© LOGOS & EPISTEME, VI, 2 (2015): 221–224 EASY KNOWLEDGE MAKES NO DIFFERENCE: REPLY TO WIELENBERG1 Juan COMESAÑA and Carolina SARTORIO ABSTRACT: We have recently proposed a diagnosis of what goes wrong in cases of 'easy-knowledge.' Erik Wielenberg argues that there are cases of easy knowledge that our proposal cannot handle. In this note we reply to Wielenberg, arguing that our proposal does indeed handle his cases. KEYWORDS: easy knowledge, evidential support, reliability, Erik Wielenberg We have recently proposed a diagnosis of what goes wrong in cases of 'easyknowledge.'2 Erik Wielenberg argues that there are cases of easy knowledge that our proposal cannot handle.3 In this note we reply to Wielenberg, arguing that our proposal does indeed handle his cases. We claim that cases of easy knowledge violate the following constraint on evidential support: Epistemic DM2: E evidentially supports P (relative to a background of evidence B) only if it's not the case that not-E evidentially supports P (relative to B). Wielenberg presents one of his cases as follows:4 Suppose that Roxanne has no idea whether her car's fuel gauge is reliable. She checks the fuel gauge and reasons as follows (where 'X' indicates some precise level of fuel in the tank – e.g., completely full, one-half full, etc.): Reasoning C (4) The gas gauge indicates X. 1 Thanks to Eric Wielenberg for his note and for comments on drafts of this note. Thanks also to the editors of Logos and Episteme for the opportunity to reply. 2 Juan Comesaña and Carolina Sartorio, "Difference-Making in Epistemology" Noûs 84, 2 (2014): 368-87. For further relevant discussion, see also Juan Comesaña, "Reply to Prior," in Contemporary Debates in Epistemology, 2nd edition, eds. Matthias Steup, John Turri, and Ernest Sosa (Oxford: Wiley-Blackwell, 2014), 239-243. 3 Erik Wielenberg, "Difference-Making and Easy Knowledge: Reply to Comesaña and Sartorio," Logos and Episteme VI, 1 (2015): 141-146. 4 Completely analogous remarks apply to Wielenberg's other case. Juan Comesaña and Carolina Sartorio 222 So, (5) the gas tank is X. Therefore, (6) on this occasion, the reading on the gas gauge corresponded exactly to the amount of gas in the tank. As before, Roxanne can use the same sort of reasoning on multiple occasions to build a solid inductive case for the reliability of the gas gauge. So, suppose she draws on multiple instances of reasoning C to arrive at: (7) The gas gauge is very reliable – it's disposed to indicate the level of fuel in the tank with a high degree of accuracy.5 According to Wielenberg, this is a case of easy knowledge that does not violate Epistemic DM2. This is because "the conjunction of not-(4) and not-(5) does not imply (6)."6 From the fact that the gauge does not indicate X and that the tank is not X Roxanne cannot conclude that the reading on the gauge corresponds exactly to the amount of gas on the tank – only that the gauge did not err this time by reading X while the tank is not X. We agree that the conjunction of not-(4) and not-(5) does not imply (6) – but, nevertheless, we shall argue that Reasoning C is not a counterexample to Epistemic DM2. Let us start by being more precise about Roxanne's inference in Reasoning C. Let 'G ' be the proposition that the gas gauge reads X and 'T ' be the proposition that the tank is X. (4) and (5) then are, respectively, just 'G ' and 'T '. But how should we understand (6) and (7)? That the reading of the gauge corresponds exactly to the amount of gas in the tank is a disjunction of conjunctions: either the gauge reads full and the tank is full, or the gauge reads one-half and the tank is one-half full, etc. Remember that, in Wielenberg's presentation, ' ' is functioning not as a variable but as corresponding to "some precise level of fuel in the tank." Let us suppose that the gas gauge can indicate readings between and , for some finite . Then (6) should be read as: (6*): Either G and T , or ... , or G and T . Notice that (4) and (5) support (6*) only because they support one of the disjuncts: (6.1): G and T . 5 Wielenberg, "Difference-Making and Easy Knowledge," 143-144. 