Preface Paradox Research Articles

Truthlikeness and the Lottery Paradox via the Preface Paradox

ABSTRACTIn a 2017 AJP paper, Cevolani and Schurz (C&S) propose a novel solution to the Preface Paradox that appeals to the notion of expected truthlikeness. This discussion note extends and analyses their approach by applying it to the related Lottery Paradox.

The Lottery, the Preface, and Conditions on Permissible Belief

This paper defends the permissibility solution to the lottery paradox against an objection by Anna-Maria Asunta Eder. Eder argues that the permissibility solution should also be applicable to the preface paradox, but conflicts with a plausible principle about epistemic permissions when so applied. This paper replies by first criticizing Eder’s considerations in defense of her principle; in particular, it argues that the plausibility of her principle is to a large extent parasitic on the spurious plausibility of the principle of factual detachment. The paper then presents a direct argument against Eder’s principle, which shows that her principle conflicts with a Pareto-style condition on permissible belief.

Deductive Cogency, understanding, and acceptance

Deductive Cogency holds that the set of propositions towards which one has, or is prepared to have, a given type of propositional attitude should be consistent and closed under logical consequence. While there are many propositional attitudes that are not subject to this requirement, e.g. hoping and imagining, it is at least prima facie plausible that Deductive Cogency applies to the doxastic attitude involved in propositional knowledge, viz. (outright) belief. However, this thought is undermined by the well-known preface paradox, leading a number of philosophers to conclude that Deductive Cogency has at best a very limited role to play in our epistemic lives. I argue here that Deductive Cogency is still an important epistemic requirement, albeit not as a requirement on belief. Instead, building on a distinction between belief and acceptance introduced by Jonathan Cohen and recent developments in the epistemology of understanding, I propose that Deductive Cogency applies to the attitude of treating propositions as given in the context of attempting to understand a given phenomenon. I then argue that this simultaneously accounts for the plausibility of the considerations in favor of Deductive Cogency and avoids the problematic consequences of the preface paradox.

K ⊈ E

In a series of very influential works, Tim Williamson has advanced and defended a much discussed theory of evidence containing, among other claims, the thesis that, if one knows P, P is part of one's evidence (K ⊆ E). I argue that K ⊆ E is false, and indeed that it is so for a reason that Williamson himself essentially provides in arguing against the thesis that, if one has a justified true belief in P, P is part of one's evidence: together with a very plausible principle governing the acquisition of knowledge by non‐deductive inference based on evidence, K ⊆ E leads, in a sorites‐like fashion, to what would seem a series of unacceptably bootstrapping expansions of one's evidence. I then develop some considerations about the functions of and conditions for evidence which are suggested by the argument against K ⊆ E. I close by discussing the relationship of the argument with anti‐closure arguments of the style exemplified by the preface paradox: I contend that, if closure is assumed, it is extremely plausible to expect that the diagnosis of what goes wrong in the preface‐paradox‐style argument cannot be used to block my own argument.

Probability, Approximate Truth, and Truthlikeness: More Ways out of the Preface Paradox

ABSTRACTThe so-called Preface Paradox seems to show that one can rationally believe two logically incompatible propositions. We address this puzzle, relying on the notions of truthlikeness and approximate truth as studied within the post-Popperian research programme on verisimilitude. In particular, we show that adequately combining probability, approximate truth, and truthlikeness leads to an explanation of how rational belief is possible in the face of the Preface Paradox. We argue that our account is superior to other solutions of the paradox, including a recent one advanced by Hannes Leitgeb (Analysis 74.1).

Two Facets of Belief

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.

Fallibilism, Verisimilitude, and the Preface Paradox

The Preface Paradox apparently shows that it is sometimes rational to believe logically incompatible propositions. In this paper, I propose a way out of the paradox based on the ideas of fallibilism and verisimilitude (or truthlikeness). More precisely, I defend the view that a rational inquirer can fallibly believe or accept a proposition which is false, or likely false, but verisimilar; and I argue that this view makes the Preface Paradox disappear. Some possible objections to my proposal, and an alternative view of fallible belief, are briefly discussed in the final part of the paper.

