Diachronic Dutch Books and Evidential Import

A handful of well‐known arguments (the ‘diachronic Dutch book arguments’) rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not ‘diachronically Dutch book‐able’) if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non‐trivial assumptions about which evidence you might acquire—in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non‐(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid.     

Anti-Positionalism’s Regress

This paper is about the Problem of Order, which is basically the problem how to account for both the distinctness of facts like a’s preceding b and b’s preceding a, and the identity of facts like a’s preceding b and b’s succeeding a. It has been shown that the Standard View fails to account for the second part and is therefore to be replaced. One of the contenders is Anti-Positionalism. As has recently been pointed out, however, Anti-Positionalism falls prey to a regress argument which is to prove its failure. In the paper we spell out this worry, show that the worry is a serious one, and distinguish four possible strategies for Anti-Positionalism to deal with it.     

The Smith-Walley Interpretation of Subjective Probability: An Appreciation

The right interpretation of subjective probability is implicit in the theories of upper and lower odds, and upper and lower previsions, developed, respectively, by Cedric Smith (1961) and Peter Walley (1991). On this interpretation you are free to assign contingent events the probability 1 (and thus to employ conditionalization as a method of probability revision) without becoming vulnerable to a weak Dutch book. Special Issue Formal Epistemology I. Edited by Branden Fitelson     

Constructive Thinking and Burnout among Secondary School Teachers

The present study investigated the relationship between Epstein’s (1998, Constructive thinking: The key to emotional intelligence. London: Praeger publisher.) components of constructive thinking and burnout as experienced by a sample of Dutch secondary school teachers. A postal questionnaire was sent to teachers from randomly selected secondary schools. The response rate was 54.1% (N=433). Four components of constructive thinking significantly contributed to the explained variance in emotional exhaustion (17%), depersonalization (21%), and personal accomplishment (20%). The results of the study suggest that secondary school teachers’ maladaptive thinking processes prevent them from rational thinking during their work, which significantly contributes to the onset of burnout. Burnout intervention programs for teachers are likely to be more effective when the participator’s maladaptive thinking system is taken into consideration. This stems from the idea that personality factors are a probably easier point of departure to tackle burnout symptoms than organizational factors.     

A Psychometric Analysis of the Revised Child Anxiety and Depression Scales—Parent Version in a School Sample

The Revised Child Anxiety and Depression Scale—Parent Version (RCADS-P) is a parent-report questionnaire of youth anxiety and depression with scales corresponding to the DSM diagnoses of separation anxiety disorder, social phobia, generalized anxiety disorder, panic disorder, obsessive-compulsive disorder, and major depressive disorder. The RCADS-P was recently developed and has previously demonstrated strong psychometric properties in a clinic-referred sample (Ebesutani et al., Journal of Abnormal Child Psychology 38, 249–260, 2010b). The present study examined the psychometric properties of the RCADS-P in a school-based population. As completed by parents of 967 children and adolescents, the RCADS-P demonstrated high internal consistency, test-retest reliability, and good convergent/divergent validity, supporting the RCADS-P as a measure of internalizing problems specific to depression and five anxiety disorders in school samples. Normative data are also reported to allow for the derivation of T-scores to enhance clinicians’ ability to make classification decisions using RCADS-P subscale scores.     

Vague Expectation Value Loss

Vague subjective probability may be modeled by means of a set of probability functions, so that the represented opinion has only a lower and upper bound. The standard rule of conditionalization can be straightforwardly adapted to this. But this combination has difficulties which, though well known in the technical literature, have not been given sufficient attention in probabilist or Bayesian epistemology. Specifically, updating on apparently irrelevant bits of news can be destructive of one’s explicitly prior expectations. Stability of vague subjective opinion appears to need a more complex model.     

Implications of the Dutch Book: Following Ramsey��s axioms

The Dutch Book Argument shows that an agent will lose surely in a gamble (a Dutch Book is made) if his degrees of belief do not satisfy the laws of the probability. Yet a question arises here: What does the Dutch Book imply? This paper firstly argues that there exists a utility function following Ramsey’s axioms. And then, it explicates the properties of the utility function and degree of belief respectively. The properties show that coherence in partial beliefs for Subjective Bayesianism means that the degree of belief, representing a belief ordering, satisfies the laws of probability, and that coherence in preferences means that the preferences are represented by expected utilities. A coherent belief ordering and a utility scale induce a coherent preference ordering; a coherent preference ordering induces a coherent belief ordering which can be uniquely represented by a degree-of-belief function. The preferences (values) and beliefs are both incoherent or disordered if a Dutch Book is made.     

