Understanding, proofs, and compositionality
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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In Michael Dummett’s manifestability challenge to truth conditional semantics, it is argued that the meaning of sentence cannot be its truth conditions, for then a speaker’s knowledge of the meaning would not in all cases be manifestable. In those cases, the speaker would not know how to ﬁnd out whether the truth conditions are satisﬁed or not. By contrast, knowledge of what counts as a proof of a sentence would pass the manifestability test, since a speaker is supposed always to be capable of deciding whether or not a given object is a proof of a given sentence. There is a problem for the positive part, however, for there is no guarantee that a compositional proof-theoretic semantics in all cases provides knowledge suﬃcient for recognizing any proof of a provable sentence for which the meaning is given. In those cases, the speaker need not know how to ﬁnd out whether a given object is a proof of the sentence. Hence, if knowledge of meaning is required to be manifestable, there is no guarantee in general is compositionally speciﬁable.
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