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

The 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).     

An analytic tableau calculus for a temporalised belief logic

A tableau is a refutation-based decision procedure for a related logic, and is among the most popular proof procedures for modal logics. In this paper, we present a labelled tableau calculus for a temporalised belief logic called TML⁺, which is obtained by adding a linear-time temporal logic onto a belief logic by the temporalisation method of Finger and Gabbay. We first establish the soundness and the completeness of the labelled tableau calculus based on the soundness and completeness results of its constituent logics. We then sketch a resolution-type proof procedure that complements the tableau calculus and also propose a model checking algorithm for TML⁺ based on the recent results for model checking procedures for temporalised logics. TML⁺ is suitable for formalising trust and agent beliefs and reasoning about their evolution for agent-based systems. Based on the logic TML⁺, the proposed labelled tableau calculus could be used for analysis, design and verification of agent-based systems operating in dynamic environments.     

Thinking about representations: the case of opaque contexts

To address the question of whether young children are differentially sensitive to referential opacity, an advanced Theory of Mind skill, we assessed 4-, 6-, and 8-year-olds on three types of opaque contexts: epistemic, quotational, and intentional. Children’s performance improved as a function of age and varied significantly by opacity type. Performance was best for epistemic opacity (using the verb “know”) and poorest for intentional opacity (using “mean to”), with quotational opacity (using “said”) falling in-between. Importantly, the current results suggest that children’s sensitivity to referential opacity is not an all-or-nothing competence but rather one that varies across the contexts examined. Possible reasons for this variability are discussed.     

聋童与正常儿童对多种信念的认知

选取了122名3～12岁聋童,并分别用65名3～5岁的正常儿童作对照,开展了2个实验系列,探讨了儿童的正确信念、一级错误信念及二级错误信念认知的发展特点.结果如下: (1)聋童及正常儿童信念认知的发展过程中,无论是关于正确信念,还是关于一级错误信念,都是先发展自我信念认知,再发展他人信念认知;(2)关于正确信念、一级错误信念和二级错误信念认知的发展,聋童都比正常儿童滞后,但两者的发展趋势一致; (3)手语聋童在信念认知上略好于口语聋童; (4)父母为聋人或父母会手语的聋童,以及兄弟姐妹会手语的聋童,其信念认知水平要比其他聋童好.     

Iterated Belief Change and the Recovery Axiom

The axiom of recovery, while capturing a central intuition regarding belief change, has been the source of much controversy. We argue briefly against putative counterexamples to the axiom—while agreeing that some of their insight deserves to be preserved—and present additional recovery-like axioms in a framework that uses epistemic states, which encode preferences, as the object of revisions. This makes iterated revision possible and renders explicit the connection between iterated belief change and the axiom of recovery. We provide a representation theorem that connects the semantic conditions we impose on iterated revision and our additional syntactical properties. We show interesting similarities between our framework and that of Darwiche–Pearl (Artificial Intelligence 89:1–29 1997). In particular, we show that intuitions underlying the controversial (C2) postulate are captured by the recovery axiom and our recovery-like postulates (the latter can be seen as weakenings of (C2)). We present postulates for contraction, in the same spirit as the Darwiche–Pearl postulates for revision, and provide a theorem that connects our syntactic postulates with a set of semantic conditions. Lastly, we show a connection between the contraction postulates and a generalisation of the recovery axiom. Portions of this paper were originally presented at ECAI 2002.     

New Foundations for a Relational Theory of Theory-revision

AGM-theory, named after its founders Carlos Alchourrón, Peter Gärdenfors and David Makinson, is the leading contemporary paradigm in the theory of belief-revision. The theory is reformulated here so as to deal with the central relational notions ‘J is a contraction of K with respect to A’ and ‘J is a revision of K with respect to A’. The new theory is based on a principal-case analysis of the domains of definition of the three main kinds of theory-change (expansion, contraction and revision). The new theory is stated by means of introduction and elimination rules for the relational notions. In this new setting one can re-examine the relationship between contraction and revision, using the appropriate versions of the so-called Levi and Harper identities. Among the positive results are the following. One can derive the extensionality of contraction and revision, rather than merely postulating it. Moreover, one can demonstrate the existence of revision-functions satisfying a principle of monotonicity. The full set of AGM-postulates for revision-functions allow for completely bizarre revisions. This motivates a Principle of Minimal Bloating, which needs to be stated as a separate postulate for revision. Moreover, contractions obtained in the usual way from the bizarre revisions, by using the Harper identity, satisfy Recovery. This provides a new reason (in addition to several others already adduced in the literature) for thinking that the contraction postulate of Recovery fails to capture the Principle of Minimal Mutilation. So the search is still on for a proper explication of the notion of minimal mutilation, to do service in both the theory of contraction and the theory of revision. The new relational formulation of AGM-theory, based on principal-case analysis, shares with the original, functional form of AGM-theory the idealizing assumption that the belief-sets of rational agents are to be modelled as consistent, logically closed sets of sentences. The upshot of the results presented here is that the new relational theory does a better job of making important matters clear than does the original functional theory. A new setting has been provided within which one can profitably address two pressing questions for AGM-theory: (1) how is the notion of minimal mutilation (by both contractions and revisions) best analyzed? and (2) how is one to rule out unnecessary bloating by revisions?     

The relationship between susceptibility to false memories, dissociativity, and paranormal belief and experience

One hundred participants completed a News Coverage Questionnaire concerning personal memories of where they were, what they were doing and who they were with when footage of dramatic news events was first shown on television, as well as asking them to recall details of the footage itself. These news items included four events that are known to have been captured on film and one item concerning non-existent footage of the bombing of a nightclub in Bali. Overall, 36% of respondents reported false memories of the alleged footage of the Bali bombing. Participants reporting false memories were found to score significantly higher than those who did not report such memories on the Australian Sheep–Goat Scale, on various subscales of the Anomalous Experiences Inventory (Belief, Experience and Ability) and on the Dissociative Experiences Scale, supporting the hypothesis that believers in the paranormal may be more susceptible to false memories than non-believers.     

“This way!”, “No! That way!”—3-year olds know that two people can have mutually incompatible desires

In theory of mind research, there is a long standing dispute about whether children come to understand the subjectivity of both desires and beliefs at the same time (around age 4), or whether there is an asymmetry such that desires are understood earlier. To address this issue, 3-year olds’ understanding of situations in which two persons have mutually incompatible desires was tested in two studies. Results revealed that (i) children were quite proficient at ascribing incompatible desires to two persons, and in simpler scenarios even incompatible desire-dependent emotions; (ii) children showed this proficiency even though they mostly failed the false belief task. Overall, these results suggest that there is an asymmetry such that young children come to understand the subjective nature of desires before they understand the corresponding subjectivity of beliefs. Possible explanations for this asymmetry are discussed in light of conceptual change and information-processing accounts of theory of mind development.     

Précis of <Emphasis Type="Italic">A Virtue Epistemology</Emphasis> (Oxford University Press, 2007)

This is a summary of A Virtue Epistemology, the book that is the subject of this book symposium.