Do You Know Everything That You Know?

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<ul><li><p>Canadian Journal of Philosophy</p><p>Do You Know Everything That You Know?Author(s): Steven R. LevySource: Canadian Journal of Philosophy, Vol. 9, No. 2 (Jun., 1979), pp. 315-322Published by: Canadian Journal of PhilosophyStable URL: http://www.jstor.org/stable/40231097 .Accessed: 09/06/2014 21:38</p><p>Your use of the JSTOR archive indicates your acceptance of the Terms &amp; Conditions of Use, available at .http://www.jstor.org/page/info/about/policies/terms.jsp</p><p> .JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range ofcontent in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new formsof scholarship. For more information about JSTOR, please contact support@jstor.org.</p><p> .</p><p>Canadian Journal of Philosophy is collaborating with JSTOR to digitize, preserve and extend access toCanadian Journal of Philosophy.</p><p>http://www.jstor.org </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/action/showPublisher?publisherCode=cjphttp://www.jstor.org/stable/40231097?origin=JSTOR-pdfhttp://www.jstor.org/page/info/about/policies/terms.jsphttp://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>CANADIAN JOURNAL OF PHILOSOPHY Volume IX, Number 2, June 1979 </p><p>Do You Know </p><p>Everything That You Know? </p><p>Steven R. Levy, , University of California, Riverside </p><p>In the ongoing attempt to provide a satisfactory analysis of </p><p>knowledge numerous conditions have been proposed as necessary and sufficient - the most noteworthy being justification, truth, and belief. In addition, various epistemic principles are frequently employed. In this paper I intend to show how the seemingly innocuous justification condition, along with two relatively uncontroversial epistemic principles, can give rise to a paradoxical situation. </p><p>Let us begin by examining an interesting principle, which emerges from time to time and which has been most recently endorsed by D.M. Armstrong.1 The principle, which Armstrong calls the principle of the conjunctivity of knowledge, states that if a person, S, knows that p and knows that q, etc., then it is rational for S to believe the </p><p>conjunction of p and q, etc. </p><p>[1] (KSp &amp; Ksq ...)- RBs(p &amp; q ...)2 </p><p>1 In Belief, Truth and Knowledge (Cambridge, 1973), p. 186. </p><p>2 Of course it may be rational for S to believe something that he does not, in fact, believe (perhaps he has never thought about it). So the satisfaction of </p><p>315 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Steven R. Levy </p><p>This principle should not be confused with </p><p>[2] (RBSp&amp;RBsq ...) / RBs(p&amp;q...) </p><p>which gives rise to the now famous lottery paradox' and which is thus not widely accepted.3 The principle of the conjunctivity of knowledge [1] has a stronger antecedent condition than does [2]. While "mere" rational belief in each of a series of propositions does not necessarily carry over into a rational belief of the conjunction of those propositions, it is claimed that if one has knowledge of each then it is rational for him to believe their conjunction. It may be rational for me to believe, for each particular lottery ticket, that it will lose - but it is not rational for me to believe that all of the lottery tickets will lose (or even that all of a large subset will lose). But although it is rational for me to believe that any given lottery ticket will lose, I cannot properly be said to know that any one of them will lose. There is an initial plausibility in supposing that given a large subset of the lottery tickets issued, if I knew that each would be a loser, then it is perfectly rational for me to believe that they are all losers. Aprima facie case has thus been made for [1]. </p><p>Armstrong feels that the principle of the conjunctivity of knowledge is so secure that he rests a rather important argument on it (the conclusion of which is that we must demand absolute empirical reliability for our non-inferential knowledge). But far from being secure, it seems that [1 ] can be shown to be false by a relatively simple counterexample. The counterexample takes as a presupposition that absolute certainty on S's part is not a requirement for S's knowledge </p><p>[3] (KSP A Csp) </p><p>This presupposition is accepted by most who are currently interested in providing requirements for knowledge and I take a defense of it </p><p>the antecedent of [1 ] does not entail that S believes that (p &amp; q ...) - only that such a belief would be rational. Throughout this discussion we shall also make the usual additional assumptions required by epistemic principles such as [1]: (1) that S understands the logical entailment between the components of a conjunction and the conjunction itself, (2) that S correctly deduces the conjunction as a result of his understanding of the