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Ahmad, Rashed. A Recipe for Paradox
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, 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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Grover, Dorothy, Joseph Kamp, Nuel Belnap. A Prosentential Theory of Truth
1975, Philosophical Studies 27(1): 73-125.
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Added by: Jamie Collin
Summary: Classic presentation of the prosentential theory of truth: an important, though minority, deflationist account of truth. Prosententialists take 'It is true that' to be a prosentence forming operator that anaphorically picks out content from claims made further back in the anaphoric chain (in the same way that pronouns such as 'he', 'she' and 'it' anaphorically pick out referents from nouns further back in the anaphoric chain).

Comment: Good as a primary reading on a course on truth, philosophy of language, or on deflationism more generally. Any course that treats deflationary accounts of truth in any detail would deal with the prosentential theory of truth, and this is one of the most historically important presentations of that theory. Would be best used in advanced undergraduate or graduate courses.

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Grover, Dorothy. How Significant is the Liar?
2008, In J. C. Beall & Bradley Armour-Garb (eds.), Deflationism and Paradox. OUP Oxford.
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Added by: Jamie Collin
Summary: Grover argues that one should be unconcerned about the liar paradox. In formal languages there are uniform ties between syntax and semantics: a term, in all its occurrences, carries a fixed meaning; and sequences of sentences that are (syntactically) proofs are always (semantically) inferences. These two features do not hold of natural languages. Grover makes use of this claim to argue that there are no arguments to contradictions from liar sentences in natural languages, as the relevant syntactic 'moves' do not come with relevant semantic 'moves'.

Comment: This would be useful in a course on truth, the philosophy of language or paradoxes. It provides a very up to date account of the prosentential theory of truth and how it may be able to deal with semantic paradoxes. Not as technical as some literature on the topic.

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Grover, Dorothy. Inheritors and Paradox
1977, Journal of Philosophy 74(10): 590-604
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Added by: Jamie Collin
Summary: Classic account of the way in which the prosentential theory of truth handles the liar paradox. Prosententialists take 'It is true that' to be a prosentence forming operator that anaphorically picks out content from claims made further back in the anaphoric chain (in the same way that pronouns such as 'he', 'she' and 'it' anaphorically pick out referents from nouns further back in the anaphoric chain). Liar sentences have no proposition-stating antecedents in the anaphoric chain. As a result, the problem of the liar does not arise.

Comment: Good as a primary reading on a course on truth, paradox, philosophy of language, or on deflationism more generally. Any course that treats deflationary accounts of truth in any detail would deal with the prosentential theory of truth, and this is one of the most historically important presentations of that theory. This is particularly useful in courses on paradox, as it is a rare articulation of the idea that the liar paradox is not "deep" and does not require large revisions to classical logic. Would be best used in advanced undergraduate or graduate courses.

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Gupta, Anil. A Critique of Deflationism
1993, Philosophical Topics 21: 57-81.
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Added by: Jamie Collin
Summary: Argues against deflationary conceptions of truth. Deflationism provides a descriptive account of the term 'true', but these claims, argues Gupta, are both very strong and problematic.

Comment: This would be very useful in a course on the nature of truth, or any course in which deflationary conceptions of truth are relevant. The paper is not technical and provides a good account of deflationism about truth. This would be suitable for undergraduates or graduates.

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Gupta, Anil. Do the Paradoxes Pose a Special Problem for Deflationism?
2006, In J. C. Beall and Bradley Armour-Garb (eds.), Deflationism and Paradox, Oxford University Press. 133-147.
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Added by: Jamie Collin
Summary: The Liar and other semantic paradoxes pose a difficult problem for all theories of truth. Any theory that aims to improve our understanding of the concept of truth must, when fully stated, include an account of the paradoxes. Not only deflationism but also its competitors - for instance, correspondence and coherence - must ultimately address the paradoxes. The question that concerns me in this essay is whether it is especially urgent for deflationism to do so. Are the paradoxes a special threat, a special problem, for deflationism? I will argue that they are not.1 Deflationists can leave the paradoxes to the specialists to puzzle over. It is the specialists who will be well served if they keep some insights of deflationism firmly in view.

Comment: This would be useful in a course on the nature of truth, or on paradoxes. This is slightly more specialised than 'A Critique of Deflationism' but still good reading material for an advanced undergraduate or graduate course. The paper is not easy, but clear and not very technical.

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Gupta, Anil. Truth
2001, In Lou Goble (ed.), The Blackwell Guide to Philosophical Logic. Blackwell
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Added by: Franci Mangraviti
Abstract:

The concept of truth serves in logic not only as an instrument but also as an object of study. Eubulides of Miletus (fl. fourth century BCE), a Megarian logician, discovered the paradox known as ‘the Liar,’ and, ever since his discovery, logicians down the ages - Aristotle and Chrysippus, John Buridan and William Heytesbury, and Alfred Tarski and Saul Kripke, to mention just a few - have tried to understand the puzzling behavior of the concept of truth.

Comment: Can be used in an advanced course on (formal approaches to) truth or the Liar paradox. Familiarity with the semantics of first-order classical logic and transfinite induction is assumed (for the latter, Ch.3 of the Blackwell Guide might be of help - using the Blackwell Guide as a blueprint may also be a way to incorporate this reading in a general advanced course on philosophical logic).

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