Abstract
Yehoshua Bar-Hillel and Rudolph Carnap’s classical theory of semantic information entails the counterintuitive feature that inconsistent statements convey maximal information. Theories preserving Bar-Hillel and Carnap’s modal intuitions while imposing a veridicality requirement on which statements convey information—such as the theories of Fred Dretske or Luciano Floridi—avoid this commitment, as inconsistent statements are deemed not information-conveying by fiat. This paper produces a pair of paradoxical statements that such “veridical-modal” theories must evaluate as both conveying and not conveying information, although Bar-Hillel and Carnap’s theory accommodates these statements without inconsistency. Moreover, the paradoxes are independently interesting as the mode in which they self-refer bears on their evaluation.
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Notes
Note that Alfred Tarski’s example of Tarski (1944) refers to itself by means of the definite description “[t]he sentence printed in this paper on p. 347, l. 31” and may be likewise thought of as a contingently paradoxical form of the Liar.
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Acknowledgments
I am grateful to Graham Priest and two anonymous referees for very helpful and challenging comments. Also, I appreciate the feedback of participants of the Sixth Workshop on the Philosophy of Information, especially the critical remarks of Orlin Vakarelov.
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Ferguson, T.M. Two paradoxes of semantic information. Synthese 192, 3719–3730 (2015). https://doi.org/10.1007/s11229-015-0717-1
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DOI: https://doi.org/10.1007/s11229-015-0717-1