<p>This sentence is whatever truth is <em>not</em>. The subject of this master’s thesis is the power, influence, and solvability of the liar paradox. This paradox can be constructed through the application of a standard conception of truth and rules of inference are applied to sentences such as the first sentence of this abstract. The liar has been a powerful problem of philosophy for thousands of years, from its ancient origin (examined in Chapter One) to a particularly intensive period in the twentieth century featuring many ingenious but ultimately unsuccessful solutions from brilliant logicians, mathematicians and philosophers (examined in Chapter Two, Chapter Three, and Chapter Four). Most of these solutions were unsuccessful because of a recurring problem known as the liar’s revenge; whatever truth is <em>not</em> includes, as it turns out, not <em>just</em> falsity, but also meaninglessness, ungroundedness, gappyness, and so on. The aim of this master’s thesis is to prove that we should not consign ourselves to the admission that the liar is and always will just be a paradox, and thus unsolvable. Rather, I argue that the liar <em>is</em> solvable; I propose and defend a novel solution which is examined in detail in the latter half of Chapter Two, and throughout Chapter Three. The alternative solution I examine and endorse (in Chapter Four) is not my own, owing its origin and energetic support to Graham Priest. I argue, however, for a more qualified version of Priest’s solution. I show that, even if we accept a very select few true contradictions, it should <em>not</em> be assumed that inconsistency inevitably spreads throughout other sets of sentences used to describe everyday phenomena such as motion, change, and vague predicates in the empirical world.</p> / Master of Arts (MA)

My thesis aims at contributing to classifying the Liar-like paradoxes (and related Truth-teller-like expressions) by clarifying distinctions and relationships between these expressions and arguments. Such a classification is worthwhile, firstly, because it makes some progress towards reducing a potential infinity of versions into a finite classification; secondly, because it identifies a number of new paradoxes, and thirdly and most significantly, because it corrects the historically misplaced distinction between semantic and set-theoretic paradoxes. I emphasize the third result because the distinction made by Peano [1906] and supported by Ramsey [1925] has been used to warrant different responses to the semantic and set-theoretic paradoxes. I find two types among the paradoxes of truth, satisfaction and membership, but the division is shifted from where it has historically been drawn. This new distinction is, I believe, more fundamental than the Peano-Ramsey distinction between semantic and set-theoretic paradoxes. The distinction I investigate is ultimately exemplified in a difference between the logical principles necessary to prove the Liar and those necessary to prove Grelling’s and Russell’s paradoxes. The difference relates to proofs of the inconsistency of naive truth and satisfaction; in the end, we will have two associated ways of proving each result. ¶ Another principled division is intuitively anticipated. I coin the term 'hypodox' (adj.: 'hypodoxical') for a generalization of Truth-tellers across paradoxes of truth, satisfaction, membership, reference, and where else it may find applicability. I make and investigate a conjecture about paradox and hypodox duality: that each paradox (at least those in the scope of the classification) has a dual hypodox.¶ In my investigation, I focus on paradoxes that might intuitively be thought to be relatives of the Liar paradox, including Grelling’s (which I present as a paradox of satisfaction) and, by analogy with Grelling’s paradox, Russell’s paradox. I extend these into truth-functional and some non-truth-functional variations, beginning with the Epimenides, Curry’s paradox, and similar variations. There are circular and infinite variations, which I relate via lists. In short, I focus on paradoxes of truth, satisfaction and some paradoxes of membership. ¶ Among the new paradoxes, three are notable in advance. The first is a non-truth functional variation on the Epimenides. This helps put the Epimenides on a par with Curry’s as a paradox in its own right and not just a lesser version of the Liar. I find the second paradox by working through truth-functional variants of the paradoxes. This new paradox, call it ‘the ESP’, can be either true or false, but can still be used to prove some other arbitrary statement. The third new paradox is another paradox of satisfaction, distinctly different from Grelling’s paradox. On this basis, I make and investigate the new distinction between two different types of paradox of satisfaction, and map one type back by direct analogy to the Liar, and the other by direct analogy to Russell's paradox.

<p>The purpose of this dissertation is to provide a proper treatment for two groups of logical paradoxes: semantic paradoxes and set-theoretic paradoxes. My main thesis is that the two different groups of paradoxes need different kinds of solution. Based on the analysis of the diagonal method and truth-gap theory, I propose a functional-deflationary interpretation for semantic notions such as ‘heterological’, ‘true’, ‘denote’, and ‘define’, and argue that the contradictions in semantic paradoxes are due to a misunderstanding of the non-representational nature of these semantic notions. Thus, they all can be solved by clarifying the relevant confusion: the liar sentence and the heterological sentence do not have truth values, and phrases generating paradoxes of definability (such as that in Berry’s paradox) do not denote an object. I also argue against three other leading approaches to the semantic paradoxes: the Tarskian hierarchy, contextualism, and the paraconsistent approach. I show that they fail to meet one or more criteria for a satisfactory solution to the semantic paradoxes. For the set-theoretic paradoxes, I argue that the criterion for a successful solution in the realm of set theory is mathematical usefulness. Since the standard solution, i.e. the axiomatic solution, meets this requirement, it should be accepted as a successful solution to the set-theoretic paradoxes.</p> / Doctor of Philosophy (PhD)