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1 1 Some philosophers distinguish between those beliefs that merely guide behavior, but which we would not be inclined to positively endorse on reflection (e.g. our suppressed beliefs, including those which might be painful to consider), from those we would be inclined to affirm as true. Ernest Sosa (e.g. 2017) terms the former “functional” beliefs and the latter “judgmental” beliefs. For the present purposes, we'll be referring to beliefs in a general sense. However, the distinction between functional and judgmental beliefs will be revisited in Chapter 11.

2 2 The reader can assume that by “justified” we will always mean (throughout the discussion in this book) “epistemically justified” – viz. justified from the point of view where what matters is things like truth and knowledge – unless explicitly stated otherwise.

3 3 The careful reader might have caught something here that seems problematic; what if some of the beliefs you have include words like “right” and “wrong”, “good” and “bad”, “justified” and “unjustified”? Given that the helmet – by stipulation – scans all of your beliefs, won't it scan these beliefs, too? And if so, then isn't it incorrect to suppose that the helmet does not detect normativity? Here it is important to distinguish between (i) the scientists' describing, without passing judgment, that you have some belief that includes a normative term (e.g. your belief that murder is wrong), and (ii) the scientists' being able to tell whether your beliefs actually have some kind of normative status (e.g. whether they are justified, unjustified). On the situation we're inviting you to imagine here, suppose what the helmet cannot do is, specifically, (ii).

4 4 Flipping a coin is certainly a method you could apply! But it is an unreliable method, one that would lead you astray as easily as not.

5 5 The philosophical strategy, more generally, of constraining our epistemological theorizing with reference to our judgments about obvious cases is developed in a notable way in epistemology by Roderick Chisholm (1973).

6 6 But wait! Could there be a simple shortcut? What about the following “obvious” rule: “Put all and only justified beliefs in Your Book of Justified Beliefs.” Following the “obvious rule” would result in your achieving your goal – for if you followed this rule, you'd get the easy cases (B1 and B2) right, along with all the rest. The obvious problem with the obvious rule, though, is that this rule doesn't actually help you do what you're trying to do. It doesn't help you work out which beliefs in Your Book of Beliefs are justified and which are not. You think you already know the easy cases. You're not sure about the rest. And you're not sure why the easy cases are right.

7 7 For a discussion of the principle (under a less snazzy name), see Goldman (1999b, p. 2).

8 8 The gist of the idea would be to, first, find some feature, F, that B1 has but B2 doesn't have, which could plausibly account for why B1, but not B2, is justified. Next, extrapolate from this difference between B1 and B2 to generate a rule, framed with reference to F, that looks something like this: “Include all and only beliefs with feature F in Your Book of Justified Beliefs.”

9 9 What does “adequate” mean? A piece of evidence might provide some support for a belief without providing adequate support for a belief. We might say that a piece of evidence, E, supports your belief in p if adding E to your set of evidence increases p's probability. If the increase is very small, the evidence might support p without providing adequate support. The observation that someone is about to swim laps is some evidence that they'll drown and the observation that someone has been handed a lottery ticket is some evidence that they'll soon be rich. These observations increase the probability of the relevant beliefs ever so slightly. They don't provide an adequate basis for belief, however. We will discuss this further in the chapter on inference.

10 10 Typically, skeptics about epistemic justification (particularly those persuaded by the kind of regress argument we are discussing in this chapter) have embraced not only the contingent, descriptive thesis that no beliefs are justified, but, even more, the necessary, modal thesis that epistemic justification is impossible. For the present purposes, we'll sidestep this distinction – for the contingent descriptive thesis that no beliefs are justified suffices for at least one interesting kind of skepticism – and return to it in Chapter 11.

