LOGOS & EPISTEME, VII, 1 (2016): 75-81 A FAILED TWIST TO AN OLD PROBLEM: A REPLY TO JOHN N. WILLIAMS Rodrigo BORGES ABSTRACT: John N. Williams argued that Peter Klein's defeasibility theory of knowledge excludes the possibility of one knowing that one has (first-order) a posteriori knowledge. He does that by way of adding a new twist to an objection Klein himself answered more than forty years ago. In this paper I argue that Williams' objection misses its target because of this new twist. KEYWORDS: defeasible reasoning, Peter Klein, second-order knowledge, John N. Williams This is a reply to John N. Williams' paper "Not Knowing You Know: A New Objection to the Defeasibility Theory of Knowledge."1 That paper argues that Peter Klein's defeasibility theory of knowledge excludes the possibility of one knowing that one has (fırst-order) a posteriori knowledge. Klein himself answered a version of this objection in "A Proposed Defınition of Propositional Knowledge."2 Williams' paper adds a new twist to the objection Klein answered more than forty years ago. I will argue that Williams' objection misses its target because of this new twist. 1. The Old Problem and the Old Solution When fully spelled out, Klein's analysis of knowledge comes down to this: (Defeasibility) S knows that α iff (1) α; (2) S believes that α; (3) S is justifıed in believing that α; (4) there is no truth, d, such that the conjunction of d and S's justifıcation, j, fails to justify S in believing that α.3 1 John N. Williams, "Not Knowing You Know: A New Objection to the Defeasibility Theory of Knowledge,"Analysis 75 (2015): 213-17. 2 Peter Klein, "A Proposed Defınition of Propositional Knowledge,"The Journal of Philosophy (1971): 471-82. 3 Since a truth may misleadingly suggest the falsehood of something one is justifıed in believing truly (as in the Grabit Case introduced in the literature by Keith Lehrer and Thomas Paxson, "Knowledge: Undefeated Justifıed True Belief," The Journal of Philosophy 66 (1969): 225-37. In that case the truth "Tom's mother said that Tom has an identical twin who is also in the library" misleadingly suggests that "Tom stole the book" is false.), Klein's view incorporates a distinction Rodrigo Borges 76 Towards the end of his paper,4 Klein considered the following objection to Defeasibility:5 If the defınition were accepted, it would never be true that S knows that she knows that x because she could never know that the fourth condition held. In reply to this objection Klein points out that, given Defeasibility, S knows that she knows x if and only if S knows "S knows that x" satisfıes each of the necessary conditions in Defeasibility. In other words, S knows that she knows that x if and only if each of the following statements is true: (I) S knows that x (II) S believes that S knows that x (III) S is justifıed in believing that she knows that x (IV) There is no truth, d, such that the conjunction of d and one's justifıcation, j, fails to justify S in believing that S knows that x. As Klein6 points out, because knowing entails that there is no defeater of one's justifıcation, S is justifıed in believing she knows that x only if she is justifıed in believing there is no defeater of her justifıcation for believing that x. In other words, III is true only if S is justifıed in believing there is no defeater of her justifıcation for believing x. In the same paper Klein argued that there is no reason to think that S is never justifıed in believing there is no defeater of the justifıcation she has for her fırst-order belief. This, in a nutshell, is Klein's solution to the old problem. Before we look at John Williams' new version of this objection, let me substantiate Klein's reply by between truths that actually defeat one's justifıcation (i.e., genuine defeaters) and truths that only appear to defeat one's justifıcation (i.e., misleading defeaters). Only the former truly defeats. In this paper I will refer only to genuine defeaters, but will drop the qualifıer "genuine" for ease of exposition. Nothing in my exchange with Williams depends on this issue. See Peter Klein, Certainty: A Refutation of Scepticism (Minnesota: University of Minnesota Press, 1981), 148-166 for his treatment of the distinction. 4 Klein, "A Proposed Defınition," 480. 5 Even though I follow the argument in Klein, "A Proposed Definition" here, I have updated the nomenclature he used in that paper to a more current one, in line not only with Klein's later work (e.g., Klein, Certainty and Peter Klein, "Useful False Beliefs," in New Essays in Epistemology, ed. Quentin Smith (New York: Oxford University Press, 2008)) but also with more widespread use in current epistemology. The nomenclature in Klein, "A Proposed Definition" followed closely the nomenclature in Roderick Chisholm, Theory of Knowledge (Upper Saddle River: Prentice Hall, 1966). Nothing of substance hinges on these changes. 6 Klein, "A Proposed Definition," 481. A Failed Twist to an Old Problem: A Reply to John N. Williams 77 providing a logically possible case in which I through IV are all true. This should establish that Defeasibility does not exclude second-order knowledge. As I look up I undergo the experience as of something being a computer screen in front o f me. I thereby form the belief that (p) there is a computer screen in front of me. Since this is a normal case of perceptual experience, I satisfy all conditions in Defeasibility, i.e., (I*) I know that p.7 Suppose further that I reflect on whether I know that p, realize that it is a normal case of perceptual experience, and come to believe I do know it. That is, the following is true: (II*) I believe I know that p. I* and II* entail that I have a true second-order belief. Now, according to Klein, S is justifıed in believing that α if and only if, given S's evidence, S's belief in α satisfıes some (perhaps contextually