© LOGOS & EPISTEME, V, 2 (2014): 133–140 HOW TO MOORE A GETTIER: NOTES ON THE DARK SIDE OF KNOWLEDGE Rodrigo BORGES ABSTRACT: The Gettier Problem and Moore's Paradox are related in a way that is unappreciated by philosophers. If one is in a Gettier situation, then one is also in a Moorean situation. The fact that S is in a Gettier situation (the fact that S is "Gettiered"), like the fact that S is in a Moorean situation (the fact that S is "Moored"), cannot (in the logical sense of "cannot") be known by S while S is in that situation. The paper starts the job of mapping what can be said about this feature of Gettier situations. The goal is to stimulate further exploration into this yet uncharted territory. KEYWORDS: Gettier problem, Moore's paradox, luminosity, blindspot The state of being Moored (p is true, but S does not know that p is true) and the state of being Gettiered (S is has a justified true belief that p, but S fails to know that p) are importantly connected. If one is in the first state, then one is also in the second state. Contemporary philosophy has failed to acknowledge this important fact. In this paper I begin exploring some of the ways in which being Moored and being Gettiered are related. Most prominently, it is logically impossible for one to know that one is in either of those states, while one is in those states. As with all first explorations into uncharted territory, the task of these notes is to partially map conceptual space and not to arrive at any particular conclusion. Hopefully, what I say here will be enough to stimulate others to look further into these issues. 1. Being Moored It is possible for it to be raining and for me not to know that it is raining. That happens whenever it is raining while I am sleeping, or whenever it rains and I am working in my windowless office. Let such facts be called "Moorean facts," after G.E Moore, and the state the relevant person is in one of being "Moored."1 Now, it can be easily shown that it is logically impossible for S to know she is Moored while she is Moored: 1. Ks(p&¬Ksp) [assume for a reductio ad absurdum] 2. Ksp&Ks¬Ksp [1, by distribution of knowledge over conjunction] 1 I borrow the label "Moored" from Michael Veber "I Know I Am Not Gettiered," Analytic Philosophy 54, 4 (2013): 401–420. Rodrigo Borges 134 3. Ksp [2, by conjunction elimination] 4. Ks¬Ksp [2, by conjunction elimination] 5. ¬Ksp [4, by the factivity of knowledge] 6. ¬Ks(p&¬Kp) [1, 2-5 by reductio ad absurdum] We should understand each step of this argument as being indexed to a certain time t, for one can clearly know sometime after t that one is Moored at t.2 Moorean facts present a synchronic, rather than a diachronic puzzle. The argument then shows that S may not know that she is Moored at the time she is Moored. Since it may well be true that p and that S fails to know that p, being Moored is not an impossible state like "S is wet and S is not wet" is at any given time t. What is more, someone other than S may come to know, at t, that S is Moored at t. So, Moorean facts not only pose a synchronic puzzle, but they pose a synchronic puzzle to a particular subject, namely, the person who is Moored.3 Thus, Moorean facts have the weird characteristic of being out of the cognitive reach of the individual who is a part of that fact, while, at the same time, being within the cognitive reach of others.4 Things get worse, however. A different Moorean fact holds whenever p is the case, but one fails to believe that p is the case. Even though p is true and S does not believe that p is true, S cannot know she is in that situation. The argument is similar to the one about knowledge: 1. Ks(p&¬Bsp) [assume for a reductio ad absurdum] 2. Ksp&Ks¬Bsp [1, by distribution of knowledge over conjunction] 3. Ksp [2, by conjunction elimination] 4. Ks¬Bsp [2, by conjunction elimination] 5. ¬Bsp [4, by the factivity of knowledge] 6. Bsp [3, knowledge entails belief] 7. ¬Ks(p&¬Kp) [1, 2-5 by reductio ad absurdum] 2 G.E. Moore, "Moore's Paradox," in G. E. Moore: Selected Writings, ed. Thomas Baldwin (New York: Routledge, 1993), 207-212. 3 This is not meant to exclude the possibility that groups may be Moored. Roy Sorensen argues that groups of people are sometimes Moored. In the case of groups, the "individual" is the relevant group of individuals. See Roy Sorensen, Blindspots (Oxford: Oxford University Press, 1998). 