The Bayesian Objection Ch 4 of Seemings and Epistemic Justification Luca Moretti University of Aberdeen l.moretti@abdn.ac.uk PLEASE DO NOT QUOTE WITHOUT PERMISSION 4. The Bayesian Objection 4.1 Introduction In this chapter I analyse an objection to phenomenal conservatism to the effect that phenomenal conservatism is unacceptable because it is incompatible with Bayesianism. I consider a few responses and dismiss them as misled or problematic. Then, I argue that the objection doesn't go through because it rests on an implausible formalization of the intuitive notion of seeming-based justification. In the final part of the chapter, I investigate how seeming-based justification and justification based on one's reflective belief that one has a seeming interact with each other. 4.2 White's objection According to the phenomenal conservative, (PC) If it seems to S that P, S thereby has prima facie justification for believing P. As clarified in §2.1, the 'thereby' in (PC) indicates that S's justification for P rests solely on S's appearance that P, which need not be justified. S's justification for P is thus immediate because it is not based on any independent justification of S. Furthermore, S's justification for P is non-inferential because it is not available to S through some inference or possible inference of S. Schiffer (2004), Cohen (2005), White (2006), and Wright (2007) have all argued that (PC) is flawed or very problematic because it is at odds with Bayesianism. These objections are very similar. I focus on White (2006) because White's objection is the most detailed and clear, and the most discussed in the literature. All these authors crucially rely on the same implausible formalization of the intuitive notion of seeming-based justification, which I criticize and reject in this chapter. Thus, my reply to White is meant to respond –– indirectly –– to the other Bayesian objections as well. 2 White specifically targets perceptual dogmatism –– namely, phenomenal conservatism circumscribed to perceptual justification. White's challenge could nevertheless be re-formulated to target phenomenal conservatism in other domains.1 The Bayesian assumes that our degrees of rational confidence –– or credences –– obey probability calculus. Furthermore, the Bayesian conceives of both hypotheses and evidence as propositions held to be true by the subject with a degree of rational confidence enclosed between 0 and 1, where 0 represents certainty in the proposition's falsehood and 1 certainty in its truth.2 The charge raised by White against (PC) is to the effect that (PC) is inconsistent with the Bayesian account of how perceptual evidence rationally affects our credences in hypotheses. Given its intuitive appeal, ductility and an impressive list of insightful analyses, Bayesianism is enormously influential in today's epistemology. If (PC) were actually incompatible with Bayesian reasoning, many would conclude that it is (PC) that has to go to the wall. At any rate, this clash would generate a philosophical puzzle with no easy solution. White (2006) formulates his argument synchronically. Since it actually concerns epistemic processes (i.e. acquisition of evidence and credence revision), I prefer to re-formulate it diachronically. Let Pr be the credence function of a rational subject S, and let PrF be S's credence function updated upon S's learning F. I take the updating procedure to be standard conditionalization, according to which PrF(P) = Pr(P|F) and PrF(F) = 1. These identities state that for any propositions P and F on which Pr is defined, as S learns F, S's credence that P equates to the conditional credence that P given F that S had before learning F, and S's credence that F becomes the highest possible. White assumes that S's degree of epistemic justification for believing a proposition P that S has in a given situation and S's degree of confidence that P that S should rationally have in the same situation coincide, or –– at least –– that the second provides an accurate model of the first. The last assumption has a strong intuitive appeal, so I will take it on board. From this assumption, White infers that S acquires some 1 In which case my response can be adjusted accordingly. 2 A good introduction to Bayesian methodology is Weisberg (2011). 3 justification for believing a proposition P from evidence F if and only if S's credence that P should increase upon S's learning F.3 Let's stipulate that: P = 'this is a hand', F = 'it appears to S that P', SH = 'this is a fake-hand'. A fake-hand is everything that isn't a hand but cannot be visually distinguished from a hand. 