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.
Truth
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.
A Recipe for Paradox
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.
How Significant is the Liar?
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’.
Do the Paradoxes Pose a Special Problem for Deflationism?
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.
A Critique of Deflationism
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.
Inheritors and Paradox
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.
A Prosentential Theory of Truth
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).