determined) threshold for knowledge-grade justifıcation.8 This means that I know I have knowledge-grade justifıcation for believing there is a computer screen in front of me only if I know that my justifıcation for believing that there is one is not defeated. But my total evidence bearing on the issue of whether I am justifıed in believing that p includes not only my knowledge that p, but also my knowledge that this is a normal case of perceptual experience, that I am not drugged or otherwise visually impaired, and so on. Thus, we may plausibly argue that, given my evidence, I am in a position to know that there is no defeater of my justifıcation for believing that p. Defeaters prevent one from knowing by preventing one's justifıcation from satisfying the (perhaps contextually determined) threshold for knowledge-grade justifıcation. They prevent S's justifıcation from satisfying this threshold by either undermining the support her evidence provides to her belief, or by making probable the denial of what she believes given her evidence.9 In the case at hand, there would be a 7 Although this is a case of non-inferential knowledge, the same could be said, mutatis mutandis, about inferential knowledge. 8 This is, roughly, what Klein means by his notion of confirmation, which is the centerpiece of his account of justifıcation. See Klein, Certainty, 61-7. 9 According to the nomenclature popularized by John Pollock, the fırst kind of defeater is an undermining defeater, while the latter kind of defeater is a rebutting defeater. See John Pollock, "Defeasible Reasoning," in Reasoning: Studies of Human Inference and Its Foundation, eds. Jonathan Adler and Lance J. Rips (Cambridge: Cambridge University Press, 2008) for a recent statement of Pollock's view. Rodrigo Borges 78 defeater of my justifıcation for believing that there is a computer screen in front of me if, for example, I had taken a drug which causes hallucinations 80 percent of the time, or if ¬p were true. But, by assumption, nothing like that is true in this situation. In other words, both III* and IV* are true: (III*) I am justifıed in believing I know that p. (IV*) There is no truth, d, such that the conjunction of d and my justifıcation, j, for believing that I know that p fails to justify me in believing that I know that p. Claims I* through IV* all seem to be true in this case; so, it is plausible to think that I know that I know that p. The upshot is that Defeasibility does not make it impossible for there to be second-order knowledge. I conclude, then, that contrary to what Williams would have us believe it is logically possible for Klein' Defeasibility to be true and for one to know that one has fırst-order a posteriori knowledge. 2. Williams' New Twist Williams' new twist to the old objection comes in the form of a principle about concepts he fınds "plausible:" 10 (CLAIM) If the satisfaction of a condition at least partly constitutes an instance of a concept, then knowing that such an instance obtains requires you to know a priori that the condition is satisfıed.11 10 Williams, "Not Knowing," 215. 11 Although Williams does not explicitly formulate CLAIM as requiring a priori knowledge, one must read CLAIM in this way lest his argument against Klein be made invalid (see below), for Williams explicitly requires that S know a priori that she satisfıes the no-defeater condition in order for her to know that she knows. If I am wrong about this and Williams' argument is invalid, then so much the worse for his argument. More precisely, this is what I take to be Williams' argument: 1. If the satisfaction of a condition at least partly constitutes an instance of a concept, then knowing that such an instance obtains requires you to know a priori that the condition is satisfıed. [CLAIM/Assumption] 2. If the satisfaction of a condition at least partly constitutes an instance of knowledge, then knowing that such an instance obtains requires you to know a priori that the condition is satisfıed. [KLAIM/ from 1] 3. The satisfaction of the no-defeater condition partly constitutes instances of knowledge. [from Defeasibility] 4. For any instance k of knowledge, if you know that k obtains in case C, then you know a priori that the no-defeater condition is satisfıed in case C. [from 2 and 3] A Failed Twist to an Old Problem: A Reply to John N. Williams 79 To get a feel for how CLAIM works, consider Williams' own example:12 since x being three-sided partially constitutes x being a triangle, I know that x is a triangle only if I know that x is three-sided. Now, CLAIM and Defeasibility together entail that one knows that one knows α only if one knows a priori that one's justifıcation satisfıes the no-defeater condition. Williams then argues that, since one cannot know a priori that one's knowledge that α satisfıes the no-defeater condition, one cannot know that one knows that α. This is Williams' new twist to the old objection: it is not enough that S knows that her fırst-order knowledge satisfıes all conditions on knowledge, if she wants to know that she knows, she must know a priori that her fırst-order a posteriori knowledge satisfıes all the conditions on knowledge. Let us look more closely at CLAIM and at Williams' new twist. Our assessment will reveal that CLAIM and the instance of this principle Williams applies to knowledge are both false. Suppose that satisfying the condition (*) S can prove (some) mathematical theorems partially constitutes the concept mathematician. The assumption is plausible because we commonly think of mathematicians as people who can prove at least one mathematical theorem. Now, consider Timmy, who is a freshman in college and not particularly math-savvy. If Timmy were confronted with a proof of a mathematical theorem he would not be able to follow it; he would not even be able to grasp any of the concepts in the