show that, in the end, this line of argument fails. But seeing why this is so involves disentangling some points of interest, concerning thought and its indexical representation.

2. Indexical predication — a brief outline

Before turning to Burge’s observation and considering its ramifications, I shall set the scene by sketching some of the central ideas about indexical predication and how it might apply in the realm of our thought about meaning and the psychological. (Readers are referred to the earlier mentioned papers for a fuller account.)

Consider utterances of this form:

(1) My curtains are coloured thus {specimen of red material}


(2) Mary sang thus {a singing by me of Pop Goes the Weasel}.

What is the role here of ‘thus’ and what follows it? The complete vehicle of communication here is formed by some words, including the indexical ‘thus’, together with a complement provided by a specimen or performance of some kind. But the specimen or performance is not itself referred to in the remark. So (3) is importantly different, in logical and epistemological ways, from

(3) My curtains are the same colour as this piece of material {specimen of red material}.

And (2) is similarly different from (4)

(4) Mary did some singing qualitatively similar to this {a singing by me of Pop Goes the Weasel}.

Nevertheless the role of the specimen or performance in (1) and (2) is crucial. It is there to make available for predicatival attribution the predicate correlate (the property — colour, manner, action or whatever) which the remark as a whole ascribes to the subject — my curtains or Mary in the examples above. It makes it available by instantiating it in the context of the utterance and so making ‘thus’ able to latch on to it. This is the hallmark of indexical predication.

We can also say

(5) My curtains are this colour {specimen of red material}


(6) Mary sang this {a singing by me of Pop Goes the Weasel}.

The shift from ‘thus’ to ‘this’ marks our willingness to think in terms of colours or tunes and to represent what curtains or people do as having some relation to these (non-concrete, non-particular) entities. Some will take it that what we have here is indexical identification of a ‘universal’ — or at least of some entity of that broad, non-concrete, category. Nominalists would not happy with that and would seek to explain away the locutions. Many familiar philosophical puzzlements arise at this point. My purpose in mentioning them here is only to set them on one side. For our purposes the important thing is the similarity of (1), (2), (5) and (6) and their difference from (3) and (4). The indexicality of (1), (2), (5) and (6), however exactly we unpack it in metaphysical terms, has to do with characterising my curtains or Mary, i.e. has to do with saying how they stand vis a vis universals and other related abstract entities (if such exist). And so for our purposes (1), (2), (5) and (6) are all indexical predications.

Indexical predication is a useful resource when the vocabulary of our language does not provide standard non-indexical words for the property (colour, manner, action, or whatever) we wish to ascribe, but where we do have, or can at will produce, specimen of it. Indexical predication will be particularly useful in enabling us to talk and think about intricate human performances, as for example in music, where we have a know-how of producing them but lack explicit analytic vocabulary for specifying all the important differences of which are implicitly aware. Suppose, for example, I am familiar with the tune Pop Goes the Weasel and can sing it but do not know its name and cannot give an analytic musical description of it. In that case (2) or (6) is the obvious resource for conveying to you what Mary did.

Talking and thinking provide other example of such intricate human performances. Hence the suggestion that we can and standardly do represent them using the resources of indexical predication. So we should see

(7) Galileo said that the Earth moves

as an indexical predication which attributes to Galileo a performance the semantic character of which is made available to the hearer by his or her appreciating the semantic character of the complement clause. So we could represent its structure in this way

(8) Galileo said that {a saying by me that the Earth moves}.

As with Davidson’s proposal, what occurs in the complement clause is present in order to support and engage with an indexical, in such way as to complete the whole claim, to fix its truth conditions, appropriately. But the indexical is predicatival and not referential (at least, no reference to a particular is involved). Hence we avoid many of the objections to which Davidson’s account is open.

An implication of this construal of the linguistic structure of (7) is an indexical reading of the structure of the thought which (7) expresses. It is obvious that one who understands (7), whether speaker of hearer, must at least exercise in combination his or her concepts of Galileo and of saying and of some indexical concept. This much is what is involved in understanding the first three words of the sentence. But what of the later words? The indexical account of indirect speech stresses that the words in the complement clause play the same role there as they do when unembedded. So what is involved in understanding them runs parallel to what is involved in understanding ‘Galileo’ or ‘said’, namely both speaker and hearer exercise (in combination) their concepts of the Earth and of moving. What ties the whole lot together, so asto constitute a representation in thought of Galileo’s action, is that the thinking of ‘the Earth moves’ is itself picked out by the indexical concept expressed by ‘that’ and so gets to contribute to the truth conditions of the whole. This thinking of ‘the Earth moves’ instantiates and so makes available for indexical attribution, the semantic properties of the performance which it is the purpose of the whole thought to attribute to Galileo.

