Antecedents and Consequents V. H. Dudman



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Antecedents and Consequents

V.H. DUDMAN

This is an essay in English grammar, but addressed to logicians and aimed at persuading them to approach their subject grammatically. On the one hand I shall stress the hazards of ignoring the grammatical approach: half of the time the logicians’ “antecedents” and “consequents” are spectral (Part 3), and even when they exist the relation between them is botched (Part 2). On the other hand, no grammatically tenable theory of antecedents and consequents yet existing, I am emboldened to venture a proposal or two of my own (Part 4) in a treatment which I conceive to recommend the attractions of starting with grammar.



1.
Grammar distinguishes sentences from the informational burdens they are uttered to convey, which I call messages. The distinction is thrust upon us by examples like
(1) If the telephone rang he would ignore it
which can convey either a generalisation about the past or a more particular claim about the future. It is the message that determines the sentence, and not the other way round: English generates the same sentence (1) from two different messages. –By two different encoding programs: the feted connection between “complete” messages and “complete” sentences is that one message is encoded as one sentence by one start-to-finish run through some encoding program of the language. When a sentence S is generated from a message m, I call m an interpretation of S and say that m is encoded as S. English grammar is the empirical study of how English generates sentences from their interpretations.1
Although the sentence does not determine its interpretations, there will often be one interpretation that springs to the hearer’s mind ahead of any other. For example, it is not easily remembered that
(2) If Sir Jasper fell he would be killed,
no less than (1) can be generated from a generalization about the past: at first presentation, (2) automatically exacts its future interpretation. Quite adventitiously, of course. When this sort of thing happens, it is convenient to refer to the dominant message as the ‘natural’ interpretation of its sentence – convenient, at any rate, while no deeper significance is read into the epithet. I shall identify the natural interpretation of the sentence (n) where it exists, as mn. Thus m2 is the future interpretation of (2).

Messages are often ignored by contemporary logicians and philosophers, who concentrate on sentences instead. When they speak of ‘conditionals’, for example, they are referring to ‘if’-sentences. The term is thereby wasted: the limitations of a theory of “conditionals” as ‘if’-sentences will be gauged by its impotence in the fade of (1), which is the same ‘if’-sentence said either way, with the ambiguity, obvious focus of interest, still to explain. But in what follows I shall be concentrating on two other terms of art, ‘antecedent’ and ‘consequent’.



2.
Antecedents and consequents are usually introduced by contemporary logicians and philosophers as constituent sentences of ‘if’-sentences. In their terms, the sentence (4) is the “consequent” of the ‘if’-sentence (3), and the sentence (5) its “antecedent”:
(3) If Socrates is a man Socrates is mortal

(4) Socrates is mortal

(5) Socrates is a man
(See e.g. Quine 1962:14). For me, however, consequent and antecedent are component messages, messages ingredient in interpretations of ‘if’-sentences. My consequent is not the sentence (4) but the proposition that Socrates is mortal, an interpretation of (4); and it is consequent of not (3) but m3. Similarly for my antecedent. My consequent and antecedent are the prior messages m4 and m5, from which (4) and (5) are separately generated when (3) is being generated from m3. To refer to the constituent sentences I use the terminology of traditional grammar. (5) is a dependent sentence because introduced by a subordinating conjunction, here ‘if’, while (4) is the independent sentence in as much as it is unencumbered by any conjunction. (‘Subordinating conjunction’ will have to wait until Part 5).

Empirical scrutiny discovers the two constituent sentences playing quite unequal roles in the ‘if’-sentence. Comparing (3), (6) and (7), for example, we observe that the dependent sentence can precede, follow or even interrupt the independent sentence:


(6) Socrates is mortal if Socrates is a man

(7) You are, if my informants in Trieste have not lied, now on your final

assignment. [Anthony Burgess 1966]
But the independent sentence never interrupts the dependent. And through it all ‘if’ remains firmly glued to the front of the dependent sentence. We have to regard (3), then, as result of taking the already sentence (4) and elaborating, by intruding the prefabricated string
(8) If Socrates is a man
And the same goes, mutatis mutandis, for the generation of (9) from m9.
(9) Although/as/because/since/unless/while Socrates is a man, Socrates is mortal.
Indeed, we can set down the encoding program exactly. Let us call it Recipe 1.
Recipe 1: First, generate the independent sentence from the consequent. Next, select a subordinating conjunction while at the same time separately generating the dependent sentence from the antecedent; prefix the conjunction to the antecedent. Finally, amalgamate the result with the independent sentence.
The intended sense of ‘amalgamate’ will be sufficiently clear from (3), (6) and (7). The freedom with which the dependent sentence and its introductory conjunction can invade the independent is exploited to obvious effect in
(10) The dog, if it was a dog, ran off.
When a message m is encoded as a sentence S by Recipe 1, I call m a first-category interpretation of S.
Recipe 1 provides for the observed unequal roles of (4) and (5) in (3). Under a first-category interpretation, the independent sentence is an immediate constituent of the ‘if’-sentence and the dependent sentence not. Under m3, (3) has just two immediate constituents, (4) and (8).

