Sensitivity Theory and the Individuation of Belief-Formation Methods

Erkenn (2009) 70:271 281 DOI 10.1007/s10670-008-9127-9 ORIGINAL ARTICLE Sensitivity Theory and the Individuation of Belief-Formation Methods Mark Alfano Received: 22 August 2007 / Accepted: 2 October 2008 / Published online: 24 October 2008 Ó Springer Science+Business Media B.V. 2008 Abstract In this paper it is argued that sensitivity theory suffers from a fatal defect. Sensitivity theory is often glossed as: (1) S knows that p only if S would not believe that p if p were false. As Nozick showed in his pioneering work on sensitivity theory, this formulation needs to be supplemented by a further counterfactual condition: (2) S knows that p only if S would believe p if p were true. Nozick further showed that the theory needs a qualification on the method used to form the belief. However, when these complications are spelled out in detail, it becomes clear that the two counterfactuals are in irresolvable tension. To jibe with the externalist intuitions that motivate sensitivity theory in the first place, (1) needs a fine-grained grouping of belief-formation methods, but (2) needs coarse-grained grouping. It is therefore suggested that sensitivity theory is in dire straits: either its proponents need to provide a workable principle of method individuation or they must retrench and give up their claims to providing sufficient conditions for knowledge. 1 Introduction This paper aims to show that one externalist account of knowledge Robert Nozick s sensitivity theory suffers from a fatal defect. According to sensitivity theory, S knows that p only if S wouldn t believe that p if p were false. 1 As Nozick showed in his pioneering work on sensitivity theory, this formulation needs to be supplemented by a further counterfactual condition: S knows that p only if S would believe p if p were true. My claim is that this expanded version of sensitivity theory 1 Cf. Nozick (1981, p. 177). M. Alfano (&) c/o Program in Philosophy, CUNY Graduate Center, 365 Fifth Avenue, New York, NY 10016, USA e-mail: mark.alfano@gmail.com

272 M. Alfano contains problems so deep that Nozick s project is doomed. In particular, I argue that the very cases that motivate externalists to accept sensitivity theory can be modified in such a way that they tell against Nozick s view. I believe that careful appraisal reveals a prima facie conflict between Nozick s two counterfactual conditions, and I adduce examples to suggest that this conflict cannot be resolved. For externalists, then, this paper poses the direct problem of accounting for a clash of intuitions over Nozick s two counterfactual conditions. In so doing it lends comfort to internalists, who, though they may not feel the pull of the examples, will be thrilled to learn that their dialectical opponents house is not in order. Nozick begins his discussion with a simplified version of sensitivity theory (ST). According to this simplified version, ST: S knows that p if and only if: (i) S believes that p, (ii) p, and (iii) If *p were the case, S would not believe that p. For reasons that will be discussed below, Nozick rejects ST as too liberal: it overascribes knowledge. He supplements it with a fourth condition, yielding ST 0 : ST 0 : S knows that p if and only if: (i) S believes that p, (ii) p, (iii) If *p were the case, S would not believe that p, (iv) If p were the case, S would believe that p. 2 Condition (iv) is not directly implied by (i) and (ii) because in ST 0 the subjunctive conditional is analyzed not according to Lewis s (1973) semantics (viz. x? y is true just in case the closest x-world is also a y-world), but rather according to the notion of a belt or neighborhood of worlds surrounding the actual world (viz. x? y is true just in case the set of close x-worlds contains only y-worlds). ST, by contrast, analyzes the subjunctive conditional in Lewis s way. 3 Despite its parsimony, ST does not supply sufficiently stringent conditions for knowledge. Nozick in his pioneering work on sensitivity theory illustrates this deficiency with a skeptical scenario in which the subject call him Hilary truly believes that he is in the skeptic tank: Imagine as actual a world in which he is in the tank and is stimulated to believe he is, and consider what subjunctives are true in that world. It is not true of him there that if he were in the tank he would believe it; for in the close world (or situation) to his own where he is in the tank but [the scientists] don t give him the belief that he is (much less instill the belief that he isn t) he 2 I will use the following abbreviations throughout the paper: Bp for S believes that p, and x? y for the subjunctive conditional If x were the case, then y would be the case. 3 Of course, a compromise could be made by giving yet a third reading to the subjunctive conditional. Say x? y is true just in case the closest non-actual-x-world is a y-world. To my knowledge only Michael Levin has proposed this rather obvious reading (forthcoming: Sensitivity Training ).

