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.     

What is wrong with Allais' Certainty Effect?

Several choice situations are constructed to explore whether the violation of expected utility theory in an Allais paradox choice situation can be attributed to what Tversky and Kahneman (1986) describe as the Allais certainty effect. Problems are developed where the Allais certainty effect would be expected to occur but results show it does not. Other problems demonstrate that the Allais ‘paradox’ is observed in the absence of the Allais certainty effect. The study concludes that, although expected utility theory is known to be wrong through the Allais paradox, the Allais certainty effect does not appear to be able to rescue it.     

Explaining the harmonic sequence paradox

According to the harmonic sequence paradox, an expected utility decision maker's willingness to pay for a gamble whose expected payoffs evolve according to the harmonic series is finite if and only if his marginal utility of additional income becomes zero for rather low payoff levels. Since the assumption of zero marginal utility is implausible for finite payoff levels, expected utility theory - as well as its standard generalizations such as cumulative prospect theory - are apparently unable to explain a finite willingness to pay. This paper presents first an experimental study of the harmonic sequence paradox. Additionally, it demonstrates that the theoretical argument of the harmonic sequence paradox only applies to time-patient decision makers, whereas the paradox is easily avoided if time-impatience is introduced.     

Arrows,Balls and the Metaphysics of Motion

The arrow paradox is an argument purported to show that objects do not really move. The two main metaphysics of motion, the At–At theory of motion and velocity primitivism, solve the paradox differently. It is argued that neither solution is completely satisfactory. In particular it is contended that there are no decisive arguments in favor of the claim that velocity as it is constructed in the At–At theory is a truly instantaneous property, which is a crucial assumption to solve the paradox. If so the At–At theory faces the threat that most of our physical theories turn out to be non-Markovian. Finally it is considered whether all those threats and paradoxes are dispelled if only a new metaphysics of persistence is taken into account, namely four-dimensionalism.     

The inconsistency of higher order extensions of Martin-Löf's type theory

Martin-Löf's constructive type theory forms the basis of this paper. His central notions of category and set, and their relations with Russell's type theories, are discussed. It is shown that addition of an axiom — treating the category of propositions as a set and thereby enabling higher order quantification — leads to inconsistency. This theorem is a variant of Girard's paradox, which is a translation into type theory of Mirimanoff's paradox (concerning the set of all well-founded sets). The occurrence of the contradiction is explained in set theoretical terms. Crucial here is the way a proof-object of an existential proposition is understood. It is shown that also Russell's paradox can be translated into type theory. The type theory extended with the axiom mentioned above contains constructive higher order logic, but even if one only adds constructive second order logic to type theory the contradictions arise.     

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.     

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.     

Minimalism and Paradoxes

This paper argues against minimalism about truth. It does so by way of acomparison of the theory of truth with the theory of sets, and considerationof where paradoxes may arise in each. The paper proceeds by asking twoseemingly unrelated questions. First, what is the theory of truth about?Answering this question shows that minimalism bears important similaritiesto naive set theory. Second, why is there no strengthened version ofRussell's paradox, as there is a strengthened Liar paradox? Answering thisquestion shows that like naive set theory, minimalism is unable to makeadequate progress in resolving the paradoxes, and must be replaced by adrastically different sort of theory. Such a theory, it is shown, must befundamentally non-minimalist.     

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。     

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.     

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.     

Beltrami's model and the independence of the parallel postulate

In their correspondence in 1902 and 1903, after discussing the Russell paradox, Russell and Frege discussed the paradox of propositions considered informally in Appendix B of Russell's Principles of Mathematics. It seems that the proposition, p, stating the logical product of the class w, namely, the class of all propositions stating the logical product of a class they are not in, is in w if and only if it is not. Frege believed that this paradox was avoided within his philosophy due to his distinction between sense (Sinn) and reference (Bedeutung). However, I show that while the paradox as Russell formulates it is ill-formed with Frege's extant logical system, if Frege's system is expanded to contain the commitments of his philosophy of language, an analogue of this paradox is formulable. This and other concerns in Fregean intensional logic are discussed, and it is discovered that Frege's logical system, even without its naive class theory embodied in its infamous Basic Law V, leads to inconsistencies when the theory of sense and reference is axiomatized therin. therein.     

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 LOTTERY PARADOX AND OUR EPISTEMIC GOAL

Abstract: Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no valid reason not to give preference to the derived accounts over the accounts from which they come.     

Rosser-Type Undecidable Sentences Based on Yablo’s Paradox

It is widely considered that Gödel’s and Rosser’s proofs of the incompleteness theorems are related to the Liar Paradox. Yablo’s paradox, a Liar-like paradox without self-reference, can also be used to prove Gödel’s first and second incompleteness theorems. We show that the situation with the formalization of Yablo’s paradox using Rosser’s provability predicate is different from that of Rosser’s proof. Namely, by using the technique of Guaspari and Solovay, we prove that the undecidability of each instance of Rosser-type formalizations of Yablo’s paradox for each consistent but not Σ₁-sound theory is dependent on the choice of a standard proof predicate.     

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.     

How Braess’ paradox solves Newcomb's problem*

Newcomb's problem is regularly described as a problem arising from equally defensible yet contradictory models of rationality. Braess’ paradox is regularly described as nothing more than the existence of non‐intuitive (but ultimately non‐contradictory) equilibrium points within physical networks of various kinds. Yet it can be shown that Newcomb's problem is structurally identical to Braess’ paradox. Both are instances of a well‐known result in game theory, namely that equilibria of non‐cooperative games are generally Pareto‐inefficient. Newcomb's problem is simply a limiting case in which the number of players equals one. Braess’ paradox is another limiting case in which the ‘players’ need not be assumed to be discrete individuals. The result is that Newcomb's problem is no more difficult to solve than (the easy to solve) Braess’ paradox.     

A New Solution to Moore's Paradox

Moore's paradox pits our intuitions about semantic oddnessagainst the concept of truth-functional consistency. Most solutions tothe problem proceed by explaining away our intuitions. But``consistency' is a theory-laden concept, having different contours indifferent semantic theories. Truth-functional consistency is appropriateonly if the semantic theory we are using identifies meaning withtruth-conditions. I argue that such a framework is not appropriate whenit comes to analzying epistemic modality. I show that a theory whichaccounts for a wide variety of semantic data about epistemic modals(Update Semantics) buys us a solution to Moore's paradox as a corollary.It turns out that Moorean propositions, when looked at through the lenseof an appropriate semantic theory, are inconsistent after all.     

Another Paradox In Naive Set-Theory

Reasonning in naive set theory (with unlimited comprehension), we derive a paradox (a formal contradiction) which can be seen as a variant of the Burali-Forti paradox. Presented by Robert Goldblatt