'Examples of fake-hands include [for instance] perfect plastic replicas of hands, and moving projected holograms of hands' (2006: 528), and –– I would add –– hallucinations of hands induced by a Cartesian demon. SH stands therefore for any error conjecture that S can conceive of, which is incompatible with P but entails F or makes F highly probable. White imagines a scenario in which S looks at her hand for the first time –– so S has a perceptual appearance that P –– and he analyses the bearing of this perceptual evidence on S's credence that P and SH. Before proceeding any further with the presentation of White's argument, let me clarify a crucial point. White relies on a formal model that takes S's perceptual evidence to be a reflective belief of S about her own perceptual appearance that P –– that is to say, S's reflective belief that (F) it appears to S that P, entertained by S with the highest possible confidence. The phenomenal conservative –– on the other hand –– would take S's perceptual evidence to be S's appearance that P. White doesn't think that there is a substantive mismatch here. For he claims that S's perceptual appearances and S's correlated reflective beliefs have the same justifying force (at least in the cases relevant to his Bayesian proof). Unlike White, I find this claim very problematic. For the sake of discussion, I will nevertheless question it only in the next section. 3 The only if direction of this biconditional is controversial (cf. Wright 2011 and Moretti and Piazza 2013). I won't press this objection here because it would distract us from more serious difficulties of White's arguments. 4 To forestall possible confusion, let me sharply distinguish between 'S's having an appearance that P' and 'S's being reflectively aware of an appearance that P'.4 These two expressions don't refer to the same mental states. The first expression refers to a mental state of S –– her appearance that P –– which can exist in S's mind even if she doesn't reflect on her own mental states. The second expression refers to a more complex state of S, one that encompasses at least these three items: (i) S's appearance that P, (iii) S's reflective acquaintance with her appearance that P,5 and (ii) S's reflective belief that (F) S has an appearance that P, based on her acquaintance with her appearance that P. This is White's argument. It looks true that PrP(F)  PrSH(F)  1 –– namely, S's credence that F should be close to certainty when S learns P or SH. Furthermore, since S shouldn't in general expect to have an experience of a hand, Pr(F) << 1 –– namely, S's prior credence that F should be far from certainty. Thus PrP(F) > Pr(F) and PrSH(F) > Pr(F). The first inequality entails via probability calculus that PrF(P) > Pr(P). The second inequality entails via probability calculus that PrF(SH) > Pr(SH). So, when S learns F –– or, equivalently for White, when S has an appearance that P –– S acquires some justification for believing both P and SH. Let's focus on PrF(SH) > Pr(SH). This inequality implies via probability theory that (1) PrF(¬SH) < Pr(¬SH). (1) states that when S learns F, S's credence that ¬SH (i.e. that SH is false) should decrease. Hence, when S has an appearance that P, S cannot acquire justification for believing ¬SH. Now note that given that P entails ¬SH, it follows through probability calculus that (2) PrF(P) ≤ PrF(¬SH). That is to say, when S learn F, S's credence that ¬SH cannot be smaller than S's credence that P. Finally, (2) and (1) trivially entail by transitivity that (3) PrF(P) < Pr(¬SH). 4 There is a third expression that one might want to distinguish from these two expressions, that is to say: 'S's directing her attention to her appearance (or appearance-part) that P'. This expression refers to S's act of selecting just one of her concurrent mental states. This act of S doesn't require S to become reflectively aware –– in the sense I clarify above –– of the selected state. 5 Here 'reflective acquaintance' can be intended as a form direct awareness, in Fumerton (1995)'s sense, or as an introspective appearance, in Huemer (2007: 46)'s sense. 5 (3) shows –– according to White –– that 'its appearing to [S] that this is a hand can render [S rationally] confident [to any degree] that it is a hand, only if [S is] already [rationally] confident that it is not a fake-hand [to a higher degree]' (2006: 534). We saw before that when S has an appearance that P, in White's model, S does acquire some justification for believing P. (3) places an upper bound on the strength of this justification. For it shows –– according to White –– that its appearing to S that P can give S some degree of justification for believing P only if S has already, and so independently, a higher degree of justification for believing ¬SH. This entails that when S has an appearance that P, unless S has independent justification sufficient to believe ¬SH, S cannot have justification sufficient to believe P. White takes this proof to show that, against (PC), S's appearance that P cannot give S immediate prima facie justification for believing P (cf. Tucker 2013: 18). 