the paradox of indicative conditionals

The Paradox Of Indicative Conditionals

D.K. JohnstonDepartment of Philosophy

University of VictoriaVictoria, Canada V8W 2Y2

e-mail: [email protected]

c© Philosophical Studies.All rights reserved.

THE PARADOX OF INDICATIVE CONDITIONALS 1

In his 1987 book Conditionals, Frank Jackson presents an argument to theeffect that the indicative conditionals of natural language have the sametruth conditions as the material conditional of truth-functional logic. ThisJackson refers to as the “Paradox of Indicative Conditionals”. I offer a so-lution to this paradox by arguing that some conditionals that appear tobe in the indicative mood are actually subjunctives, to which the paradoxdoes not apply. I support this proposed solution with some historical ob-servations on the evolution of the English verb phrase. I then examinesome examples of indicative conditionals that are subject to the paradox,and argue that they need not be considered problematic. Finally, I showthat if -clauses have other functions besides the conditional one, but that aunivocal analysis can still be given of the particle if.

1. Material Implication and Indicative Conditionals.

Perhaps the best-known philosophical puzzle concerning conditionals isthe so-called “Paradox of Material Implication”. According to the standardtruth-functional account, a material conditional of the form “P ⊃ Q”1 willbe true when either its antecedent is false or its consequent true. But thesedo not seem to be the truth conditions of typical conditional sentences suchas:

(1) If the door isn’t closed, then the buzzer sounds.

We would be inclined to say that a true assertion of sentence (1) wouldrequire that a causal connection obtain between the events designated byits antecedent and consequent. But the antecedent might be false, or theconsequent true, when such a relationship does not exist. Thus, a materialconditional would be true in circumstances where we would not want tosay that sentence (1) is true.

Furthermore, we would be inclined to say that sentence (1) is inconsis-tent with the sentence:

If the door isn’t closed, then the buzzer doesn’t sound.

1Following Jackson (1987), I will use the symbol “⊃” exclusively to designate materialimplication.


But the truth conditions for the material conditional will allow both of thesesentences to be truly asserted in contexts where their common antecedentis false.

It is tempting to avoid the Paradox of Material Implication simply byclaiming that the material conditional is a philosopher’s illusion, and thatit does not exist in natural language. For example, one might attribute theillusion to an uncritical acceptance of the Law of Excluded Middle; sincesentence (1) would not be said to be false when either its antecedent is falseor its consequent true, one might argue on the basis of Excluded Middlethat the conditional must be true. But this would be as much an argumentagainst the universal applicability of the Law of Excluded Middle, as itwould be for the existence of the material conditional in natural language.

However, the Paradox of Material Implication is not so easily avoided;despite our contrary intuitions, a convincing case can be made for iden-tifying the truth conditions of the philosopher’s material conditional withthose of the indicative conditionals of natural language, such as example(1) above. Frank Jackson2 has called this the “Paradox of Indicative Condi-tionals” (PIC), and it follows from three quite plausible principles:

(a) The Truth-Functionality Principle: The material conditional “A ⊃ B” isequivalent to “Not-A or B”.

(b) The Uncontested Principle: The indicative conditional “If A then B” im-plies the material conditional “A ⊃ B”.3

(c) The Passage Principle: Given the disjunction “A or B”, we can infer theindicative conditional “If not-A then B”.

Suppose now that the material conditional “P ⊃ Q” is true. “Not-P or Q”follows by the Truth-Functionality Principle. But then the indicative condi-tional “If not-not-P then Q” follows by the Passage Principle. And this givesus the indicative conditional “If P then Q” by Double Negation. Thus, wecan infer the indicative conditional from the material conditional. But theUncontested Principle tells us that the material conditional can be inferred

2(1987), pp. 4-6.3Since the truth of A and the falsity of B imply the falsity of the indicative condi-

tional, the falsity of the material conditional implies the falsity of the indicative condi-tional. Hence, it is claimed, the Uncontested Principle follows by Contraposition.


from the indicative conditional. It follows that the material and indicativeconditionals must have the same truth conditions. But of course we cannotdeny that the indicative conditional occurs in natural language. Conse-quently, the puzzles associated with the Paradox of Material Implicationstill remain.

