Barker, John A.

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272Notre Dame Journal of Formal LogicVolume XVII, Number 2, April 1976NDJFAMPRESUPPOSITION AND ENTAILMENTJOHN A. BARKER1 In a recent paper1 Mitchell Ginsberg has argued that in light of certainfacts about presupposition the traditional conception of entailment should bemodified. It has traditionally been maintained that the following principleholds for entailment:(I) If A entails B, then if B is false then A is false.But, as Ginsberg points out, it seems pre-analytically clear that, forexample, the statement:(1) Vita, whose husband is a lawyer, is an artist,entails the statement:(2) Vita is an artist.And if (2) is false, it may be the case that (1) is not false, since (1) may betruthvalueless due to the falsity of the presupposition that Vita's husband isa lawyer. In general,"if . . . a given A entails some B such that A has a presupposition P whichB does not have, then it will be possible for A to be without truth value (beneither true nor false), for example when P is false, while B might be eithertrue or false."2Ginsberg suggests that (I) be replaced by the principle:(II) If A entails B, then if B is false then A is not true.If this is done, then we can say, for example, that (1) does entail (2), sinceif (2) is false, (1) will be either false or truthvalueless. As a bonus,Ginsberg argues, we would also be able to accept the principle:(III) If A presupposes B, then A entails B,a principle which conflicts with the generally accepted principle:(IV) If A presupposes B, then if B is false, then A is neither true nor false.For example, since (1) presupposes(3) Vita's husband is a lawyer,Received September 5, 1973PRESUPPOSITION AND ENTAILMENT 273it follows via (IV) that if (3) is false, then (1) is neither true nor false. Butif (IΠ) were accepted, then since (1) presupposes (3), it would follow that (1)entails (3). We would then find ourselves in conflict with (I), which wouldcommit us to holding that if (3) is false, then (1) is false rather thantruthvalueless. Ginsberg argues that in replacing (I) with (II), we would becommitted instead to the acceptable consequence that if (3) is false, then (1)is either false or truthvalueless. As a result, (III) could be accepted.I will try to show that the rejection of (I) has undesirable conse-quences. I will then go on to sketch an alternative solution which will allowus to hold both (I) and (III). Thus, we shall not only be able to retain thetraditional conception of entailment, but also we shall be able to say thatwhenever A presupposes B, A entails B.2 If we reject (I), then Modus Tollens for entailment:A entails B, not-B, :. not-Awould also have to be rejected. For given that A entails B and that not-B,it may happen that A is truthvalueless, in which case we cannot concludethat not-A. Similarly, rejection of (I) will entail rejection of Reductio adAbsurdum for entailment:A entails B, A entails not-B, :. not-A.Given that A entails a contradiction, we could not infer that not-A, since Amight be truthvalueless. It may, of course, be possible to justify intro-ducing a qualified version of these argument forms in which the conclusionis appropriately weakened. Nevertheless, it would seem preferable to tryto find a way to save the traditional principle, (I).3 Instead of attempting to modify the traditional conception of entailment,then, let us focus on the conception of presupposition which Ginsbergemploys. A fundamental aspect of this conception is embodied in (ΓV),according to which the falsity of a presupposition renders the presupposingstatement truthvalueless. This view apparently arises from considerationssuch as the following. The truth of(3) Vita's husband is a lawyeris a necessary condition of the truth of(1) Vita, whose husband is a lawyer, is an artist,since if (3) is false then (1) is not true. But the truth of (3) is also anecessary condition of the truth of(4) It is false that Vita, whose husband is a lawyer, is an artist,since if (3) is false then (4) is not true. Consequently, it seems, the truthof (3) is a necessary condition of the truth and of the falsity of (1).Obviously, this argument takes (4) to be what logicians would call acontradictory of (1), i.e., (1) is false if and only if (4) is true. Fully stated,the argument runs as follows. If (3) is false then (1) is not true. And if (3)274 JOHN A. BARKERis false then (4) is not true. But since (4) is a contradictory of (1), if (4) isnot true then (1) is not false. Hence if (3) is false then (1) is neither truenor false.4 We should note, however, that the truth of (3) is a necessary condition ofthe truth not only of (1) and of (4), but apparently of every logical compoundstatement containing (1) as a component. For example, it appears that thetruth of (3) is a necessary condition of the truth of each of the followinglogical compounds:(5) If Vita, whose husband is a lawyer, is an artist, then Vita is anarchitect.(6) If Vit? is an architect, then Vita, whose husband is a lawyer, is anartist.