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Plural signification and the Liar paradox

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Abstract

In recent years, speech-act theory has mooted the possibility that one utterance can signify a number of different things. This pluralist conception of signification lies at the heart of Thomas Bradwardine’s solution to the insolubles, logical puzzles such as the semantic paradoxes, presented in Oxford in the early 1320s. His leading assumption was that signification is closed under consequence, that is, that a proposition signifies everything which follows from what it signifies. Then any proposition signifying its own falsity, he showed, also signifies its own truth and so, since it signifies things which cannot both obtain, it is simply false. Bradwardine himself, and his contemporaries, did not elaborate this pluralist theory, or say much in its defence. It can be shown to accord closely, however, with the prevailing conception of logical consequence in England in the fourteenth century. Recent pluralist theories of signification, such as Grice’s, also endorse Bradwardine’s closure postulate as a plausible constraint on signification, and so his analysis of the semantic paradoxes is seen to be both well-grounded and plausible.

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Notes

  1. A new edition of the text, with English translation, can be found in (Bradwardine 2008). (An earlier but unreliable text is found in [Roure 1970]).

  2. This passage occurs in an additional chapter found in only two of the thirteen manuscripts: see §2 below.

  3. Bradwardine (2008) §ad A.4.3: “It must be said that any proposition signifying itself not to be true or itself to be false necessarily signifies itself to be true, as was decisively shown above by the second thesis.”

  4. See (Martin 1984: p. 4)

  5. The Latin terms are simpliciter (absolutely) and ut nunc (as a matter of fact).

  6. Explicit Insolubilium tractatus Magistri Thome de Anglia (“Here end the Insolubles of Master Thomas of England”).

  7. The Latin terms are significare precise (signify exactly) and pretendere (say explicitly).

  8. The Latin terms are ex impossibili quodlibet and necessarium ad quodlibet, respectively.

  9. The Latin terms are consequentia formalis de forma (formal consequence in form) and consequentia formalis de materia (formal consequence in matter).

  10. The Latin terms contrast signifying naturaliter (naturally) as against ad placitum or voluntarie (conventionally).

  11. Grice (1989): pp. 214–215.

  12. Grice (1989): p. 349; cf. p. 291.

  13. Ockham (William of Ockham 1974) I 1 p. 8: “And in this way a sound signifies naturally, just as any effect signifies at least its cause, and also just as the barrel-hoop signifies wine in the tavern.”

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Read, S. Plural signification and the Liar paradox. Philos Stud 145, 363–375 (2009). https://doi.org/10.1007/s11098-008-9236-y

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