Impossibility Results for Rational Belief

There are two ways of representing rational belief: qualitatively as yes‐or‐no belief, and quantitatively as degrees of belief. Standard rationality conditions are: (i) consistency and logical closure, for qualitative belief, (ii) satisfaction of the probability axioms, for quantitative belief, and (iii) a relationship between qualitative and quantitative beliefs in accordance with the Lockean thesis. In this paper, it is shown that these conditions are inconsistent with each of three further rationality conditions: fallibilism, open‐mindedness, and invariance under independent conceptual expansions. Restrictions of the Lockean thesis that have been suggested in the literature cannot remove the inconsistency. In the outlook we discuss two alternative ways of dealing with this problem: restricting conjunctive closure or going for a dual system account.     

The joint aggregation of beliefs and degrees of belief

Synthese - The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: (1) consistency and deductive closure for...     

Belief,Credence, and the Preface Paradox

Many 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 Decision-Theoretic Lockean Thesis

Abstract

Certain philosophers maintain that there is a ‘constitutive threshold for belief’: to believe that p just is to have a degree of confidence that p above a certain threshold. On the basis of this view, these philosophers defend what is known as ‘the Lockean Thesis’, according to which it is rational to believe that p just in case it is rational to have a degree of confidence that p above the constitutive threshold for belief. While not directly speaking to the controversy over the Lockean Thesis, this paper defends the general idea behind it—namely, the thesis that there is some threshold such that it is rational to believe that p if and only if it is rational to have a degree of confidence greater than that threshold. This paper identifies the threshold in question—not with the alleged constitutive threshold for belief—but with what I call ‘the practical threshold for rational belief’. Roughly, the thesis defended here is that it is rational to believe that p if and only if it is rational to have a degree of confidence that p that rationalizes engaging in certain types of practical reasoning.     

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.     

Higher‐Order Defeat is Object‐Independent

Higher‐order defeat occurs when one loses justification for one's beliefs as a result of receiving evidence that those beliefs resulted from a cognitive malfunction. Several philosophers have identified features of higher‐order defeat that distinguish it from familiar types of defeat. If higher‐order defeat has these features, they are data an account of rational belief must capture. In this article, I identify a new distinguishing feature of higher‐order defeat, and I argue that on its own, and in conjunction with the other distinguishing features, it favors an account of higher‐order defeat grounded in non‐evidential, ‘state‐given reasons’ for belief.     

The Preface Paradox Revisited

The Preface Paradox has led many philosophers to believe that, if it isassumed that high probability is necessary for rational acceptability, the principleaccording to which rational acceptability is closed under conjunction (CP)must be abandoned. In this paper we argue that the paradox is far less damaging to CP than is generally believed. We describe how, given certain plausibleassumptions, in a large class of cases in which CP seems to lead tocontradiction, it does not do so after all. A restricted version of CP canthus be maintained.     

Statistical Bias and Endorsement of Conspiracy Theories

Previous research proposes that endorsement of anomalous beliefs is associated with proneness to conjunction error. This supposition ignores important differences between belief types. Correspondingly, the present study examined the degree to which components of statistical bias predicted conspiratorial ideation and belief in the paranormal. Confirmatory factor analysis and structural equation modelling revealed that conjunction error was associated with conspiratorial ideation, whilst perception of randomness most strongly predicted belief in the paranormal. These findings opposed the notion that anomalous beliefs, by virtue of possession of common characteristics, relate similarly to conjunction error. With regard to conspiracy, conjunction‐framing manipulations produced only minor variations in relationship strength. This supported the notion that conspiratorial ideation was associated with a domain‐general susceptibility to conjunction error. Framing, however, did influence the relationship between belief in the paranormal and conjunction; whilst paranormal conjunctions were generally easier to solve, performance declined as level of paranormal belief increased.Copyright © 2017 John Wiley & Sons, Ltd.     

The Insufficiency of the Dutch Book Argument

It is a common view that the axioms of probability can be derived from the following assumptions: (a) probabilities reflect (rational) degrees of belief, (b) degrees of belief can be measured as betting quotients; and (c) a rational agent must select betting quotients that are coherent. In this paper, I argue that a consideration of reasonable betting behaviour, with respect to the alleged derivation of the first axiom of probability, suggests that (b) and (c) are incorrect. In particular, I show how a rational agent might assign a ‘probability’ of zero to an event which she is sure will occur.     

Foley's Threshold View of Belief and The Safety Condition on Knowledge

This paper introduces a new argument against Richard Foley's threshold view of belief. Foley's view is based on the Lockean Thesis (LT) and the Rational Threshold Thesis (RTT). The former thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition sufficient for belief. The latter thesis is the claim that it is epistemically rational to believe a proposition if and only if it is epistemically rational to have a degree of confidence in that proposition that meets or exceeds a specified threshold. The argument introduced here shows that the views derived from the joint endorsement of the LT and the RTT violate the safety condition on knowledge in way that threatens the LT and/or the RTT.     

On the relative independence of thinking biases and cognitive ability

In 7 different studies, the authors observed that a large number of thinking biases are uncorrelated with cognitive ability. These thinking biases include some of the most classic and well-studied biases in the heuristics and biases literature, including the conjunction effect, framing effects, anchoring effects, outcome bias, base-rate neglect, "less is more" effects, affect biases, omission bias, myside bias, sunk-cost effect, and certainty effects that violate the axioms of expected utility theory. In a further experiment, the authors nonetheless showed that cognitive ability does correlate with the tendency to avoid some rational thinking biases, specifically the tendency to display denominator neglect, probability matching rather than maximizing, belief bias, and matching bias on the 4-card selection task. The authors present a framework for predicting when cognitive ability will and will not correlate with a rational thinking tendency.     

