Knowledge Closure and Knowledge Openness A Study of Epistemic Closure Principles Levi Spectre ©Levi Spectre, Stockholm 2009 ISBN 978-91-7155-973-9 Printed in Sweden by US-AB, Stockholm 2009 Contents Preface...........................................................................................................vi Chapter 1: An Introduction to the Closure Debate in Epistemology............... 9 1.1 The Closure Debate ...............................................................................................14 1.2 Layout of the Argument ..........................................................................................17 1.3 Closure and its Motivation ......................................................................................19 1.4 What is the Closure Principle? ...............................................................................23 1.5 Debating Closure....................................................................................................29 1.5.1 Hawthorne’s Arguments.................................................................................29 1.5.2 Nozick on Closure ..........................................................................................32 1.5.3 Dretske on Closure and Heavyweight Propositions .......................................35 1.5.4 Section Summary...........................................................................................37 Chapter 2: Skepticisms and Closure............................................................ 38 2.1 Skepticism and Closure..........................................................................................38 2.1.1 Cartesian Skepticism, Moorianism, and what Comes In-Between.................41 2.2. Cartesian Skepticism.............................................................................................43 2.2.1 Immodest Skepticism .....................................................................................44 2.2.2. Modest Skepticism ........................................................................................47 2.3 Mundane Skepticism ..............................................................................................53 2.4 Live Skepticism.......................................................................................................58 Chapter Summary ........................................................................................................59 Chapter 3: The Kripke Dogmatism Puzzle and Epistemic Ascent ............... 62 Chapter Three Outline ..................................................................................................62 3.1 The Threat of Dogmatism.......................................................................................63 3.1.1 Junk Conditionals and Junk Knowledge ........................................................66 3.1.2 Junks or Knowledge? Dogmatism Repuzzled................................................68 3.1.2.1 A Short Excursion to the Bahamas........................................................77 3.2 Epistemic Ascent ....................................................................................................79 3.2.1. Dogmatism and Easy Knowledge and Bootstrapping ...................................81 3.2.2 Epistemic Ascent and Knowledge of True Belief ...........................................83 Chapter Summary ........................................................................................................87 Chapter 4: Evidence and Open Knowledge................................................. 90 Chapter outline .............................................................................................................90 4.1 The Watch Case and its Probabilistic Analysis. .....................................................91 4.1.1. Evidence and Probabilities............................................................................91 4.2. Probabilistic Argument for Evidence and Knowledge Openness ..........................96 4.3 Evidence Openness from Principles.......................................................................99 4.3.1. Equivalence, Consistency and Addition ......................................................104 4.3.2. Equivalence and Distribution.......................................................................109 4.3.3. EAD, EDIS and the Logic of Evidence ........................................................110 4.3.4. Carnap’s Matrix ...........................................................................................111 Chapter Summary ......................................................................................................114 Chapter 5: Open Knowledge – Costs and Benefits ................................... 119 5.1. From Evidence to Knowledge..............................................................................119 5.1.1. Premise (V) of the Open Knowledge Argument ..........................................124 5.1.1.1. An Objection to the Use of (V) ............................................................127 5.1.1.2. An Objection to (NED) ........................................................................132 5.2. Knowledge Without Evidence..............................................................................137 5.3. Knowledge as Evidence ......................................................................................140 5.3.1. Knowledge as Evidence: Jeffrey Conditionalization....................................142 5.3.2. Knowledge as Evidence: Standard Conditionalization................................144 5.3.3. Knowledge as Evidence: Williamson's Account..........................................148 5.3.3.1. Safety and Chance .............................................................................149 5.3.3.2. Lottery Propositions ............................................................................152 5.3.3.3. The Principal Principle and Practical Deliberation ..............................158 5.3.3.4. Fallibilism ............................................................................................162 5.3.4. Knowledge as Evidence: Conclusion ..........................................................165 5.4. Evidential Knowledge ..........................................................................................166 5.4.1. The Benefits of Epistemic Openness ..........................................................166 5.4.2. Denying Closure: Not as Bad as You Think................................................168 Chapter Summary ......................................................................................................175 Chapter 6: Concluding Remarks................................................................ 179 Appendix: A Short Overview of Bayesianism............................................. 186 A Bayesian Framework .........................................................................................187 Convergence Theorems........................................................................................192 Deep convergence ................................................................................................197 Bibliography ............................................................................................... 199 Chapter 1: An Introduction to the Closure Debate in Epistemology Those are my principles, and if you don't like them... well, I have others. Groucho Marx We know that Socrates was troubled if it is true that Socrates lived and true that, if he lived, he was troubled. We know this since we have excellent rea- son to believe that basic deductive inferences patterns are truth-preserving. If the premises of valid inference patterns are true, we have a logical guarantee that the conclusion is true as well. Such is the case with the modus ponens inference pattern, a candidate as good as any for being valid. The study of logic deals, among other things, with the identification of such patterns as well as with proof of their validity. Yet, when propositional attitudes govern the scope of the premises of provably valid inferences, even with regard to factive attitudes1 such as knowledge, there is no logical guarantee that the conclusion will also fall within their scope (K(p)∧K(p→q)⊬K(q)). Regard- less of the logical guarantee, however, the prevalent inclination is to think that these inferences actually do preserve truth from premises to conclusion. If I know that grass is green, and if I know that if something is green it has a color, I know that grass is colored. We cannot prove that I know this, but a denial would seem very odd. What else would it take for me to know that grass is colored? Not all cases inspire the same confidence as this grass example. My wife knows, since we have talked about this extensively, that if she gets extended time-off from her job, we will go to the Bahamas. She also knows, since her trusted boss has told her as much, that in the case of her husband's unfortu- nate death, she will receive extended time-off. Does she then know that, if I die, we will go to the Bahamas?2 Perhaps she does, or perhaps when she thinks about this, knowledge no longer governs the scope of the premises of this valid inference. The point is that, even though the truth of the premises guarantees the truth of the consequence, knowledge (though tightly con- 1 Factive propositional attitudes are those that entail the truth of the propositions they govern. 2 The example is inspired by Sorensen’s tennis example (1988b: