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«Three Twentieth-century Commonplaces about `If’ V. H. DUDMAN 28 Haig Street, Chatswood, NSW 2067, Australia Received June 2000 The commonplaces, ...»

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HISTORY AND PHILOSOPHY OF LOGIC, 22 (2001), 119±127

Three Twentieth-century Commonplaces about `If’

V. H. DUDMAN

28 Haig Street, Chatswood, NSW 2067, Australia

Received June 2000

The commonplaces, all grammatically confused, are that `conditionals’ are ternary in structure, have

`antecedents’ and conform to the traditional taxonomy. It is maintained en route that `The bough will not

break’ is consistent with `If the bough breaks... ’, that there is no logical difference between ``future indicatives’’ and ``subjunctives’’, and that there is a difference between the logic of propositions (e.g. `The bough broke’) and that of judgments (`The bough will/might/could/should/must/needn’t break’).

1. Introduction (A) to (E) instance what we casually call `if’-sentences:

(A) If the bough breaks, the cradle will fall (B) If the bough broke (were to break), the cradle would fall (C) If the bough had broken, the cradle would have fallen (D) If the bough broke, the cradle will have fallen (E) If the bough broke, the cradle fell Each can encode a message featuring a cradle’s falling and a bough’s breaking, two single events. Call these messages m1 to m5 respectively. I shall also be referring, as respectively m6 and m 7, to the single-future-event interpretation of (F)

and the single-past-event interpretation of (G):

(F) The bough will break (G) The bough broke Interest in messages like m1 to m5 increased exponentially among philosophers during the twentieth century, and many and diverse were the theories they proposed for them. But perhaps a few tenets were so widely espoused or at any rate acquiesced in as to be accounted among the century’s commonplaces of Englishspeaking philosophy. I think to have collected three, which I shall introduce in turn below (Sections 4, 12, 14). Each of the three is, or arises from, a fundamental grammatical mistake.

For authentication, I draw here and there upon late twentieth-century essays of Jonathan Bennett and Dorothy Edgington, and on the work of a larger ®gure, Frank Jackson.

2. Sentences and messages (A) is discovered ambiguous between our single-events interpretation m1 and a logically different interpretation formulating a present habit (`... the cradle will often/usually fall’). The mere fact of sentence-ambiguity establishes a distinction between sentences and the messages they encode. And the logician’s interest is in the messages, patently.

History & Philosophy of Logic ISSN 0144-5340 print/ISSN 1464-5149 online # 2002 Taylor & Francis Ltd http://www/tandf/co/uk/journal

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3. Times-about In my semantics the homely notion of the time(s) that a message is propounded about plays an important role. A message encoded in an `if’-sentence naturally has two times about. In each of m1 to m5, a is the time of the cradle’s falling and a’ the time of the bough’s breaking.1

4. First commonplace The aim of the empiricist in semantics must be to expound messages as articulated in the sentences found to convey them, saying how each target message is built up as its encoding sentence is generated, and out of what informational fragments. Posed about interpretations of `if’-sentences, those two questions elicit my ®rst two commonplaces.

Jackson, appreciating their primacy, answers both questions in his opening sentence: `if, then’ is a `dyadic sentential connective’ (1987: 1). `Dyadic’ means that `if’-sentences encode structures along the lines of A4C, and `sentential’ means that A and C are interpretations of sentences, i.e. messages. And those understandings provide respectively my ®rst and second commonplaces.

The same ternary structure espoused by Jackson is employed by Bennett, but I miss in his essay any clear avouchment of it. Rather, it is attributed to use and

custom: urging two types of ``conditionals’’, he continues (p.331):

The former are often expressed by a straight arrow (A?C), and the latter with a corner symbol (A4C).

Edgington is if anything more oblique, acquiescing uncritically in the ternary convictions of others, but as far as I see saying nothing of her own to choose between the ternary structure and, say, some If-A+C one.

Not every twentieth-century authority proclaims the ternary structure, then. But many who do not seem still to think and work in terms of it, like Bennett and Edgington. Now let me explain why it cannot be right.

5. Ternary structure untenable Examples like the following demonstrate that an `if’-sentence has a string

beginning with `if’ for a constituent:

... the moment for such frivolities, if it had ever existed, was now past. (Anthony Powell 1960: 160) The knowledge that there was a leak, if it became public, could be more damaging than the leak itself. (Graham Green 1978: 37) In them we descry that string interrupting a prior sentence (`The moment for such frivolities was now past’, `The knowledge that there was a leak could be more damaging than the leak itself’) which it could synonymously have preceded or followed: there is no doubting its integrity. And then the point is simply that the commonplace ternary structure would sunder this undoubted constituent.

1 Dudman 1998, pp.283±284 pursues some intricacies of time-about.





Three Twentieth-century Commonplaces about `If’ 121

6. Prior messages Now, a prior sentenceÐany sentenceÐcan appear with its own full stop, `stand on its own’. But a string beginning with `if’ never can: it occurs only to elaborate some prior sentence. The right way to expound interpretations of `if’sentences, then, is as informational elaborations of the prior messages their prior sentences encode.

Brie¯y, the prior messages of our examples are all simple messages (=df messages encoded in subject-predicate sentences). Simple messages divide into propositions and judgments. Propositions are statements of fact about their tenses; they have a identical with the A-series time t registered formally as present or past in the predicates of their encoding sentences. The prior message of m5 is a proposition.