Intellectual Humility: Lessons from the Preface Paradox

Intellectual Humility: Lessons from the Preface Paradox

The problem of logical omniscience, the preface paradox, and doxastic commitments

The main goal of this paper is to investigate what explanatory resources Robert Brandom’s distinction between acknowledged and consequential commitments affords in relation to the problem of logical omniscience. With this distinction the importance of the doxastic perspective under consideration for the relationship between logic and norms of reasoning is emphasized, and it becomes possible to handle a number of problematic cases discussed in the literature without thereby incurring a commitment to revisionism about logic. One such case in particular is the preface paradox, which will receive an extensive treatment. As we shall see, the problem of logical omniscience not only arises within theories based on deductive logic; but also within the recent paradigm shift in psychology of reasoning. So dealing with this problem is important not only for philosophical purposes but also from a psychological perspective.

Preface Writers are Consistent

AbstractThe preface paradox does not show that it can be rational to have inconsistent beliefs, because preface writers do not have inconsistent beliefs. I argue, first, that a fully satisfactory solution to the preface paradox would have it that the preface writer's beliefs are consistent. The case here is on basic intuitive grounds, not the consequence of a theory of rationality or of belief. Second, I point out that there is an independently motivated theory of belief – sensitivism – which allows such a solution. I sketch a sensitivist account of the preface writer's (consistent) doxastic state.

Belief, Credence, and the Preface Paradox

ABSTRACTMany discussions of the ‘preface paradox’ assume that it is more troubling for deductive closure constraints on rational belief if outright belief is reducible to credence. I show that this is an error: we can generate the problem without assuming such reducibility. All that we need are some very weak normative assumptions about rational relationships between belief and credence. The only view that escapes my way of formulating the problem for the deductive closure constraint is in fact itself a reductive view: namely, the view that outright belief is credence 1. However, I argue that this view is unsustainable. Moreover, my version of the problem turns on no particular theory of evidence or evidential probability, and so cannot be avoided by adopting some revisionary such theory. In sum, deductive closure is in more serious, and more general, trouble than some have thought.

The Calendar Paradox

In this paper I present an underappreciated puzzle about intention. The puzzle is analogous to the famous Preface Paradox for belief, and arises for any theory according to which intentions are all or nothing states governed by two popular and plausible rational norms. It shows that at least one of these three assumptions must be substantially revised, and thus that many standard views about intention cannot be true. I consider two general strategies for responding to the puzzle. The more conservative approach retains the assumption that intentions are all or nothing states, and attempts to marshal independent arguments for modifying one of the two puzzle-generating norms. I briefly discuss this line of response and conclude that there is prima facie reason to reject the more commonly defended of the two, the Consistency norm, which requires a particular relationship between one’s intentions and one’s beliefs about those intentions’ execution. I then explore a more radical approach: a solution that parallels the well-known partial belief response to the Preface Paradox. According to this solution, the puzzle about intention ultimately derives from the mistaken thought that the paradigmatic conclusions of deliberation are fully committed states of intention. Instead, I suggest that what we call intentions, and think of as all or nothing states, may in fact often be only partially committed states, which I call states of inclination, and which must be governed by slightly different norms. In addition to showing that my theory of inclination may give us a motivated way out of the puzzle, I provide independent arguments for thinking that we have such mental states, and I say what I can about their nature and the norms that regulate them. These arguments do not depend on the viability of the more radical response to the puzzle. They purport to show that inclinations are psychologically real, and that countenancing them is necessary for vindicating plausible descriptive and normative truths about mental phenomena.

No Match Point for the Permissibility Account

In the literature, one finds two accounts of the normative status of rational belief: the ought account and the permissibility account. Both accounts have their advantages and shortcomings, making it difficult to favour one over the other. Imagine that there were two principles of rational belief or rational degrees of belief commonly considered plausible, but which, however, yielded a paradox together with one account, but not with the other. One of the accounts therefore requires us to give up one of the plausible principles; whereas the other allows us to save them both. The fact that it allows us to save both of the plausible principles might well be considered a strong reason in favour of the relevant account. The permissibility-account-based resolution of the lottery paradox suggests that the permissibility account is a candidate for being supported in this way, since the account seems to save two plausible principles of rational belief and rational degrees of belief. I argue that even if the permissibility account were supported in this way the support would be defeated, since one cannot provide an analogous resolution of the preface paradox. The principles remain unsaved by the permissibility account.

Multi‐Peer Disagreement and the Preface Paradox

AbstractThe problem of multi‐peer disagreement concerns the reasonable response to a situation in which you believe P1 … Pn and disagree with a group of ‘epistemic peers’ of yours, who believe ∼P1 … ∼Pn, respectively. However, the problem of multi‐peer disagreement is a variant on the preface paradox; because of this the problem poses no challenge to the so‐called ‘steadfast view’ in the epistemology of disagreement, on which it is sometimes reasonable to believe P in the face of peer disagreement about P. After some terminology is defined (§1), Peter van Inwagen's challenge to the steadfast view will be presented (§2). The preface paradox will then be presented and diagnosed (§3), and it will be argued that van Inwagen's challenge relies on the same principle that generates the preface paradox (§4). The reasonable response to multi‐peer disagreement will be discussed (§5), and an objection addressed (§6).