Can QOL Researchers Learn Anything “Scientifically” Meaningful from Popular Cultural Icons Who Speak on Happiness and Well-Being?

This is review of two books written by “gurus” who address the topic of happiness and well-being from a spiritual perspective. One book is Matthieu Ricard’s Happiness: A Guide to Developing Life’s Most Important Skill (published by Little, Brown and Company, 2003). The other book is Eckhart Tolle’s A New Earth: Awakening to Your Life’s Purpose (published by A Plume Book, 2005). The books are thought provoking and interesting reading for the layperson. From a scientific perspective, they should not be treated with any credibility. They advocate an image of the human condition and well-being that is not based on a good and scientific understanding of human nature.     

Diachronic Dutch Books and Sleeping Beauty

Hitchcock advances a diachronic Dutch Book argument (DDB) for a 1/3 answer to the Sleeping Beauty problem. Bradley and Leitgeb argue that Hitchcock’s DDB argument fails. We demonstrate the following: (a) Bradley and Leitgeb’s criticism of Hitchcock is unconvincing; (b) nonetheless, there are serious reasons to worry about the success of Hitchcock’s argument; (c) however, it is possible to construct a new DDB for 1/3 about which such worries cannot be raised.     

If Logic, Definitions and the Vicious Circle Principle

In a definition (∀x)((xєr)↔D[x]) of the set r, the definiens D[x] must not depend on the definiendum r. This implies that all quantifiers in D[x] are independent of r and of (∀x). This cannot be implemented in the traditional first-order logic, but can be expressed in IF logic. Violations of such independence requirements are what created the typical paradoxes of set theory. Poincaré’s Vicious Circle Principle was intended to bar such violations. Russell nevertheless misunderstood the principle; for him a set a can depend on another set b only if (bєa) or (b ⊆ a). Likewise, the truth of an ordinary first-order sentence with the G?del number of r is undefinable in Tarki’s sense because the quantifiers of the definiens depend unavoidably on r.     

Toward a More Natural Expression of Quantum Logic with Boolean Fractions

This paper uses a non-distributive system of Boolean fractions (a|b), where a and b are 2-valued propositions or events, to express uncertain conditional propositions and conditional events. These Boolean fractions, ‘a if b’ or ‘a given b’, ordered pairs of events, which did not exist for the founders of quantum logic, can better represent uncertain conditional information just as integer fractions can better represent partial distances on a number line. Since the indeterminacy of some pairs of quantum events is due to the mutual inconsistency of their experimental conditions, this algebra of conditionals can express indeterminacy. In fact, this system is able to express the crucial quantum concepts of orthogonality, simultaneous verifiability, compatibility, and the superposition of quantum events, all without resorting to Hilbert space. A conditional (a|b) is said to be “inapplicable” (or “undefined”) in those instances or models for which b is false. Otherwise the conditional takes the truth-value of proposition a. Thus the system is technically 3-valued, but the 3rd value has nothing to do with a state of ignorance, nor to some half-truth. People already routinely put statements into three categories: true, false, or inapplicable. As such, this system applies to macroscopic as well as microscopic events. Two conditional propositions turn out to be simultaneously verifiable just in case the truth of one implies the applicability of the other. Furthermore, two conditional propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the non-distributive system of conditional propositions just in case b=d, their conditions are equivalent. Since all aspects of quantum mechanics can be represented with this near classical logic, there is no need to adopt Hilbert space logic as ordinary logic, just a need perhaps to adopt propositional fractions to do logic, just as we long ago adopted integer fractions to do arithmetic. The algebra of Boolean fractions is a natural, near-Boolean extension of Boolean algebra adequate to express quantum logic. While this paper explains one group of quantum anomalies, it nevertheless leaves no less mysterious the ‘influence-at-a-distance’, quantum entanglement phenomena. A quantum realist must still embrace non-local influences to hold that “hidden variables” are the measured properties of particles. But that seems easier than imaging wave-particle duality and instant collapse, as offered by proponents of the standard interpretation of quantum mechanics. Partial support for this work is gratefully acknowledged from the In-House Independent Research Program and from Code 2737 at the Space & Naval Warfare Systems Center (SSC-SD), San Diego, CA 92152-5001. Presently this work is supported by Data Synthesis, 2919 Luna Avenue, San Diego, CA 92117.     