(7) If Vita, whose husband is a lawyer, is not an artist, then Vita is anarchitect.(8) Vita, whose husband is a lawyer, is an artist only if she is an architect.(9) Either Vita, whose husband is a lawyer, is an artist, or she is anarchitect.(10) Unless Vita, whose husband is a lawyer, is an artist, she is anarchitect.(11) It is possible that Vita, whose husband is a lawyer, is an artist.Thus, there seems to be nothing special about the fact that the truth of (3)is a necessary condition of the truth of (4), since (4) is merely one of themany logical compounds which can be formed from (1), and each of thesecompounds requires the truth of (3) as a precondition of its truth.Evidently a presupposed proposition is simply one which is not affectedby the logical compounding operations of natural languages by whichcomplex statements are constructed out of more elemental parts. Forexample, (5) states that Vita's being an architect is implied by Vita's beingan artist, and does not claim that her husband's being a lawyer is somehowinvolved in this implication. The proposition that Vita's husband is alawyer is something which, so to speak, stands outside the operation bywhich the hypothetical statement is constructed. Analogous considerationsapply to the other statements in the above list. Many statements, we cansay, are composed of several propositions having differing statuses-certain propositions involved in a given statement are focused on, whileothers are presupposed. Logical compounding operations of natural lan-guages affect only the focus propositions, leaving the presuppositionsuntouched. The resultant compounds continue to require the truth of thepresuppositions of the components as a precondition of the truth of thecompounds. This will explain why it happens that when the relevantnegating operation is applied to (1) to form(4) It is false that Vita, whose husband is a lawyer, is an artist,only the focus proposition of (1), i.e., that Vita is an artist, is affected.This fact is even clearer in the statementPRESUPPOSITION AND ENTAILMENT 275(12) Vita, whose husband is a lawyer, is not an artist,which is equivalent to (4).5 We should, then, avoid confusing the truth conditions of a given statementwith the truth conditions of certain compounds of the statement formed innatural languages. With this in mind, let us hypothesize that not only is thetruth of (3) a necessary condition of the truth of (1), but also the falsity of(3) is a sufficient condition of the falsity of (1). Since the truth of (3) is anecessary condition of the truth of (4), we cannot now hold that the truth of(4) is a necessary condition of the falsity of (1). (1) may be false because(3) is false, even though the falsity of (3) also makes (4) false. Obviously,we cannot go on to claim that (4) is a "logician's contradictory" of (1), forit is not the case that (1) is false if and only if (4) is true. This is not tosay that a "logician's contradictory" of (1) cannot be formed in naturallanguages. Such a contradictory, however, will not be a natural languagelogical compound of (1). For example, both of the statements:(13) It is false that Vita is an artist and her husband is a lawyer,(14) Either Vita is not an artist or her husband is not a lawyer,are true if and only if (1) is false. Nevertheless, normally a speaker whoobjected to (1) would believe himself to be in a position to make one of thefollowing statements:(15) Vita is not an artist,(16) Vita's husband is not a lawyer.Hence, such a speaker would not be inclined to state either (13) or (14).Indeed, doing so would normally be misleading, since it would normallyindicate that the speaker did not believe he was in a position to state either(15) or (16).6 We can go on to hypothesize that from a logical point of view a statementcan be identified as the conjunction of the proposition focused on and theproposition(s) presupposed.3 "Two" statements are the same statement ifand only if they consist of the same proposition focused on and the samepresupposition(s). Thus, for example, the "two" statements:(1) Vita, whose husband is a lawyer, is an artist,(17) Vita, who is married to a lawyer, is an artist,are the same statement, while the two statements:(18) Vita is an artist and her husband is a lawyer,(19) Vita, who is an artist, is married to a lawyer,are statements distinct both from each other and from (1) and (17), despitethe fact that all four statements have the same truth conditions. A logicalcompound statement will also be a conjunction of the focus proposition andpresupposition(s), but in this case the presupposition(s) of the variouscomponents, instead of entering into the focus proposition, become pre-suppositions) of the compound. For example, the statement276 JOHN A. BARKER(5) If Vita, whose husband is a lawyer, is an artist, then Vita is anarchitect,is the same statement as(20) If Vita is an artist, then Vita, whose husband is a lawyer, is anarchitect,since each consists of a conjunction of the focus proposition, i.e., that ifVita is an artist then she is an architect, and the