proof. Now, suppose Timmy's Calculus professor, a skillful mathematician, satisfıes condition (*), and that on the fırst day of class she tells Timmy and all the other students in Timmy's class that she can prove many mathematical theorems. Intuitively, Timmy knows his teacher is a mathematician even though this concept is partially constituted by condition (*) and his knowledge that the professor satisfıes (*) is a posteriori, for it is based on his experience as of something being his calculus professor telling him she satisfıes (*). But if that is the case, then CLAIM is false on account of the fact that Timmy knows the concept mathematician is instantiated by his professor, even though he does not know a priori t hat the professor satisfıes a condition that partially constitutes that concept. As a matter of fact, it seems to me that Timmy would know a posteriori that his professor is a mathematician even if she had not told the class that she satisfıes (*), 5. You cannot know a priori that the no-defeater condition is satisfıed in C. [Assumption] You do not know that k obtains in C. [from 4 and 5 by modus tollens] 12 Williams, "Not Knowing," 215. Rodrigo Borges 80 but told them only that she is a mathematician. Either version of the case counterexemplifıes CLAIM. Now, consider CLAIM as it applies to knowledge: (KLAIM) If the satisfaction of a condition at least partly constitutes an instance of knowledge, then knowing that such an instance obtains requires you to know a priori that the condition is satisfıed. KLAIM is false because of Williams' new twist. To see that, let us look at what happens when we apply KLAIM to the other traditional conditions on knowledge (i.e., the justifıcation, belief, and truth conditions). Take justifıcation and belief fırst. If KLAIM is true, then one cannot know a posteriori that those conditions are satisfıed. This is a bad result because our secondorder knowledge that those conditions are satisfıed is sometimes justifıed a posteriori. I am completely ignorant of quantum mechanics, but if Stephen Hawking were to tell me that q is a testable prediction of the theory, then, assuming this is a normal case of transmission of knowledge via testimony, I not only come to know that q is a testable prediction of quantum mechanics, but I am also in a position to know both that I believe that q and that I am justifıed in believing that q. The problem for KLAIM is that my justifıcation for believing that I believe that q with justifıcation is arguably a posteriori, for it includes the justifıcation that emerges from my undergoing a particular experience: if I had not experienced Stephen Hawking, the celebrated physicist, asserting to me that q, I would not have believed that q, nor would I have been justifıed in believing that q. Things get worse when we apply KLAIM to the truth condition on knowledge. Williams faces a dilemma: if KLAIM is true, then, necessarily, either there is no second-order knowledge or no fırst-order a posteriori knowledge. That there is such a dilemma should be reason enough to reject KLAIM and Williams' argument, which relies on it. No epistemology that accepts either (or both) of those horns should be deemed satisfactory. Here is how KLAIM forces this dilemma on Williams. As before, let "p" stand for the claim that there is a computer screen in front of me. Also as before, suppose that I know that p and that I know that p in virtue of my true belief being suitably related to my experience as of something being a computer screen in front of me. As a result, the justifıcation for my knowledge that p is a posteriori. Suppose I reflect on the question of whether I know that p and come to believe I do know it in virtue of reliably assessing my perceptual experience as veridical. Now, a condition on knowledge is that the known proposition be true. Because knowledge entails truth, it follows from KLAIM that I know that I know that p only if I know a priori that my belief that p satisfıes this condition; that is, given KLAIM, I know that I A Failed Twist to an Old Problem: A Reply to John N. Williams 81 know that p only if I know a priori that my belief that p is true. But if one knows that a belief is true, then one knows the truth the belief is about. So, given KLAIM, I know that I know that p only if I know a priori that p. But, by assumption, I know that p a posteriori. We have derived a contradiction from KLAIM by applying it to a seemingly innocent case. Something's gotta give. I think KLAIM has got to go. If KLAIM is true, then either my knowledge that p is not a posteriori or I can't know that I know that p. The fırst horn of this dilemma seems false on its face, and the second one leads to a curious form of skepticism: considering that there is nothing special about this case, the result of this argument generalizes to all cases of fırstorder a posteriori knowledge. 3. Conclusion In sum, John Williams' new twist on the old problem for Defeasibility fails. His problem for Defeasibility arises only when the requirements for iterative knowledge are made too high. What is more, this lesson applies to a number of other views that also incorporate a no-defeater clause in their defınition of knowledge.13,14 13 e.g., Keith Lehrer, Theory of Knowledge 2nd ed. (Boulder: Westview Press, 1990), John Pollock and Joseph Cruz, Contemporary Theories of Knowledge (Lanham: Rowman and Littlefıeld, 1999), and Marshall Swain, Reasons and Knowledge (Ithaca: Cornell University Press, 1981). 14 I am very grateful to Cherie Braden, Peter Klein, and John N. Williams for discussion and feedback on different drafts of this paper. I am happy to acknowledge that the research in this paper was partly funded by the CAPES/Fulbright Commission. I am also grateful for the partial support my research received from the São Paulo Research Foundation (FAPESP) through grant 2015/02419-4.