Sensitivity Theory and the Individuation of Belief-Formation Methods 273 doesn t believe he is in the tank. Of the person actually in the tank and believing it, it is not true to make the further statement that if he were in the tank he would believe it so he does not know he is in the tank. (1981, pp. 176 177) ST gives the wrong result in this situation. Since the closest world at which Hilary is not in the skeptic tank is also one at which he believes he is not, (iii) is satisfied, but we obviously do not want to say that Hilary knows he is in the tank. His belief that he is in the tank does not co-vary across worlds with his being in the tank. ST 0, by contrast, deals successfully with this scenario. According to ST 0, Hilary does not know he is in the tank because (iv) is violated: the close worlds where he is not stimulated to believe he is in the tank (but nevertheless is in it) are not worlds where he believes he is in the tank. In the balance of this paper, therefore, I will deal with ST 0. In outline, my argument is that (iii) and (iv) are in irresolvable tension. Both must be supplemented with a rider specifying which method is used to form the belief, but (iii) needs to cut belief-formation methods finely and (iv) needs to cut them coarsely. ST 0 needs to distinguish believing via one method from believing via another, but it cannot make a principled distinction that gives the desired results for both (iii) and (iv). Whereas (iii) becomes easier to satisfy the more finely we slice methods, (iv) fails to do its designated work when methods grow too specific. Conversely, if one opts for coarse-grained grouping, (iv) is satisfied in the right situations but (iii) becomes too liberal. I want to suggest that there is no middle ground where both counterfactual conditions function properly. 2 Individuation of Methods is Not Optional Nozick notices early in his account that he needs a requirement on the method used to form a belief. Examples like Grandma bring this out: Grandma. Grandma believes that her darling grandson Bobby is well. This is because he just visited her and she looked him up and down before serving him an overcooked brisket. However, if Bobby were not well, the family would call grandma and tell her he was healthy why pile woes upon widows? 4 Grandma is a counterexample to ST 0 as formulated above. In this story, we want to say that Grandma knows that Bobby is healthy, but condition (iii) is violated. If Bobby were sick, Grandma would believe he was healthy. Nozick s solution to the Grandma problem and similar scenarios is to say that, although Grandma would nevertheless believe that Bobby is healthy were he sick (i.e., *p? Bp, which implies *[*p? *Bp]), she would come to believe in a different way or via a different method. Rather than visually inspecting Bobby, she would receive testimony from her children. But presumably were she to see Bobby (in a slightly more removed world in which he is sick and she manages to visit him) 4 Cf. Nozick (1981, p. 179).