法律信仰转型中人的主体性

在西方法律传统的演变中,法律信仰的转型是伴随着人的主体性的凸显而发生的。基督教理论承认人的有限自由意志,在上帝之下,君主必须服从神法和以神法为依据的法律,个人意志可以高于君权,由此形成了神权保护民权、对抗王权的局面。在自然法理论中,自由意志被理性所取代,人依赖理性就可以制定出符合神法和自然法的世俗法。理性主义则认为,人不再需要神的帮助,仅凭理性的命令就可以制定出符合理性本身的法律,获得对法律的信仰。西方法律信仰的转型经历了从自由意志到理性主义的演变历程。当代中国法律信仰的基础是理性主义,将“公平”、“正义”等法治观念建立在理性的基础上,对处于目前文化境遇中的中国人来说是必然的选择。     

Belief,credence, and norms

There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered.     

Misperception of Chance,Conjunction, Framing Effects and Belief in the Paranormal: A Further Evaluation

Studies exploring relationships between belief in the paranormal and vulnerability to cognitive bias suggest that believers are liable to misperception of chance and conjunction fallacy. Research investigating misperception of chance has produced consistent findings, whilst work on conjunction fallacy is less compelling. Evidence indicates also that framing biases within a paranormal context can increase believers' susceptibility. The present study, using confirmatory factor analysis and structural equation modelling, examined the contribution of each bias to belief in the paranormal and assessed the merits of previous research. Alongside, the Revised Paranormal Belief Scale, participants completed standard and paranormal framed perception of randomness and conjunction problems. Perception of randomness was more strongly associated with belief in the paranormal than conjunction fallacy. Inherent methodological issues limited the usefulness of framing manipulations; presenting problems within a paranormal context weakened their predictive power.Copyright © 2016 John Wiley & Sons, Ltd.     

The moderating influence of variability on belief revision

The variability of the information on which a belief was initially based should moderate the degree to which the belief is revised when new disconfirming information is received. Reasoning from everyday intuitions, psychological theories of concept representation, and a rational mathematical analysis, we inferred that as variability increased, resistance to disconfirming information would also increase. Participants’ judgments of the central tendencies of distributions of numerical information confirmed this prediction.     

Iterative and fixed point common belief

We define infinitary extensions to classical epistemic logic systems, and add also a common belief modality, axiomatized in a finitary, fixed-point manner. In the infinitary K system, common belief turns to be provably equivalent to the conjunction of all the finite levels of mutual belief. In contrast, in the infinitary monotonic system, common belief implies every transfinite level of mutual belief but is never implied by it. We conclude that the fixed- point notion of common belief is more powerful than the iterative notion of common belief.     

The Modal Logic of Discrepancy

Discrepancies between an agents goals and beliefs play an important, if implicit, role in determining what a rational agent is motivated to do. This is most obvious in cases where an agent achieves a complex goal incrementally and must deliberate anew as each milestone is reached. In such cases the concept of goal/belief discrepancy defines an appropriate space to which a degree-of-achievement yardstick can be applied. This paper presents soundness and completeness results concerning a logic for reasoning about goal/belief discrepancy, and it is suggested that a certain species of goal/belief discrepancy captures the concept of desire.     

Justified inference

This paper proposes a general account of the epistemological significance of inference. This account rests on the assumption that the concept of a ??justified?? belief or inference is a normative concept. It also rests on a conception of belief that distinguishes both (a) between conditional and unconditional beliefs and (b) between enduring belief states and mental events of forming or reaffirming a belief, and interprets all of these different kinds of belief as coming in degrees. Conceptions of ??rational coherence?? and ??competent inference?? are then formulated, in terms of the undefeated instances of certain rules of inference. It is proposed that (non-accidental) rational coherence is a necessary and sufficient condition of justified enduring belief states, while competent inference always results in a justified mental event of some kind. This proposal turns out to tell against the view that there are any non-trivial cases of ??warrant transmission failure??. Finally, it is explained how these proposals can answer the objections that philosophers have raised against the idea that justified belief is ??closed?? under competent inference.     

The Irreducibility of Iterated to Single Revision

After a number of decades of research into the dynamics of rational belief, the belief revision theory community remains split on the appropriate handling of sequences of changes in view, the issue of so-called iterated revision. It has long been suggested that the matter is at least partly settled by facts pertaining to the results of various single revisions of one’s initial state of belief. Recent work has pushed this thesis further, offering various strong principles that ultimately result in a wholesale reduction of iterated to one-shot revision. The present paper offers grounds to hold that these principles should be significantly weakened and that the reductionist thesis should ultimately be rejected. Furthermore, the considerations provided suggest a close connection between the logic of iterated belief change and the logic of evidential relevance.     

The Price of Innocent Millianism

According to the view I call `innocent Millianism', that-clauses differing only for occurrences of co-referential names provide the same contribution to the intensional profile of a belief report. It is widely believed by friends and foes of innocent Millianism alike that this approach entails either the denial of what I label a `naïve' account ofbelief reports, or a dismissive attitude towards our semantic intuitions. In this essay, I counter that the conjunction of innocent Millianism and the naïve view of belief reports is compatible with our intuitions of truth-conditions. In order to defend this conclusion, I defend an independently motivated approach, in which utterances endowed of the same intension may nevertheless differ in truth-conditions.