The effects of payout and probability magnitude on the Allais paradox

The Allais paradox decision bias was first offered as a challenge to the expected utility theory over 60 years ago. Although the Allais paradox is a standard challenge for normative theories of risky choice, its causes are not well understood. The present experiment uses two manipulations of the Allais paradox to investigate the commonly proposed probability-weighting explanation of the paradox. Reducing the magnitude of the outcomes did not affect the size of the Allais paradox, contradicting previous literature and supporting the probability weighting hypothesis. Reducing the probability of the nonzero outcomes to eliminate certainty reduced, but did not eliminate, the Allais paradox, a result inconsistent with probability weighting and other theories of the Allais paradox. The results suggest that the certainty effect alone cannot explain the Allais paradox.     

The revenger's paradox

Conclusion Unlike the more commonly discussed paradoxes of deontic logic, the revenger's paradox is present not only in strong logics such as SDL, but also in much weaker logics that have been constructed to avoid the paradoxes of SDL. The paradox shows that any deontic logic with intersubstitutivity makes counter-intuitive truth assignments to some deontic expressions.However, the revenger's paradox does not pose as serious a problem as does Ross's paradox to the logics in which it occurs. A deontic logic in which Ross's paradox does not arise is preferable to one in which it does arise, even if the latter is subject to the revenger's paradox.     

The logic of Simpson’s paradox

There are three distinct questions associated with Simpson’s paradox. (i) Why or in what sense is Simpson’s paradox a paradox? (ii) What is the proper analysis of the paradox? (iii) How one should proceed when confronted with a typical case of the paradox? We propose a “formal” answer to the first two questions which, among other things, includes deductive proofs for important theorems regarding Simpson’s paradox. Our account contrasts sharply with Pearl’s causal (and questionable) account of the first two questions. We argue that the “how to proceed question?” does not have a unique response, and that it depends on the context of the problem. We evaluate an objection to our account by comparing ours with Blyth’s account of the paradox. Our research on the paradox suggests that the “how to proceed question” needs to be divorced from what makes Simpson’s paradox “paradoxical.”     

On Kripke’s Dogmatism Paradox: A Logical Dynamical Analysis

As a byproduct of solving the surprise-exam paradox, Saul Kripke formulates a “dogmatism paradox” which seems to show that knowledge entails dogmatism. In this paper, the author analyzes the nature of the dogmatism paradox from a logical dynamical perspective. The author suggests that the dogmatism paradox is better understood as a paradox of knowledge attribution rather than of knowledge. Therefore, the dogmatism paradox could be solved without sacrificing the principle of epistemic closure. Based on a famous version of relevant alternatives theory, the author formalizes a logic of knowledge attribution in the style of logical dynamics, namely, public retraction logic, and analyzes how knowledge attributions are retracted with the expansion of relevant alternatives.     

The Paradox of Belief Instability and a Revision Theory of Belief

The epistemic paradox of 'belief instability' has recently received notable attention from many philosophers. In this paper I offer a new proposal, which I call a 'revision theory of belief'. This theory is in many respects an application of Gupta's and Belnap's revision theory of truth. They argue that the Liar paradox arises because our notion of truth is circular. I offer a similar proposal for handling the paradox of belief instability. In particular, I argue that our notion involved in the paradox of belief instability is circular, and this circularity of belief is the source of the paradox.     

Some Irreverent Thoughts on Paradox

There is currently great interest in the use of paradox in psychotherapy. Unfortunately, there is also considerable confusion and misunderstanding of paradox, owing, in part, to the lack of a comprehensive theory that explains the role of paradox in human problems. This paper does not address itself to such theory but explores some cultural and epistemological components of therapists' misperceptions and misattributions of “paradox.”     

Natural Deduction and Curry's Paradox

Curry's paradox, sometimes described as a general version of the better known Russell's paradox, has intrigued logicians for some time. This paper examines the paradox in a natural deduction setting and critically examines some proposed restrictions to the logic by Fitch and Prawitz. We then offer a tentative counterexample to a conjecture by Tennant proposing a criterion for what is to count as a genuine paradox.     

PARADOXICAL PROPOSITIONS

This paper concerns two paradoxes involving propositions. The first is Russell's paradox from Appendix B of The Principles of Mathematics, a version of which was later given by Myhill. The second is a paradox in the framework of possible worlds, given by Kaplan. This paper shows a number of things about these paradoxes. First, we will see that, though the Russell/Myhill paradox and the Kaplan paradox might appear somewhat different, they are really just variants of the same phenomenon. Though they do this in different ways, the core of each paradox is to use the notion of a proposition to construct a function, f, from the power set of some set into the set itself. Next we will see how this paradox fits into the Inclosure Schema. Finally, I will provide a model of the paradox in question, showing its results to be non‐trivial, though inconsistent.     