It follows further that the indicative conditional will be true when eitherits antecedent is false or its consequent true. This corollary can be derivedwithout using the Uncontested Principle. Supposing “P ” to be false givesus “P ⊃ Q” by simple truth-functional logic. This yields “Not-P or Q” bythe Truth-Functionality Principle, and the Passage Principle together withDouble Negation then gives us the indicative conditional “If P then Q” asbefore. Similarly, supposing “Q” to be true gives us “P ⊃ Q”, so againthe indicative conditional can be derived. Thus, rejecting the UncontestedPrinciple would still leave us with an equally problematic form of the PIC.

There are two possible strategies for dealing with the PIC. The first in-volves blocking the derivation of the indicative conditional from the ma-terial conditional. This would be possible if reasons could be found forrejecting either the Passage Principle or the Truth-Functionality Principle.The latter might seem the more likely target, for it requires the validity ofthe rule of Addition; since “A” will imply “not-A ⊃ B”, “A or B” followsby the Truth-Functionality Principle. But when applied to the or of naturallanguage, Addition produces unnatural results. For example, many compe-tent speakers would be surprised to find themselves committed to “Eithersnow is white or Goldbach’s conjecture is false”, simply because they holdthat snow is white. Nevertheless, in what follows I will assume that the orof natural language does conform to Addition. This is not because I thinkthis is true, but rather because I want to propose another way of blockingthe derivation.

Jackson adopts a second strategy for dealing with the PIC. His solutioninvolves making a distinction between the truth conditions of a sentence,and its “assertibility” conditions. Jackson’s claim is that material and in-dicative conditionals do have the same truth conditions, as implied by thePIC. However, these conditionals do not have the same assertibility condi-tions. Thus, on Jackson’s view a conditional like (1) will indeed be truewhenever its antecedent is false or its consequent true; but it need not beassertible under these circumstances.


With this distinction in hand, it can be argued that our reluctance toaccept a sentence like (1), given only a false antecedent or true consequent,is due to the non-fulfilment of the assertibility conditions of the sentence,rather than its truth conditions. Thus, the PIC does not present a counter-intuitive result, for it does not imply that the indicative conditional has thesame assertibility conditions as the material conditional.4

However, there are consequences of the PIC for which Jackson’s solu-tion is less than satisfactory. It is easily demonstrated that the materialconditional conforms to the rule of Contraposition: that is, “A ⊃ B” isequivalent to “not-B ⊃ not-A”. It also conforms to the rule of Strengthen-ing the Antecedent: that is, from “A ⊃ B” we can infer “(A and C) ⊃ B”for an arbitrary sentence “C”. Thus, the PIC implies that the indicative con-ditional must also conform to these inference rules, because it has the sametruth conditions as the material conditional.

Now consider the following sentences:

(2) If he made a mistake, then it wasn’t a big one.

(3) If my partner is cheating me, then I’ll never know it.

The rule of Contraposition would have it that these sentences are equiva-lent to:

If he made a big mistake, then he didn’t make a mistake.

If I know that my partner is cheating me, then my partneris not cheating me.

But these sentences are obviously false; indeed, on intuitive grounds atleast, they should be classified as self-contradictory. Furthermore, the ruleof Strengthening the Antecedent would have it that sentence (1) aboveimplies:

If the door doesn’t close and the battery is flat, then thebuzzer sounds.

4The same reasoning might be used against those who are suspicious of the rule ofAddition. It might be claimed that the or of natural language does have the same truthconditions as truth-functional disjunction, and that any apparent counter-examples aremerely violations of assertibility conditions. This is another reason why I have chosen toaccept the Truth-Functionality Principle without a fight.


Of course, this sentence could well be false in circumstances where (1)would be true.

On Jackson’s view, it would follow that each of these examples wouldbe true (although presumably not assertible) in any context where its al-leged logical equivalent (1), (2) or (3) were true. Jackson himself bothrecognises and accepts this consequence, and provides a detailed defenseof his position.5 However, avoiding such counter-intuitive consequences isgenerally preferable to having to explain them away. For this reason, I willadopt the first of the two strategies mentioned above, and argue that con-ditionals like (1) cannot be derived from material conditionals. However,it will turn out that my solution does not require the rejection of either thePassage Principle or the Truth-Functionality Principle.

2. Indicative and Subjunctive Conditionals.

As Jackson points out,6 the PIC cannot be extended to subjunctive condi-tionals. As an illustration, consider the three sentences:

(4) Either the butler or the maid did it.

(4a) If the butler didn’t do it, then the maid did.

(4b) If the butler hadn’t done it, then the maid would have.