274 M. Alfano she would recognize that he is unwell. Hence, she knows that he is healthy. Thus, we add an epicycle to the theory: ST 00 : S knows via method M that p if and only if (i) Bp via M, (ii) p, (iii 0 ) *p? *(Bp via M), and (iv 0 ) p? Bp via M. So far, so good. But now the inevitable question arises: what is a method? More specifically, how are methods to be individuated? 5 When are two belief-formation events m 1 and m 2 tokens of the same method type M? Ideally, we would like to define a binary relation R such that: ð8m 1 Þð8m 2 Þ½R M ðm 1 ; m 2 Þðm 1 2 M & m 2 2 MÞŠ; where m 1 and m 2 range over belief-formation events and M is a method type. 3 What is the Logic of Sorting Methods? Nozick is not altogether clear about how to sort methods. 6 I will consider three ways of symbolizing via M in the third and fourth conditions, arguing that only one of them plausibly accomplishes the task at hand. First, consider a material conditional rendering: (iii 0 ) *p? *(S uses M. *Bp) (iii 00 ) tells us to look at the belt of close *p-worlds. At each such world, if S either does not believe that p or does not use method M, then the subjunctive conditional is true. This version is unsatisfactory because (iii 00 ) is trivially true if, at all the nearby *p-worlds, S does not use M. We want to know whether the method tracks truth, not just whether it is isolated in modal space. Next, consider a nested subjunctive conditional: (iii 000 ) *p? (S uses M? *Bp) According to (iii 000 ), we should first go to the belt of *p-worlds around the actual world @, and then take another trip to the M-using-worlds in and around this belt. The problem with this interpretation is that, the larger the belt of M-worlds around the *p-worlds close to @, the greater the chance it may contain p-worlds. Consider the following: (iii 000 ) first sends us to W2 and W3. Then it tells us to look at W3 and W4. (iii 000 )is satisfied because *Bp is true at W3 and W4. But obviously W4 is a problem: S s belief is false at W4. 5 As Quine s famous slogan puts it, There is no entity without identity (1981, p. 102), so if we are to countenance doxastic methods, we need a clear principle of individuation. 6 For instance, he rewords (iii 0 ) as If p weren t true and S were to use M to arrive at a belief whether (or not) p, then S wouldn t believe, via M, that p (1981, p. 179). M occurs in both the antecedent and the consequent of the subjunctive conditional here. Need it?

Sensitivity Theory and the Individuation of Belief-Formation Methods 275 Fig. 1 Countermodel to (iii 000 ) @ W1 W2 W3 W4 p p ~p ~p p S uses M ~(S uses M) ~(S uses M) S uses M S uses M Bp Bp Bp ~Bp ~Bp Finally, consider the reading I prefer: (iii 0000 ) (*p & S uses M)? *Bp. This translation tells us to consider only the worlds near @ at which both pis false and M is used. The analogous version of the fourth condition is: (iv 00 ) (p & S uses M)? Bp. In terms of Fig. 1 above, (iii 0000 ) is satisfied. (iv 00 ), however, is violated by W4. First we look at @ and W4. At W4, we do not have Bp. Thus, we get the desired result: since (iv 00 ) is false, knowledge is not ascribed, and the counterexample to (iii 000 ) is deflected. In the balance of this paper, I will therefore construe sensitivity theory as follows: ST 000 : S knows via method M that p iff (i) Bp via M, (ii) p, (iii 0000 )(*p& S uses M)? *Bp, and (iv 00 ) (p & S uses M)? Bp. 4 Condition (iii 0000 ) Presupposes Fine-Grained Individuation Examples like Dack and Redwood require fine-grained method grouping to avoid underascription of knowledge through violation of (iii 0000 ). Dack. Suppose Oscar is standing in an open field containing Dack the dachshund. Oscar sees Dack and (noninferentially) forms a belief in [p]: The object over there is a dog. [ ] Further suppose that Oscar has a tendency to mistake wolves for dogs (he confuses them with malamutes, or German shepherds). Then if the object Oscar saw were Wiley the wolf, rather than Dack the dachshund, Oscar would (still) believe [p]. (Goldman 2005, p. 92) Goldman takes Dack to show that method grouping must follow stringent lines. Indeed, he proposes that m 1 and m 2 count as tokens of the same method type just in case they are perceptually equivalent. That is, he counts two tokens as being of the same method type only if the percepts they produce are indistinguishable ( from the inside, as one says). 7 In this way, he avoids the unwanted result that Oscar does not 7 A perceptual equivalent of an actual state of affairs is a possible state of affairs that would produce the same, or a sufficiently similar, perceptual experience (Goldman 2005, p. 93). If not for the sufficiently similar rider, this would be a very helpful definition. The whole problem is how similar is similar enough.