A Berry and A Russell Without Self-Reference

In this paper I present two new paradoxes, a definability paradox (related to the paradoxes of Berry, Richard and König), and a paradox about extensions (related to Russell’s paradox). However, unlike the familiar definability paradoxes and Russell’s paradox, these new paradoxes involve no self-reference or circularity.     

意外考试悖论的博弈分析

本文从博弈的角度分析了意外考试悖论,指出了以往解决方案的不足,给出了一种新的方案。根据这个新方案,考试悖论的推理中使用了倒推法和弱下策反复剔除法。本文接着讨论了这些博弈推理方法的不足。然后把这个新的博弈方案用到卡片悖论和方格悖论这些考试悖论的变种里。最后指出,在考试悖论里,比起倒推法,弱下策剔除法是引起悖论的更根本的原因。     

How Braess’ paradox solves Newcomb's problem: Not!

In an engaging and ingenious paper, Irvine (1993) purports to show how the resolution of Braess’ paradox can be applied to Newcomb's problem. To accomplish this end, Irvine forges three links. First, he couples Braess’ paradox to the Cohen‐Kelly queuing paradox. Second, he couples the Cohen‐Kelly queuing paradox to the Prisoner's Dilemma (PD). Third, in accord with received literature, he couples the PD to Newcomb's problem itself. Claiming that the linked models are “structurally identical”, he argues that Braess solves Newcomb's problem. This paper shows that Irvine's linkage depends on structural similarities—rather than identities—between and among the models. The elucidation of functional disanalogies illuminates structural dissimilarities which sever that linkage. I claim that the Cohen‐Kelly queuing paradox cloaks a fine structure that decouples it from both Braess’ paradox and the PD (Marinoff, 1996a). I further assert that the putative reduction of the PD to a Newcomb problem (e.g. Brams, 1975; Lewis, 1979) is seriously flawed. It follows that Braess’ paradox does not solve Newcomb's problem via the foregoing and herein sundered chain. I conclude by substantiating a stronger claim, namely that Braess'paradox cannot solve Newcomb's problem at all.     

Is the paradox of fiction soluble in psychology?

If feeling a genuine emotion requires believing that its object actually exists, and if this is a belief we are unlikely to have about fictional entities, then how could we feel genuine emotions towards these entities? This question lies at the core of the paradox of fiction. Since its original formulation, this paradox has generated a substantial literature. Until recently, the dominant strategy had consisted in trying to solve it. Yet, it is more and more common for scholars to try to dismiss it using data and theories from psychology. In opposition to this trend, the present paper argues that the paradox of fiction cannot be dissolved in the ways recommended by the recent literature. We start by showing how contemporary attempts at dissolving the paradox assume that it emerges from theoretical commitments regarding the nature of emotions. Next, we argue that the paradox of fiction rather emerges from everyday observations, the validity of which is independent of any such commitment. This is why we then go on to claim that a mere appeal to psychology in order to discredit these theoretical commitments cannot dissolve the paradox. We bring our discussion to a close on a more positive note by exploring how the paradox could in fact be solved by an adequate theory of the emotions.     

Russell’s Paradox of Predicates

Russell’s letter to Frege of June 16, 1902 contains the famous paradox of the class of all classes which are not members of themselves as well as a second paradox of the predicates that cannot be predicated of themselves. The latter paradox arises out of Russell’s theory of classes and class concepts in Principles of Mathematics.     

On Russell's vulnerability to Russell's paradox

Influenced by G. E. Moore, Russell broke with Idealism towards the end of 1898; but in later years he characterized his meeting Peano in August 1900 as ‘the most important event’ in ‘the most important year in my intellectual life’. While Russell discovered his paradox during his post-Peano period, the question arises whether he was already committed, during his pre-Peano Moorean period, to assumptions from which his paradox may be derived. Peter Hylton has argued that the pre-Peano Russell was thus vulnerable to (at least one version of) Russell's paradox and hence that the paradox exposes a pre-existing difficulty in Russell's Moorean philosophy. Contrary to Hylton, I argue that the Moorean Russell adhered to views which insulated him against the paradox. Further, I argue that Russell became vulnerable to his paradox as a result of changes in his Moorean position occasioned, first, by his acceptance of Cantor's theory of the transfinite, and, second, by his correspondence with Frege. I conclude with some general comments regarding Russell's acceptance of naïve set theory.     