The disjunction (4) implies the indicative conditional (4a), in accordancewith the Passage Principle. But (4) does not imply the subjunctive con-ditional (4b). Thus, the Passage Principle does not apply to subjunctiveconditionals, and consequently a counterpart to the PIC cannot be derived.

There is a form of the Passage Principle that does apply to subjunctiveconditionals. If the disjunction is itself in the subjunctive mood, the cor-responding subjunctive conditional can be inferred. For example, sentence(4b) can be inferred from the subjunctive disjunction:

(4c) Either the butler or the maid would have done it.

5See especially his Chapter Four.6(1987), p.6.


But this is not enough to extend the PIC to subjunctive conditionals, forneither the material conditional nor the indicative disjunction will implythe subjunctive disjunction. For example, consider a standard “detectivemystery” context in which the indicative disjunction (4) is asserted on thebasis of a process of elimination; the deed was done by someone, and wedetermine that only the butler or the maid could possibly have done it.But the subjunctive disjunction (4c) might be false in such a context, for itimplies that both the butler and the maid had sufficient motive to do thedeed.

The fact that the indicative conditional (4a) does not imply its sub-junctive counterpart (4b) contrasts with the case of example (1), for thissentence does imply its subjunctive form:

(1a) If the door weren’t closed, then the buzzer would sound.7

This contrast between (1) and (4a) is more fundamental than might at firstappear; it turns out that sentences like (1) are really subjunctive condition-als, rather than indicatives.

In Old English, the subjunctive and indicative moods were marked bydistinct inflections. And it was the subjunctive that was the mood mostcommonly used in if -clauses: that is, in many contexts where Modern En-glish appears to have the indicative in an if -clause, Old English would haveused the subjunctive. But it would be wrong to conclude that the subjunc-tive came to be replaced by the indicative in the evolution of the Englishverb phrase. What happened was that the distinctive subjunctive and in-dicative inflections became phonetically indistinguishable through the lev-elling of their vowels. This levelling affected all types of inflection, andoccurred for purely phonetic reasons. Eventually, the distinctive verb end-ings were dropped altogether, first in speech, and much later in writing.8

7This is only to say there is no context in which one of the sentences would be trueand the other false. This does not mean that these sentences can be interchanged inany context, for their illocutionary forces, conversational implicatures, etc. might be quitedifferent.

8See the Appendix for an example of this historical process. The details of the evolu-tion of the English verb can be found in numerous histories of English: Strang [1970] isespecially recommended.


Modern English now makes use of an extensive system of auxiliary verbsto indicate tense, aspect, and mood.9 For example, the future tense is oftenindicated by using the auxiliary verb will, together with the infinitive ofthe main verb, as in John will arrive tomorrow. For the most part, these“periphrastic” forms were lacking in Old English. In fact, Old English simplydid not mark many of the tense and aspect distinctions that we find inModern English. For example, there was no distinct inflection for the futuretense, nor for the perfect. The inflection system really only distinguishedpast from non-past, with other distinctions being made contextually, orthrough the use of adverbial phrases. This is still evident in Modern English,where besides John will arrive tomorrow, which marks the future tensewith an auxiliary verb, we have John arrives tomorrow, which uses only thesimple present.10

For our purposes here, the important point is that what appears to bean indicative conditional in Modern English may instead be a survival ofthe original inflected subjunctive. The grammatical form of a verb phrasein Modern English is not enough in itself to distinguish the indicative fromthe inflected subjunctive. However, we are not without the means of mak-ing the distinction between these moods, for we need only compare theconditional in question with its periphrastic subjunctive form. If the truthconditions are the same, then we have a survival of the inflected subjunc-tive; while if they are different, we have an indicative. To avoid confusion,I will refer to the latter as “non-subjunctive” conditionals, rather than in-dicatives. And to avoid needless complexity, I will refer to survivals of theinflected subjunctive conditional simply as “inflected subjunctives”, despitethe fact that they no longer show any trace of the original inflections.

Thus, conditionals such as our example (1) turn out to be inflectedsubjunctives; as we saw above, (1) and its periphrastic subjunctive form(1a) have the same truth conditions. Consequently, conditionals like (1)

9The Modern English verb exhibits remarkably few inflections. All past tense formsare identical, while in the present tense, only the third person singular indicative is dis-tinguished. The copula be is exceptional, having three distinct forms in the present tense(am, is, are), and two in the past (was, were). Note that the so-called “modal” auxiliaries,such as shall, will, may, etc., do not distinguish the third person singular of their presenttense.