This paper surely contains some errors

The preface paradox can be motivated by appealing to a plausible inference from an author’s reasonable assertion that her book is bound to contain errors to the author’s rational belief that her book contains errors. By evaluating and undermining the validity of this inference, I offer a resolution of the paradox. Discussions of the preface paradox have surprisingly failed to note that expressions of fallibility made in prefaces typically employ terms such as surely, undoubtedly, and bound to be. After considering what these terms mean, I show that the motivating inference is invalid. Moreover, I argue that a closer consideration of our expressions of fallibility suggest that epistemically responsible authors would not be rational to believe that their books contains errors. I conclude by considering alternative expressions of fallibility that employ terms such as possible and probable, and discuss the role that expressions of fallibility play in conversation.

A way out of the preface paradox?

The thesis defended in this article is that by uttering or publishing a great many declarative sentences in assertoric mode, one does not actually assert that their conjunction is true – one rather asserts that the vast majority of these sentences are true. Accordingly, the belief that is expressed thereby is the belief that the vast majority of these sentences are true. In the article, we make this proposal precise, we explain the context-dependency of belief that corresponds to it, we point out why our everyday oral practice of single assertions is not affected by it, and we argue that the proposal leads to a way out of the Paradox of the Preface.

The Review Paradox: On The Diachronic Costs of Not Closing Rational Belief Under Conjunction

AbstractWe argue that giving up on the closure of rational belief under conjunction comes with a substantial price. Either rational belief is closed under conjunction, or else the epistemology of belief has a serious diachronic deficit over and above the synchronic failures of conjunctive closure. The argument for this, which can be viewed as a sequel to the preface paradox, is called the ‘review paradox'; it is presented in four distinct, but closely related versions.

Epistemic closure under deductive inference: what is it and can we afford it?

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic uncertainty in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge.

A springboard for exploring the many approaches to degrees of belief

Degrees of Belief is a strong collection of essays distinguished by its inclusion of an unusually wide array of approaches to understanding its subject. The book consists mainly of recent works (growing out of a 2004 conference at the University of Konstanz) from perspectives as diverse as probabilism (the view that degrees of belief ought to be probabilities), Dempster-Shafer theory, possibility theory, ranking theory, AGM (Alchourron-Gardenfors-Makinson) belief-revision theory, and others. The essays are varied in focus, but many are concerned with outlining formal axiomatizations of degree of belief (variously understood), and several of them are surveys of their respective sub-fields. As one might expect, the discussion is often technical and sometimes dense, and so the book is best suited for formally proficient advanced students (graduate or upper-level undergraduate) or professionals seeking to explore other approaches to degree of belief than the ones in which they currently work. Some recurrent themes in the book include the relation of degree of belief to full belief, how degree of belief ought best to be understood (its purpose and function), and the formal laws (so understood) it ought to obey. There is limited reference in some articles to applications (e.g., in computer science), but the main focus of the book is theoretical. What follows is only a small sample of the rich content contained in the book. After a clear and concise preview of the book’s contents, written by one of the editors (Franz Huber), Part I of the book concentrates on how belief relates to degree of belief. The lottery paradox is key here (and also the related preface paradox), and accordingly, the section begins with one exposition of it, by Richard Foley (a revision of Chapter 4 of Foley 1993). The lottery paradox arises from the so-called Lockean thesis that belief is just sufficiently high degree of belief. For example, if I believe p just in case my degree of belief in it is at least 99%, then I’ll

Logical questions behind the lottery and preface paradoxes: lossy rules for uncertain inference

We reflect on lessons that the lottery and preface paradoxes provide for the logic of uncertain inference. One of these lessons is the unreliability of the rule of conjunction of conclusions in such contexts, whether the inferences are probabilistic or qualitative; this leads us to an examination of consequence relations without that rule, the study of other rules that may nevertheless be satisfied in its absence, and a partial rehabilitation of conjunction as a ‘lossy’ rule. A second lesson is the possibility of rational inconsistent belief; this leads us to formulate criteria for deciding when an inconsistent set of beliefs may reasonably be retained.