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Abstract: Radical sceptical possibilities challenge the anti-realist view that truth consists in ideal rational acceptability. Putnam, as part of his defence of an anti-realist view, subjected the case of the brain in a vat to a semantic externalist treatment, which aimed to maintain the desired connection between truth and ideal rational acceptability. It is argued here that self-consciousness poses special problems for this externalist strategy. It is shown how, on a standard model of first-person reference, Putnam's brain in a vat will be mistaken in its rational self-ascription of externalist predicates. The natural response, which employs an alternative model of first-person reference, is shown to have the equally realist consequence that there are enquiry-transcendent truths about the self.