10Of course, the evolution of the modern system of auxiliary verbs was not unconnectedwith the decline of the inflection system.


do not conform to the Passage Principle, and so cannot be derived froma material conditional. It follows that the PIC does not apply to them.11

Hence, despite apparent grammatical similarities, conditionals like (1) arefundamentally different from non-subjunctive conditionals like (4a).

It appears, then, that the PIC applies only to non-subjunctive condition-als, which have truth conditions different from their periphrastic subjunc-tive counterparts. This class of conditionals is worthy of special attention,since it contains such famous examples as:

(5) If Oswald didn’t shoot Kennedy, then someone else did.

Obviously, this is a non-subjunctive conditional; its truth conditions arequite different from the corresponding periphrastic subjunctive If Oswaldhadn’t shot Kennedy, then someone else would have.

However, in the specific case of example (5), the PIC is not problematic:that is, there is nothing paradoxical in saying that sentence (5) has thesame truth conditions as a material conditional. The truth of this sentencedepends upon the fact that Kennedy was shot, and hence that he was shotby someone. Let the logical form of the sentence Someone shot Kennedybe represented as (∃x )Fx. Given this rendering, the logical form of thesentence Oswald didn’t shoot Kennedy can be represented as ¬Fa. ApplyingExistential Instantiation to the first formula gives us Fb, and this togetherwith ¬Fa gives us (a 6= b) by the Indiscernibility of Identicals. Conjunctionnow gives us:

Fb ∧ (a 6= b)

and by applying Existential Generalisation to this, we get:

(∃x )(Fx ∧ (a 6= x))

which is the logical form of the consequent of (5). Thus, sentence (5)is logically entailed by the assumption that someone shot Kennedy; given

11Likewise, we need not be concerned that these conditionals do not conform to the ruleof Strengthening the Antecedent. It is possible to construct a semantics for subjunctiveconditionals in which this rule fails: for example, see Stalnaker (1968).


this assumption, we can logically deduce the consequent of (5) from itsantecedent.12

Now suppose that the antecedent of (5) is false. Thus it is true that Os-wald shot Kennedy, and it follows trivially that someone shot Kennedy. Butas we have just demonstrated, sentence (5) is entailed by this assumption.Assuming that the consequent of (5) is true yields the same result, for ittoo implies that someone shot Kennedy. Thus, in the case of sentence (5),there is nothing counter-intuitive in saying that it has the same truth condi-tions as a material conditional. And consequently there is no need to claimthat the assertibility conditions of the sentence have not been satisfied, asJackson would have us do.

The non-subjunctive conditional (4a) can be dealt with in a similar man-ner. The conditional is being asserted on the basis of the disjunction (4),which logically entails it; indeed, this entailment represents little more thanan instance of the rule of Disjunctive Syllogism. But we are assuming thatthe rule of Addition applies universally.13 Thus, either the falsity of theantecedent of (4a), or the truth of its consequent, will entail sentence (4).

It is unwise to make linguistic generalisations on the basis of only twocases, and I want to stress that I do not claim that all non-subjunctive condi-tionals can be dealt with in the same manner as our examples (4a) and (5).There may well be several different types of non-subjunctive conditional,each requiring a different analysis.14 Many more cases will need to be ex-amined before the matter can be resolved. For the moment, all I can sayis that I have been unable to discover further examples of non-subjunctiveconditionals that do not fit the pattern of (4a) and (5). No doubt the readerwill form their own opinion about why this is so; in my own defense, Ioffer the observation that non-subjunctive conditionals are much less com-mon than inflected subjunctives. This is just what we should expect given

12Note that this argument does not assume the rule of Conditional Proof, which ofcourse applies to material conditionals. All that is needed here is the weaker assumptionthat the derivability of consequent from antecedent is a sufficient condition for the truthof a non-subjunctive conditional.

13If we do not assume the rule of Addition in this case, the Truth-Functionality Principlemust be rejected as well, and the PIC will not apply.

14To repeat a crucial point: a non-subjunctive conditional is one that can be true whenits periphrastic subjunctive form is false, or false when its periphrastic subjunctive form istrue.


Old English usage, where conditionals with subjunctive if -clauses were thenorm.

