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5. A Puzzle for Dogmatism

© 2017 Mark McBride, CC BY 4.0 https://doi.org/10.11647/OBP.0104.07

Returning to dogmatism and the pattern of objection, I present an apparently more serious puzzle for dogmatism. It seems that one must have had warrant to believe the conclusion of (EK)-reasoning antecedently to the perceptual evidence.

0.1 I want to consider a puzzle in the realm of confirmation theory. The puzzle arises from consideration of reasoning with an argument, given certain epistemological commitments. Here is the argument (preceded by the stipulated justification for the first premise):

(JUSTIFICATION FOR 1) The table looks red.

(EK)

(1) The table is red.

(2) If the table is red, then it is not white with red lights shining on it.

(3) The table is not white with red lights shining on it.

As we’ve seen, (EK) — the easy knowledge argument (aka (TABLE)) — has received much epistemological scrutiny of late.1

0.2 The plan: First, I set out the epistemological commitments in play. Second, I set out an example, leading to the puzzle, which is putatively troubling for dogmatism. Finally, I consider the implications of the puzzle for dogmatism.

1. Epistemological Commitments

1.1 Suppose that the mere having of the experience described in (JUSTIFICATION FOR 1) can give one defeasible perceptual justification2 to believe (1) — that is, it is the subject’s having the experience, rather than the subject’s beliefs about the experience, that makes it epistemically appropriate for the subject to believe (1). And we might go further in claiming that this justification can (suffice to) give one knowledge of (1). This supposition and claim are distinctive features of dogmatist accounts of justification and knowledge respectively (see Pryor 2000, 2004). To refer specifically to dogmatism about justification, I’ll use ‘j-dogmatism’, to refer to dogmatism about knowledge, I’ll use ‘k-dogmatism’, and to refer to dogmatism generically, I’ll use ‘dogmatism’. I take it the truth of k-dogmatism entails the truth of j-dogmatism; but the converse entailment does not hold.

Dogmatists are (necessarily?) fallibilists about knowledge: “[W]e can have knowledge on the basis of defeasible justification, justification that does not guarantee that our beliefs are correct” (Pryor 2000: 518).3 It’s the defining feature of dogmatism that the justification one gets for (1) is immediate: you don’t need antecedent justification for any other propositions in order for the having of the experience described in (JUSTIFICATION FOR 1) to give one justification for (1). Some find dogmatism an appealing way to think of perceptual justification and knowledge. So let’s suppose, pro tem, we’re dogmatists and fallibilists — that is, we are fallibilists in this dogmatist sense.4

1.2 At a highly general level, it seems that dogmatists must give some account of the defectiveness of (certain instances of) reasoning by means of (EK). Why so? Here’s the worry: on a dogmatist view, the mere having of a perceptual experience (giving justification for and, say, knowledge of, (1)), combined with some elementary logical reasoning (via (2)), can seemingly lead us — all too easily — to knowledge of the falsity of certain sceptical hypotheses ((3)). Thus the problem of easy knowledge (discussed at length in Chapters Two and Three). Our ensuing puzzle uses tools from confirmation theory to challenge dogmatism more directly.

2. Example, Leading to the Puzzle for Dogmatism

2.1 Example: Let us, for simplicity, consider only red tables and white tables,5 and only red light and white (natural) light. Suppose that the prior probabilities are divided equally between red table (RT) (0.5) and white table (WT) (0.5) and in the ratio 1:2 between red light (RL) (0.33) and white light (WL) (0.67). So the prior probabilities of the four hypotheses (assuming the table colour and the light colour are independent) are: (RT&RL) 0.167; (RT&WL) 0.33; (WT&RL) 0.167; (WT&WL) 0.33.6 Now I have a visual experience as of a red table. We know that the posterior probability of each of the four hypotheses is proportional to the product of the prior probability and the likelihood (that is, the probability of the evidence given the hypothesis). Keeping things simple, suppose that the probability of a table looking red is the same given (RT&RL), or given (RT&WL), or given (WT&RL). Suppose (idealising) that the probability of a table looking red given (WT&WL) is zero. Then the posterior probabilities are: (RT&RL) 0.25; (RT&WL) 0.5; (WT&RL) 0.25; (WT&WL) 0.