entailment, and (3) that S believes the conjunction as a result of (1) and (2). At certain points in the discussion we shall stop short of making the third assumption for reasons that will become obvious. </p><p>3 See, e.g., H. E. Kyburg, Probability and the Logic of Rational Belief (Middletown,1961). </p><p>316 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Do You Know Everything That You Know? </p><p>here to be unnecessary. Armstrong himself defends such a view.4 Nevertheless, in light of our final results, [3] will be one principle for which a reexamination may be necessary. </p><p>Consider the following case : S is given a written examination. The examination consists of a very large number of short-answer </p><p>questions (1,000; 100,000; ...). Suppose further that S knows the answers to all of the questions on the test. The questions may be like the following: </p><p>1. In what year were you born? </p><p>2. In what city were you born? </p><p>3. How many planets are currently thought to comprise our solar system? </p><p>4. Do you in fact know everything that you think you know? </p><p>S answers the questions, '1946', 'Los Angeles', '9', 'No', ....The answer to question 4 will, of course, be 'no' because S is not </p><p>absolutely certain of everything that he knows and he knows that somewhere in his vast collection of beliefs there is something that he thinks that he knows which is really false. Perhaps because of </p><p>gerrymandered boundary lines he wasn't really born in Los Angeles or perhaps another planet was recently discovered and he hasn't yet heard the news. The examination given to S just turned out to be such that he did know the answers to all of the questions. If one of the </p><p>questions had been about the color of S's car he would not have fared so well - he would have answered that it was red when, in fact, while he was taking the test vandals had painted it green (thus ensuring that S's answer to question 4 was correct). </p><p>Is it rational for S to believe that he scored 100 percent on the examination? Given his answer to question 4 and given that the number of questions is sufficiently large, it seems quite obvious that it need not be rational for S to believe the conjunction of all of his answers (i.e., that he scored 100 percent). The rational belief would </p><p>4 Op. cit., p. 139. </p><p>317 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Steven R. Levy </p><p>be that he scored very well but that on at least one occasion, he had given an incorrect answer. Here we have a case in which S knows that p and S knows that q, etc., but in which it would not be rational for S to believe the conjunction of p and q etc.5 </p><p>Note that this example would not work if question 4 were: </p><p>4'. Do you in fact know all of the answers to this test? </p><p>For if S answered 'yes' and this answer were correct, then it is a much more difficult matter to determine whether or not it is rational for him to believe that he scored 100 percent. We shall consider this question shortly. Any other outcome with regard to question 4' (an incorrect 'yes' or a 'no', correct or incorrect) would fail to satisfy the antecedent of[1]. </p><p>Of course it is not necessary to the counterexample that question 4 actually be included in the examination. All that is necessary is that S recognize the fact that he is fallible. S's failure to recognize this would be wholly arrogant and dogmatic.6 But the hypothesis is stated more strongly than it need be stated. It is not necessary to the counterexample that S know that he is fallible (although I think that this is something that he can know) - all that is necessary is that it is rational for S to believe that he is fallible: </p><p>[4] RBs(Fallibles)7 </p><p>Indeed, if asked S may even be able to give a good inductive argument for his own fallibility - time and time again he has found himself in error about matters in which he had complete confidence. S's evidence for his own fallibility may even be greater than his evidence for his own birth date. So if he knows his birth date, certainly he knows that he is fallible. If it is rational for him to believe that a certain date is his birth date, then it is rational for him to believe that he is fallible. </p><p>5 A similar point was made by Alan H. Goldman, "A note on the conjunctivity of Knowledge/' Analysis (1975). </p><p>6 Keith Lehrer makes a related observation in "When Rational Disagreement is Impossible/' Nous (1976). </p><p>7 With the supposition stated in this way, the counterexample works when modified so as to omit question 4 from the examination but to allow that S rationally believes that he does not know everything that he thinks he knows. </p><p>318 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Do You Know Everything That You Know? </p><p>We can now embrace the denial of [1] as being possible (and probably true for all of