The distinction between inflected subjunctive and non-subjunctive con-ditionals provides more than just an alternative means of resolving theParadox of Indicative Conditionals. As I observed earlier, one’s first in-clination upon confronting the Paradox of Material Implication is simply todistinguish the material conditional from conditionals like (1), and to denythat the former exist in natural language. This way of avoiding the para-dox is made even more tempting by the availability of alternative “possibleworlds” accounts of the truth conditions of conditionals like (1). For exam-ple: for each possible world w, define a set of possible worlds R(w) that are“accessible” from w in some relevant respect. Then let a conditional like(1) be true in a world w if and only if every member of R(w) that has theantecedent true, also has the consequent true.15

This analysis of truth conditions avoids the Paradox of Material Implica-tion. For if the consequent of sentence (1) happens to be true at w, it mightstill be false in some member of R(w) where the antecedent is true. If suchis the case, (1) will be false at w. Similarly, the falsity of the antecedentat w does not in itself prevent it from being true in some member of R(w)

where the consequent is false. Again, if such is the case, (1) will be false atw.

Of course, such possible worlds analyses were originally intended todeal with (periphrastic) subjunctive conditionals such as (1a). In this ca-pacity, these analyses have received a great deal of attention. They havealso achieved a great deal of success, especially when compared to tradi-tional truth-functional approaches to conditionals like (1). But philoso-phers have been reluctant to extend the possible worlds account to con-ditionals like (1), presumably because of their apparent similarity to con-ditionals like (5), to which the analysis does not apply. One needs a wayof distinguishing between these grammatically similar types; but basingsuch a distinction on the fact that an analysis works for the first, but not

15There are other ways of formulating the truth conditions of conditionals within apossible worlds semantics. The formulation I have given here is for illustrative purposesonly, and indeed is not the most appropriate for conditionals like (1). See Stalnaker (1968)and Lewis (1979) for alternative formulations. The exact nature of the “accessibility”relation is a matter of some importance, but need not concern us here.


for the second, would provoke well-founded objections of circular reason-ing. However, the distinction I have made here between inflected sub-junctive and non-subjunctive conditionals is characterised independentlyof the possible worlds analysis, and can be accounted for on purely his-torical grounds. Thus, there is no reason to withhold the possible worldsanalysis from conditionals like (1).

We have still to deal with the problematic examples (2) and (3). Likesentence (1), they have the same truth conditions as their periphrastic sub-junctive forms:

If he had make a mistake, then it wouldn’t have been a big one.

If my partner were cheating me, then I would never know it.

However, unlike (1), sentences (2) and (3) violate the rule of Contrapo-sition, and will not readily submit to a possible worlds analysis. In whatfollows, I will argue that these sentences are really “pseudo-conditionals”,in the sense that their subordinate if -clauses do not specify conditions un-der which their main clauses would be true. But before proceeding to this,it will be helpful to determine more precisely the function of the particleif. This is best done by examining what might be called the “grammaticalmechanics” of causal conditionals.

3. Causality and Coincidence.

Conditionals like:

(6) If the pressure increases, then the temperature rises.

are generally taken to imply or presuppose that a causal connection ex-ists between the events designated by their antecedent and consequent.16

However, it is easily demonstrated that such implications or presupposi-tions must be pragmatic, rather than semantic. Consider the followingsequence of sentences:

16Such connections between events may be other than causal, as is the case with sen-tences like She gives me a biscuit if I behave.


(6a) The pressure increased at noon.

(6b) The temperature rose at noon.

(6c) The temperature rose when the pressure increased.

(6d) The temperature rises when the pressure increases.

(6e) The temperature rises if the pressure increases.

Sentences (6a) and (6b) have no causal content: that is, there would be noneed to mention a causal connection between events in any description oftheir truth conditions.17 When one of these sentences is asserted, all that isrequired for truth is that the designated event occur at the time indicatedby the accompanying prepositional phrase.

Sentence (6c) is (semantically) entailed by sentences (6a) and (6b).Hence (6c) cannot have any causal content either, for no sentence can havemore semantic content than the sentences that entail it. (6c) differs from(6b) only in using a subordinate when-clause to designate a particular time,rather than a prepositional phrase. The when-clause brings about the re-quired temporal correlation by designating an event that occurs at the rel-evant time. Again, all that is required for truth is that the event designatedby the main clause occur at this time.

When a sentence like (6c) is used, it may well be that the events des-ignated by the main clause and the subordinate clause are causally con-nected. Indeed, a speaker might deliberately choose to use (6c) ratherthan a sentence like (6b) in order to bring such a connection to the atten-tion of their audience. But a causal connection between the designatedevents is not a necessary condition of the truth of the assertion. As far asthe truth conditions of the sentence are concerned, the coincidence of thesetwo events might just as easily be due to chance. A speaker might some-times mislead by uttering (6c) when there is no causal connection, but theywill not speak falsely.