Logicians often call ‘if’ a “binary connective”, meaning thereby that it evenhandedly joins two prior sentences to form a third. (Thus e.g. Quine loc.cit.). For them, (3) has three immediate constituents, (4), (5) and ‘if’. I can only repeat that, as a matter of observation, the conjunction attaches to just one of the constituent sentences. Such observations go direct to the absolutely fundamental question of the message’s outermost structure, and the toiling grammarian, seeking an empirical theory of how English turns messages into sentences, simply cannot afford to ignore them.

The only tenable semantic theories of first-category interpretations, I conclude, are those which recognise (4) and (8) as (3)’s immediate constituents under m3, and Part 4 will be devoted to expounding such a theory.

So far there has been a measure of agreement between logicians and me: we both react to the first category by diagnosing antecedents and consequents. Of course our antecedents and consequents are different things, but there remains this firm connection, that mine are simply interpretations of theirs. Alas, this happy relationship is about to end.



3.0
Compare the natural, future interpretations of (11), (2) and (12), the natural, present interpretations of (13) and (14), and the natural, past interpretation of (15):
(11) If Sir Jasper falls he will be killed

(12) If the auditors had come tomorrow they would have found our books in perfect order

(13) If Her Majesty was [were] here now she would be embarrassed

(14) If Her Majesty had been here now she would have been embarrassed

(15) If Sir Jasper had fallen he would have been killed
There is a definite pattern to these messages: the time that the message is about is always later than the time registered by the form. – Given, that is, that ‘will’, ‘can’, ‘may’, ‘must’, etc. and the ‘V-s form all register presentness, while ‘would’, ‘could’, ‘might’ and the ‘V-ed form all register pastness, in accordance with received grammatical wisdom (see e.g. Huddleston 1984: 131f, 169f). Thus we find form (i) below registering presentness while accessible to future messages, form (ii) registering pastness while accessible to present and future messages alike, and form (iii) registering past-pastness, and then accessible to messages relating not only to the past and the present but – examples like (12) are usually overlooked – to the future as well.
(i) If a U-s ..., b will/can/may/must/should/ought to/ needn’t/ daren’t V ...

(ii) If a U-ed ..., b would/could/might/should V

(iii) If a had U-en ..., b would/could/might/should have V-en ...
Unmistakeably, all this is the work of a single encoding program; and when a message m is encoded into its sentence S by this program, I call m a third-category interpretation of S.

‘If’-sentences under third-category interpretations always contain secondary auxiliaries. These, by definition, are inflectional forms of modals. English has eight modals, of which four, WILL, CAN, MAY and SHALL have two inflectional forms, while the other four – MUST, OUGHT, NEED, DARE – have only one. Already, then, we descry one factor in a third-category message, the one responsible for the choice of modal.. Current logical thought concentrates almost exclusively here on the case where the modal is WILL; but this is poor methodology, ignoring as it does one whole dimension of what after all is a single problem.

Many logicians resist my division between the first and third categories, preferring an analysis which classifies (11) with (3), rather than with (2) and (12) to (15). To me this is like classifying merinos with kangaroos and not with other sheep. But at all events the onus is surely upon them to defend this startling decision; and should they invoke a conception of “the subjunctive”, the onus will fall instantly upon them to defend that too.

My own account of the third category is sketched in section 3.3 below. It recognises no component messages in a third-category interpretation: no antecedent, and no consequent. There is just one message, the overarching third-category message itself. Conformably, I recognise no constituent sentences in (11) under m11.



3.1
And indeed it would be indefensible to maintain that ‘Sir Jasper falls’ occurred as a sentence under m11, or ‘Her Majesty had been here’ under m14. If one thing is certain about third-category messages, it is that ‘if’-sentences do not have two constituent sentences under them. Accordingly, when logicians diagnose “antecedents” and “consequents” in the third-category, they are abandoning their beginners’ doctrine that antecedent and consequent are constituent sentences.

Which, then, is to be ditched, ‘constituent’ or ‘sentence’? It may be that not every logician sees the problem, but those who do generally surrender ‘constituent’ and keep ‘sentence’. Thus David Lewis (1973: 21) teaches that ‘Her Majesty is here’ is the antecedent of (13) and ‘Sir Jasper fell’ the antecedent of (15), while Ernest Adams (1975: 11, 14, e.g.) takes it that


(16) Sir Jasper will fall
is the antecedent of (11). For these thinkers an “antecedent” can be a sentence not part of its parent sentence.

