A Defense of Trivialism Paul Douglas Kabay Submitted in total fulfillment of the requirements of the degree of Doctor of Philosophy August 2008 School of Philosophy, Anthropology, and Social Inquiry The University of Melbourne Abstract That trivialism ought to be rejected is almost universally held. I argue that the rejection of trivialism should be held in suspicion and that there are good reasons for thinking that trivialism is true. After outlining in chapter 1 the place of trivialism in the history of philosophy, I begin in chapter 2 an outline and defense of the various arguments in favor of the truth of trivialism. I defend four such arguments: an argument from the Curry Paradox; and argument from the Characterization Principle; an argument from the Principle of Sufficient Reason; and an argument from the truth of possibilism. In chapter 3 I build a case for thinking that the denial of trivialism is impossible. I begin by arguing that the denial of some view is the assertion of an alternative view. I show that there is no such view as the alternative to trivialism and so the denial of trivialism is impossible. I then examine an alternative view of the nature of denial – that denial is not reducible to an assertion but is a sui generis speech act. It follows given such an account of denial that the denial of trivialism is possible. I respond to this in two ways. First, I give reason for thinking that this is not a plausible account of denial. Secondly, I show that even if it is successful, the denial of trivialism is still unassertable, unbelievable, and severely limited in its rationality. In chapter 4 I examine two important arguments that purport to show that it is impossible to believe in trivialism: one from Aristotle and a more recent one from Graham Priest. According to Aristotle, it is not possible to believe in trivialism because such a belief is incompatible with being able to act in a discriminating manner. 2 According to Priest, belief in trivialism is incompatible with being able to act with a purpose. I show that there are a number of ways to respond to such arguments, and so it is far from obvious that it is impossible to believe in trivialism. In chapter 5 I reply to one of the few sustained arguments against the truth of trivialism. According to this argument, trivialism cannot be true because it entails that every observable state of affairs is contradictory - which is clearly not the case. After raising a number of objections to this line of reasoning, I argue that a contradictory state of affairs will necessarily appear consistent. As such, that the world appears consistent is not a good reason for thinking that it fails to be contradictory. In chapter 6 I defend the claim that the observable world is indeed contradictory in the way that trivialism implies. I show that a dialetheic solution to Zeno’s paradox of the arrow requires one to postulate that a body in motion is located at every point of the path of its journey at every instant of the journey. 3 Declaration This is to certify that i. the thesis comprises only my original work towards the PhD, ii. due acknowledgement has been made in the text to all other material used, iii. the thesis is less than 100,000 words in length, exclusive of tables, maps, bibliographies and appendices. Signed ______________________________________ 4 Preface The majority of chapter 5 was published in my article “When seeing is not Believing: A Critique of Priest’s Argument from Perception,” Australasian Journal of Philosophy 84, no. 3 (2006): 443-60. 5 Acknowledgements It never ceases to astound me that Graham Priest was willing to take this project seriously enough to act as its supervisor – a clear demonstration of the philosophical spirit. He was always attentive and thorough – and never short on criticism. Thanks Graham. Thank you to my parents, Dave and Dale, for all the encouragement and financial support - the thesis would have been rather difficult to write without this. But the thing that really got me through this was my own little family – without them I see little reason to do anything. I love you Pidor, Elfine, Roy, and Basil. I dedicate this thesis to the little one growing in Pidor’s womb. I can’t wait to hold you. 6 Table of Contents Introduction 10 Chapter 1: A History of Trivialism 1. What is Trivialism and What do People think of it? 29 2. The Pre-Socratics 32 3. Nicholas of Cusa 36 4. Spinoza 37 5. Hegel 40 6. Hua-Yen Buddhism 41 7. Azzouni: a modern advocate 42 Chapter 2: Arguments for Trivialism 1. Introductory Comments 48 2. The Explosive Liar 49 3. The Curry Paradox 54 4. The Argument from the Characterization Principle 56 5. The Argument from Possibilism 63 6. A Cosmological Argument for a Trivial Entity 68 7. Concluding Remarks 76 Chapter 3: On the Impossibility of the Denial of Trivialism 1. Introductory Comments 77 7 2. What does it mean to deny something? 