Durham E-Theses Conceivability, Apriority and Modality WINSTANLEY, PAUL How to cite: WINSTANLEY, PAUL (2011) Conceivability, Apriority and Modality, Durham theses, Durham University. Available at Durham E-Theses Online: http://etheses.dur.ac.uk/860/ Use policy The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that: • a full bibliographic reference is made to the original source • a link is made to the metadata record in Durham E-Theses • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders. Please consult the full Durham E-Theses policy for further details. Academic Support Oce, Durham University, University Oce, Old Elvet, Durham DH1 3HP e-mail: [email protected] Tel: +44 0191 334 6107 http://etheses.dur.ac.uk Conceivability, Apriority and Modality Paul Winstanley Submitted for the degree of PhD Department of Philosophy University of Durham 2011 Abstract I aim to understand whether apriority entails necessity, aposteriority entails contingency and conceivability entails possibility; that is, the relationship between, and the nature of, rationality and modality. The thesis is split into two parts: one on apriority and modality (chs. 2-4), and another on conceivability, apriority/aposteriority and modality (chs. 5 to 7). In Chapter 1, I discuss ‘two-dimensional modal semantics’, arguing that it is ill-equipped to provide a substantive account of rationality and modality, before setting out the basis of such an understanding. I begin the first part of the thesis (in Chapter 2) by outlining a preliminary account of the a priori: it is, strictly, not defeasible by empirical evidence; it involves a kind of necessity (‘rational necessity’); and it is (at least in its prima facie variant) fallible. In Chapter 3 I discuss the contingent a priori, arguing that genuine apriority entails necessity, before placing apriority qua ‘rational necessity’ (and ‘rational modality’ more widely) with respect to other kinds of modality (in Chapter 4). I conclude Part I of the thesis, by arguing that the a priori is not coextensive with, but is grounded in, metaphysical necessity. Part II of the thesis begins with a discussion of the necessary a posteriori (Chapter 5), where I argue that there are no genuine cases, thus aposteriority entails contingency and conceivability entails possibility. I then deal with Frege’s and Kripke’s puzzles (Chapter 6), which I claim (as with the necessary a posteriori) pose no genuine problem for conceivability- possibility reasoning. Finally (in Chapter 7), I offer a deeper account of rational modality together with a tentative account of metaphysical modality (and essence). I then conclude that genuine apriority qua rational necessity entails metaphysical necessity; similarly, strictly, aposteriority (rational contingency) entails metaphysical contingency and, (in)conceivability (rational (im)possibility) entails metaphysical (im)possibility. Acknowledgements Much of the research for the thesis has been presented at seminars and conferences in the UK and Europe. In particular, Chapter 1 draws on material presented at the 2005 Durham-Bergen seminar in Bergen, Norway (subsequently published in the proceedings, as ‘Conceivabilities and possibilities’), and on a paper presented at the 2005 National Postgraduate Analytic Philosophy Conference in York (subsequently published in Percipi, as ‘Conceivability, Possibility and Two-Dimensional Semantics’). Chapter 3 draws on work presented at the First SIFA Graduate Conference in Padova, 2007 (subsequently published in the proceedings, as ‘‘I exist’: the contingent a priori and indexicality’). I am grateful to the organisers and editors concerned for allowing me to present this material here. I am further grateful to several audience members (notably Timothy Williamson) for forcing me to think more deeply about some of the relevant issues. I am, of course, deeply indebted to my supervisor, Jonathan Lowe. I should also mention Durham’s postgraduate philosophy community. I have had many very helpful discussions with Tuomas Tahko, Donnchadh O’Connaill and Michael Turp. I have also had much, general, philosophical support from my good friend, Tony Booth, who deserves a particular mention. Finally, I would like to thank my wife, Emma, for her continuing love and understanding, especially during the last, rather taxing months of the PhD. Contents Chapter 1: From Metaphysics to Semantics: Two-Dimensionalism, Rationality and Modality 1 Introduction 1 2 From Kripkean to two-dimensional semantics 4 3 The real issues 12 4 Thesis outline 20 PART I: APRIORITY AND MODALITY Chapter 2: The A Priori: Preliminaries 1 Introduction 25 2 A negative account? 