presupposition, i.e., thatVita's husband is a lawyer. In contrast, the statements(21) If Vita is an artist and her husband is a lawyer, then Vita is anarchitect,(22) If Vita, who is an artist, is married to a lawyer, then Vita is anarchitect,are distinct both from each other and from (5) and (15). In this case thetruth conditions of the statements also differ. While (5) and (20) are nottrue unless Vita's husband is a lawyer, the truth of (21) and of (22) is notruled out by her husband's not being a lawyer. On the other hand, (22),unlike the other statements, cannot be true unless Vita is an artist.Since on our hypothesis a statement is a conjunction of the propositionfocused on and the presupposition(s), the truth of the principle:(III) If A presupposes B, then A entails Bis immediate. For example, since (1) consists of a conjunction of theproposition focused on, i.e., that Vita is an artist, and the propositionpresupposed, i.e., that Vita's husband is a lawyer, it is clear that (1)entails its presupposition, (3). Nevertheless, since the falsity of a pre-supposition renders the presupposing statement false, it follows that weneed not reject the principle:(I) If A entails B, then if B is false then A is false.Instead, we reject the claim:(IV) If A presupposes B, then if B is false then A is neither true nor false,a claim whose plausibility can be accounted for by the principle:(V) If A presupposes B, then if B is false, then A is not true and everylogical compound of A is not true.We can go on to accept the traditional principle of bivalence:(VI) A is true or A is false,in accordance with which (V) yields the following principle:(VII) If A presupposes B, then if B is false then A is false and every logicalcompound of A is false.It should be noted that in holding that both of the statements:(1) Vita, whose husband is a lawyer, is an artist,(12) Vita, whose husband is a lawyer, is not an artist,PRESUPPOSITION AND ENTAILMENT 277are false if Vita's husband is not a lawyer, we are in effect committed tothe rejection of the traditional principle of excluded middle:(VIII) A or not-A,where 'not-A' represents the result of applying a natural language negationoperation to Ά ' . Nevertheless, as we noted above, we are not committed toholding that there is no way to form in natural languages a "logician'scontradictory" of a statement having a presupposition. For example, wehave seen that the statement:(13) It is false that Vita is an artist and her husband is a lawyer,is true if and only if (1) is false. Representing such a contradictory as'NOT-A', we can accept the following modified form of the principle ofexcluded middle:(IX) A or NOT-A.4Thus, we are not committed to holding that there are any built-in limita-tions on what can be expressed in natural languages.7 I have tried to show that there are undesirable features associated withGinsberg's proposal that we modify the traditional conception of entailmentin order to be able to hold that a statement having a presupposition canentail a statement not having the presupposition. I have gone on to sketch aproposal for replacing the conception of presupposition underlying Gins-berg's view with a conception which at once seems to save the appearancesconcerning presupposition and to eliminate the conflicts with the traditionalconception of entailment. The extent to which this new conception ofpresupposition can handle the full range of presuppositional phenomenaremains as a subject for further investigation.5NOTES1. Mitchell Ginsberg, "The entailment-presupposition relationship/' Notre DameJournal of Formal Logic, vol. XIII (1972), pp. 511-515.2. Ibid., p. 512.3. For discussion of a similar view of statements, see my "Pragmatics and definitedescriptions/' Tulane Studies in Philosophy, vol. XXI (1972), pp. 63-84, Section 6.4. Some qualification to this principle may have to be made if there are genuinestatements in which the truth of the presupposition is a necessary condition notonly of the truth of the statement, but also of the truth of the focus propositioninvolved. For a discussion of such cases, see ibid., p. 79ff.5. For an excellent discussion of a number of these phenomena, see Lauri Karttunen,"Presuppositions of compound sentences/' Linguistic Inquiry, vol. IV (1973), pp.169-193. Among the many types of statements discussed by Karttunen, there isone which may appear to be especially damaging to my thesis. The statement(23) If Vita is married, then Vita's husband is a lawyer278 JOHN A. BARKERmay be true even if(24) Vita is marriedis false. And yet (23) seems to be a natural language logical compound composed(in part) of(3) Vita's husband is a lawyer,and hence should presuppose (24) just as (3) does. On this point see Section 8 ofmy "Hypotheticals: Conditionals and theticals," forthcoming in PhilosophicalQuarterly, in which I argue that such statements as (23) are not genuine logicalcompounds.Southern Illinois University at EdwardsvilleEawardsυille, Illinois

Presupposition and entailment

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