79 3. The Denial of Trivialism is Impossible 85 4. The Consequences of the Impossibility of the Denial of Trivialism 92 5. What if Denial is Sui Generis Speech Act? 97 6. Concluding Remarks 103 Chapter 4: Is it Possible to Believe in Trivialism? 1. Is it Possible to Believe in Trivialism? 106 2. Is Belief in Trivialism Compatible with Discriminating Behavior? 109 3. First Response to Aristotle 113 4. Is Belief in Trivialism Compatible with Purposeful Behavior? 115 5. First Response to Priest 117 6. Response 2: Need the Trivialist Believe Everything Entailed by Trivialism? 121 7. Response 3: Have Priest and Aristotle Misunderstood the Nature of Belief? 128 8. Concluding Remarks 131 Chapter 5: Is it Possible to Observe a Contradictory State of Affairs? 1. The Argument 134 2. Various Objections 139 3. Contradictory Perceptions as Non-Veridical: The Case of Escher’s Belvedere 143 8 4. The Inconsistent Observer 149 5. Do the Conjuncts of a Contradiction Act Independently? 158 Chapter 6: Zeno’s Arrow Paradox and the Contradictory Nature of the World 1. Introduction 168 2. The Orthodox Account of Motion 169 3. Zeno’s Paradox of the Arrow 170 4. Priest’s Hegelean Solution to the Paradox of the Arrow 175 5. A New Version of the Paradox of the Arrow 178 6. The Arrow Paradox and the Ontology of Points 181 7. A Solution to the New Paradox of the Arrow 184 8. Various Objections 185 9. Is this Really an Improvement for the Hegelean Theory of Motion? The Problem of Perception 190 Conclusion: Summary and Existential Implications 194 Bibliography 200 9 Introduction It is a characteristic of humans that they are stingy in their dealings with reality (a fact that is also reflected in their dealings with one another). Their sciences and logical systems all seem to have in common the fact that they privilege off a certain class of propositions as true – the rest are left to flounder as second class citizens. But Reality does not so discriminate. Unlike humans, Being exhibits a generosity that is without limit, and it will not allow itself to be contained by the rationings of mere humans. In this thesis I argue for the truth of a claim that, to put it mildly, violates commonsense in a way that no other philosophical theory to date has achieved. In this regard it even surpasses Berkeley’s idealism or Lewis’s modal realism or the Indian philosophy of Advaita Vedanta. I have in mind here the theory of trivialism. Trivialism is the claim that every proposition is true. This is such a bizarre view that one wonders why anyone would have taken an interest in it – let alone think that it is true. The reason why there is an interest in trivialism is due to the fact that there has been a revival in a view known as dialetheism - the claim that some contradictions are true. Trivialism is often understood as an extreme form of dialetheism (all, as opposed to some, contradictions are true). There has been pressure on dialetheists to distinguish their own view from trivialism. There is no doubt that there is a tendency to conflate the two. This dates back to Aristotle’s formulation and defense of the Law of Non- Contradiction in his Metaphysics Γ.1 It is clear, given Aristotle’s intended target, that he is 1 Aristotle, The Metaphysics , 86-110. Although not everyone agrees that Aristotle is making a mistake here. Berto, How to Sell a Contradiction , 279-80, argues that Aristotle was onto something quite significant concerning the relationship between dialetheism and trivialism. 10 often defending the Law of Non-Triviality, i.e. the law that there is at least one proposition that fails to be true. So, these passages are misunderstood if they are interpreted to be an attack on dialetheism solely and not also trivialism. But the temptation to conflate the two positions remains today. Priest reports that: I often find myself being asked the following question: ‘Since you believe some contradictions, but not all, you must have a criterion for deciding between those that are true and those that are not. What is it?’ 2 According to Priest, the implication of such a query is that the questioner is unable to see how the slippery slope toward trivialism can be avoided. But, of course, there is a reason intrinsic to classical logic that is the probable source of the accusation that dialetheism amounts to, or at least leads to, trivialism.