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The results reported in this essay were obtained for the most part in February and March 1980 during my stay at the University of Pittsburgh. I discussed these results in informal talks given at the University of Pittsburgh in March and April 1980, and in my seminar on logic given in the Fall of 1980 at McGill University. More recently, talks based on this paper were given at Syracuse University (November 1981) and at the Eastern Division meetings of the American Philosophical Association (December 1981).
In preparing this essay I have incurred a number of debts. My first and foremost is to my teacher and friend Professor Nuel Belnap. During my stay in Pittsburgh in the Winter semester of the academic year 1979–80, he willingly and generously spent many hours working with me on the ideas reported here. He helped me to find my way out of numerous blind alleys, and he made numerous positive suggestions that have greatly benefitted my work. The proof of the main lemma given in section II, in particular, would have been much more inelegant were it not for his suggestions. It would be difficult now to detail his contributions exactly. Let me just say that they are very great indeed. At Pittsburgh, I also benefitted from discussions with Professor Richmond Thomason. He raised the question of how non-vicious reference should be defined. My answer to his question is given in the definition of the Thomason model (Section IV). To Professor Allen Hazen I am indebted for correspondence on the problem of the paradoxes and for useful comments on the first draft. Professor John Macnamara also read the first draft and made numerous suggestions for improvement. With my student Mr. John Hawthorn, who is writing his doctoral dissertation on the liar paradox, I have had fruitful discussions for over three years. I have discussed this subject with many other people as well. I would like to mention especially David Conter, Steven Davis, François Dongier, Vishwas Govitrikar, Dorothy Grover, Lily Knezevich, Storrs McCall and Michel Paquette.
As the present essay was nearing completion, I received three recent papers from Professor Hans Herzberger: his “Notes on Naive Semantics”, “Notes on Periodicity”, and “Naive Semantics and the Liar Paradox”. These papers develop a theory which is, in many respects, similar to the one presented in this essay. Professor Herzberger has studied the notions of stability, paradoxicality, etc., in the context of Definition 2. The main areas of overlap in the results we have obtained appear to be facts 4 to 11. The main area that he has studied that I have not is the cycling of the revision process. I hope to take account of his important work on cycling in a later essay.
I have not attempted to deal with all the approaches to the paradoxes that are found in the literature. I have discussed only those that give (or attempt to give) a systematic solution to the first problem of Section I. The bibliography lists the most important recent papers on the liar paradox known to me.
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Gupta, A. Truth and paradox. J Philos Logic 11, 1–60 (1982). https://doi.org/10.1007/BF00302338
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DOI: https://doi.org/10.1007/BF00302338