4.3 Responding to White's objection The responses to White given by supporters of (PC) fall within either of these categories: the revisionary ones, which agree with White that (PC) is incompatible with Bayesianism but propose revising Bayesianism to resolve the incompatibility, and those that retort that (PC) and Bayesianism haven't actually been shown to be incompatible by White. Revisionary responses propose, for instance, to replace the probability function with an original superadditive function (cf. Pryor 2007); to switch to imprecise probabilities and introduce a nonstandard conditionalization procedure (cf. Weatherson 2007); to re-interpret Bayesian formalism in a non-standard way (cf. Kung 2010); and to replace the probability function with an intuitionist probability function (cf. Jehle and Weatherson 2012). I won't discuss these proposals because I think they are on the wrong track.6 In this section I will argue that White hasn't actually proven that (PC) and 6 It is fair to say that these revisionary proposals aren't ad hoc. They are typically introduced as means to respond to White and –– simultaneously –– resolve independent shortcomings of Bayesianism; for instance, its inability to provide states of uncertainty (or absence of evidence) or defeaters of certain types with adequate formalizations. 6 Bayesianism are incompatible. Silins (2007) has made a case for the same conclusion.7 Before laying down my response to White, let me detail Silins' response and the reasons of my discontent with it. The salient formal result of White's objection is the proposition that (3) PrF(P) < Pr(¬SH). White takes (3) to contradict (PC). Silins agrees that (3) models an important feature of perceptual justification but insists that (3) doesn't establish that S's having independent justification for believing ¬SH is a condition necessary and basing for S's acquiring perceptual justification for P. (3) only establishes –– according to Silins –– that S's having independent justification for believing ¬SH is a condition necessary for S's acquiring perceptual justification for believing P. Silins concludes that since (PC) doesn't disallow conditions for perceptual justification that are necessary but not basing, White's inequality doesn't contradict (PC). Silins gives a few examples of conditions for perceptual justification that are necessary but not basing, and that aren't disallowed by (PC). Let's consider two of them. Take the conceptually true proposition that (R) a hand is a hand. S does have (a priori) justification for believing R if S possesses the concepts required to entertain R. Presumably, S can have a seeming that (P) this is a hand, only if S has the concepts required to represent that P. But these include the concepts required to entertain P, and thus R. Consequently, if S has an appearance that P, S possesses prima facie justification for believing P but also independent justification for believing R. S's having independent justification for R is thus a necessary condition for S's having perceptual justification for P, but it doesn't look like a basing condition for it. For S's perceptual justification for believing P doesn't appear to be constituted by, among other things, S's independent justification for believing R. 7 To be accurate, Silins (2007) aims to defend, not (PC), but a position that he calls liberalism, following Pryor (2004). According to liberalism: In some case C, S's visual appearance that P gives S some justification for believing P, and what makes S's appearance capable of giving S some justification for believing P doesn't include S's having some independent justification for believing other propositions. (Cf. 2007: 111-112) Silins (2007: 108) makes it clear that one C-case is the one inspected by White (2006), in which P states that there is a hand. It is quite clear that for Silins (PC) and liberalism largely overlap. 