11 11 Interestingly, many of the philosophers associated with the doctrine of skepticism about epistemic justification would be disinclined to say that they know or even justifiably believe the doctrine to be true. Pyrrhonian skeptics typically were led, through argument, to a position called equipollence, which involved withholding assent entirely, on either all propositions (as in the case of rustic Pyrrhonians) or on controversial propositions (as in the case of urbane Pyrrhonists). Academic skeptics were more inclined to assert philosophical doctrines (such as the thesis that skepticism about epistemic justification is true); however, as Michael Frede (1998) has noted, even these bolder skeptics were often disinclined to say they knew the truth of their own skeptical doctrine, even if (unlike Pyrrhonian skeptics) they were inclined to assert the theses.

12 12 See, most notably, Sextus Empiricus' Outlines of Pyrrhonism (1976). Unlike the radical skeptic of Descartes' Meditations who denies that any of our beliefs are known, the Pyrrhonian skeptic denies that beliefs even attain the status of being justifiably held. For some helpful contemporary discussion of how to interpret the Pyrrhonian's controversial epistemological thesis, see Burnyeat and Frede (1997) and, in particular, Barnes (1998) and Frede (1998). Cf. Fine (2000) for related discussion concerning the distinction between Cartesian and Pyrrhonian skepticism.

13 13 See, for example, Turri and Klein (2014, p. 3).

14 14 It is possible to be a skeptical infinitist by insisting that the structure of justification is as the infinitist says it is, and then to submit further that this structure is not instantiated in any human mind. See, for example, Aikin (2005). For our purposes, we will be discussing only non‐skeptical infinitism.

15 15 This is a paraphrased reconstruction of the argument as stated initially by Turri and Klein (2014, p. 3).

16 16 That's not to say there are not various in‐house disputes between coherentists and foundationalists that lead some coherentist and foundationalist views to end up looking very different from one another.

17 17 This line of reply is briefly canvassed by Sosa (1980, p. 10).

18 18 Recall that in attempting to come up with a method for determining which entries in Your Book of Beliefs should be included in Your Book of Justified Beliefs, you are in the main searching for some feature which could potentially serve to distinguish the justified from the unjustified beliefs; the feature of being justified by further beliefs is but one such candidate potential feature. As we'll see in Section 1.5, foundationalists are disinclined to think the feature of being justified by further beliefs is the feature we should be looking for.

19 19 The sense of “availability” at issue here will be of relevance to the viability of infinitism; we engage with this point later in this section.

20 20 For presentational purposes, we are setting aside the contested question of what basing a belief on a reason involves. Some philosophers think it is a matter of a reason causing your belief. Others think it is a matter of having beliefs about your reasons supporting your beliefs. Others still take the notion to be a theoretical primitive. See Korcz (2015) for an overview and Carter and Bondy (eds.) (2019), for a recent volume of papers that engages with a range of contemporary views on epistemic basing.

21 21 Turri (2013, pp. 791–792).

22 22 Note that for the purposes of this discussion, we are setting aside issues to do with the distinction between inductive and deductive support relations, which is a central topic in Chapter 4, on inference.

23 23 Note that Podlaskowski and Smith offer a more sophisticated normativity‐based argument which builds on the argument we are discussing in this chapter. For space constraints, we won't be surveying the normativity argument.

24 24 Dispositions are often theorized in terms of counterfactual conditionals. For example, the disposition “flammability” corresponds with the counterfactual conditional: if it were struck (in appropriate conditions), it would catch fire. For an overview, see Choi and Fara (2016).

25 25 See, for example, Turri (2013). For a counterreply to Turri, see Podlaskowski and Smith (2014).

26 26 Recall that doxastic justification for the infinitist requires two components: first, that the belief be propositionally justified, and, second, that the agent cite enough of the reasons from the series to satisfy contextual demands. If the notion of availability is weakened in the sense that it might have to be in order to get around Podlaskowski and Smith's objection, then it looks as though the infinite series of reasons “available” to you in such an attenuated sense has a marginalized role to play in explaining your doxastic justification. And, correspondingly, the reasons you cite to satisfy contextual demands play a comparatively larger role in accounting for your doxastic justification. But at this point, the position begins to look like a version of foundationalism rather than infinitism! Doxastic justification would in the main be a matter of citing a finite number of reasons (the last of which plays a special role in “clinching” the contextual provision demand), whereas the infinite series that is available to you includes reasons you'd more likely than not fail to cite correctly.

