countering the counting problem: a reply to holton

Countering the counting problem: a reply to Holton JULIAN DODD

1 . It has become commonplace to claim that ‘the counting problem’ for Donald Davidson’s paratactic account of oratio obliqua can be met only by admitting propositions into one’s onto1ogy.l In a recent note, Richard Holton (1 996) has disputed this. The purpose of this brief reply is to argue that Holton’s rearguard action against propositions is unsuccessful. He has not succeeded in showing that we can hold on to the nominalistic ontology which Davidson takes to be concomitant on his paratactic proposal.

2. As Holton (1996: 46) explains, the counting problem emerges when we imagine the following monologue:

(1) The Earth moves. Galileo said that. The Earth moves. That’s another thing Galileo said.

Once it is granted that Galileo uttered only one sentence, we will want to say that the final sentence of (1) is false. Davidson, however, would seem to be unable to account for this result. Because Davidson holds that the thing said by Galileo (the thing named by the reporter’s utterance of the demonstrative ‘that’) is the reporter’s utterance of ‘The Earth moves’; and because the two occurrences of ‘that’ in (1) name different utterances, this means that the final sentence of (1) has the wrong truth-value. It comes out true.

How should Davidson reply to this problem? Holton’s suggestion is as ingenious as it is unexpected to anyone familiar with Davidson’s paratactic logical form proposal. This proposal, we may remind ourselves, was said by Davidson (1969: 106) to amount to the claim that sentences in oratio obliqua wear their logical form on their sleeves, except for one small point. Take ‘said’ to be a two-place predicate, insert a full stop after ‘that’, take ‘that’ to be a demonstrative referring to the utterance of the sentence which follows it, and there you have it. Consequently, we can represent David- son’s logical form proposal for

1 This has been argued by Ian McFetridge (1975) and Ian Rumfitt (1993). I argue for such a view in my 1997, with the proviso that propositions be treated as utterance- types rather than as inhabitants of a ‘third realm’. For the origin of this conception of propositions, see Michael Dummett 1986.

ANALYSIS 56.4, October 1996, pp. 239-245. 0 Julian Dodd

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(2) Galileo said that the Earth moves as

( 3 ) Said (Galileo, that). The Earth moves. If the logical form proposal is correct, then extensionality is preserved without there being a need to follow Frege (1892) in having the words of the content-sentence shift their reference.

Having set out Davidson’s proposal in this way, it comes as something of a surprise to be told by Holton (1996: 46) that Davidson gives the logical form of (2) as

(4) 3x(Galileo’s utterance x and my next utterance make us samesayers). The Earth moves.

Things, he says (1996: 46), are not ‘so simple’ as Davidson’s initial remarks suggest. I shall return to this reading of Davidson presently. For now, we should note how, with (4) in place, Holton’s reply to the counting problem can proceed.

If Holton is correct in thinking that the logical form of (5) Galileo said that

is given by the first part of (4), that is to say, by

(6) 3x(Galileo’s utterance x and my next utterance make us samesayers),

then ( 5 ) already involves quantification over utterances of Galileo’s. As such, Holton has a neat explanation of why (5) entails

(7) Galileo said something. This entailment goes through, not on the basis of quantifying into the place held by ‘that’, but because the ‘something’ in (7) corresponds to the exis- tential quantifier in (6). The quantifier in (7) ranges over Galileo’s utterances, not those of the reporter, the logical form of (7) being repre- sentable as

(8) 3 x ( x is an utterance of Galileo’s). When it comes to the counting problem, Holton’s suggestion is that we treat the quantifier ‘another thing’ in (1) in the same way as the ‘something’ in (7) , as ranging over utterances of Galileo’s, so that (1) is represented as

(9) The Earth moves. 3x(Galileo’s utterance x and my last utterance make us samesayers). The Earth moves. 3y(Galileo’s utterance y and my last utterance make us sarne- sayers, and y # Galileo’s utterance reported above).

COUNTERING THE COUNTING PROBLEM 241

As Holton (1 996: 48) points out, the final sentence of (9) would only be true if Galileo had made two utterances which match an utterance of ‘The Earth moves’ in content.

3. So much for Holton’s reply to the counting problem. Zfhe is right that (5) involves quantification over utterances of Galileo’s - if, that is, he is correct in giving the logical form of ( 5 ) as (6), and hence the logical form of (2) as (4) - is reply succeeds. However, the first thing I want to argue is that Holton is quite mistaken in thinking that Davidson gives the logical form of ( 5 ) as (6), and hence, pace Holton (1996: 48), that Holton’s reply, elegant though it is, is unavailable to Davidson.

