John N. Williams argued that Peter Klein's defeasibility theory of knowledge excludes the possibility of one knowing that one has 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

Borges, Rodrigo

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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

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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 second-order 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 fırst-order  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. 

A Failed Twist to an Old Problem

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A Failed Twist to an Old Problem: A Reply to John N. Williams

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