This general idea of an indexical structure in representation of items with semantic properties can clearly also be applied when what I am talking or thinking about is someone else’s thoughts rather than her speech. So if I think the thought expressed by

(9) Mary believes that the Earth moves

what I do is exercise my concepts of Mary and believing together with some indexical, and then complement this by exercising my concepts of the Earth and movement. So my thinking has roughly this structure:

(10) Mary believes this {a thinking by me that the Earth moves}.

3. Indirect speech and formal validity: a problem for Davidson’s account

Let us now turn to Burge’s argument. As we have already reminded ourselves. Davidson’s proposal is that indirect speech is indexical, but the indexicality is of the familiar referential kind. So for him ‘Galileo said that the Earth moves’ claims the existence of a relation (here represented by the verb ‘said’) between Galileo and a particular utterance produced by me, which is the referent of the indexical referring term ‘that’. (Davidson himself gives a vivid informal characterisation of the logical form he is trying to get us to grasp by using the notion of samesaying. What I do, he suggests, is refer to an utterance of mine and claim that some utterance of Galileo’s samesaid it. Compare the form of (3) or (4) above.)

Let us now look again at the argument (A).

(A) Galileo said that the Earth moves


Galileo said that the Earth moves.

We seem to have here an indubitable specimen of a formally valid inference, the deduction of a claim from itself. On Davidson’s account of indirect speech, however, (A) has the same form as

(B) That cat {Tabitha} is friendly


That cat {Tibbles} is friendly.

Now even if Tabitha and Tibbles are both friendly, this clearly does not make (B) into a formally valid argument. But on Davidson’s construal of indirect discourse (A) can be no better than (B). This is because, according to him the two ‘that’s of the premise and conclusion refer to two different particular utterances of mine, say U1 and U2. And, just as Tabitha’s friendliness cannot logically guarantee the existence and friendliness Tibbles, the fact that Galileo ‘said’ U1 (in Davidson’s sense of ‘said’) cannot logically guarantee the existence of U2 and his ‘saying’ of it. To put this another way, the fact that I do produce two specimens of ‘the Earth moves’, and that each does in fact have the same content as some remark of Galileo’s, so that Galileo can be truly reported as ‘saying’ each, no more makes (A) formally valid than the existence and friendliness of both Tabitha and Tibbles make (B) formally valid.

It does not help if we suppose that it is somehow obvious from the appearance of Tabitha and Tibbles that they are twins and share the same temperament. The inference (B) may, if this extra information is included as a premise, look more respectable. But our task is to explain why (A) is formally valid just as it stands. To show that, regarded as an enthymeme, the inference can be seen as valid does not address the point.

This is in effect the objection Burge brings against Davidson. Does a shift to indexical predication produce an account which escapes any version of this difficulty? It looks at first glance as if it might, because the shift allows us to say that the indexicals in premise and conclusion serve to identify the same property. Hence, it seems, we can say that premise and conclusion serve to make the same claim about Galileo, unlike Davidson’s account where they make different claims. And so we seem to have saved the formal validity.

But things are not so simple. Let us return to referential indexicals and note that things are not guaranteed to improve, even if we take cases where the indexically identified particular is the same in premise and conclusion — and hence where, in some sense of ‘same claim’, premise and conclusion make the same claim. Consider

(C) That cat {Tabitha} is friendly


That cat {Tabitha} is friendly.

Is this formally valid? It is not. Imagine that I direct the premise at Tabitha’s tail as she stands behind a broad pillar and I direct the conclusion at the head of a cat (Tabitha as it happens) protruding at the other side. Although I do in fact pick out the same cat, I am not entitled without contingent information about spatio-temporal continuity to the assumption that she is the same. (The pillar is broad enough, let us suppose to allow for two curving cat-width tunnels behind. So, for all I can see, it could be Tabitha’s tail on one side and Tibbles’ head on the other.) I am not entitled to the inference. But then the inference can hardly be formally valid.

Now consider

(D) The brooch is this shape {specimen of complicated shape}


The brooch is this shape {specimen of same shape but upside down}.