276 M. Alfano know that p. If there were not a dog over there but Wiley the wolf instead, Oscar would still believe p, but he would be using a different method because he had a different percept. Hence, (iii 0000 ) is not violated and ST 000 is saved. The moral of Redwood is similar: Redwood. Suppose Scotty sees and correctly identifies a redwood as a tree. Suppose further that there are plants nearby that Scotty would mistake for bonsai trees if he were to see them and that Scotty would have seen them if he did not see the redwood. Nevertheless, it seems, Scotty knows that he sees a tree. The way out is again to individuate methods via perceptual equivalence. Since Scotty would draw on a doxastically non-equivalent percept, the method he would use to come to believe he does not see a tree is different from the method he actually uses. Hence, (iii 0000 ) is not violated; the mere presence of bonsai-like plants does not disqualify Scotty s knowledge. If, however, there were some fake Redwoods nearby (to mimic the timeworn barn scenario) Scotty would not know that he sees a tree. If Goldman is right, perceptual equivalence is the way to sort methods. This is basically the same principle of individuation suggested by Nozick: Usually, a method will have a final upshot in experience on which the belief is based, such as visual experience, and then (a) no method without this upshot is the same method, and (b) any method experientially the same, the same from the inside, will count as the same method. (1981, pp. 184 185) However, perception is not the only source of belief; we also want to talk about beliefs caused by testimony, memory, deduction, induction, and perhaps abduction and intuition. We therefore want a more general characterization along Goldman s and Nozick s lines. The notion of perceptual equivalence clearly suggests the notion of doxastic equivalence. Roughly put, doxastic equivalence is equivalence of belief-causing power. We may formulate relation R above as follows: (R1) R(m 1, m 2 ) just in case m 1 is doxastically equivalent to m 2. If m 1 and m 2 would lead to all and only the same beliefs, they are doxastically equivalent and therefore tokens of the same method type. As already mentioned, this cuts the dough of method very thin. According to (R1), seeing a Dell-like laptop is not the same method as seeing an Apple-like laptop (given that S is familiar enough with laptops to distinguish Dells from Apples). Indeed, according to (R1), seeing a familiar face in head-on is not the same method as seeing that face in three-quarters profile. Footnote 7 continued Note that Goldman is working with reliabilism rather than sensitivity theory. The two are contrapositive cousins (reliabilism says Bp? p and *Bp? *p where sensitivity theory says p? Bp and *p? *Bp). Although the counterfactual conditional cannot be validly contraposed, results that apply to one theory can often be applied with at most minor modifications to the other.

Sensitivity Theory and the Individuation of Belief-Formation Methods 277 5 Condition (iv 00 ) Demands Coarse-Grained Individuation In my view, the almost-exclusive attention paid to (iii 0000 ) in the literature has led epistemologists to ignore the competing claims of (iv 00 ). The explication of beliefformation methods has privileged (iii 0000 ), and in so doing has produced an analysis of R that does not work for (iv 00 ). (R1) seems too extreme to many theorists: a method should be a robust process that can be used in many circumstances, not something that can only be used a couple of times in the course of human history. Doxastic equivalence seems too high a bar to set for same-method-hood. In this section, I will argue that this intuition is well grounded. If distinctions between methods are too precious, we end up overascribing knowledge. Recall that Nozick initially proposes (iv 00 ) to rule out non-knowledge beliefs that (iii 0000 ) fails to disqualify. If Hilary is in the skeptic tank and is stimulated to believe that he is in the tank, (iii 0000 ) is satisfied. He believes truly that he is in the tank, and if he were not in the tank, he would not believe it (because he would never have been there in the first place, and so would not have beliefs artificially instilled in him by the scientists), but we resist saying that Hilary knows he is in the tank. (iv 00 ) is intended to save us from this admission. Since there are close worlds at which Hilary would not believe he is in the tank, even though he is, (iv 00 ) is violated. Note, however, that doxastic equivalence is too stringent to allow for this interpretation. (R1) lets us consider only the close worlds at which Hilary is in the tank and the neurologists cause him to think he is. If he weren t caused to have this belief, he would not have used a doxastically equivalent method. Obviously his belief is true at all such worlds. For (iv 00 ) to perform its intended labor, methods must be individuated more coarsely. To further motivate this conclusion, consider the following scenario: Steel Penny. Ferris is a blind boy whose father is a numismatist with a huge collection of steel pennies from the war years. Ferris has, in fact, never encountered a copper penny. On the day he receives his first allowance, he goes to the local convenience store and buys a chocolate bar. His change is $1.01, and by a stroke of luck he receives a steel penny the only one in the till. The coin drops on the counter as the cashier tries to hand it to him, and, hearing the telltale steel clink, Ferris comes to believe that a penny just dropped. If, however, he had received one of the many copper pennies, he would not have recognized it as a penny. In Steel Penny, p= a penny just dropped. If we follow Goldman in defining R according to (R1), however, Ferris uses a different method to form a belief that *p at the close possible world W where he heard a copper penny. At @, m 1 causes him to believe that p, but at W, m 2 causes him to believe that *p. Since m 1 and m 2 are not doxastically equivalent, Ferris does not use the same method at @ and W, so (iv 00 ) is not violated. Schematically, this situation is represented in Fig. 2: The only way to say that (iv 00 ) is violated in the case of Steel Penny is to admit that Ferris does use the same method in both worlds. And this indicates that (R1) is not a proper interpretation of R.