Let us return to Holton’s claim that Davidson gives the logical form of (2) as (4). Davidson does no such thing. In fact, (4) is a conflation of David- son’s logical form proposal with his informal gloss of the relation expressed by the ‘said’ of indirect speech. But don’t just take my word for it. Here’s Davidson charging John Foster with having made exactly the same mistake:

The paratactic semantic approach to indirect discourse tells us to view an utterance of ‘Galileo said that the Earth moves’ as consisting of the utterance of two sentences, ‘Galileo said that’, and ‘The Earth moves’. The ‘that’ refers to the second utterance, and the first utterance is true if and only if an utterance of Galileo’s was the same in content as (‘translates’) the utterance to which the ‘that’ refers. (Foster wrongly says my analysis of ‘Galileo said that’ is ‘Some utterance of Galileo and my last utterance make Galileo and me samesayers’. This is not an analysis, but a rephrasal designed to give a reader a feeling for the semantics; an expository and heuristic device.) (1976: 176-77.)

According to Davidson, then, sentences in oratio obliqua really do wear their logical forms on their sleeves. While ( 5 ) may be rephrased as (6 ) , this is not to give its logical form.

Holton may well object that the distinction between a logical form proposal and ‘a rephrasal designed to give the reader a feeling for the semantics’ is not sufficiently clear to tell against his account. For if (6) really does give one a feeling for the semantics of ( 5 ) , then, on the most natural understanding of this phrase, this means that ( 5 ) really does involve quantification over utterances of Galileo’s; and this is all Holton needs for his solution to the counting problem to get going. The remainder of this note is devoted to showing why such an objection ultimately fails.

4. To be sure, Davidson’s own distinction between a logical form proposal and a rephrasal which gives a feeling for the semantics seems to be merely

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verbal. But this should not distract us from the key issue: whether ( 5 ) involves quantification over utterances of Galileo’s. Holton’s account trades on the idea that it does. Davidson, I shall argue, is correct in thinking that it doesn’t. In the course of my argument to this effect, two things should become clear: what it is to give the logical form of a sentence; and what (6) is doing, if not representing the logical form of (5 ) .

In the context of a discussion of his theory of the logical form of action sentences (1967), Davidson says the following:

To know the logical form of a sentence is to know, in the context of a comprehensive theory, the semantic roles of the significant features of the sentence. ... To know the logical form of ‘The rain caused the flood’ is to know whether ‘caused’ is a sentential connective or a two- place predicate (or something else), but it hardly begins to be knowledge of an analysis of the concept of causality (or the word ‘caused’). Or perhaps it is the beginning; but that is all. (1970: 146)

The distinction being made here is that between explaining the semantic function of the expressions that make up a sentence (explaining what these familiar words are doirzg here2) and giving a philosophical analysis of the concepts expressed by these words. And it is a grasp of this distinction that sheds light on our question. For the properly Davidsonian thing to say3 about ( 5 ) and (6) is this. The rephrasal of (5) as ( 6 ) is not intended to explain the semantic functions of the constituent expressions of (5). (5) is not really a quantified sentence. In this sense, (6) does not give the logical form of (5 ) . Rather, (6) constitutes an informal philosophical account (which forms part of a philosophical analysis) of the concept expressed by the ‘said’ of indirect discourse.

This much is obvious, if we contrast the motivation for Davidson’s account of the logical form of sentences in indirect speech with the motivation for his rephrasal of (5) as (6) . When it comes to his logical form proposal (that is to say ( 3 ) ) , Davidson’s aim is to explain how extensionality may be preserved, and hence how such sentences may fall within the scope of a compositional, truth-theoretic semantics. This he does by making claims about the semantic function of the familiar words, notably by claiming that (2) consists of two sentences, and that the first sentence - ( 5 ) - consists of a two-place predicate flanked by a name of a person and a demonstrative which refers to the utterance of the sentence immediately following it. The informal gloss on the saying relation, by contrast, scratches a very different itch. It is, in essence, an attempt to explain how

2 This paraphrases the way Davidson (1969: 94-95) himself puts it.

3 As opposed to what he actually says (see above).


Galileo can (literally) have said a reporter’s utterance of ‘The Earth moves’. The explanation goes like this: Galileo said the utterance made by a reporter just in case he produced an utterance which matches in content the reporter’s utterance. But this is not a semantic claim (to the effect that ( 5 ) is a disguised quantified sentence). It is the solution to a philosophical puzzle (that of how it is possible for Galileo to say an utterance of the reporter’s), and, as such, constitutes a part of an analysis of the concept of saying. To think that (6) reveals the semantics of ( 5 ) , that it gives the latter’s logical form, is akin to thinking that one’s favoured definition of the concept of knowledge shows up in the semantics of

(10) Galileo knows that the Earth moves. With the distinction between logical form and the analysis of predicates

in place, there would seem to be no good reason for replacing Davidson’s own view about the logical form of ( 5 ) (that it is composed of a name, a two-place predicate and a demonstrative) with ( 6 ) . Of course, had Holton shown that representing the logical form of ( 5 ) as (6) enables us to explain hitherto inexplicable inferential connections between ( 5 ) and other sentences, he would have thereby provided us with an adequate motivation for his proposal. But the plain fact is that any such phenomenon that (6) can explain is as easily explained on the assumption that the logical form of ( 5 ) is just as it seems.

