University of Miami Scholarly Repository Open Access Dissertations Electronic Theses and Dissertations 2011-11-29 Truth is a One-Player Game: A Defense of Monaletheism and Classical Logic Benjamin Burgis University of Miami, [email protected] Follow this and additional works at: https://scholarlyrepository.miami.edu/oa_dissertations Recommended Citation Burgis, Benjamin, "Truth is a One-Player Game: A Defense of Monaletheism and Classical Logic" (2011). Open Access Dissertations. 677. https://scholarlyrepository.miami.edu/oa_dissertations/677 This Open access is brought to you for free and open access by the Electronic Theses and Dissertations at Scholarly Repository. It has been accepted for inclusion in Open Access Dissertations by an authorized administrator of Scholarly Repository. For more information, please contact [email protected]. UNIVERSITY OF MIAMI TRUTH IS A ONE-PLAYER GAME: A DEFENSE OF MONALETHEISM AND CLASSICAL LOGIC By Benjamin A. Burgis A DISSERTATION Submitted to the Faculty of the University of Miami in partial fulfillment of the requirements for the degree of Doctor of Philosophy Coral Gables, Florida December 2011 ©2011 Benjamin A. Burgis All Rights Reserved UNIVERSITY OF MIAMI A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy TRUTH IS A ONE-PLAYER GAME: A DEFENSE OF MONALETHEISM AND CLASSICAL LOGIC Benjamin A. Burgis Approved: ________________ _________________ Otávio Bueno, Ph.D. Terri A. Scandura, Ph.D. Professor of Philosophy Dean of the Graduate School ________________ _________________ Edward Erwin, Ph.D. Risto Hilpinen, Ph.D. Professor of Philosophy Professor of Philosophy ________________ Hartry Field, Ph.D. Professor of Philosophy New York University BURGIS, BENJAMIN (Ph.D., Philosophy) Truth is a One-Player Game: A Defense of Monaletheism and (December 2011) Classical Logic Abstract of a dissertation at the University of Miami. Dissertation supervised by Professor Otávio Bueno. No. of pages in text. (241) The Liar Paradox and related semantic antinomies seem to challenge our deepest intuitions about language, truth and logic. Many philosophers believe that to solve them, we must give up either classical logic, or the expressive resources of natural language, or even the “naïve theory of truth” (according to which ! and Tr<!> [“it is true that !”] always entail each other). A particularly extreme form of radical surgery is proposed by figures like Graham Priest, who argues for “dialetheism”—the position that some contradictions are actually true—on the basis of the paradoxes. While Priest’s willingness to dispense with the Law of Non-Contradiction may be unpopular in contemporary analytic philosophy, figures as significant as Saul Kripke and Hartry Field have argued that, in light of the paradoxes, we can only save Non-Contradiction at the expense of the Law of the Excluded Middle, abandoning classical logic in favor of a “paracomplete” alternative in which ! and ¬! can simultaneously fail to hold. I believe that we can do better than that, and I argue for a more conservative approach, which retains not only “monaletheism” (the orthodox position that no sentence, either in natural languages or other language, can have more than one truth-value at a time), but the full inferential resources of classical logic. For Ryan, who told me he’d only pay my bar tab if I agreed to do my Ph.D. at Miami. """! ! Acknowledgements I’d like to acknowledge the help and encouragement of my excellent advisor, Otávio Bueno. He got me interested in these questions in my first year of graduate work at Miami and he has helped me bounce around my ideas about them, and helped me refine and sharpen those ideas in light of his endless stream of objections and counter- arguments, ever since. I’d like to thank my good friends Ryan Lake, for coining the word in the title, Robin Neiman, for telling me that this would make a more interesting dissertation project than the alternative I’d been considering during my last semester of coursework, and Mark Warren, for many hours of fruitful philosophical conversation over glasses of peaty and delicious single malt whisky. I’d be absurdly remiss if I didn’t also thank my wonderful parents, Richard and Kathy Burgis, for inadvertently planting the seeds of my interest in logic by going through a great many math problems with me with a ballpoint pen and various El Azteco restaurant napkins over the course of my childhood. (At the time, I wasn’t always grateful.) I’d obviously like to think my committee members Risto Hilpinen and Ed Erwin, and my outside member Hartry Field, a giant in the field who I felt honored to work with. Finally, I’d be remiss if I didn’t thank Graham Priest, whose arguments functioned like water balloons dropped from a great height on my sleeping head, to force me to wake up, confused and alarmed, from my dogmatic slumber. "#! ! Table of Contents Chapter One: Monaletheism and Dialetheism 1 Chapter Two: The Very Possibility of the Debate 17 Chapter Three: Motivations for Dialetheism 41 Chapter Four: Liars and Gluts 78 Chapter Five: Liars and Gaps 94 Chapter Six: Liars and Meaninglessness 110 Chapter Seven: Meaninglessness and Revenge 136 Chapter Eight: $%&'&!