28 2.1 Independence 30 2.2 Experience 34 3 A positive account? 39 4 Justifiability, objectivity and subjectivity 43 5 Euclid and defeasibility 47 6 Fallibility 58 Chapter 3: Coincidence, Goldbach and the Contingent A Priori 1 Introduction 62 2 The coincidence thesis and Goldbach’s conjecture 63 3 The contingent a priori 68 3.1 Problems with the metre stick 70 3.2 ‘I exist’: a better example? 80 3.3 Apriority, indexicality and Evansian, ‘superficial’ contingency 83 3.4 Apriority, introspection and causation 92 4 Conclusion 99 Chapter 4: Rational, Epistemic, Logical and Metaphysical Modalities 1 Introduction 103 2 Rational necessity, rational insight and metaphysical modality 105 2.1 The regress problem 112 2.2 Apriority and rational necessity; certainty and objectivity 117 3 Rational, epistemic and logical modalities 121 3.1 Rational and epistemic necessity 122 3.2 Rational necessity and the logical necessities 127 4 Apriority as rational necessity 134 PART II: RATIONALITY AND MODALITY Chapter 5: The Necessary A Posteriori, Conceivability and Possibility 1 Introduction 141 2 A Kripkean argument for the necessary a posteriori 144 3 How many propositions? 155 4 Another argument? 164 5 The necessary a posteriori conceivability and possibility 175 Chapter 6: Frege and Kripke’s Problems, Conceivability and Possibility 1 Introduction 181 2 Frege’s problem and Kripke’s puzzle 183 2.1 Frege’s problem 183 2.2 Kripke’s puzzle 190 3 Conceivability, rational and metaphysical modalities 200 3.1 The problems, conceivability and possibility 201 3.2 (In)conceivability and (im)possibility: Goldbach’s conjecture again 203 Chapter 7: Rationality, Modality and Essence 1 Introduction 215 2 The nature of metaphysical modality 215 2.1 ‘Actual’ and ‘possible’ worlds 216 2.2 Possible worlds, ‘realism’ and essentialism 221 2.3 Problems with possibilism and merits of modalism 224 2.4 The grounding of modality 230 3 Thesis summary 235 4 Issues, objections and replies 243 4.1 Fallibilism, justifiability, circularity and two-dimensionalism 244 4.2 The possibility of modal error 248 Bibliography 257 Chapter 1 From Metaphysics to Semantics: Two-Dimensionalism, Rationality and Modality 1 Introduction Philosophy, at least as traditionally conceived, is a deeply modal and broadly a priori discipline. Philosophers are interested in necessary and possible 1 conclusions, and whether, for example, a priori or conceivability-based reasoning justifies these; whether apriority entails necessity and ‘conceivability’ entails possibility.2 The empirical sciences (again, as trad- itionally understood) are, as the ‘empirical’ suggests, largely a posteriori. Scientists are interested in contingent truths about the natural world and are generally less interested in whether, for example, aposteriority entails contingency. Broadly stated then, a simple, traditional demarcation of philosophy and science would have the latter exemplified by a posteriori investigation of contingent truths (or probabilities), with the former consisting of putatively a priori-necessary and conceivability-possibility forms of reasoning. After the seminal work of Kripke on the ‘contingent a priori’ and ‘necessary 1 I intend metaphysical modality here—but this is a topic of dispute throughout. I begin to clarify this issue towards the end of this section and throughout the remainder of the thesis. 2 There is a lot of shorthand here, which I explain in more detail later. The scare quotes indicate the contentiousness of ‘conceivability’. I offer working understandings of modality shortly, and of apriority and conceivability in §3 below. 2 a posteriori’3 there appeared to be much to challenge such an understanding of philosophy, science, rationality and modality. Specifically, the contingent a priori (if genuine) invalidates any entailment from apriority to necessity. Similarly, the necessary a posteriori (if genuine) undermines (for example) philosophy’s position as the main provider of necessary or essentialist conclusions, since if a posteriori justification can result in necessary conclusions, empirical science (perhaps alone) can establish essentialist results; i.e. scientific essentialism. Moreover, the necessary a posteriori would also appear to further challenge the methodology of traditional philosophy, viz the conceivability-possibility form of reasoning; if p is necessary and a posteriori, ¬p is impossible but, apparently, ‘a priori possible’ or ‘conceivable’— that is, ‘conceivability’ does not entail possibility. In short, whilst having significant ramifications for the status of both philosophy and science, apriority, conceivability (i.e. rationality)