Free Assumptions and the Liar Paradox

1998

It is proposed that "This sentence is not true" may be true under some interpretations and false under others. The revenge challenge given by "This sentence is false in at least one interpretation" is handled through the observation that a sentence is arguable true under all interpretations if and only if it is provable. This makes the revenge challenge equivalent to the one given by "This sentence is not provable." Apart from arguing a link with Gödel's first incompleteness theorem we also argue that the way a Liar sentence may be true under one interpretation and false under another is related to the way a "many-valued function" in mathematics may have more than one value. We set up a mathematical framework where sentences may be given many different interpretations. Examples are also given of how Liar sentences may be given many interpretations in practice depending on the intentions of speakers and how they are understood, and our approach to dealing with Liar sentences is compared to those of others.

It seems that the most common strategy to solve the liar paradox is to argue that liar sentences are meaningless and, consequently, truth-valueless. The other main option that has grown in recent years is the dialetheist view that treats liar sentences as meaningful, truth-apt and true. In this paper I will offer a new approach that does not belong in either camp. I hope to show that liar sentences can be interpreted as meaningful, truth-apt and false, but without engendering any contradiction. This seemingly impossible task can be accomplished once the semantic structure of the liar sentence is unpacked by a quantified analysis. The paper will be divided in two sections. In the first section, I present the independent reasons that motivate the quantificational strategy and how it works in the liar sentence. In the second section, I explain how this quantificational analysis allows us to explain the truth teller sentence and a counter-example advanced against truthmaker maximalism, and deal with some potential objections.

Principia: an international journal of epistemology, 2018

In this paper we intend to outline an introduction to Situation Theory as an approach to the liar paradoxes. This idea was first presented by the work of Barwise and Etchemendy (in their (1987)). First (section 1) we introduce the paradoxes in their most appealing and important versions. Second (section 2) we show that non-classical approaches on the problem usually get puzzled by the revenge problem on one side and loss of expressive power on the other side. Last (sections 3 and 4), we present Situation Theory and try to show how it is capable of solving the old paradoxes and blocking revenge. The price we pay on this view is universality, since it would allow a new revenge situated liar. We don’t intend to address the problem of universality here, but we try at least to motivate the reader to make sense of this theory.

In The Philosophy of David Kaplan, Edited by J. Almog and P. Leonardi, Oxford University Press, 2009

Lecture Notes in Computer Science, 2012

We model lying as a communicative act changing the beliefs of the agents in a multi-agent system. With Augustine, we see lying as an utterance believed to be false by the speaker and uttered with the intent to deceive the addressee. The deceit is successful if the lie is believed after the utterance by the addressee. This is our perspective. Also, as common in dynamic epistemic logics, we model the agents addressed by the lie, but we do not (necessarily) model the speaker as one of those agents. This further simplifies the picture: we do not need to model the intention of the speaker, nor do we need to distinguish between knowledge and belief of the speaker: he is the observer of the system and his beliefs are taken to be the truth by the listeners. We provide a sketch of what goes on logically when a lie is communicated. We present a complete logic of manipulative updating, to analyse the effects of lying in public discourse. Next, we turn to the study of lying in games. First, a game-theoretical analysis is used to explain how the possibility of lying makes games such as Liar's Dice interesting, and how lying is put to use in optimal strategies for playing the game. This is the opposite of the logical manipulative update: instead of always believing the utterance, now, it is never believed. We also give a matching logical analysis for the games perspective, and implement that in the model checker DEMO. Our running example of lying in games is the game of Liar's Dice.

Truth and Paradox, 2004

Reviews the standard semantic paradoxes, and constructs a simple formal language in which the paradoxical reasoning can be reconstructed. Particular attention is paid to Löb's paradox, which allows for the derivation of any sentence in the language as a theorem. The advantages of a natural deduction system over an axiomatic logic is discussed.

2006

Stephen Read’s criticism of Buridan’s solution of the Liar Paradox is based on the charge that while this solution may avoid inconsistency, it does so at the expense of failing to provide a theory of truth. This paper argues that this is one luxury Buridan’s logical theory actually can afford: since Buridan does not define formal consequence in terms of truth (and with good reason), his logic simply does not need it. Therefore, Buridan’s treatment of the paradox should be regarded as an attempt to eliminate a problem concerning the possibility of the consistent use of semantic predicates under the conditions of semantic closure, rather than as an attempted solution of a problem for a theory of truth. Nevertheless, the concluding section of the paper argues that Buridan’s solution fails, because it renders his logical theory inconsistent. A postscript, however, briefly considers an interpretation that may quite plausibly save the consistency of Buridan’s theory.

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2018

SU M M A RY: Our approach to the liar paradox is based on the Wittgensteinian approach to semantic and logical paradoxes. The main aim of this article is to point out that the liar sentence is only seemingly intelligible, and that it has not been given any sense. First, we will present the traditional solutions of the paradox, especially those which we call modificational. Then we will determine what the defects of these solutions are. Our main objection is that the modificational approaches assume that we can express in languages certain senses which are improper. Next, we will explain why we think that the liar sentence is a mere nonsense. This sentence does not have any role in any language game – it is completely useless. We will also respond to several objections to our approach. 1. That it is not consistent with the principle of compositionality of sense. 2. According to the Quineian philosophy of logic, paradoxical sentences can be conceived as false assumptions leading to cr...