Thus, given the evidence described in (JUSTIFICATION FOR 1), the probability of premise (1) [that is, red table with either red light or white light] is raised from 0.5 to 0.75; the probability of premise (2) is 1 because it is a priori true; and the probability of the conclusion (3) [~(WT&RL)] is decreased from 0.833 to 0.75. That is, the probability of the ‘sceptical hypothesis’, (WT&RL), is increased from 0.167 to 0.25 (essentially because one of the hypotheses, (WT&WL), has been eliminated by the evidence and its share of the prior probability has been redistributed amongst the remaining three hypotheses). The ratio of the posterior probabilities of premise (1) — that is, RT — and the ‘sceptical hypothesis’ (WT&RL) is 3:1. But this is so only because the ratio of their prior probabilities was 3:1. The evidence described in (JUSTIFICATION FOR 1) is not diagnostic between these two hypotheses.

2.2 The foregoing worked example, though simplified and idealised, serves to support premise (iii) in the following argument against j-dogmatism, viz. getting (JUSTIFICATION FOR 1) diminishes the credence one ought to have in (3).7 Similarly, the worked example serves to support premise (iii*) in the subsequent argument against k-dogmatism. Here, first, is the argument against j-dogmatism:

(i) If one has justification to believe (1) after getting (JUSTIFICATION FOR 1), one has justification to believe (3) after getting (JUSTIFICATION FOR 1).

(ii) If having a certain experience diminishes the credence one ought to have in a proposition, then, if one has justification to believe the proposition after having the experience, one must have had justification to believe the proposition antecedently to the experience.

(iii) Getting (JUSTIFICATION FOR 1) diminishes the credence one ought to have in (3).

(iv) Therefore, if one has justification to believe (1) after getting (JUSTIFICATION FOR 1), one must have had justification to believe (3) antecedently to getting (JUSTIFICATION FOR 1).

(v) Therefore j-dogmatism is false: (JUSTIFICATION FOR 1)’s ability to provide justification to believe (1) is not independent of whether one has antecedent justification to believe (3).8

The argument against k-dogmatism is similar:

(i*) If one knows (1) after getting (JUSTIFICATION FOR 1), one is in a position to know (3) after getting (JUSTIFICATION FOR 1).

(ii*) If having a certain experience diminishes the credence one ought to have in a proposition, then if one is in a position to know the proposition after having the experience, one must have been in a position to know the proposition antecedently to the experience.

(iii*) Getting (JUSTIFICATION FOR 1) diminishes the credence one ought to have in (3).

(iv*) Therefore, if one knows (1) after getting (JUSTIFICATION FOR 1), one must have been in a position to know (3) antecedently to getting (JUSTIFICATION FOR 1).

(v*) Therefore k-dogmatism is false: (JUSTIFICATION FOR 1)’s ability to confer knowledge of (1) is not independent of whether one is antecedently in a position to know (3).9

Note that this second argument contains the locution ‘in a position to know’ at several junctures. I take it that one is in such a position just in case one has (evidential) justification for the true proposition in question, and some anti-luck condition is fulfilled thwarting Gettierisation. Admittedly this account is vague and context-dependent at a number of points (cf. Williamson 2000: 95), but this working definition will do for our purposes.

I take it that, with these two arguments, we’ve identified the major puzzle in confirmation theory for dogmatism. They purport to establish, contra dogmatism, that the role of a perceptual experience (of the table looking red) in providing justification to believe (1), and ultimately knowledge of (1), depends on an antecedently available justification to believe (3), or on being antecedently in a position to know (3). Each argument has three premises. Unless there is some flaw in the reasoning that takes us from the three premises to the interim conclusion, and thence to the conclusion, the dogmatist must identify a false premise. Each of the premises, however, is plausible.

3. Implications of the Puzzle

3.1 The arguments comprising our puzzle for dogmatism (see 2.2) are valid, so let’s isolate a premise on which some doubt might be cast. An obvious move at this stage, given the apparent security of the second and third premises,10 is to flag premises (i) and (i*):

(i) If one has justification to believe (EK1) after getting (JUSTIFICATION FOR 1), one has justification to believe (EK3) after getting (JUSTIFICATION FOR 1).

(i*) If one knows (EK1) after getting (JUSTIFICATION FOR 1), one is in a position to know (EK3) after getting (JUSTIFICATION FOR 1).

Each premise, respectively, presupposes (something like) the following (single-premise) closure principles:

(J-Closure) If one has justification to believe P and can tell that P entails Q then — ceteris paribus — one has justification to believe Q.

(K-Closure) If one knows P and competently deduces Q from P, thereby coming to believe Q, while retaining one’s knowledge that P, one comes to know that Q.

A defender of j-dogmatism or k-dogmatism who wants to question the truth of (i) or (i*) should offer reasons to reject (J-Closure) or (K-Closure), respectively.11 However, these are highly plausible closure principles. Thus dogmatism is — or seems very likely to be — false.12


1 See, notably, Cohen (2002, 2005). Likewise for our (MOORE) argument (in respect of which the puzzle to come can, mutatis mutandis, also be run).