7 Take now the contingent proposition that (R*) S exists. Whenever S has a perceptual appearance that P, and thus prima facie justification for believing P, S also has a cogito-style independent justification for believing R*. In this case too, S's having independent justification for R* is a necessary condition for S's having perceptual justification for P, but this doesn't appear to be a basing condition for it. I find Silins' response to White problematic for at least two reasons. This is the first: suppose that S's possessing independent justification for ¬SH were actually a necessary but not basing condition for S's having perceptual justification for P. A consequence of this would be that if S had a seeming that P but no independent justification for ¬SH, S would not have prima facie justification for believing P, in which case (PC) would be false. Therefore, if S's having independent justification for ¬SH were actually a necessary but not basing condition for S's having perceptual justification for P, the phenomenal conservative would be committed to claiming that S does have some sort of default justification for ¬SH that is not constitutive of S's perceptual justification for P. Indeed, the phenomenal conservative would be committed to making the same claim about any conceivable error conjecture relevant to the content of any perceptual seeming falling within (PC)'s domain. Note that showing that S has default justification of this sort8 is much more demanding than showing that S has independent justification for relatively trivial truths like R or R*. A line of response to White that did not embark the phenomenal conservative on such an arduous enterprise would be preferable. Another problem of Silins' response is that it concedes to White that S's having independent justification for ¬SH is a condition necessary for S's having perceptual justification for P. Silins concedes this because he endorses White's assumption that perceptual appearances and correlated reflective beliefs have, in the circumstances of White's thought experiment, the same justificatory force (cf. 2007: 125n22). Given that this assumption is implausible, Silins' thesis that S's having independent justification for ¬SH is a condition necessary for S's having justification for P is ungrounded. This is my second reason why I take Silins' response to White to be inadequate. 8 See Wedgwood (2013) for an ingenious attempt. See also Balcerak-Jackson (2016)'s objections. 8 I now explain why White's assumption is implausible. I will then argue that since White's case crucially relies on this assumption, it doesn't get off the ground. The phenomenal conservative takes S's perceptual evidence to be S's perceptual appearance. White, on the other hand, relies on a formalism in which S's perceptual evidence is S's reflective belief that S has a perceptual appearance. The result is that when the phenomenal conservative identifies the evidential basis of S's perceptual justification for believing a proposition X with S's appearance that X, White's formalism identifies the evidential basis of S's perceptual justification for believing the same proposition X with S's reflective belief (Y) that S has an appearance that X. White's formalism can accurately model the notion of justification deployed by the phenomenal conservative and describe important features of it only if the justifying force of S's perceptual appearance that X and the justifying force of a correlated reflective belief that Y of S are identical or very similar, at least when X and Y are propositions relevant to White's proof. This is precisely what White assumes. For example, White (2006: 535) considers whether the formal step in his objection constituted by (1) PrF(¬SH) < Pr(¬SH) can be interpreted as describing a feature of the justifying force of S's appearance that P (rather than S's reflective belief that F) with respect to ¬SH. White takes it to be true that if S happens to have a perceptual appearance that P accompanied by a correlated reflective belief that F, the strength of S's justification for ¬SH should be identical to the strength of S's justification for ¬SH depending on S's sole belief that F. (I agree with White on this point. I return to it in the next section.) Considering what (1) specifically states, this means that when S has a perceptual appearance that P accompanied by a correlated reflective belief that F, the strength of S's justification for ¬SH should decrease. White then suggests that: 9 If the rational response to its appearing that this is a hand, when [S] also believe[s] that it appears that this is a hand, is to decrease [S's] confidence that it is not a fake-hand,9 then surely this is the rational response to the same experience when [S does] not even consider how things appear to [her]. (535) In conclusion, according to White, S's appearance that P alone should lessen S's justification for ¬SH, exactly as S's belief that F alone does. Despite White's conviction, it appears false or very implausible that S's appearance that P should lessen S's justification for ¬SH, as S's belief that F does. One might find it intuitive that appearances and correlated reflective beliefs must always have the same justifying force. However, our intuitions about this matter crucially depend on the conception of appearance we work with. If one adopts the conception presupposed