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Abstract
I begin by contrasting two facets of belief: that belief is a response to a sufficiency of evidence and that belief plays a role in one’s representation of reality. I claim that these conceptions of belief are in tension because whilst the latter – Representationalism – requires Logical Coherence of belief the former – Thresholdism – conflicts with Logical Coherence. Thus we need to choose between conceptions. Many have argued that the Preface Paradox supports Thresholdism. In contrast I argue that Representationalism has a more plausible response to the paradox.
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Acknowledgements
The paper was presented in my department at the University of Cape Town and at a conference on naturalism and phenomenology held at the University of Johannesburg in 2014. I’d like to express my thanks to audiences at both of those events for their comments; to Jack Ritchie and David Papineau for their discussions; and, finally, to two anonymous reviewers for the journal for their feedback on a previous draft.
Disclosure statement
No potential conflict of interest was reported by the author.
Notes
1 So I’m thinking of credence as a measure of the confidence that a believer ought to have in the truth of a proposition, given her state of information in relation to that proposition.
2 The reason for taking this to be a normative requirement is that I shall want to allow that on a representational view beliefs can fail to participate in what deserves to be called a description of reality.
3 I imagine that there might be different forms of the view, each of which is distinguished by the ways in which it thinks beliefs need to ‘hang together’. Plausibly these differences will be driven by differing metaphysical views about the nature of reality.
4 Thresholdism seems to align with a naturalistic view of belief – belief as an agent’s reaction to the input of her surroundings – and Representationalism with the phenomenological tradition – belief as first personal account of one’s world. Though this is highly suggestive, the story is likely to be far more complex.
5 There is, of course, considerable debate in the literature over whether normative principles derived from Consistency and Closure apply to belief. Macfarlane (Citationunpublished) provides an exhaustive discussion of these principles, which he dubs ‘Bridging Principles’. Though he is sceptical about many forms of Bridging Principle, he is inclined to endorse a version according to which one should not disbelieve known logical consequences of one’s beliefs. I don’t think my discussion below is affected by the precise nature of accepted bridging Principles, since the Preface Paradox might be set up in a variety of ways, each of which targets a different Bridging Principle. I think my proposal can be adopted by an adherent of any plausible Bridging Principle. So I shall stick with the above as unpacking Logical Coherence.
6 See his 2004 sections 4.1 and 4.2.
7 To be sure, some semantic deflationists argue against the representational import of (one or another piece of) semantic theory, but: (i) their motivations for doing so have nothing to do with a Threshold conception of belief; (ii) while questioning the substance and/or explanatory power of semantic and representational notions, they do not reject those conceptions. So, though they might adopt a preferred construal of the representational role of belief, they need not reject such a view.
8 Reason for my caution here will emerge when I turn to discuss treatments of the issue.
9 See Christensen Citation2004; Sturgeon Citation2008; Weintraub Citation2001; Foley Citation1992 inter alia. The reasoning in some of these papers is applied to the Lottery rather than or as well as the Preface Paradox. When it is applied to the former there are obvious enough extensions to the latter.
10 Of course the Preface Paradox is just one arena in which Logical Coherence has been brought into question. Since there may be others, my argument cannot pretend to be exhaustive. Indeed the Lottery Paradox is often cited, in addition. I largely ignore it here because in many versions Logical Coherentists have a good response in arguing that we ought not to believe of each ticket that it won’t win; and in other versions it raises much the same issues as the Preface Paradox.
11 Obviously this is an inconsistent set of beliefs. The logical machinery then kicks in simply to make the inconsistency explicit by deriving a contradiction.
12 I’ll sometimes call the proposition believed here ‘Book’.
13 The easiest way to note this is to define the Risk of a proposition, R(P) as 1-Cr(P). Then R(C)≤R(P1)+…+R(Pn), since C is only false when at least one of P1 to Pn is false. See Sturgeon, Citation2008.
14 See Sturgeon Citation2008.
15 We may suppose that this argumentation employs claims that are taken to be uncontroversial and certainly are not intended to fall within the scope of the author’s Preface proposition.
16 To be sure Christensen has raised some doubts about this. I don’t think these need detain us for the following reasons: (i) Christensen’s reasons arise from thinking about how an agent should integrate her ‘first order’ credences with ‘second order’ beliefs about her own competence. But for the beliefs involved in Book this isn’t relevant. (ii) Secondly, if we turn to the integration of the second order beliefs, we are essentially tackling the sort of problem thrown up by the Preface Paradox. I’m the process of arguing that belief, despite the Preface Paradox, requires Logical Coherence and to suppose that beliefs may fail to adhere to the laws of probability is to beg the question. In fact the example I go on to construct is near enough the same as the one Christensen uses to argue his point. (iii) I don’t need the claim in full generality, just the claim that credences are not purely subjective measures of confidence and the supposition that logical and mathematical truths warrant a credence of 1.
17 Let it be said that my experience is that the position does elicit some fierce incredulity. I’m tempted to say it expresses a belief that I have, but which is probably false.
18 Here’s another such example, taken from the closing sentences of Dummett’s Truth and Other Enigmas. Having presented his view that philosophy, since Frege, has at last found its true method Dummett admits that the history of such predictions is replete with disappointment and concludes thus: ‘by far the safest bet would be that I was suffering from a similar illusion in making the same claim for Frege. To this I can offer only the banal reply which any prophet has to make to any sceptic: time will tell’ (Citation1978, 458). Clearly Dummett thinks that from a certain objective point of view his belief is likely to be false, but this doesn’t lead him to relinquish it.
19 Note that my imagined generous reader would have to reject assimilation of the current scenario to those of Moore’s Paradox. For in the latter scenarios the agent’s state of mind is incomprehensible.
20 See Christensen Citation2004 for examples.
21 Recall, though, that in the section entitled ‘Thresholdism and Logical Coherence’ I argued against a combining Thresholdism with the broad conception of credences.
22 See Quine’s classical statement (Citation1953), also Quine and Ullian (Citation1970, ch. 2) and Tennant (Citation2012).
23 There is a third, more technical problem. Tennant (Citation2006) argues that for finite schemes of belief it is false to suppose that systematic removal of a belief, p, followed by its replacement will restore the original situation in that all the original consequences of p (together with one’s other beliefs) will flow back into the scheme of belief. What holds of a single belief will hold of whole systems of beliefs.
24 See his (Citation2012).