2 ‘Justification’ is used in this chapter as a broad term of epistemic appraisal and is interchangeable with ‘warrant’.

3 If one wants to frame fallibilism in terms of conditional probabilities (cf. Pryor MS), one will claim that a subject, S, can know a proposition, p, when the probability of p conditional on S’s evidence, e, is less than 1. Note that conditional probabilities involve two propositions: one about the world, p, and one about the subject’s evidence, e. However the subject does not have to believe the proposition about evidence in order to possess the evidence.

4 This supposition keeps things manageable. Our puzzle assumes fallibilism. Note, however, that one can (see Hawthorne 2004: 75–77) give a rendering of a similar puzzle on the assumption of infallibilism (fallibilism’s negation).

5 One could, to make things more realistic, generate a similar example by considering, say, ten equiprobable colours the table might be.

6 The prior probability assigned to the ‘sceptical hypothesis’ (WT&RL) is low because the prior probabilities favour the white (natural) light hypothesis over the red (tricky) light hypothesis. It might seem like a reasonable prior, but it would not be acceptable to the (local) sceptic (cf. Wright 2007, 2008).

7 In itself, that a piece of evidence disconfirms a hypothesis (known to be) entailed by a hypothesis that the evidence confirms is not problematic. Consider the following thesis (cf. Hempel 1945, whose theory of confirmation lacks the following property):

(CC) If E confirms H and H entails H´, then E confirms H´.

Due to counterexample(s), we have good reason to reject (CC). (Of course, principle (CC) is fine if by ‘E confirms H’ we mean only that the probability of H given E is greater than some threshold (e.g. 0.9). If the probability of H given E > 0.9 and H entails H´, then the probability of H´ given E > 0.9. However the principle (CC) is not fine if by ‘E confirms H’ we mean that E raises the probability of H (i.e. the probability of H given E is greater than the prior probability of H). It is thus this latter understanding of confirmation with which we are operating here.) Consider: E = card is black, H = card is the ace of spades, and H´ = card is an ace. Clearly, H entails H´ while E confirms H but not H´. Note the following weaker thesis, however:

(CC*) If E confirms H and H entails H´, then E doesn’t disconfirm H´.

While the counterexample we considered to (CC) is not a counterexample to (CC*), Pryor’s (2004: 350–51) case of ‘Clio’s pet’ plausibly is.

8 I take something like this argument to be extractable from White (2006), whose focus is specifically on j-dogmatism. Cf. also Schiffer (2004) and Wright (2007). Note premises (i) and (i*) each rest on a closure principle; I explore this further in section 3. Note also premises (iii) and (iii*) can form the basis for an explication of the phenomenon of transmission failure (cf. Okasha (2004), Chandler (2010), and Moretti (2012)). Note, finally, that if one added a further premise to these arguments that we don’t in fact have justification to believe — aren’t in fact in a position to know — (3) prior to experiencing (JUSTIFICATION FOR 1), one would have the makings of a full-fledged argument for scepticism.

9 I take something like this argument to be extractable from Hawthorne (2004: 73–75), whose (effective) focus is specifically on k-dogmatism. Cf. also Cohen (2005: 425).

10 In the coming Interim Review, I suggest a line of argument to the effect that their security is only apparent. I thus do not mean to commit to the ensuing move being the most promising way for dogmatism to get out of the puzzle; just an obvious way.

11 Note that (K-Closure) is difficult to distinguish from a principle about transmission (here, transmission of epistemic status). One might then ask: would there not be a similar principle about justification, that would speak of coming to have a justified belief? The principle that White calls ‘Justification Closure’ (2006: 528) would seem to be like this (using, as it does, the ‘justified in believing’ nomenclature — a nomenclature I noted in the Introduction to be associated with doxastic justification).Why, then, is it important here to have (J-Closure) be a principle about (propositional) justification to believe rather than about (doxastic) justified belief (or being justified in believing)? First, even though White uses nomenclature associated with doxastic justification, it is not unequivocally so associated, and White’s surrounding remarks suggest instead a propositional focus. Second, as can be seen from the argument, a propositional justification closure principle is all White needs — and this is a good thing, given the familiar counterexamples to doxastic justification closure principles. Finally, see Lasonen-Aarnio (2008) for an interesting exploration of so-called deductive risk — a phenomenon which provides a novel basis for questioning (K-Closure).

12 As hinted (n. 10), I consider, and canvass, a range of possible dogmatist responses to these arguments in the coming Interim Review.