Sleeping Beauty and Self-location: A Hybrid Model

The Sleeping Beauty problem is test stone for theories about self- locating belief, i.e. theories about how we should reason when data or theories contain indexical information. Opinion on this problem is split between two camps, those who defend the “1/2 view” and those who advocate the “1/3 view”. I argue that both these positions are mistaken. Instead, I propose a new “hybrid” model, which avoids the faults of the standard views while retaining their attractive properties. This model appears to violate Bayesian conditionalization, but I argue that this is not the case. By paying close attention to the details of conditionalization in contexts where indexical information is relevant, we discover that the hybrid model is in fact consistent with Bayesian kinematics. If the proposed model is correct, there are important lessons for the study of self-location, observation selection theory, and anthropic reasoning.     

Stakes and beliefs

The idea that beliefs may be stake-sensitive is explored. This is the idea that the strength with which a single, persistent belief is held may vary and depend upon what the believer takes to be at stake. The stakes in question are tied to the truth of the belief—not, as in Pascal’s wager and other cases, to the belief’s presence. Categorical beliefs and degrees of belief are considered; both kinds of account typically exclude the idea and treat belief as stake-invariant, though an exception is briefly described. The role of the assumption of stake-invariance in familiar accounts of degrees of belief is also discussed, and morals are drawn concerning finite and countable Dutch book arguments.     

The puzzle of the hats

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty.     

The grammar of approximating number pairs

In the present article, we studied approximating pairs of numbers (a, b) that were used to estimate quantity in a single phrase (“two, three years ago”). Pollmann and Jansen (1996) found that only a few of the many possible pairs are actually used, suggesting an interaction between the ways in which people estimate quantity and their use of quantitative phrases in colloquial speech. They proposed a set of rules that describe which approximating pairs are used in Dutch phrases. We revisited this issue in an analysis of Swedish and American language corpora and in a series of three experiments in which Swedish and American adults rated the acceptability of various approximating pairs and created approximating pairs of their own in response to various estimation tasks. We found evidence for Pollmann and Jansen’s rules in both Swedish and English phrases, but we also identified additional rules and substantial individual and cross-language variation. We will discuss implications for the origin of this loose “grammar” of approximating pairs.     

Erotic Motherhood and the Ideal Son: Mythology as Psychotherapy in the Krishna-Bhakti Tradition

Through the lenses of D.W. Winnicott’s theory of development and Sudhir Kakar’s theory that the flux between fusion with and separation from Krishna in the Krishna-bhakti tradition is a reflection of the early childhood relational dynamics of mother and son, I will argue that the mythology of Krishna found in the Bhagavata Purana Book X implements the traditional Hindu notion of moksha but reshapes it in a uniquely psychologically adaptive way. In an attempt to meet the psychological needs of sons and mothers, the mythology of this text maintains a theme of fluctuation between fusion and separation between the gopis who function as mother figures and Krishna, the ideal son. Through the thematic focus on the flux between the gopis’ fusion with and separation from Krishna, the text embodies the Hindu soteriological concept of moksha as well as plays out the cultural relationship between mother and son.     

Knowability and the capacity to know

This paper presents a generalized form of Fitch’s paradox of knowability, with the aim of showing that the questions it raises are not peculiar to the topics of knowledge, belief, or other epistemic notions. Drawing lessons from the generalization, the paper offers a solution to Fitch’s paradox that exploits an understanding of modal talk about what could be known in terms of capacities to know. It is argued that, in rare cases, one might have the capacity to know that p even if it is metaphysically impossible for anyone to know that p, and that recognizing this fact provides the resources to solve Fitch’s paradox.     

Reichenbach’s Posits Reposited

Reichenbach’s use of ‘posits’ to defend his frequentistic theory of probability has been criticized on the grounds that it makes unfalsifiable predictions. The justice of this criticism has blinded many to Reichenbach’s second use of a posit, one that can fruitfully be applied to current debates within epistemology. We show first that Reichenbach’s alternative type of posit creates a difficulty for epistemic foundationalists, and then that its use is equivalent to a particular kind of Jeffrey conditionalization. We conclude that, under particular circumstances, Reichenbach’s approach and that of the Bayesians amount to the same thing, thereby presenting us with a new instance in which chance and credence coincide.