The prior messages of our other four examples are judgments. A judgment has a verdict v, expressed by a modal, for an immediate informational factor. The English modals are WILL, CAN, MAY, MUST, SHOULD, OUGHT, NEED, DARE and SHALL.

There are two grammatical categories of judgment. The prior message of m4 is a prActical judgment, intuitively a judgment `as to fact’: its verdict is applied to the cradle’s actually falling in the past. The prior messages of m1, m2 and m3 are projEctives, and it is the speciality of Es to lack the {+actual} understanding that characterises As.

7. The string beginning with `if’ They are matters of observation that in (D) under m4 and (E) under m5, `the bough broke’ means something it can mean when it occurs with its own full stop, whereas nothing comparable is true of (A), (B) or (C). I urge a grammatical explanation, that in (D) and (E) `if’ is externally pre®xed to the sentence `the bough broke’, whereas in (A) under m 1, (B) under m2 and (C) under m3 `if’ is ®rst word of what is called a `conditional clause’. That is one point, that our strings beginning with `if’ are put together in two ways. My next is that `if’-strings combine with prior sentences in different ways.

8. Structure When `if’ is pre®xed to a sentence, the resulting string is not embedded in the prior sentence but always an external accompaniment to it. In m4 and m5 I recognize two immediate informational factors then, one encoded in the `if’-string and the other in the prior sentence.

How `if’-string and prior sentence amalgamate under m1, m 2 and m3 is a question I have often botched, and as recently as (Dudman 1998: 277, 282).

According to the proposal I now prefer, smiling like a sheep, (A)’s prior sentence has WILL for an immediate constituent, while (A) itself has `WILL if the bough breaks’ in its place.

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10. Wodehouse Note that there is nothing wrong with af®rming m1 while simultaneously maintaining that the bough will not break. For a reason about to emerge, I call this the Wodehouse proposition. Prima facie there should be nothing wrong logically: the two tenets are sustained by quite independent reasoning, the former’s perhaps premissed on the observation that the cradle depends wholly from the bough, the latter’s on the logically indifferent observation that the bough is a foot thick.

And anyway, the concatenation is found in received English:

If Mr Winship performs the miracle of winning this election, which he won’t, he will be an ordinary, humble back-bencher... (P.G. Wodehouse 1971: 79) Examples can be multiplied. 2 In contrast, we cannot say `If the bough broke, which it didn’t, the cradle fell [will have fallen]’ (unless with the interpolation kept apart thematically from the rest, e.g.

said as an aside). The speaker maintaining that the bough did not break retreats from that position by adding `If it did, the cradle fell [will have fallen]’, the resultant effect hardly to be distinguished from that of `The bough didn’t break, or if it did, the cradle fell [will have fallen]’.

My explanation is that, when `if’ is pre®xed to a sentence, it introduces that sentence’s then interpretation as a hypothesis, i.e.df as treated as true (if a proposition) or as accepted (if a judgment) regardless of whether it really is, and accordingly that `If the bough broke, which it didn’t,... ’ attempts, inconsistently, to treat m7 as true and simultaneously to af®rm its negation.3 By contrast, Wodehousian dicta make sense because in the conditional clause of (A) under m1 is encoded no message, hence nothing that might be inconsistent with `The bough will not break’ (They are however further matters of observation that, although [i] `The bough broke, but it won’t have broken’ is unsayable, it nevertheless makes perfect sense to say [ii] `If the bough broke, which it won’t have,... ’. How are these to be explained? [i] combines af®rmation of a fact and a contrary opinion as to that same matter of fact. [ii] combines the announcement that something is being treated as a fact regardless of whether it actually is with an opinion that it actually isn’t. A speaker can follow through the consequences of a propositional hypothesis she openly opines to be false, but af®rming something rules out opining its falsity).

11. Logical differences among m1 to m 5 From casual examination of our ®ve examples, it would be no surprise to ®nd m 5 logically different from the ®rst four, because (E) lacks a lexeme shared by (A) to (D).

(A) to (D) use every lexeme used by (E) plus the modal WILL. And therefore the modality will (which= df the meaning of WILL) is an informational factor, unshared 2 `But call me earlier if there’s anything to report, won’t you?’ `There won’t be. But yeah, sure, if there is.’ (Gabrielle Donnelly 1991: 20) `Well, let me know if you have any more trouble with him, but you won’t.’ (Pamela Hansford Johnson 1987: 14) `I will arrive on the 10 o’clock plane. If I don’t arrive on that plane, I will arrive on the 2 o’clock plane.

(Adams 1965: 171).

3 It is as well one cannot deny that the bough broke while hypothesizing that it did. Otherwise `if A, C would follow, `paradoxically’, from `not-A’, familiar problem. For both steps in the argument `notA; therefore not-A or C; therefore if A, C’ are widely relied upon, and logically impeccable.

Three Twentieth-century Commonplaces about `If’ 123 by m5, of m 1, m 2, m3 and m4. Moreover, from comparison of `The cradle will fall’, `...

can’t fall’, `... may fall’, `... must fall’ and the like, it is evident that the role played by the modality in the prior messages of m1 to m4 is no minor one. So m5 lacks what is a major factor in the prior messages of other four, good reason for expecting a semantic difference large enough to be logical.



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