In the case of sentence (6d), the implication of a causal connectionseems inescapable. But the only grammatical difference between (6c) and(6d) is that the latter uses the simple present tense instead of the simple

17Although of course one might have to mention a causal connection in accounting forwhy utterances of these sentences are true in a particular case.


past. In English, a verb in the simple present often has what is called“habitual” or “durative” aspect: that is, it implies that the designated actionpersists or recurs over a period of time. In this use, the simple presentcontrasts with the periphrastic or “progressive” present that we see in thesentence The temperature is rising. Here, the present participle of the mainverb is attached as complement to a finite form of be. A verb that occursin the progressive present implies only that the designated action occurs atthe time of utterance.18

The use of the simple present in the subordinate clause of (6d) willimply that the event described by that clause recurs from time to time.Hence, the when-clause will correlate the utterance with an indefinite setof moments of time: those moments at which the given event occurs.19 Andin order for the assertion as a whole to be true, the event designated by themain clause must occur at each of these moments. But again, this is all thatthe truth conditions of the sentence require: the invariable coincidence (or“constant conjunction”) of these two events. Of course, the ways of theworld are such that a coincidence of this sort would not occur unless theevents are causally connected in some way. But this is a matter of empiricalfact, and does not have a place in the semantic analysis of the sentenceitself.20

Now consider sentence (6e). Like (6d), its subordinate clause is in thesimple present. And like (6d), its truth conditions require that the eventdesignated by the main clause occur whenever the event designated by thesubordinate clause occurs. Thus, it is plausible to attribute to the subordi-nate clause of (6e) the same grammatical function that it has in (6d): thatis, the determination of the moments of time at which the event designatedby the main clause must occur.

This way of characterising the function of the subordinate clause in (6e)allows us to account for the causal implication of this sentence in the same

18Curiously, the periphrastic present tense is unique to English.19I describe this set as “indefinite” because no times are explicitly indicated, as they are

by prepositional phrases such as in the morning or before midnight. However, this set isstill “well-defined”, in the sense that, for any given moment of time, we can tell whetheror not it is in the set.

20Indeed, someone who believes in such things as divine intervention might truthfullyand properly assert sentence (6d) in circumstances where they would deny the existenceof any causal connection.


way as we did in the case of (6d). As a matter of empirical fact, the co-incidence of events required for the truth-conditions of the sentence to befulfilled would not occur in the real world unless a causal connection didexist. Hence, this sentence does have a causal implication, but as in thecase of (6d), this implication is pragmatic, not semantic.

The only thing that distinguishes (6d) from (6e) is that (6d) implies thatthe event designated by the subordinate clause does actually occur: that is,that the pressure in fact increases from time to time. But (6e) has no suchimplication. So, when the subordinate clause is modified by when, theremust be some moments of time when the event designated by the clauseoccurs. But when the clause is modified by if, the event it designates neednot occur at any time.

This suggests that the only function that if has in (6e) is to neutralisethe assertive force of the subordinate clause that it modifies. Since thisforce is neutralised, there need not be any actual manifestations of theevent that the clause designates. But when has no such neutralising effecton the clause it modifies. Thus there must be some occasions on which thisevent actually occurs.

This way of accounting for if has the virtue of being rather simpler thanmany of the analyses that have traditionally been given of this troublesomeword. And it does appear to be all that is needed in order to explain howif -clauses can be used to form conditional sentences. But there are othergrounds for characterising the function of if in this way.

A standard “assertion-cancelling” device in English is subject-operatorinversion.21 In independent clauses, this usually has the effect of trans-forming the indicative mood into the interrogative: for example,

The pressure was increasing⇒ Was the pressure increasing?

But in subordinate clauses, subject-operator inversion often has much thesame effect as using an if -clause: for example,

21The operator of a verb phrase is simply its initial auxiliary. When a verb phrase doesnot contain an auxiliary, a finite form of the verb do is used to provide one. For example,the interrogative form of The pressure increased would be Did the pressure increase?


The temperature would have risen had the pressure increased.

The temperature would rise were the pressure to increase.

The temperature will rise should the pressure increase.

So here we have examples where a cancelled assertion is clearly being usedto produce a conditional assertion.

Furthermore, classifying if as an assertion-canceller fits neatly with itshistorical origins. The Oxford English Dictionary describes the etymology ofif as follows:

By many considered to represent one or more cases of the substantiverepresented by Old High German iba “condition, stipulation, doubt”,Old Norse if, ef . . . “doubt, hesitation” (whence ifa, efa vb. to doubt. . .