The policy of ignoring messages and confining discussion to strings of words emerges at this point as especially feeble, there being no way one might justify or even explain such attributions without appealing to the disdained informational contents. Why is (16), rather than any other English sentence, “antecedent” of m11? It can only be because m16 is believed an ingredient of m11. One had better said straight out that consequent and antecedent were component messages – in which sense Adams’ doctrine is that m11 has m16 for its antecedent.

Adams’ doctrine is enthusiastically shared by those many linguists who maintain that English puts ‘V-s’ instead of ‘will V’ in future-referring clauses of time and condition. Its adherents also number, willy-nilly, every logician who diagnoses modus ponens in

If Sir Jaspers falls he will be killed. Sir Jasper will fall.

Therefore Sir Jasper will be killed.
Nevertheless, Adams’ doctrine is a simple fallacy, as we shall see before this section is over.

First, though, let me stress what a radical proposal this is, as a piece of grammatical thought. For it entails nonstandard encodement, the idea that m16 is encoded into (11) nonstandardly, as the string ‘Sir Jasper falls’. The notion is that a message different from any message accessible to a string s when s might occur as a separate sentence is nevertheless encoded as s in special circumstances. Meanwhile this message, like any other, is recognisable only as an interpretation of some sentence S, necessarily distinct from s. Radical? Very: it means abandoning the basic principle that a string occurs as a sentence exactly when it encodes a message. Furthermore, what is being postulated is an entirely arbitrary and pointless complication of the system, an anomaly in the English language.

The whole idea is in any case misconceived. If English puts ‘V-s’ when it ought to put ‘will V’, why do we encounter (18) as well as (17)?
(17) If it is cooler after sundown I may drop in then

(18) If it will be cooler after sundown I may drop in then.


Moreover, comparison of m17 and m18, irrefutably different messages, discloses that it is the latter that has m16 for an antecedent, exactly as a simple theory would predict. Sympathetic listening discovers ‘it is cooler’ doing something in (17) which is quite different from what ‘it will be cooler’ does in (18), indeed something which no string, it or another, ever does when standing alone. In short, m16 is not, and never was an ingredient in m11. When logicians nominate (16) as the “antecedent” of (11), it is for no better reason than that they need a sentence with a future interpretation and can think of no other.

3.2
But by parity of reasoning, they need a sentence with a future interpretation – (16) again, then – to play “antecedent” to (2). So now we have two sorts of nonstandard encodement, each covertly encoding the same antecedent message into two different ‘if’-sentences. – Better make that three, so as to allow for the phenomenon of (12) and all that it entails.

And if we enquire for a moment how the consequent message is encoded in these cases, we discover yet further private little encoding recipes in operation – with the additional oddity that this time one of them is the standard one: under m11, runs the doctrine, ‘Sir Jasper will be killed’ means Sir Jasper will be killed.

Nonstandard encoding recipes can be arresting to a degree. For example the alleged common consequent of m13 and m14 is the proposition that Her Majesty is embarrassed. The sudden accession of ‘would’ and ‘would have’ for encoding an interpretation of ‘Her Majesty is embarrassed’ into a string leaves the grammarian flabbergasted.

Nor are we at the end of our perplexities. Comparing the cases of (2) and (13), we discover that ‘would V’ is a nonstandard encodement now for (“for”) ‘will V’ and now for ‘V-s’. It is an interesting question how many different sorts of nonstandard encodement a theory might feel entitled to evoke, but to bring this discussion to a point let me try to sketch what seems to me the logician’s inevitable analysis of the range of third-category messages represented by m2 and m11 to m15.

To make a start with future cases, the doctrine must be that the forms (i), (ii) and (iii) of section 3.0 all have interpretations with the same future antecedent, an interpretation of ‘a will U ...’, and the same future consequent, an interpretation of ‘b will V ...’. These three interpretations are themselves all different: compare m11, m2 and m12. And each of them has its own nonstandard encoding program. These three encoding programs are of a most unusual kind: each has two recipes, one for encoding the antecedent, and the other, never the same, for encoding the consequent.

And from here, it seems to me, the doctrine must proceed as follows. The three different overall messages are three different conceptual elaborations of the same two component messages. And when such an overall message is being encoded into its ‘if’-sentence, what conditions the speaker’s choice between the three bipartite nonstandard encoding programs available to him is his semantic choice between these three conceptual ways of mocking up an overall message out of two component ones. The speaker opts for the nonstandard encoding program proper to his intended elaboration. All three of these elaborations, however, call for ‘if’ to register them. And thus we have three different messages all encoded by the following routine: first select ‘if’; then separately encode the consequent and the antecedent using that nonstandard bipartite program which registers the other factors in your message, viz. which of the three elaborations you intend. Finally, prefix ‘if’ to the string nonstandardly encoding the antecedent and amalgamate the results with the string encoding the consequent.