6 Wielenberg, "Difference-Making and Easy Knowledge," 144. Easy Knowledge Makes No Difference 223 What about (7)? What is it for a gauge to accurately indicate the level of fuel in the tank? It is for the tank to be full if the gauge reads full, half-full if the gauge reads half-full, etc. So, to a first approximation, (7) should be read along these lines: (7*) For all x, if the gauge reads x, then the tank is x. Wielenberg incorporates reliability considerations into the content of (7) itself – but, more plausible, what is reliable is the inference from repeated instances of (6*) to (7*) – after verifying (6*) over and over, Roxanne becomes more and more confident of (7*). But perhaps repeated instances of (6*) justify Roxanne in drawing a stronger inference – not only does the gas gauge happen to correctly indicate the content of the tank, but it does so in a modally robust way. If so, then perhaps we should reformulate (7*) as follows: (7**) For all x, if the gauge were to read x, then the tank would be x. Consider now how to apply Epistemic DM2 to Reasoning C. We start with the negation of (4), which supports the negation of (5) provided that (4) supports (5): not-(4): not-G not-(5): not-T Now, Wielenberg is correct that we cannot get to (6*) from not-(4) and not- (5). But getting to (6*) from (4) and (5) is not an instance of easy knowledge – or, at least, it is not (6*) that almost everyone finds objectionable (a bit more on this below). What almost everyone finds objectionable is, rather, the inference to (7*) and (7**). And notice that, whereas not-(4) and not-(5) don't entail (6*), they do support (7*) and (7**). For not-(4) entails: (8): not-(G and not-T ) That is to say: from the fact that the gauge does not read, for instance, onehalf, it follows that it is not the case that both the gauge reads one-half but the tank is not one-half. In other words, from the fact that the gauge does not read one-half it follows that either it does not read one-half or the tank is one-half. In still other words, the following conditional (read as a material conditional) follows from not-(4): (8*) If G , then T Juan Comesaña and Carolina Sartorio 224 Roxanne can now rely on multiple instances of the reasoning from not-(4) to (8*) to conclude with a high degree of confidence, just as before: (7*) For all , if the gauge reads , then the tank is ; and (7**) For all x, if the gauge were to read x, then the tank would be x. So, not-(4) supports (7*) and (7**) if (4) does. After all, repeated instances of (8*) support (7*) and (7**).7 So, if (4) supports (7*) and (7**), then not-(4) supports them as well. Therefore, Epistemic DM2 does block the move from (4) to (7*) and (7**), and so does explain why there is no easy knowledge in Wielenberg's case. There is a residual question: what about the move from (4) to (6*)? Isn't that an inference that should also be banned? On this question, we wish to make two points. First, notice that (6*) is entailed by (6.1), and that (6.1) follows from (4) is barely more than the statement of the views that allow for easy knowledge. So (6*) is not, as we remarked before, what almost everyone finds objectionable about those views (nor does Wielenberg claim that it is). The objection is that, once we get to (6*), the move to (7*) and (7**) cannot be stopped, and it is those further inferences that are objectionable. Our view explains why those further inferences are objectionable, and so explains what is wrong with easy knowledge. Second, notice that (6*) entails (8*). So, given a proper closure principle, (4) supports (6*) only if (4) supports (8*). Therefore, modulo that closure principle, Epistemic DM2 entails that (4) does not support (6*). Some philosophers might prefer to give up the corresponding closure principle before giving up the claim that (4) supports (6*). Epistemic DM2 is consistent with that position as well. In sum, Epistemic DM2 can handle Wielenberg's case. 7 (7*) and (7**) entail (8*). Therefore, one way in which (7*) and (7**) could be false is for (8*) to be false. Given that the falsity of (8*) would refute (7*) and (7**), its truth supports them. Indeed, under standard assumptions, a probabilistic construal of the evidential support relation guarantees that (8*) supports (7*) and (7**). As in our previous paper, we do not assume that this probabilistic construal is correct in the details, but we do believe that it gives the right result in this case. This is compatible, of course, with the claim that (6*) also supports (7*) and (7**), and indeed compatible also with the claim that (6*) supports those propositions more than (8*) does.