So, the English if is descended from older Germanic words that could mean“doubt” or “hesitation”, as well as “condition”.22 It is not difficult to under-stand why affixing a marker of doubt or hesitation to a clause should serveto neutralise its assertive force. And the above examples of subject-operatorinversion demonstrate that conditional assertions can be formed by usingsuch neutralised clauses. Thus, the “condition” sense of if that we findin sentences like (6e) can be explained as deriving from this more basic“doubt” or “hesitation” sense.

4. Non-Conditional If -Clauses.

It is common practice in philosophy to refer to any sentence that has asubordinate if -clause as a conditional. But clearly there are conditionalsentences that do not contain if -clauses. Sentence (6d), which contains asubordinate when-clause, is as worthy of the title “conditional” as (6e); forin both cases, the subordinate clause describes the conditions under whichthe event described by the main clause will occur.

Nor is every sentence that contains an if -clause to be classified as aconditional. In his article “Ifs and Cans”, Austin gave a famous example ofsuch a sentence that does not have a conditional sense:

22This was noticed by J.L. Austin in his 1956 article “Ifs and Cans”. See Austin (1970),pp. 211-212.


(7) There are biscuits on the sideboard if you want them.23

Clearly the purpose of the if -clause of this sentence is not to describe condi-tions under which its main clause would be true; the presence of biscuits onthe sideboard is not conditional upon the desires of the audience. As Austinpoints out, the sentence implies “There are biscuits on the sideboard” sim-pliciter. But of course a conditional “If P then Q” will not imply “Q”. Nordoes sentence (7) conform to the rule of Contraposition; your lack of desirefor biscuits cannot be inferred from their absence on the sideboard.

The assertion-canceller analysis of if is enough to account for this typeof case as well. Obviously, the point of uttering a sentence like (7) would beto make an offer to one’s audience. But this same illocutionary purpose canalso be achieved by applying subject-operator inversion to the subordinateclause, as in:

(7a) There are biscuits on the sideboard: Do you want them?

(7b) There are biscuits on the sideboard should you want them.

Of course, when one is making an offer, the question of whether one’saudience wants what is on offer is relevant. By using a subordinate clausethat attributes this desire to the audience, and then applying an assertion-cancelling device to that clause, the speaker can make the illocutionaryforce of the main clause clear. In some contexts, this force might not beclear from the utterance of a simple sentence like There are biscuits on thesideboard.

We can now deal with the troublesome example of sentence (2). Likesentence (7), the if -clause of sentence (2) is not being used to describeconditions under which its main clause will be true; it is not being claimedthat his having made a mistake guarantees that he didn’t make a big one.Indeed, like sentence (7), sentence (2) implies its apparent “consequent”,He didn’t make a big mistake. Hence, sentence (2) is not a conditional, andconsequently the fact that it does not conform to the rule of Contrapositionis of no philosophical significance.

23Ibid. p.210. Paradoxically, this type of sentence is often referred to as an “Austinianconditional”.


The function of the if -clause of sentence (2) can be accounted for inmuch the same way as that of sentence (7). An audience might take the un-modified utterance “He didn’t make a big mistake” to indicate the speaker’sbelief that some mistake was still made. In the same way, saying “He doesnthave a big car” would often be taken to imply24 that he does have a car. Thespeaker can ensure that such an implication will not be made by using theif -clause, since it attaches an explicit indicator of doubt to the relevantproposition. Thus, as in the case of sentence (7), the if -clause of sentence(2) serves to make the illocutionary force of the utterance more precise.

It is clear that the if -clause of sentence (3) does not have a conditionalfunction either; in uttering this sentence, a speaker clearly would not beclaiming that their partner’s cheating them is a sufficient condition of theirnot knowing it. However, the if -clause of (3) has a different function thanthe if -clauses of examples (2) and (7). Sentence (3) is synonymous with:

(3a) I will never know if my partner is cheating me.

And this sentence in turn is synonymous with:

(3b) I will never know whether my partner is cheating me.25

The subordinate clause in (3b) modifies the verb know, and serves to spec-ify the proposition whose truth value the speaker claims to be ignorant of.The same function can thus be attributed to the if -clauses of both (3) and(3a).