by the phenomenal conservative –– according to which appearances are non-doxastic attitudes that represent states of affairs as actualized –– one will naturally conclude that appearances and correlated introspective beliefs may often have very dissimilar justifying force. In the case in point, note that the content of S's belief that F –– the proposition that it appears to S that this is a hand –– and the content of S's appearance that P –– the proposition that this is a hand –– are about disparate states of affairs, where the first concern S's mind and the second the external world. Furthermore, note that these contents don't stand in the same logical relation with SH –– the proposition that this is a fake-hand. Because of all of this, S's belief that F and S's appearance that P presumably don't have, when separately considered, the same evidential bearing on SH, and thus on ¬SH. Since SH entails F or makes F highly probable, it is intuitive that S's coming to believe F should result in S's acquiring justification for SH, and so lessening her justification for ¬SH. On the other hand, since P is logically incompatible with SH, it is very implausible that S's appearance that P –– in which it seems to S to ascertain that P –– could result in S's acquiring justification for SH.10 It is much 9 White's original passage omits 'not' and literally reads 'it is a fake-hand'. This is certainly a typo. 10 Pryor acknowledges this when he writes: 'My view is that whenever you have an experience as of P, you thereby have immediate prima facie justification for believing P ... Your experiences do not, in the same way, give you immediate prima facie justification for believing that you are dreaming, or being deceived by an evil demon, or that any of the skeptic's other hypotheses obtain.' (2000: 536). 10 more plausible that S's appearance that P should result in S's acquiring justification for ¬SH, and so in S's lessening her justification for SH. Since S's appearance that P and S's correlated belief that F turn out to have divergent evidential force in the case just considered, it is very dubious that White's formalism could accurately model the notion of seeming-based justification that (PC) aims to account for. Thus, it is very dubious that the consequences that White draws from his formal framework could capture key features of that notion of perceptual justification. To persuade the unimpressed reader that White's objection actually goes off the track, let me reformulate it directly in terms of seeming-based justification. If White's objection goes through, this reformulation of it must also go through. But it doesn't. Since S knows that P entails ¬SH and degrees of justification are presumably closed under known entailment, when S has an appearance that P, S has some degree of justification for believing P only if S has at least the same degree of justification for believing ¬SH given the same appearance that P. Therefore, considering that S's appearance that P lowers S's degree of justification for ¬SH, S can have some degree of justification for believing P when S has an appearance that P only if S has already –– and so independently –– a higher degree of justification for believing ¬SH. Since it is false that S's appearance that P lowers S's degree of justification for ¬SH, this argument is unsound. To salvage the cogency of White's argument, one might think of re-formulating it by replacing F with P itself. The hope might be that since a belief that P and an appearance that P share the same content, believing P could prove a closer surrogate than believing F for having an appearance that P. This would require replacing PrF(P), PrF(SH) and PrF(¬SH) with, respectively, PrP(P), PrP(SH) and PrP(¬SH), which refer to the degrees of confidence in P, SH and ¬SH that S should rationally have 11 when S comes to believe P (rather than F) with certainty. The goal would be proving that PrP(P) < Pr(¬SH). It is easy to show, however, that this proposition is false. In fact, note that PrP(P) = 1.11 Hence, given that 1 is the highest possible degree of credence, it cannot possibly be that PrP(P) < Pr(¬SH). One might perhaps think of proving the weaker proposition that (3*) PrP(P) ≤ Pr(¬SH). (3*) can be interpreted as indicating that when S has an appearance that P, unless S has independent justification sufficient to believe ¬SH, S doesn't have justification sufficient to believe P. However, (3*) is also false. Since P entails ¬SH, PrP(¬SH) = 1. Furthermore, since S cannot be just certain that ¬SH, Pr(¬SH) < 1. Thus, PrP(¬SH) > Pr(¬SH). The latter inequality and the proposition that PrP(P) = 1 = PrP(¬SH) jointly entail that PrP(P) > Pr(¬SH). Another suggestion might be that of replacing F with P while deploying Jeffrey