('&!)*!$'+&!,*-.'/0"1."*-2! 154 Chapter Nine: 3*-/4&.%&"25!/-0!)&6/."*-! 789! ! :&;&'&-1&2! <=8 #!! Chapter One: Dialetheism And Monaletheism Dialetheism, also called “strong paraconsistency,” is the position in the philosophy of logic, championed chiefly by Graham Priesqt, according to which there are true statements of the form (! " ¬!). By contrast, less extreme paraconsistent views either reject or are agnostic about the possibility of true contradictions, but still reject the classical principle that “from a contradiction, everything follows” for various other reasons. If dialetheism is at the far left wing of the spectrum and weaker forms of paraconsistency are somewhere in the middle, I situate myself at the extreme right: There are no true contradictions. As such, the “explosion” of inferences derivable from contradictions in classical logic is (vacuously) truth-preserving, and we have no good reason to reject classical logic in favor of any sort of weaker, inconsistency-tolerant (or “paraconsistent”) logical framework. My perspective is classical monism, the claim that classical logic is currently our best overall theory of the world (that is to say, of which inferences are truth-preserving and hence of what’s true), relative to the level of abstractness and generality at which formal logics operate. In what follows, I will be defending that view against the dialetheist challenge. Debates about whether dialetheism is correct are often described as debates about the Law of Non-Contradiction, but that isn’t quite right. If the Law of Non-Contradiction is simply a logical formula that tells us that for any conjunction of a statement and its 1 2 negation, the negation of that conjunction is true, there is no reason that a dialetheist should have to deny this in order to be a dialetheist, so long as they hold that some such conjunctions are also true. It is simply the case that for any ! such that (! " ¬!) is a true contradiction, [(! " ¬!) " ¬(! " ¬!)] is also a true contradiction.1 As such, we might do better to think of the orthodox logical position that the dialetheist is challenging not as “the Law of Non-Contradiction,” but as “monaletheism.”2 Just as dialetheism is the claim that a statement can have both of the values “true” and “false,” monaletheism is the claim that no statement can have more than one of them at a time.3 Note first of all that monaletheism--like dialetheism--is neutral about whether there can be “truth-value gaps,” statements that are neither true nor false.4 (We will return 1 More to the point, not only could the dialetheist take this position on the LNC (after all, they could take it on anything!), but important dialetheists do take exactly this stand, adopting the LNC as a logical truth in their preferred logics at the same time as they assert that it has true exceptions. Interesting alternate suggestions that might also do the expressive work for which I’m adopting “monaletheism” are ‘the LNC taken as a metaphysical principle’ and ‘the rationality LNC.’ The former is due to Takho (2009), pp. 32-47, and the latter is due to Beall (2009), p. 101. In the former case, I decline to use it (despite a sense that Takho is getting at much the same idea that I am) because Takho means only to rule out Graham Priest’s “metaphysical dialetheism,” whereas I also want to rule out positions like Edwin Mares’ “semantic dialetheism” and Beall’s version of dialetheism (according to which there would be no true contradictions if we hadn’t enhanced our language with a truth predicate as a convenient expressive tool for making certain sorts of generalizations) as well. In the latter case, my hesitation is due to the fact that the ‘Rationality LNC’ is expressed in acceptance/rejection talk, and (as discussed in Chapter Seven, when we to a revenge paradox about rejection), I don’t think that, given the Liar reasoning Beall endorses in other cases, acceptance/rejection talk can do the work in clarifying different positions on truth and paradox that Beall thinks it does. 2 Thanks to Ryan Lake for coining this word, in conversation. 3 The issue of whether, as some proponents of the A-Theory of Time argue, propositions change truth- values over time, or, as B-Theorists have it, they have eternal and unchanging truth-values, is a separate issue that need not concern us here. 4 Even if some very prominent dialetheists like Priest reject the possibility of gaps that are not gluts, that doesn’t mean that dialetheism itself is incompatible with gap theory.