27 27 Incidentally, this is a point that Sosa (1980, p. 19) appeals to in objecting as well to coherentism.

28 28 The fact that it makes little sense to support the more certain with the less certain is why Wittgenstein objected to G.E. Moore's (1939) famous attempt to prove through argument that the external world exists – something Moore knows if he knows anything at all (including the reasons he could cite as evidence for it). For further discussion of Moore's proof, see Chapter 11 on skepticism.

29 29 Ernest Sosa (1980, p. 8) refers to this general position – that justification is a matter of relations between beliefs – as an Intellectualist Model of Justification.

30 30 This line of thinking could be further developed so as to indicate that your belief that the singular proposition “There is a tomato” is true, after the reveal, will accompany not only other demonstrative singular propositions (e.g. such as that the thing on the platter looks like a tomato) but also general propositions – for example, that something is on the table. Our response to the worry (expressed without reference to general propositions) applies mutatis mutandis to a version of the worry that included general propositions. For discussion about the difference between the two, see Fitch and Nelson (2016).

31 31 For helpful discussions of irrationality and delusion, see Bortolotti (2014) and Sacks (1985). The example of people who believe that there had been spaceships shaped like cars is taken from Wright (2013).

32 32 Note that some self‐described forms of coherentism maintain that coherence cannot justify beliefs from scratch but maintain nonetheless that coherence can justify beliefs that already have some initial degree of justification (even if miniscule) from something other than coherence. As Olsson (2014, Section 1) observes, however, such views might be better described as weak foundationalism as opposed to coherentism.

33 33 Note that the Regress Argument, understood as an argument for foundationalism, is distinct from the more general Regress Problem canvassed in Section 1.1.

34 34 See Pryor (2014, p. 206).

35 35 We assume our readers will be familiar with sudoku. If you are not, you can check out the rules here: https://sudoku.com/how‐to‐play/sudoku‐rules‐for‐ complete‐beginners.

36 36 For a discussion of defeat in terms of warrants rather than in terms of evidence, see Lyons and Graham (2020).

37 37 See Pollock (1986, pp. 29–30, 37–58) for the classic presentation of defeaters in epistemology.

38 38 According to some foundationalists, the relevant property here is simply the truth of the belief. On such views, foundational beliefs are self‐justifying. According to Turri and Klein (2014, pp. 6–7), this kind of position is usually associated with what they call “traditional” foundationalism, whereas those they term meta‐ justificatory foundationalists deny that the property doing the justifying work for foundational beliefs must be the truth of such beliefs.

39 39 At least, this assumption seems innocent enough provided we are taking responsible beliefs to be those beliefs that are not irresponsibly held. Some philosophers build further requirements into the notion of a responsible belief, beyond it not being held irresponsibly. Linda Zagzebski (1996) requires that a responsibly held belief is in some way praiseworthy – viz. attributable to some kind of intellectual virtue on the part of the subject. It is more contentious whether responsible beliefs must be not merely not‐irresponsible but also praiseworthy. Sosa (2017, pp. 147–149), for example, suggests that the belief one has that the room has just gotten dark, immediately as the light goes off, is not something that can be credited to one's agency, given that in such circumstances, one couldn't help but to form such a belief (e.g. if one tried to believe the room was not dark, one would fail). Putting this all together: if the requirement that beliefs be responsibly held is unpacked in a robust way so as to involve praiseworthiness on the part of the agent, Assumption 1 looks less plausible. If read as a minimal claim to the effect that justified beliefs cannot be irresponsibly held, the claim looks beyond reproach.