conditionalization rather than standard conditionalization. Suppose X is an evidential proposition of S. Jeffrey conditionalization enables S to update her credence function on uncertain evidence –– i.e. on a mere change of S's confidence in X that may not result in S's holding X with credence 1. Let Prold be S's credence function before S changes her credence that X, and let Prnew be S's credence function upon S's changing her credence that X. Let Y be any proposition on which Prold is defined. On Jeffrey conditionalization, (JC) Prnew(Y) = Prnew(X) Prold(Y|X) + Prnew(¬X) Prold(Y|¬X). (JC) states that S's credence that Y upon S's changing her credence that X equates to the sum of two things: the product of S's new credence that X by S's conditional credence that Y given X before S changed her credence that X, and the product of S's new credence that ¬X by S's conditional credence that Y given ¬X before S's changed her credence that X. Suppose now that S's evidential proposition X is P. Jeffrey conditionalization enables S to update her credence function on a mere increase in her rational confidence that P. A mere increase in 11 I follow White (2006) in assuming that Pr(P) > 0 so that P can actually be learned by S. 12 S's confidence in P might appear to be a very close surrogate for S's having an appearance that P. One might hope to rehabilitate White's argument by showing that (3+) Prnew(P) ≤ Prold(¬SH). However, (3+) is false because one of its instances is false. To see this, consider that standard conditionalization is just a special case of Jeffrey conditionalization in which the evidential proposition is held by S with credence 1.12 Given this, in any case in which the evidential proposition P is held by S with credence 1, the formalism of Jeffery conditionalization can be replaced salva veritate with the formalism of standard conditionalization. For example, in these cases, we can replace Prnew(P) = 1 with PrP(P) = 1, and Prold(¬SH) = n with Pr(¬SH) = n. A consequence of this is that in any case in which the evidential proposition P is held by S with credence 1, (3+) Prnew(P) ≤ Prold(¬SH) can be re-written salva veritate as (3*) PrP(P) ≤ Pr(¬SH). This shows that (3*) is actually an instance of (3+). Since we have seen that (3*) is false, (3+) is also false. At this point, one might still hope to obtain a working variant of White's argument by showing that (3+) is true for some specific range of values of Prnew(P), not inclusive of 0 and 1, suitable to formalize the epistemic import of S's entertaining an appearance that P. But this looks like something very hard to show. To wrap up, White hasn't actually shown that (PC) is incompatible with Bayesianism. For the formal notion of justification at work in his argument doesn't provide a sufficiently accurate model of the intuitive notion of seeming-based justification, and there is no easy way to produce a working variant of White's argument that relies on a more accurate formalization. 4.4 Perceptual appearances and reflective justification Before concluding this chapter, I would like to probe a few interesting issues that might have crossed the mind of the reader in the course of the former discussion. My investigation will pave the way for the task of appraising the actual antisceptical bite of phenomenal conservatism, carried out in the next 12 In fact note that when Prnew(X) = 1, (JC) reduces to Prnew(Y) = Prold(Y|X). 13 chapter. Phenomenal conservatives can and should generalise the thesis that S's appearance that P and S's reflective belief that F have different evidential force with respect to SH and ¬SH to other propositions. Consider any appearance that X of a subject S capable of entertaining beliefs about her own seemings. The phenomenal conservative can legitimately claim that the justifying force of S's appearance that X, with regard to a given proposition Z, and the justifying force of S's reflective belief that (Y) S has an appearance that X, with regard to the same proposition Z, need not coincide and may diverge. This claim prompts the following question: how do the justifying force of S's seeming that X and the justifying force of S's reflective belief that Y generally work together to determine S's justification for Z? It is intuitively plausible that when S has a reflective belief that Y, the justifying force of S's appearance that X becomes irrelevant to S's epistemic standing with regard to Z. We can rephrase this epistemological thesis by stating that the evidential import that S's sole appearance that X has for Z is overridden by the evidential import that S's reflective belief that Y has for Z, when S also entertains this reflective belief. When the evidential import that S's appearance that X has for Z is overridden