Now, if some such strategy is what logicians are bent upon, then the sheer complexity of the job is going to defeat them. Let us unfold the plan a little further, to see where it is leading. Of interpretations relating dually to the present we discover some conveyed by the form (ii) and some conveyed by the form (iii): cf. (13) and (14). Now, are m13 and m14 same or different? To hold them identical were to recognise yet another dimension of nonstandardness: cases where two different nonstandard bipartite encoding programs were chosen between freely, i.e. on the basis of no informational difference whatever. The alternative is to say that the syntactical choice registers, as before, a choice between two different kinds of elaboration – whereupon the problem presents itself of explaining why these two different elaborations sound so terribly alike. And the next question that looms is whether either of these elaborations is the same as any of the three recently invoked for the future cases. And then there is the same question about the elaboration, again registered by ‘if’, which concocts m15 out of the propositions that Sir Jasper fell and that Sir Jasper was killed. David Lewis, among other authorities, evidently sees the latter as the same as the one registered by the (ii) form in (13); and certainly we need to be told which of them is which.

Ah, but I have been forgetting: we must also consider the interpretations with present antecedents and future consequents, past antecedents and future consequents, and so on. Evidently there are more nonstandard bipartite encoding programs yet.

It must at all events be plain that anyone, logician or no, who coveted such a theory would have a job of work ahead of him. It will also be plain, I trust, that the onus would be on him to furnish all the details. Nor need I add that the author of such a tract would ipso facto consign himself to the very verges of sanity.

Attempts are sometimes made to confirm some hypothesis of nonstandard encodement by claiming that a certain nonstandardly generated sentence is merely a stylistic variant of another in which both antecedent and consequent are standardly encoded. We are told (e.g. by Aune 1967: 28) that (13) ‘can be rewritten as’ (19):


(19) If it were the case that Her Majesty is here, it would be the case that Her Majesty is embarrassed.
According to this contention, the elaboration itself becomes overtly registered by the whole complex
If it were the case that ..., it would be the case that ...,
- though not, alas, in a way that enlightens. But no wonder: (19) is not a sentence of English at all, so if it encodes m13, it does so in some unexplained language.

3.3
This section attempts a lightning sketch of a grammatical theory with pretensions to handling third-category messages without nonstandard encodement. The presenting problem for the third category is that the message always relates to a time later than the time registered formally in the sentence. (section 3.0). My solution (1984b: 159ff.; 1985: 170ff) is that third-category interpretations are judgements arrived at by imaginatively thinking futurewards from historical realities of some time whose location as present, past or past past is registered by the form. Why does a speaker assert (12) rather than (20) when, disastrously, the auditors have come a day early?
(20) If the auditors come tomorrow, they will find our books in perfect order.
Because by saying ‘had come’ and ‘would have found’ he can retreat to a point which is past with respect to the already past time of the auditors’ surprise visit and imagine developments unfolding from there, thus setting aside the historical reality of their inopportune arrival. If he says ‘come’ and ‘will find’, the imagined developments begin at the point of speech, and he can set aside no historical fact whatever.

In their simplest versions, these judgements are in fact expressed without the aid of ‘if’-clauses. Thus the various sentences (21) all have interpretations which are judgements arrived at by setting out from certain present facts and picturing subsequent developments:


(21) Sir Jasper will/can/may/shall/must/ought to/ needn’t/ daren’t be killed
Under these interpretations, the sentence divides into a subject ‘Sir Jasper’ and a predicate comprising everything else. This predicate, in its turn, consists of a verb phrase, here ‘be killed’, preceded by a secondary auxiliary. It is the kind of judgement, we observe that conditions the choice of modal (cf. section 3.0), while what the judgement is about, Sir Jasper’s being killed, is responsible both for the choice of subject and the choice of verb phrase.

Now, in my submission, the effect of adding an ‘if’-clause to such a sentence is simply to modify the judgement pronounced by the secondary auxiliary:


Sir Jasper will-if-he-falls be killed
Under m11, (11) is a subject-predicate sentence, indiscernible in outermost structure from (21) under m21. Under m11, the subject of (11) is ‘he’ and the predicate is everything else. But this time the predicate is complex in as much as containing, along with the mandatory secondary auxiliary and verb phrase, an entire subordinate clause whose first word is ‘if’. And the message, as before, is a judgement concerning Sir Jasper’s being killed in developments subsequent to the point of speech; only this time the judgement is arrived at by gratuitously including, in these imagined future developments, the imagined future satisfaction of a condition – here that of Sir Jasper’s falling – encoded in the subject and verb phrase of the ‘if’-clause.

It is therefore quite wrong to regard


(22) He will be killed
as a constituent sentence of (11) under m11, for under m11 ‘If Sir Jasper falls’ occurs as indiscerptible part of (11)’s predicate. Not even in this case does the third-category message have a consequent.
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