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Ahmad, Rashed. A Recipe for Paradox
2022 2022, Australasian Journal of Logic, 19(5): 254-281
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Added by: Franci Mangraviti
Abstract:

In this paper, we provide a recipe that not only captures the common structure of semantic paradoxes but also captures our intuitions regarding the relations between these paradoxes. Before we unveil our recipe, we first discuss a well-known schema introduced by Graham Priest, namely,the Inclosure Schema. Without rehashing previous arguments against the Inclosure Schema, we contribute different arguments for the same concern that the Inclosure Schema bundles together the wrong paradoxes. That is, we will provide further arguments on why the Inclosure Schema is both too narrow and too broad. We then spell out our recipe. The recipe shows that all of the following paradoxes share the same structure: The Liar, Curry’s paradox, Validity Curry, Provability Liar, Provability Curry, Knower’s paradox, Knower’s Curry, Grelling-Nelson’s paradox, Russell’s paradox in terms of extensions, alternative Liar and alternative Curry, and hitherto unexplored paradoxes.We conclude the paper by stating the lessons that we can learn from the recipe, and what kind of solutions the recipe suggests if we want to adhere to the Principle of Uniform Solution.

Comment: Appropriate for a course on logical paradoxes. Makes a natural foil to a reading defending the inclosure schema. Familiarity with sequent calculus, and with the Liar and Curry paradoxes, is required.

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Goodship, Laura. On Dialethism
1996 1996, Australasian Journal of Philosophy 74 (1):153 – 161
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Added by: Franci Mangraviti
Abstract:

The paper discusses two problems with Graham Priest's version of dialetheism: the thesis that one cannot be rationally obliged to both accept and reject something, and the use of a Contraction-less conditional in dealing with Curry paradoxes. Some solutions are suggested.

Comment: A useful supplement to any discussion of dialetheism, as the origin of what is now known in the literature as the "Goodship project". Some familiarity with Priest's account is required for context.

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