by the evidential import that S's belief that Y has for Z, the strength of S's all things considered justification for Z –– i.e. the strength of the justification for Z that S has when she entertain both the appearance that X and the correlated reflective belief that Y –– is the same as the strength of S's justification for Z based on S's reflective belief that Y alone. Let's call reflective justification S's justification for Z based on S's reflective belief that Y alone. To appreciate the intuitive plausibility of this thesis, consider the following thought experiment. S faces a randomly chosen table in a room. Since S's eyes are closed, S cannot see the colour of the table. However, S is reliably told that (BK) The room has two white tables and two red tables. One of the white tables is illuminated by a hidden red light, so that it looks red, but the other three tables are illuminated by natural light. 14 Let's stipulate that: R = 'the table is red'. A = 'it appears to S that the table is red'. SH* = 'the table is white but looks red because it is illuminated by a hidden red light'. Given BK, it is easy to determine what the strength of S's confidence in R and ¬SH* should be before S opens her eyes. Since S knows that the chance that R is 1⁄2 and the chance that ¬SH* is 3⁄4, then Pr(R) = 1⁄2 and Pr(¬SH*) = 3⁄4.13 The strength of S's credence that R and ¬SH* can be taken to indicate the strength of S's justification for believing R and ¬SH*. Considering that the justification threshold for plain belief is presumably very high and near to 1, the justification values 1⁄2 and 3⁄4 are intuitively insufficient to sustain, respectively, S's belief that R and S's belief that ¬SH*. Accordingly, before opening her eyes, S doesn't have justification sufficient to believe R or ¬SH*. Given BK, it is also easy to determine what the strength of S's confidence in R and ¬SH* should be if S believed A. Since S would know that the cases in which R is true are 2/3 of those in which A is true, and the cases in which ¬SH* is true are also 2/3 of those in which A is true, PrA(R) = PrA(¬SH*) = 2/3. Again, this level of reflective justification would intuitively be insufficient to sustain S's belief that R or that ¬SH*. So, if S believed A, S wouldn't thereby have reflective justification sufficient to believe R or ¬SH*. Now imagine that S opens her eyes and has an appearance that R. Given (PC), S must acquire prima facie justification sufficient to believe R. Furthermore, since S's seeming gives her the impression of verifying R, which is incompatible with SH*, it is plausible that S has also justification sufficient to believe ¬SH*, but not SH*. Suppose that after this, S reflects on her experience and comes to believe A. It is strongly intuitive that at this point S's appearance that R will cease to be evidentially relevant for R and ¬SH*. At this point, S's all things considered justification for R and ¬SH* will only be determined by the 13 This follows from the application of (some version of) Lewis' Principal Principle. I take S's information BK to be embedded in Pr. 15 evidential force of S's reflective belief that A. Since PrA(R) = PrA(¬SH*) = 2/3, S won't have all things considered justification sufficient to believe R or ¬SH*. Let me describe a different thought experiment which might hopefully persuade readers still unconvinced that the evidential force of S's appearance that R is overridden by the evidential force of S's reflective belief that A. Suppose an oracle –– who S knows to be virtually infallible –– tells S that S will have an appearance that R at a future time t. So, now, S already believes A without hesitation.14 Imagine, the oracle instantly adds information BK about the chance that R and ¬SH* will have at t –– which S also believes without hesitation. So, now, S has already a suitable amount of justification for R and ¬SH* based on A.15 Suppose that, at t, S actually comes to have an appearance that R. It is intuitive that S's degree of justification for R and ¬SH* shouldn't change. This suggests, again, that the evidential force of S's reflective belief that A with respect to R and ¬SH* overrides the evidential force of S's sole appearance that R with respect to R and ¬SH*. As we will see in §5.3, an independent reason to accept the thesis that the justification based on S's appearances is generally overridden by the justification based on S's correlated reflective beliefs is that this thesis plays a crucial role in resolving the problem of easy justification, which apparently afflicts phenomenal conservatism. Let me make a few final remarks. Suppose S has a seeming that X and a reflective belief (Y) that she has a seeming that X. To begin with, note that S's seeming-based justification for X and S's reflective justification for X are different in type. In particular, S's seeming-based justification for X is both non-inferential and immediate. Whereas S's reflective justification for X is both inferential and non-immediate. S's reflective justification for X is inferential because it is available to S through an inference from Y to X. (For instance, the inference from 'it appears to S that the table is red' to 'the table is red'.) S's reflective justification for X is non-immediate because it is constituted by the portion of S's justification for believing Y transmissible to X through the inference. 