This inference suffers from the same defect as (C), namely that I am not justified in endorsing it merely in virtue of the actual identity of the shape picked out, together with my understanding of the indexicals. I need, in addition, to be able to take for granted that the same shape is identified in premise and conclusion. But it is clear that, in this sort of case, I might understand both premise and conclusion perfectly well without grasping this identity.

Consider also

(E) The brooch is this shape {specimen of complicated shape}


The brooch is this shape {specimen of different shape which, however, gives the same impression as the first}.

What (C), (D) and (E) enable us to see is that, lurking behind Burge’s original problem of the different referents of the two ‘that’s in (A) (on Davidson’s construal of (A)) is another problem for indexical accounts, namely that posed by the fact of the two indexicals themselves. With an indexical, whether referential or predicatival, mere sameness of semantic correlate (whether a particular or a universal) does not secure the sort of sameness in the nature of the grasp on that correlate, which entitles a thinker to assume identity and hence to judge the inference formally valid. Also, as (C) and (E) show, there is a converse problem, namely that impression of sameness of semantic correlate can sometimes be erroneous. So are there circumstances in which the user of two different indexicals can be entitled to the assumption that the semantic correlate is the same? And if so what are they? I cannot offer a fully general answer to this question. But I think we can answer it in the case of thought.

4. The Solution — Purity of thought

Our problem is to explain why and how (A) differs from (D) and (E). Two ideas provide the key to a solution. The first is the ‘purity’ of the indexicality involved and the second is the right of a thinker to assume his or her competence in maintaining stable concepts and deploying them in a logically well-structured manner.

‘Pure’ indexicals (in the sense introduced by Kaplan) are to be contrasted with demonstrative indexicals. An indexical type is demonstrative if a token of it may need a demonstration of some element in a perceptually presented array to fix whatit latches onto. Some referential and predicatival indexicals are demonstrative. For example, ‘that cat’ may need to be supplemented by a pointing to one of a group of cats to determine its referent. Or ‘that shape’ may need supplementation by an indication of one shape among various ones exhibited in the environment.

But the rules governing some referential indexicals mean that such demonstrative support is in their case not necessary. If the rule for the indexical type, the rule which links any token to its referent in the context, is so set up that there can be only one possible contender to be that referent then further demonstrative information, even if it can be provided, is not necessary. For example a token of ‘I’ can only refer to whoever produced it. This does not mean that the referent is something it is not possible to perceive or to demonstrate. (I may point to myself as well as uttering ‘I’, but I do not need to do so.) The point is only that securing of reference need not go via such perception and demonstration.

Can predicatival indexicals also be pure, in this sense? The conditions on the well-formedness of thoughts show that it is. Consider to start with the subject slot. If I am to be credited with making a judgement of the form ‘---- said that the Earth moves’, then it must be determinate which conceptual content is playing the role of subject vis a vis the concept of the action ‘said’. I have not succeeded in making any judgement unless there is one and only one such content playing that role. The content could itself be complex, as in ‘the first notable European scientist to be offered a chair at Harvard’ or ‘either Galileo or Newton’ or ‘both Galileo and Newton’ and so on. But if it is indeterminate what content is there, then the psychological goings on in me (whatever their subjective character) do not constitute my making a well-formed judgement.

Similar observations apply with respect to what I judge Galileo to have said. It is a condition of the thought’s being well-formed that there be only one content-supplying thought in the indexically indicated complement slot. Of course that thought may itself be complex, in being disjunctive, quantificational and so forth. But unless there is one and only one thought occupying the complement place, and hence available to be latched on to by the indexical, the psychological goings on do not constitute my making any well-formed judgement about what Galileo said.

Now of course I can wonder about many people, whether they said that the Earth moves. Similarly I can wonder about many claims whether Galileo made them. But these observations must not lead us to suppose that making a judgement involves some kind of inner pointing, whereby one concept rather than another gets to be put in the subject slot or the complement slot of a judgement. What resolves my uncertainty about who said what are thought processes in which I look at evidence and ponder its force. The upshot of such investigations, if helpful evidence comes to hand, is that I come to see (what I take to be) the truth on the issues. While investigating I deploy my concepts in various ways. The inveestigating, if successful, terminates in their being assembled in my mind in one determinate way, namely that which constitutes my making the judgement which the investigation leads me to. We must not complicate matters by supposing that even when I have done the investigating and come to a conclusion, I still have to do some inner pointing in order to get my concepts in the right relations to constitute my (really) making the judgement. To think this way is to embark on an absurd infinite regress.