To summarise: the class of if -sentences must first be divided into theconditional and the non-conditional. Those if -sentences that are condi-tional must be further divided into the inflected subjunctive, the periphras-tic subjunctive, and the non-subjunctive. Once a correct classification ismade according to this scheme, examples like (2), (3), and (5) lose theirphilosophical significance.

24Of course, this would be what is commonly called a “conversational” or “pragmatic”implication, not a logical one.

25In some contexts, (3b) may mean “I will never know whether or not my partner ischeating me”, which does differ slightly in meaning from (3a). However, this “whether-or-not” meaning is also present in the sentence I will never know if my partner is cheatingme or not.


5. Concluding Remarks.

As we have seen, many conditionals that have what appear to be indica-tive verb phrases are in fact subjunctives; the apparent indicative form of averb phrase is not a reliable sign of the indicative mood. But neither is theappearance of an auxiliary verb such as should or would a reliable indicatorof the subjunctive mood. The auxiliary verbs that Modern English uses tomark the subjunctive were not specially developed for this purpose; theyalready had well-defined meanings in the language before they took ontheir additional auxiliary roles. For example, the auxiliary verbs would andshould are the past-tense forms of will and shall, and these verbs are stillcommonly used with their original senses designating volition and obliga-tion.

Thus, in some cases it will be difficult to tell whether such auxiliaryverbs are being used to mark the subjunctive mood, or whether they arebeing used simply as standard past tense forms. For example, consider thesentence:

John would help us if we needed him.

This sentence is somewhat ambiguous. If it is uttered with reference to apast time, would represents only the past tense of will. In such a context,the sentence would mean something like “John used to help us when weneeded him”. But if the sentence is uttered with reference to the present,would is being used to mark the subjunctive mood. In this type of context,the sentence would be more or less synonymous with John will help us ifwe need him. And in either context, the original volitional sense of theauxiliary verb is still evident.

Philosophers must be very cautious, then, in classifying the conditionalsentences of Modern English as indicative or subjunctive, regardless ofwhether these sentences contain auxiliary verbs. Because of the peculiarhistorical evolution of the English verb phrase, its grammatical form is nota reliable indicator of mood. Taking notice of these historical factors canhelp us to understand such puzzles as the Paradox of Indicative Condition-als.


Appendix: English Verb Paradigms

Old English Middle English Modern EnglishPres. Indic.

1st hıere here hear2nd hıerst herest hear3rd hıerth hereth hearsPl. hıerath hereth hear

Pres. Subj.1st hıere here hear2nd hıere here hear3rd hıere here hearPl. hıeren heren hear

Past Indic.1st hıerde herde heard2nd hıerdest herdest heard3rd hıerde herde heardPl. hıerdon herden heard

Past Subj.1st hıerde herde heard2nd hıerde herde heard3rd hıerde herde heardPl. hıerden herden heard

Notes:

1. The Old English paradigm gives the forms characteristic of the WestSaxon dialect, and the Middle English forms are those of the Southerndialect. Thus they represent the language as it was spoken in roughly thesame geographic region. Modern English derives from the East Midlandsdialect of Middle English.

2. The term “Old English” is generally used to refer to the language as itwas spoken in Britain up to about 1150, while the Middle English periodis taken to have lasted until about 1500. The division between Middleand Modern English is somewhat arbitrary, but the division between


Old and Middle English is less so; the Norman Conquest had significantlinguistic consequences.

3. The third-person present subjunctive form given for Modern English of-ten sounds somewhat archaic in contemporary speech, but it was com-mon even as late as the nineteenth century. The use of the correspond-ing indicative form in its place is best attributed to the effect of analogy,rather than to any change in the meaning of the indicative mood.

References

Austin, J.L. (1970) Philosophical Papers (Second Edition). Oxford Univer-sity Press.

Jackson, F. (1987) Conditionals. Basil Blackwell Limited.

Jackson, F. (editor) (1991) Conditionals. Oxford University Press.

Lewis, D. (1979) “Counterfactual Dependence and Time’s Arrow”. NousXIII. Reprinted in Jackson (1991).

Mitchell, B. and F.C. Robinson (1992) A Guide to Old English (Fifth Edi-tion). Basil Blackwell Limited.

Mosse, F. (1952) A Handbook of Middle English. Johns Hopkins UniversityPress.

Stalnaker, R. (1968) “A Theory of Conditionals”. Studies in Logical The-ory, American Philosophical Quarterly, Monograph 2. Reprinted in Jackson(1991).

Strang, B.M.H. (1970) A History of English. Methuen and Company.

the paradox of indicative conditionals

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