14 S's belief that A isn't –– rigorously speaking –– a reflective one before t, but this is irrelevant. 15 To forestall possible confusion let's make the implicit temporal references in A, R and ¬SH* explicit. Thus, A = 'it appears to S at t that the wall is red at t', R = 'The wall is red at t', and ¬SH* = 'At t the wall is white but looks red because it is illuminated by a hidden red light'. 16 Consider now any error conjecture Z that states that although S has a seeming that X, X is false. White's proof –– generalized to any perceptual proposition X, correlated reflective belief Y and correlated error conjecture Z –– shows that PrY(X) < Pr(¬Z). This means that the degree of S's reflective justification for believing X has an upper bound in the degree of independent justification that S has for believing that Z is false. However, note that we have found no reason to think that the degree of S's seeming-based justification for believing X has such an upper bound. One might suppose that the finding about reflective justification heavily relies on interpreting justification as rational credence, and so on the Bayesian machinery. This is untrue. White's Bayesian proof has a straightforward parallel informal argument that exploits basic intuitions about epistemic justification. This is a version of the argument: since S knows that X entails ¬Z and degrees of justification are presumably closed under known entailment, when S has the reflective belief that Y, S can have some degree of justification for believing X only if S has at least the same degree of justification for believing ¬Z, given the same reflective belief. Consider now that since S's reflective belief that Y increases S's degree of justification for Z at least a little bit,16 the same reflective belief cannot but lower S's degree of justification for ¬Z. Thus, S can have some degree of justification for believing P when S has the reflective belief that Z only if S has already –– and so independently –– a higher degree of justification for believing ¬Z. Finally, note that S's reflective justification for X may not suffice to support S's belief that X, though S's seeming-based justification alone may suffice to it. (This happens, for instance, in the examples about the coloured tables examined before.) This possibility indicates that S's reflective belief that Y (accompanied by suitable background information) can act as a defeater of S's seemingbased justification for Y. 4.5 Conclusions White has articulated the sharpest and most detailed Bayesian objection to (PC) delivered in the recent literature. I have argued that White's objection is nevertheless inconclusive because it relies on an 16 Note that Y = 'S has an appearance that X' and that Z entails Y and explains it to some extent. 17 implausible model of the intuitive notion of seeming-based justification. I cannot exclude that a more accurate formalization of this notion could ultimately be found. However, I have no reason to suppose that such a formalization would show that perceptual justification doesn't have the central features that (PC) credits to it. My analysis of White's objection lends support to the following propositions: seemings and correlated reflective beliefs can diverge in justifying power, the strength of reflective justification (but not the strength of the correlated seeming-based justification) has an upper bound in the strength of the justification for denying any relevant error conjecture, reflective justification generally overrides the correlated seeming-based justification, a reflective belief can act as a defeater of the correlated seeming-based justification. References Balcerak-Jackson, Magdalena. 2016. Perceptual fundamentalism and a priori bootstrapping. Philosophical Studies 173: 2087-2103. Cohen, Stewart. 2005. Why basic knowledge is easy knowledge. Philosophy and Phenomenological Research 70: 417-430. Fumerton, Richard. 1995. Metaepistemology and skepticism. Lanham, Md.: Rowman & Littlefield. Jehle, David and Brian Weatherson. (2012). Dogmatism, probability, and logical uncertainty. 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