278 M. Alfano @ p W p S uses m 1 M S uses m 2 M Bp ~Bp Fig. 2 Countermodel to doxastic equivalence This defect in (R1) is not limited to skeptic tank and auditory experience. Further examples using other sense modalities, as well as for non-perceptual sources of belief, can be constructed to illustrate why individuating methods as per (R1) does not give the desired result. I will show this with Barn Redux (vision) and Banana Republic (testimony). Barn Redux. Henry s brother Henri is traveling through barn country. He s been reading about his brother in epistemology journals, so he has decided to believe that something is a barn only if it is red. Anything that seems like a white barn is not to be trusted. Unfortunately for Henri, someone has replaced all the white facades with real white barns: everything that looks like a barn in this district really is a barn. Henri happens upon the only red barn in the district. He believes it is a barn. However, if he had not seen the red barn, he would have seen one of the white ones and thought it was not a barn. In Barn Redux, at @ S believes that p (= S sees a barn) on the basis of m 1, seeing a red-barn-like-thing. But at W, S believes that *p on the basis of m 2, seeing a white-barn-like-thing. According to (R1), m 1 and m 2 are not tokens of the same method type, so S knows he is seeing a barn. But does S really know that p? I think not, and I suspect that anyone sympathetic to the original barn scenario would agree. The only way to say he does not know, however, is to claim that (iv 00 ) is violated because m 1 and m 2 are tokens of the same method type. If this is right, doxastic equivalence is too stringent. We need a more coarse-grained grouping of tokens into types. Compare this scenario to Banana Republic, Harman s well-known example of the vacationer who believes a true newspaper report saying the dictator has died (Harman 1973, pp. 142 154). He goes on holiday soon afterwards and thus omits to read the many (false) retractions in the same newspaper saying that the dictator is in good health. We may suppose, to intensify the example, that on vacation he buys a different paper, one he normally never reads, and that this paper has not yet been updated with the retraction. Dozens of copies of his normal paper are available, but on a whim he decides to buy a different one. S does not know that the dictator is dead, but obviously he does not use a doxastically equivalent method at the close world in which he does read and believe the retraction (Harman 1973, pp. 142 154). If, as externalists tend to think, these are examples of non-knowledge, then they show that there is something wrong with (R1). It all too easily allows (iv 00 )tobe satisfied because it does not allow enough p-worlds to be considered. Furthermore, the examples seem to suggest a much coarser-grained construal of the relation R, on the basis of the modality employed in forming the belief:

Sensitivity Theory and the Individuation of Belief-Formation Methods 279 (R2) R(m 1, m 2 ) just in case m 1 and m 2 are both cases of vision or olfaction or audition or tactition or gustation or testimony or deduction or testimony. The right-hand side of this biconditional probably needs a few more disjuncts, but the idea should be intuitively clear. Yet, although (R2) gives the right result in Grandma, Steel Penny, Barn Redux, and Banana Republic, its guidance is obviously not to be trusted in Dack or Redwood. This leaves us at an impasse: is there a principled way to construe the relation R so that it gives the right results for both (iii 0000 ) and (iv 00 )? That is, can we formulate a happy compromise between the extremely fine-grained (R1) and the rather coarse-grained (R2)? 6 Compromises, Compromises It is difficult to formulate an informative analysis of R between (R1) and (R2). 8 Consider the following: (R3) R(m 1, m 2 ) just in case m 1 and m 2 are doxastically consistent (i.e. cause some of the same beliefs). This principle of individuation counts m 1 and m 2 as the same method if and only if there is some belief they would both cause. This is obviously too coarse-grained, since it gives the wrong result for Dack and Redwood, inter alia. (R4) R(m 1, m 2 ) just in case m 1 and m 2 are doxastically similar. We may say that m 1 and m 2 are doxastically similar if they cause mostly the same beliefs. (R4) wedges its way in between (R1) and (R3). It is, however and unfortunately, rather vague. It is still unclear how to apply the notion of majority. Should we just count the beliefs that m 1 and m 2 both cause, and then compare that number to the number only one of them causes? Or should we weight the beliefs in terms of relevance or importance? Probably the latter is preferable, but then the obvious question arises: how do we weight the beliefs? Aside from the worry over whether such weighting can be objective or at least intersubjective, paired scenarios like the standard barn situation and my Barn Redux are almost guaranteed to demand different weightings on any scale. That is to say, since the percepts in Barn and Barn Redux are identical, any way of weighting beliefs that gives the right result for one is guaranteed to give the wrong result for the other. Counterpart redux versions of the traditional examples like Judy & Trudy, Dack, and Redwood are easily constructed: just add to the story that S is somewhat paranoid, ignorant of some fine distinction, or has been reading contemporary epistemology. 8 In his forthcoming Sensitivity Training, Levin identifies a fallback position for reliabilism. He says that a method [M] for forming [the belief that p] is trivializing (for p) if [M] cannot be used unless p; Moore s method [seeing a hand], for instance, trivializes. Perhaps (iii 0000 ) and (vi 00 ) both give the right results if we individuate methods trivially? One obvious problem with trivializing methods is that they completely beg the question against skepticism. That aside, a decision to use trivializing methods does not give us a definition for R. Trivializing methods are compatible with m 1 and m 2 in the above examples being tokens of the same method type (since in all such cases p is true at both @ and W), but they are also compatible with m 1 and m 2 being different. The question of trivializers is thus orthogonal to our problem.

280 M. Alfano Fig. 3 Comparison of typical barn scenarios with their redux versions As Fig. 3 shows, standard barn scenarios involve beliefs that outstrip their propositional contents. The redux versions involve contents that outstrip their corresponding beliefs. 7 Upshot I do not want to claim to have proved once and for all that no correct principle of method individuation exists, but I doubt that any is forthcoming. If, as I suspect, this is because there really is none, then we need to admit that the third and fourth conditions of sensitivity theory are in irresolvable conflict. The theory can be salvaged, therefore, only by dropping one of these two conditions. However, regardless of which one is discarded, the remnant-theory will end up overascribing knowledge. The upshot is that sensitivity theory as such is in dire straits. Either its proponents need to provide a workable principle of method individuation, or they must admit that ST 000 at best establishes necessary conditions for S s knowing that p: it does not provide sufficient conditions. Acknowledgment I would like to thank Michael Levin and two anonymous referees for their helpful comments on drafts of this paper. References Goldman, A. (2005). Discrimination and perceptual knowledge. In S. Bernecker & F. Dretske (Eds.), Knowledge (pp. 86 102). Oxford: Oxford University Press. Harman, G. (1973). Thought. Princeton: Princeton University Press.

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