4 From now on I will stop emphasizing that Moorean facts present a synchronic problem. Unless, I state otherwise, this feature of Moorean facts will be presupposed. How to Moore a Gettier: Notes on the Dark Side of Knowledge 135 Both arguments about our epistemic limitation with respect to Moorean facts seem to be sound and fully general ("p" can refer to any proposition whatsoever). What is more, S can reach the conclusion that S cannot know S is Moored a priori, independently of experience. Someone different from S can also know a priori that S cannot know S is Moored. This shows that "S does not know she is Moored" is a contingent truth we know a priori to be true. This situation raises obvious problems about thought. The arguments above show that S's belief that S is Moored can never reach the status of knowledge. If a successful belief is a knowledgeable one, and knowing that one cannot successfully φ gives one sufficient reason not to φ, then the arguments above constitute an a priori reason for one not to believe one is Moored. There is a normative reason for one not to believe that one is Moored. Since believing that p is a way of thinking that p, thinking that one is Moored is always an inappropriate way of thinking about oneself. Thinking that you are Moored has a self-defeating feature to it, similar (but not identical) to believing that you have no beliefs. Moorean facts also raise problems in speech. G.E Moore argued that it is absurd for S to assert "It is raining, but I do not know that it is" or "It is raining, but I do not believe that it is."5 If proper assertion requires that one knows what one asserts, then the fact that we do not know Moorean facts explains why asserting propositions expressing those facts is inappropriate: hearers expect one to know the propositions that speakers assert, and they know the speaker does not know the Moorean fact.6 2. Being Gettiered Edmund Gettiered famously showed that one might have a justified true belief that p and yet fail to know that p.7 In one of the cases Gettier discussed, Smith infers a justified true belief that the man who will get the job has ten coins in his pocket from the false but justified belief that Jones will get the job and Jones has ten coins in his pocket. Smith is Gettiered. Like being Moored, one cannot know one is Gettiered. Here is the proof: 5 Moore, "Moore's Paradox." 6 cf. Peter Unger, Ignorance: A Case for Scepticism (Oxford: Oxford University Press, 1975); Timothy Williamson, Knowledge and Its Limits (Oxford: Oxford University Press, 2000); Keith DeRose, The Case for Contextualism: Volume One (Oxford: Oxford University Press, 2009); Matthew Benton, "Two More for the Knowledge Account of Assertion," Analysis 71, 4 (2011): 684–687; John Turri, "The Express Knowledge Account of Assertion," Australasian Journal of Philosophy 89, 11 (2011): 37–45. 7 Edmund Gettier, "Is Justified True Belief Knowledge?" Analysis 23 (1963): 121–123. Rodrigo Borges 136 1. Ks(Jsp&p&Bsp&¬Ksp) [assume for a reductio ad absurdum] 2. KsJsp&Ksp&KsBsp&Ks¬Ksp [1, by distribution of knowledge over conjunction] 3. Ks¬Ksp [2, by conjunction elimination] 4. ¬Ksp [3, by the factivity of knowledge] 5. Ksp [2, by conjunction elimination] 6. ¬Ks(Jsp&p&Bsp&¬Ksp) [7,8-11 by reductio ad absurdum] 8 As with being Moored, being Gettiered poses a synchronic, rather than a diachronic, epistemic problem. S cannot know she is Gettiered while she is Gettiered. After Smith comes to know he will get the job and that he has ten coins in his pocket, he can then come to know he had a justified true belief that the man who would get the job has ten coins in his pocket, but that he did not know that. Like being Moored, and unlike being wet and not wet, the state of being Gettiered is not an impossible one. What is more, "Gettierean facts" pose a synchronic puzzle to the individual who is Gettiered, not to others; there is no obstacle preventing epistemologists from knowing Smith is Gettiered.9 As with being Moored, S can reach the conclusion that S cannot know S is Gettiered a priori, independently of experience. Epistemologists also know a priori that Smith cannot know he is Gettiered. This shows that "S does not know she is Gettiered" is a contingent truth we know a priori to be true. Being Gettiered similarly raises problems about thought. One cannot know one is Gettiered. If a successful belief is a knowledgeable one, and knowing that one cannot successfully φ gives one sufficient reason not to φ, then the arguments 8 This argument assumes that, if one is Gettiered with respect to p, then one does not know that p. In Stephen Hetherington, How To Know: A Practicalist Conception of Knowledge (Malden: Wiley-Blackwell, 2011) it is argued that one can know that p even if one is Getteried with respect to p. For the purpose of this paper, I will assume that Hetherington is wrong about this. I discuss and reject Hetherington's radical contention in Rodrigo Borges, "Knowledge from Knowledge: an Essay on Inferential Knowledge," PhD thesis, Rutgers University, 2014. 