So, for exemple, suppose that I am wondering what Galileo said on a particular occasion. It is my appreciation of the evidence about the astronomical claim he then made which ends up by putting one and only one determinate content in the complement slot of my thought ‘Galileo said …’. There is no role here to be played by any inner analogue of demonstration. Hence, to repeat, the indexical can latch on to this embedded thought without the need of a quasi-demonstration to distinguish that thought from others. Perhaps thoughts can also be ‘introspected’ and quasi-demonstrated. But we do not have to take any stand on this issue to help ourselves to the idea that the complement-indentifying indexicals may be pure.

So (A) differs from (D) in that the indexical invoked in (A) is pure. But by itself this does not solve our problem of showing how someone could be entitled to (A), i.e. to assume that the conclusion is merely the repetition of the premise and hence that we have formal validity. Someone might object: ‘How can you be assured that the second indexically used token — the one in the conclusion "Galileo said that the Earth moves" — latches on to the same content as the first token — the one in the premise "Galileo said that the Earth moves"? I allow that both indexicals are pure’ says this objector ‘but might it not be the case that, unknown to you, the two complement thoughts are not tokens of the same type?’

With pure indexical reference we can resist this kind of move, at least in some cases, by pointing out that premise and conclusion are judged or enunciated at the same place and time and by the same person. Hence a reasoner is entitled to assume the same referent for tokens of ‘I’, ‘here’ and ‘now’ which are deployed in that way.

We can also resist worries about identity of worldly correlate, for demonstrative indexicals, by making one identification serve for both premise and conclusion. In effect, I make an anaphoric link between premise and conclusion. Thus I might fix my eye on a cat and think ‘that cat is friendly, so it is friendly’. Here I do not risk unnoticed substitution of one cat for another because I use the same perception and demonstration to identify the cat in both premise and conclusion. Analogously, on the predicatival front, I might reason: ‘That is the shape of the brooch, so it is the shape of the brooch’ — using one look at the shape to fix which shape I meant.

But it is not plausible that (A) has this last mentioned form. So let us grant that in it there are two tokens of ‘the Earth moves’, one fixing the content of Galileo’s saying for the premise and one for the conclusion, just as there are two exercises of my concept of Galileo, one for the premise and one for the conclusion. In this situation, why am I entitled to assume that I am do not make a mistake analogous to that of the reasoner in (E), who wrongly assumes the identity of two shapes which look the same? The objector may reinforce the worry by pointing out that sentences may be subtly ambiguous. Failure to detect such ambiguity, and hence mistaken apprehensions of formal validity, are a well known source of fallacious reasoning. I may think I am having the same thought aroused in my by contemplating the complement in premise and conclusion, but perhaps this is a mistaken impression.

The worry is perfectly proper one. But what has been raised is an entirely general difficulty which arises in formulating any theory of our entitlement to confidence in formal validity. It bears as much on my right to think to suppose that it is Galileo about whom I think in premise and conclusion as upon my right to take it that it is his thought about the Earth which is reported. And radical scepticism about the stability of our concepts is not something we are required to answer here. The idea of detecting and responding to formally valid inference presupposes an intact mind, entitled to the general presupposition that it can hold its ideas steady and respond appropriately to identities of concepts. Such a mind is entitled to the assumption that it can hold the indexically used specimen steady as well as the frame in which itappears.



Burge, T. (1986). ‘On Davidson’s"Saying That"’ in Lepore, E. (ed.) Truth and Interpretation (Oxford: Blackwell) 190-208.

Davidson, D. (1968). ‘On Saying That’ Synthese 19, 130-146. Reprinted in his Inquiries into Truth and Interpretation, (1984) 93-108 (Oxford: Oxford University Press).

Heal, J. (1997). ‘Indexical Predicates and Their Uses’ Mind 106, 619-640.

Heal, J. (2001). ‘On Speaking Thus: The Semantics of Indirect Discourse’ Philosophical Quarterly 51, 433-454.

Heal, J. (2003). ‘Lagadonian Kinds and Psychological Concepts’ in Heal, J. Mind Reason and Imagination Cambridge: Cambridge University Press. (Heal (1997) and Heal (2001) are also reprinted in this volume.)

Kaplan, D. (1989). ‘Demonstratives’ in J.Almog, J.Perry and H.Wettstein eds. Themes from Kaplan (Oxford: Oxford University Press) 481- 563.