Ernesto Perini-Santos - John Buridan’s Theory of Truth and the Paradox of the Liar

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Transcript of Ernesto Perini-Santos - John Buridan’s Theory of Truth and the Paradox of the Liar

  • Koninklijke Brill NV, Leiden, 2011 DOI: 10.1163/156853411X590499

    Vivarium 49 (2011) 184-213 brill.nl/viv

    vivarium

    John Buridans Theory of Truth and the Paradox of the Liar*

    Ernesto Perini-SantosUFMG, Brazil

    AbstractThe solution John Buridan oers for the Paradox of the Liar has not been correctly placed within the framework of his philosophy of language. More precisely, there are two important points of the Buridanian philosophy of language that are crucial to the correct understanding of his solution to the Liar paradox that are either misrepre-sented or ignored in some important accounts of his theory. The rst point is that the Aristotelian formula, propositio est vera quia qualitercumque signicat in rebus signica-tis ita est, once amended, is a correct way to talk about the truth of a sentence. The second one is that he has a double indexing theory of truth: a sentence is true in a time about a time, and such times should be distinguished in the account of the truth-conditions of sentences. These two claims are connected in an important way: the Aristotelian formula indicates the time about which a sentence is true. Some interpret-ers of the Buridanian solution to the paradox, following the lead of Herzberger, have missed these points and have been led to postulate truth-values gaps, or surrogates of truth-value gaps, when there is nothing of this sort in his theory. I argue against this tradition of interpretation of Buridan and propose an interpretation of his solution to the Liar.

    KeywordsParadox of the Liar, John Buridan, medieval theories of truth, medieval semantics, medieval pragmatics

    * Earlier versions of this paper were read at conferences in Bologna and Rio de Janeiro. I thank the audiences on both occasions for helpful comments. I am also grateful for the support of the Conselho Nacional de Desenvolvimento Cientco e Tecnolgico.

  • E. Perini-Santos / Vivarium 49 (2011) 184-213 185

    1. Introduction

    The solution John Buridan oers for the Paradox of the Liar is certainly among the more oft-discussed medieval approaches to the subject.1 In spite of this, I think that it has not been entirely understood, nor has it been correctly placed within the framework of his philosophy of language. More precisely, there are two important (and related) points of the Buridanian philosophy of language that are crucial to the correct understanding of his solution to the Liar paradox that are either misrepresented or ignored in some important accounts of his theory. The rst point concerns the interpretation of the formula propositio est vera quia qualitercumque signicat in rebus signicatis ita esthereafter the Aristotelian formula. The second point concerns the distinction between the time about which ( pro quo) a sentence is true and the time in which (in quo) it is true, a distinction that is at the heart of the seventh chapter of the Soph-isms, and which is taken up at the beginning of the eighth chapter, in which he discusses the Liar. I propose two main theses that are, to my mind, essential to the correct interpretation of his solution to the Liar paradox:

    (i) The Aristotelian formula, once amended, is a correct way to talk about the truth of a sentence.

    (ii) A sentence is true in a time about a time, and such times should be distin-guished in the account of the truth-conditions of sentences.

    These two claims are connected in an important way: the Aristotelian formula indicates the time about which a sentence is true. I defend these claims in sec-tions 2 and 3 of this paper. Following this, I examine some important inter-pretations of the Buridanian solution to the Liar. In the light of the results of the previous sections, we will see that they are wanting. Finally, I present my own interpretation to the Buridanian solution to the paradox of the Liar.

    The Buridanian theory of truth turns out to have a pragmatic aspect. In very general terms, pragmatics deals with linguistic phenomena that can be explained only by considering the context of production of linguistic items. Such phenomena can be divided in two very broad kinds: the dierent types of speech acts and speech products, on the one hand, and the way the content

    1) The task Buridan sets for himself in the eighth chapter is that of dispelling the air of paradox surrounding certain self-referential propositions. His analyses of these sophisms pushed termin-ist logic to new heights, and remain impressive quite apart from their historical context, as it evidenced by the large secondary literature on the topic. (Jack Zupko, John Buridan (Notre Dame, 2003), 131).