9 If it is possible for groups to know things, then, as far as I can see, nothing prevents those individuals from being Gettiered. Perhaps the following is a case in which a group is Gettiered: group A has a justified true belief that the group that won the public bidding has at least ten years of experience because they received a memo from the government asserting that organization B has ten years of experience and organization B won the bidding. However, the person typing the memo made a mistake and organization A won the bidding and A also has more than ten years of experience. Group A has a justified true belief that the group that won the bidding has at least ten years of experience, but group A does not know that, for its justified true belief depends essentially on a falsehood. How to Moore a Gettier: Notes on the Dark Side of Knowledge 137 above constitutes an a priori reason for one not to believe one is Gettiered. There is, therefore, a normative reason for one not to believe that one is Gettiered. Since believing that p is a way of thinking that p, thinking that one is Gettiered is prima facie inappropriate. If knowledge is the norm of proper assertion, then one should not assert one is Gettiered; it is clearly inappropriate for Smith to assert (before he learns he will get the job), "I am justified in believing the man who will get the job has ten coins in his pocket, it is true that he has, but I do not know that he does." There might be one subtle difference between being Moored and being Gettiered. While believing one is Moored does not prevent one from being Moored (unless believing one does not know that p automatically destroys one's belief that p), one might think that believing one is Gettiered prevents one from being Gettiered because believing one is Gettiered with respect to p destroys one's belief that one is justified in believing that p. If one believes that one is Gettiered, one acquires a defeater for the claim that one is justified in believing that p, thereby falsifying the first conjunct of "Jsp&p&Bsp&¬Ksp." The result is that one acquires a false belief whenever one believes one is Gettiered. This result, if correct, is compatible with my claim that one cannot know that one is Gettiered, while one is Gettiered. Perhaps this provides an explanation of why one cannot know one is Gettiered.10 3. The Dark Side of Knowledge That Moorean and Gettierian facts share all those features is explained by the fact that, if S is Gettiered, then S is also Moored: Jsp&p&Bsp&¬Ksp entails p&¬Ksp The converse, of course, is not the case. That is, one may be Moored but not Gettiered with respect to p. This fact rarely stressed by philosophers.11 Since being Gettiered entails being Moored, whatever "badness" we assign to the state of being Moored is also present in the state of being Gettiered. Gettiered agents are in a much worse epistemic situation than philosophers have so far realized, for Smith 10 Thanks to Georgi Gardiner for discussion here. 11 Michael Veber is the only exception I know of on this subject (see Veber, "I Know I Am Not Gettiered"). However, he mentions this point in passing, without stopping to discuss it. Here I take Veber's remark further. Rodrigo Borges 138 not only fails to know the truth he justifiably believes, but it is logically impossible for him to know he is in that situation, and, if proper assertion requires knowledge, he may not assert that she is Gettiered either. There are a few things we can say about this bad epistemic place in which Gettiered agents find themselves. The following considerations will also apply to the badness of being Moored, since one cannot know one is Moored either. Timothy Williamson has argued that no non-trivial condition C is "luminous." A condition C is luminous if it satisfies the following definition: (L) For every case α, if in α C obtains, then in α one is in a position to know that C obtains Williamson argues that no non-trivial condition satisfies (L).12 It can be shown that, given (L), being Moored and being Gettiered are non-trivial, nonluminous conditions. They are non-trivial conditions because neither of them holds necessarily or necessarily fails to hold.13 The condition of being taller than oneself satisfies (L) vacuously and is thus trivially luminous, while the