Can silence be a proper response to the liar paradox?

  • Dilin Li

Student thesis: Master's Thesis


Many attempts at solving the liar paradox involve either rejecting some principles in classical logic so as to block the argument that leads to the contradiction or modifying the notion of truth so that the liar sentence can be classified as true in one aspect while false in another. However, the prominent approaches based the above strategies may suffer from the revenge problem. That is, while they solve the pristine liar paradox, the introduction of the solution triggers another one with the same structure. In this dissertation, three prominent approaches to the liar paradox are first introduced and examined. In particular, they are, first, the Tarskian hierarchical approach, whose main idea can be roughly characterized as that a natural language is a hierarchy of a series of languages and the liar sentence is true at one level of the hierarchy and is false at another; second, Saul Kripke's paracomplete approach, whose main idea can be roughly characterized as that the liar sentence is ungrounded and has no classical truth value at all; finally, Gupta and Belnep's revision theory of truth, the main idea of which is that truth is a circular concept and that the truth predicate is circularly defined. With a new semantics and logic for circular concept and definition, one can classify the liar sentence as not categorical. Based on two general patterns that give rise to the revenge paradox by Graham Priest, it is shown that none of the above approaches can escape the revenge paradox, at least, not satisfactorily. After the examination of three prominent approaches, I provide an initial characterization of a kind of approach which I call the silence approach. The main idea of the silence approach is that, perhaps what the liar paradox teaches us is that the semantic status of the liar sentence is eventually not classifiable, in the sense that the accepted or correct semantic theory for natural language simply does not apply to the liar sentence. There are two theoretical possibilities that can evoke the failure of classification. Either there is just no semantic category that fits the liar sentence or the necessary principles for the classification do not apply to the sentence. In either case, the silence approach suggests that although the liar sentence could have a semantic status according to the accepted or correct semantic theory, but given that we cannot classify it, we cannot know it. In this dissertation, I do not provide a detailed and well-developed theory of the silence approach. Instead, after the initial characterization of this approach, I go on to introduce and examine two current theories on the liar paradox which I think satisfy at least part of my characterization of the silence approach. The first theory is the semantic epistemicism by Paul Horwich. The second one is what I call exceptional theory, which is given by Thomas Hofweber. The result of the examination is that, both theories can indeed be interpreted as a silence approach. However, although they can block both the pristine liar paradox and the revenge paradox, they suffer severely from the problem of being ad hoc. The current conclusion of this dissertation about the silence approach thus is that, it is possible to construct a silence approach which can block the pristine liar paradox and the revenge, but it is hard to find a rationale for the solution. That is, it is hard to answer the question as to why the liar sentence is not classifiable. Finally, as an overlook to the future development of the silence approach, I suggest that even if we can solve the problem of ad hocness, there remains a question as to whether the incompleteness of classification is a symptom revealing that the accepted semantic theory is defective, or it is a symptom showing that there is just no possible semantic theory that can eventually do the job. Without answering this question, the silence approach still lacks a plausible theoretical ground

Date of Award18 Nov 2020
Original languageEnglish
SupervisorStephen R PALMQUIST (Supervisor)

User-Defined Keywords

  • Liar paradox
  • Silence (Philosophy)
  • Semantics (Philosophy)

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