The truth-tellers paradox

Alexandre Billon

Abstract


Ttler=‘Ttler is true’ says of itself that it is true. It is a truth-teller. I argue that we have equally telling arguments (i) to the effect that all truth-tellers must have the same truth-value (ii) and the effect that truth-tellers differ in truth-value. This is what I call the Truth-Tellers paradox. This paradox stems from the fact that the truth-value of a truth-teller like Ttler should be determined by the fact that it says of itself that it is true (which entails (i)) but that it cannot be determined by that fact (as witnessed by (ii)). The Truth-Tellers paradox resembles the classical semantic paradoxes like the Liar. In both cases, a form of self-reference allows us to derive a contradiction from otherwise plausible semantic and logical principles. Furthermore the Truth-Tellers paradox can be formulated without using sentences which are in an intuitive sense ungrounded, it thus severs the link, almost universally taken for granted, between the semantic paradoxes and ungroundedness. Finally, some classical solutions to the Liar do not generalize to the Truth-Tellers paradox.

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