condition of being identical to oneself is trivially luminous because it obtains in every case α. To see that being Moored or being Gettiered are not luminous conditions, let us assume, with Williamson, that, if one is in a position to know that C obtains, and one has done what one is in a position to do to decide whether C obtains, then one knows that C obtains.14 The arguments in the two previous sections show that there is no case α such that S is Gettiered or Moored in α and S is in a position to know she is Gettiered or Moored in α, for there is nothing one can do in α that will give one knowledge that one is Moored or Gettiered. Thus, being Moored or being Gettiered are not luminous conditions, according to Williamson, for neither condition satisfies the definition of a luminous condition, (L). In fact, we can see that something stronger is true of the conditions of being Moored and being Gettiered, for they are not only non-trivial, non-luminous conditions, but they are, what we may call "non-trivial dark conditions." A condition C is non-trivially dark if it satisfies the following definition: (D) For every case α, if in α C obtains, then in α one is not in a position to know that C obtains (D) is not the mere denial of (L). The fact that C is not luminous is necessary, but not sufficient for C to be a dark condition. One is sometimes in a position to know that condition C obtains even if C is not luminous (that C is not 12 Williamson, Knowledge and Its Limits, 97–102. 13 Williamson, Knowledge and Its Limits, 107–8. 14 Williamson, Knowledge and Its Limits, 95. How to Moore a Gettier: Notes on the Dark Side of Knowledge 139 luminous entails only that one is not always in a position to know that C obtains). If C is a dark condition, however, then there is no case α such that one is in a position to know, in α, that C obtains. Dark conditions are not trivial conditions. The conditions of being Moored and of being Gettiered obtain in some cases but not in others, but they are always out of our cognitive reach. The arguments in the previous sections establish that being Gettiered and being Moored are dark conditions in the sense of (D). Williamson does not discuss dark conditions as I have defined them, but, given the arguments above, a full story about luminosity ought to include a discussion of conditions that, like being Gettiered and being Moored, obtain in some but not all cases and with respect to which one is never in a position to know they obtain (at the time in which they obtain). In short, a discussion of luminosity is not complete without a discussion of dark conditions. The argument in the previous section shows that being Gettiered is a cognitive "blindspot," in the sense introduced by Roy Sorensen.15 "Blindspot" is a technical term for Sorensen, to be distinguished from "blind spot." The latter term is used in physiology to refer to the area in one's retina devoid of rods and cones, and, therefore, insensitive to light. The former term refers to a relational property whose relata are a person S, a fact p, and a time t. Sorensen defines a blindspot thus:16 (B) the fact that p is a blindspot for an agent S at a time t if and only if S is not in a position to know that p at t. Notice that blindspots are dark conditions in the way defined by (D). The converse is also true: if the fact that p is a blindspot for S at t, then the condition, C, p is about is a dark condition. It is only fitting that dark conditions constitute epistemic blindspots. Even though Sorensen recognized that Moorean facts are blindspots, he failed to see that Gettierian facts are also Moorean facts. This paper contributes to the discussion of blindspots by showing that Gettierian facts are blindspots. 4. Conclusion This ends my brief exploratory notes on the striking similarities between the states of being Moored and of being Gettiered. Being Gettiered entails that one is Moored, and it is logically impossible for one to know that one is in either of those 15 Sorensen, Blindspots. 16 Sorensen, Blindspots, 1-13. Rodrigo Borges 140 states while one is in them. Those states are dark conditions, synchronically always in our cognitive blind spot.17 17 Thanks to Michael Veber for discussion on some of the issues in this paper and for the inspiration to write it. Thanks also to Georgi Gardiner for fruitful discussion on an earlier draft of this paper. Special thanks to Peter Klein for discussing with me different drafts of this paper. The research for this paper was partially funded by the Capes/Fulbright Commission. I am grateful for their support.