  • 186 E. Perini-Santos / Vivarium 49 (2011) 184-213

    of a given utterance depends on the context of its production, on the other.2 The rst domain of pragmatics deals with the dierent kinds of acts performed by an utterance, their eects, conditions of satisfaction etc. I will have nothing to say about it in this paper. On the other hand, Buridans theory of truth recognizes the need to identify the context of utterance of a sentence and to distinguish it from its circumstances of evaluation, to give its adequate truth-conditions. And this point, suggested by (ii), is crucial to his solution to the Paradox of the Liar. As I will try to show, even if there are proximities between Buridan and some contemporary theories that make room for contextual eects in the determination of the content of an assertion, there are also some important dierences. As a result, we will nd an interesting and original pic-ture of a pragmatic theory of truth.

    2. The amended Aristotelian formula is a correct way to talk about the truth of a sentence

    In his Sophisms, Buridan states explicitly that the Aristotelian formula does not oer a correct denition of truth:

    The second conclusion is that it is not required for the truth a spoken sentence that howso-ever it signies [things to be] outside [the mind] so should things signied be outside [the mind]. Or let us put this conclusion in following form: some sentence is true, yet it is not the case that howsoever it signies [things to be] outside, so are the things that are signied outside.3

    There are three arguments supporting this claim. The rst and more impor-tant argument4 is based on the fact that sentences that are not armative, in

    2) See Robert Stalnaker, Pragmatics, in Context and Content (Oxford, 1999), 34.3) John Buridan, Summulae de Dialectica, transl. G. Klima (New Haven-London, 2001), 850 (hereafter, transl. Klima). Secunda conclusio est quod non requiritur ad veritatem propositio-nis vocalis quod qualitercumque signicant ad extra, ita sint quantum ad res signicatas ad extra. Vel ponatur conclusio sub hac forma: aliqua propositio est vera, tamen non est qualitercumque signicant ad extra, ita est in rebus quae signicantur ad extra. (Summulae de Practica Sophisma-tum, ed. F. Pironet (Turnhout, 2009) II, 2 conclusio, 38, l. 7-10hereafter, Soph.,). In the quotations of Klimas translation, I replace proposition by sentence as a translation of proposi-tio, so as to have a uniform vocabulary throughout the text.4) It is the only argument present in the following texts dealing with the formula: the commen-taries to the Metaphysics, Lectura Erfordiensis in I-V Metaphysica, ed. L.M. de Rijk (Turnhout, 2008), qu. 23A, 624, p. 145, l. 10-19, the Abbrevitationes Caminenses, ed. L.M. de Rijk (Turn-hout, 2008), 92, p. 197, l. 29-33 (hereafter Lect. Erf. and Abbrev. Cam.) and the Quaestiones in Aristotelis Metaphysicam (Paris, 1518) [reprint, Frankfurt am Main, 1964], VI, qu. 9 (hereaf-

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    the present tense and de inesse may be true without being in things signied as they signify them to be. Let us consider the following sentence:

    (1) Antichrist will walk

    (1) signies the Antichrist and his future walk, but such things are nothing. According to the Aristotelian formula, a sentence is true if, and only if, how-soever it signies things outside to be, so they are. In this case, the things signi-ed do not exist, so cannot be in some way or another. The tense of the last verb of the formula does not represent the fact that a future tense sentence is true because things will be in a certain way. The same argument applies to past tense sentences, to de possibili sentences and, in a modied way, to negative sentences. None of such sentences can be true because things are the way they signify things to be

    This line of thought has two important features. On the one hand, arma-tive de inesse present tense sentences remain untouched by the argument: nothing in it prevents the application of the Aristotelian formula to such sen-tences. On the other hand, a rather straightforward amendment of the for-mula seems to make it t other kinds of sentences. Both consequences appear in more than one text. The early Erfurt commentary on the Metaphysics states the conclusion as follows:

    And I state briey [the conclusion] that we should speak dierently about present tense sentences and about past tense and future tense sentences, and [we should speak] dierently about armative sentences and about negative sentences. I state therefore that an arma-tive atomic present tense [sentence] is true because howsoever it signies [things] to be, so are the thing or the things signied. But a future tense [sentence] is true because howsoever it signies [things] coming to be, so [they] will be, and a past tense [sentence] is true because howsoever it signies [things] having been, so [they] have been.5

    ter, Quaest. Met.), the Tractatus de consequentiis, ed. H. Hubien (Louvain-Paris, 1976) I, 1, 14-27, p. 17 (hereafter, Tractatus) and the Quaestiones in Analytica Posteriora, ed. H. Hubien (unpublished) II, qu. 10a (herafter, Quaest. Analyt. Post.)in this latter text, there