Rose's Prevention Paradox

Geoffrey Rose's ‘prevention paradox’ occurs when a population‐based preventative health measure that brings large benefits to the community – such as compulsory seatbelts, a ‘fat tax’, or mass immunisation – offers little to each participating individual. Although the prevention paradox is not obviously a paradox in the sense in which philosophers understand the term, it does raise important normative questions. In particular, should we implement population‐based preventative health measures when the typical individual is not expected to gain from them? After canvassing other attempts to address the paradox, I argue that what is significant about the prevention paradox is that it involves intra‐personal trade‐offs; the costs and benefits of the choice to implement or not implement a preventative health measure fall on the same individuals. The intra‐personal nature of these trade‐offs has two implications. First, the solutions to the paradox proposed by other authors are deficient. Second, the policy choice to not implement some preventative health measures can be normatively justified.     

Explaining the Paradox of Hedonism

The paradox of hedonism is the idea that making pleasure the only thing that we desire for its own sake can be self-defeating. Why would this be true? In this paper, I survey two prominent explanations, then develop a third possible explanation, inspired by Joseph Butler's classic discussion of the paradox. The existing accounts claim that the paradox arises because we are systematically incompetent at predicting what will make us happy, or because the greatest pleasures for human beings are found in certain special goods which hedonists cannot enjoy. On the account that I develop, the paradox is a consequence of a theory about the nature of pleasure, together with a view about the requirements of rational belief. Which of these explanations is correct, I argue, bears on central questions about how to understand the nature and extent of the paradox.     

The Argument from Skepticism for Contextualism

Epistemic contextualism was originally motivated and supported by the response it provides to skeptical paradox. Although there has been much discussion of the contextualist response to skeptical paradox, not much attention has been paid to the argument from skepticism for contextualism. Contextualists argue that contextualism accounts for the plausibility and apparent inconsistency of a set of paradoxical claims better than any classical invariantist theory. In this paper I focus on and carefully examine the argument from skepticism for contextualism. I argue not only that the prima facie advantage of contextualism is specious, but also that contextualism is in fact at a competitive disadvantage with respect to two classical invariantist views. I also argue that contextualism takes an arbitrary and unsatisfying strategy in its response to skepticism. That contextualism is alone in taking this arbitrary strategy marks a second competitive disadvantage for it. In addition, I argue that the contextualist response to skeptical paradox regenerates a skeptical paradox which contextualism is powerless to solve. Consequently, the argument from skepticism for contextualism fails. Furthermore, this feature of the contextualist response to skeptical paradox completely undermines the motivation and support for contextualism deriving from its treatment of skeptical paradox. I conclude that the argument from skepticism for contextualism fails, and that the contextualist response to skeptical paradox fails to motivate contextualism, pending the success of another argument for the contextualist thesis.     

Conjunction-based Sorites: A Misguided Objection to Degree-Theoretic (Fuzzy) Solutions to Sorites Paradoxes

In 1987, Crispin Wright argued that degree-theoretic (fuzzy) solutions to the Sorites paradox fail because the solutions do not work when the paradox is restated using a conjunctive major premise. I show that Wright is incorrect: degree-theoretic solutions also work when the paradox is stated with a conjunctive major premise.     

Sacred Dialectic: The Centrality of Paradox in the Worldview of Rollo May

This article explores the fundamental significance of paradox to the worldview of Rollo May. The theme and concept of paradox is seen as constituting the essence of his thought and is believed to have strongly influenced his conception of the human psyche, health and dysfunction, and socio-cultural dynamics. Through an analysis of primary sources in May's writings, it is demonstrated that his philosophical worldview is most accurately represented by the principle of paradox, or dialectic. Specifically, both the basic characteristics of this principle, as well as its many manifestations in the form of particular paradoxes, are discussed. This discussion emphasizes the value of paradox to May's worldview and its role in shaping his critique of psychology and culture. The article concludes with an emphasis on the importance of May's view of paradox as a vital contribution to the field of psychology and broader culture, as well as its specific applicability to our own individual struggles to achieve integration and wholeness.     

Is there an auditory analogue to Fechner's paradox in binaural loudness perception?

In binocular brightness perception a phenomenon called Fechner's paradox can be observed. This paradox implies non-monotonicities in the psychometric functions of binocular brightness. Lehky (1983) proposed a model that describes such non-monotonicities. He suggested that Fechner's paradox also exists in binaural loudness perception. However, until now no sufficient data have been collected to test this hypothesis. Therefore, an experiment was conducted in which 36 psychometric functions were obtained using binaural stimuli in the range of intensities in which Fechner's paradox supposedly occurs. As a result, no significant non-monotonicities were found. However, it is shown that jnds derived from the psychometric functions contradict predictions derived from the limited binaural additivity model of Gigerenzer and Strube (1983).