So much for Holton’s specific account. There exists, nonetheless, another motivation for taking ( 5 ) to involve quantification over utterances of Galileo’s. For ( 5 ) is an action sentence, and, if Davidson’s own account of the logical form of action sentences (1967) were to be applied to ( 5 ) , its logical form would be represented as

(1 1) 3e( Said( Galileo, e, that)). Needless to say, this is some way from Holton’s account of the logical form of (5), an account, which, as we have seen, confuses the task of giving a sentence’s logical form with that of providing a philosophical analysis of one of its predicates. However, (1 1) would seem to give Holton what he needs to reply to the counting problem. For some of the events quantified over will be utterances, and so the sort of solution he envisages may yet go through.

Ultimately, though, such a reliance on Davidson’s account of action sentences is unconvincing. At the risk of repeating myself, we should give up the natural thought that ( 5 ) does not involve quantification only if there exists a compelling motivation for doing so. There are two reasons why a commitment to Davidson’s account of action sentences does not fit the bill. First, this account faces familiar difficulties, notably with attributive

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adverbs4 Second, it has a more intuitive rival - the view that adverbs are predicate modifiers - which equally well explains the semantics of adver- bial modifi~ation.~ We should disentangle Davidson’s logical form proposal for sentences in indirect speech from his more dubious excursion into the logical form of action sentences. And if this is the moral that should be drawn, we still await a persuasive argument for treating (5) as a quantified sentence.

5. Once it is granted that ( 5 ) is not an existentially quantified sentence, Holton’s reply to the counting problem collapses. How should we proceed? The neatest reply is the one which Holton rejects. In (l), we can take the two occurrences of ‘that’ to refer to the same thing: the proposition expressed by both utterances of ‘the Earth moves’. This ensures that the final sentence of (1) is false. Of course, the success of such a reply is contingent upon (at least) two conditions being satisfied: it must be explained how a proposition, being an abstract object, may be demon- strated; and propositions must be shown to be metaphysically respectable as opposed to being, for example, self-subsistent occupants of a Fregean ‘third realm’. In fact, I think that both conditions may be met,6 but I do not intend to show this here. My conclusion is just that, in the face of the failure of Holton’s reply to the counting problem, the only plausible way around is to take the demonstrative ‘that’ in (3 ) to refer to the proposition expressed by the following utterance of ‘the Earth moves’, rather than to that utterance i t ~ e l f . ~

Humanities Division, Bolton Institute Chadwick Street, Bolton BL2 1 JW

[email protected]

References Bennett, J. 1988. Events and their Names. Cambridge: Cambridge University Press. Clark, R. 1970. Concerning the logic of predicate modifiers. Notis 4: 311-35. Davidson, D. 1967. The logical form of action sentences. Reprinted in his Essays on

Davidson, D. 1969. On saying that. Reprinted in his Inquiries into Truth and Intetpre- Actions and Events. Oxford: Clarendon Press, 1984.

tation. Oxford: Clarendon Press, 1984.

This is explained with particular clarity by Simon Evnine (1991: 90).

5 The treatment of adverbs as predicate-modifiers has been set out by, among others, Romane Clark (1970), Terence Horgan (1978) and Jonathan Bennett (1988, Ch. XI).

I hold this view in my 1997.

Thanks are due to Jennifer Hornsby and, especially, Peter Smith for their helpful remarks.


Davidson, D. 1976. Reply to Foster. Reprinted in his Inquiries into Truth and Interpre-

Davidson, D. 1980. Reply to Carlile. Reprinted in his Essays on Actions and Events. Dodd, J. 1997. Indirect speech, parataxis and the nature of things said. Forthcoming

Dummett, M. 1986. Frege’s myth of the third realm. In his Frege and Other Philoso-

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Holton, R. 1996. Davidson, McFetridge, and the counting problem. Analysis 56: 46-50. Horgan, T. 1978. The case against events. Philosophical Review 87: 28-48. McFetridge, I. 1975. Propositions and Davidson’s account of indirect discourse.

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