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  • Journal of Philosophy, Inc.

    Presupposition, Implication, and Self-ReferenceAuthor(s): Bas C. van FraassenSource: The Journal of Philosophy, Vol. 65, No. 5 (Mar. 7, 1968), pp. 136-152Published by: Journal of Philosophy, Inc.Stable URL: http://www.jstor.org/stable/2024557 .Accessed: 13/02/2014 04:53

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  • 136 THE JOURNAL OF PHILOSOPHY

    What then can transpire between the first and second days to make trust in the teacher less reasonable? Given the idealizations we have assumed, the only relevant difference between the first and second days is that by the second day it will be known whether or not an examination occurred on the first. If an examination has been given on the first day, then the teacher's trustworthiness will be, if any- thing, enhanced, for his announcement will have come true, the students having had no reason to expect it then. But if an examina- tion has not been given, then the teacher's trustworthiness will in- deed be placed in question, and the students' caution confirmed; but in a curious way. It will not be because the teacher will have been proved a liar; a surprise examination may still be given. The reason is rather that events will have proved him to be a purveyor, by impli- cation, of incredible propositions. Such people cannot be trusted. You cannot trust a man if he tells you things that you cannot believe.

    This comes about because, if there is no examination on the first day, then the teacher's announcement becomes in effect the one-day paradoxical announcement considered above. For if we add el to what the teacher has said we can deduce e2* J2e2, something that the students can't believe on the second day.

    Now the students must envisage this paradoxical second-day test of their teacher's trustworthiness if their first-day doubt about their continued belief in his announcement is to be reasonably combined with their first-day trusting belief in it. But as we have seen, this doubt must be present if they are to believe it at all.

    So either directly with A5b or indirectly without it, the surprise- examination paradox reduces to the phenomenon of incredible though possibly true propositions, and it should redound to the credit of modal logic that it helps us to see this.

    ROBERT BINKLEY

    University of Western Ontario

    PRESUPPOSITION, IMPLICATION, AND SELF-REFERENCE *

    T ^ HE two aims of this paper are, first, to explicate the seman- tic relation of presupposition among sentences, and, sec- ond, to employ the distinctions made in this explication

    in a discussion of certain paradoxes of self-reference. Section I will explore informally the distinction between presupposition and im-

    * An earlier version of this paper was read at Duke University on May 12, 1967, and sections I and ii were included in a paper presented at a symposium on free logic held at Michigan State University on June 9 and 10, 1967. Acknowledgments and bibliographical references have been collected in a note at the end.

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  • PRESUPPOSITION, IMPLICATION, AND SELF-REFERENCE 137

    plication. In section ii we construct a formal paradigm in which this distinction corresponds to a substantial difference. Section ill explores the relations between presupposition and truth, and, in section Iv, the Liar and some similar paradoxes are finally broached.

    I

    The best known source for the concept of presupposition is the view (a.o. Strawson's) that a property cannot be either truly or falsely at- tributed to what does not exist. Thus, the sentence "The King of France (in 1967) is bald" is neither true nor false, on this view, be- cause the King of France does not exist.' The explicit characteriza- tion of presupposes is therefore given by

    1. A presupposes B if and only if A is neither true nor false unless B is true.

    This is equivalent to

    2. A presupposes B if and only if (a) if A is true then B is true, (b) if A is false then B is true.

    From this equivalence it is clear that presupposition is a trivial se- mantic relation if we hold to the principle of bivalence (that every sentence is, in any possible situation, either true or false). In that case, every sentence presupposes all and only the universally valid sentences.

    Why can we not say that, on Strawson's position, "The King of France is bald" implies "The King of France exists"? The reason is that presupposition differs in two main ways from implication, on any accepted account of the latter relation. For implication, modus ponens is accepted as valid; from 2(a) it is clear that an analogue of modus ponens holds also for presupposition. But modus tollens is also generally accepted as valid for implication; what of its analogue for presupposition? This question cannot be answered unless we first settle on the meaning of negation. We shall understand the negation of a sentence A to be true (respectively, false) if and only if A is false (respectively, true). This is not the only possible conven- tion, but it has the virtue of yielding the convenient further char- acterization of presupposition:

    3. A presupposes B if and only if: (a) if A is true then B is true, (b) if (not-A) is true then B is true.

    The question whether a sentence is true may be said to make sense only rela- tive to an interpretation, or to what is intended by it, and so on. Except when dealing with artificial languages, we shall avoid this issue by assuming that there is a "correct" interpretation known to the reader.

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  • 138 THE JOURNAL OF PHILOSOPHY

    From 3 it is clear that the analogue to modus tollens

    4. A presupposes B (not-B) Therefore, (not-A)

    is not valid; if the premises are true, the conclusion is not true (and not false). Secondly, 3(b) shows that the argument

    5. A presupposes B (not-A) Therefore, B

    is valid: if its premises are true, so is its conclusion. But of course the analogue of 5 for implication does not hold.

    Thus presupposition and implication are not the same, but they have something in common. What they have in common is that, if A either presupposes or implies B, the argument from A to B is valid. This is itself a semantic relation, which we shall here call "necessi- tation":

    6. A necessitates B if and only if, whenever A is true, B is also true.2

    We see here an obvious possible cause of confusion between impli- cation and presupposition. The standard logic text generally begins with an explanation that an argument is valid if and only if the con- junction of the premises implies the conclusion, if and only if the corresponding conditional is logically true. This explanation then justifies the text's concern with validating arguments (respectively, with proving logical truths) alone. But the standard logic text is concerned only with a case for which the principle of bivalence holds, and we must resist the temptation to extrapolate its teachings to other contexts.

    From 3 and 6 we obtain finally the equivalence

    7. A presupposes B if and only if: (a) A necessitates B, (b) (not-A) necessitates B.

    Thus we have an explication of presupposition in terms of standard semantic notions.

    Before turning to the task of making our account precise, we may briefly consider two questions. The first notes that we use 'if - . - then' in, for example, 3 and 6; how is this conditional to be understood? For the sake of clarity, I propose that this be understood as the ma-

    2 This relationship is usually called "semantic entailment," but in the present context that terminology might be confusing. Note that the 'whenever' does not refer to times, but to possible situations.

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  • PRESUPPOSITION, IMPLICATION, AND SELF-REFERENCE 139

    terial conditional. This yields at once the limiting case that, if B is universally valid, every sentence presuppose it. The second question notes that every case of implication or presupposition is a case of ne- cessitation; does the converse hold? This question is not necessarily decidable at this point, because we have not given a complete account of implication (nor presume to be able to do so). But in section III we present a case of necessitation which is not one of presupposition and which, we shall argue, is also not a case