us) </p><p>[5] [(Ksp &amp; KSq ...) -RBs(p &amp; q ...)] </p><p>But this leads to a very surprising result. Almost all analyses of what it is for S to know that p include a requirement to the effect that S be justified in believing that p (at least for "non-basic" propositions). And there is no analysis of justification under which a person may be justified in believing a proposition that it is not rational for him to believe. Most use the phrases 'S is justified in believing that p' and 'it is rational for S to believe that p' interchangeably Thus, for any non basic proposition p, if S knows that p then it is rational for him to believe that p: </p><p>[6] Ksp-^RBSP </p><p>Now suppose that [5] is true of S. This means that S knows that p and S knows that q etc., but that it is not rational for S to believe the conjunction of p and q etc. However by [6] if it is not rational for S to believe the conjunction of p and q, etc., then S cannot properly be said to know the conjunction of p and q, etc. We are left with the paradoxical result that although S knows that p and S knows that q, etc., S does not know the conjunction of p and q, etc. </p><p>[7] Ksp - Ksq...&amp;~Ks(p&amp;q...) </p><p>S does not know everything that he knows ! Of course S does know everything that he knows when we consider each proposition individually. But when taken together it can no longer be correctly said that S has knowledge. </p><p>So from the suppositions that knowledge does not entail certainty, that it can be rational for us to believe that we are fallible, and that knowledge entails rational belief, we arrive at the puzzling conclusion that we do not know everything that we know. </p><p>There has been an attempt to modify the principle of the conjunctivity of knowledge [1], the denial of which gives rise to the above paradox. Goldman8 argues that only when S knows that he knows each of a set of propositions is it entailed that it is rational for </p><p>8 Op.,cit. </p><p>319 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Steven R. Levy </p><p>him to believe their conjunction. He schematizes his claim in this way: </p><p>[8] Ks(Ksp &amp; Ksq ...) - *-RBs(p &amp; q ...) </p><p>This is analogous to the case in which S correctly answers 'yes' to question 4' on the test. The denial of [8] conflicts with two other widely accepted epistemic principles: that it is rational for S to believe a logical consequence of a proposition that he knows, </p><p>[9] Ksp &amp; (p - q) - RBsq </p><p>and that truth is a necessary condition of knowledge, </p><p>[10] Ksp- p </p><p>However we need not be too hurried in our acceptance of [9]. Suppose that S knows that p, that p entails q, and that S correctly infers q from p. We may, perhaps, be tempted to approve any belief formed by S that q, as a result of this process is a rational belief without inquiring further into the matter. But to do so would be a mistake. Suppose that S also has a firm belief that r (it makes no difference whether or not this belief is rational). Suppose further, that r entails not-q and that S correctly infers not-q from r. In such a situation it would hardly be rational of S to believe that q. Rather, S should be required to escape the dilemma either by further inquiry or by suspending any belief that q or that not-q. Thus, even though the antecedent of [9] is satisfied, given S's other beliefs it would not be rational for him to believe q. So [8] need not be accepted because of its logical relationship with [9] and [10]. Neither, however, should it be rejected due to the failure of [9]. </p><p>A consideration of [8] gives rise to some intriguing questions. Excluding a situation such as described above the conditional as a whole seems plausible. But how does the consequent emerge from the antecedent? My example of the examination demonstrates that the knowledge operator cannot be factored out of a conjunction. Can it be distributed into a conjunction ? Nothing that has been said so far precludes this possibility. Furthermore, it seems reasonable to suppose that it can. Suppose that on the examination described above the answer to question 1 is p and the answer to question 2 is q and so on. If we can accurately say of S that he knows that p and q, etc., then it is hard to imagine how we can avoid saying that he knows that p and he knows that q, etc., i.e. that he knows the answer to each question. It is not hard to imagine how S can know that he scored 100 </p><p>320 </p><p>This content downloaded from 194.29.185.90 on Mon, 9 Jun 2014 21:38:26 PMAll use subject to JSTOR Terms and Conditions</p><p>http://www.jstor.org/page/info/about/policies/terms.jsp</p></li><li><p>Do You Know Everything That You Know? </p><p>percent on the test without knowing the answer to each question. Supposing that the test were a multiple choice one and that S had procured a copy of the grading key before taking the examinatio...</p></li></ul>