Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

-/- Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures (such as fields, group, and graphs) to various natural classes of complete metric structures (such as probability algebras, Hilbert spaces, and Banach spaces). With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result? -/- The primary purpose (...) of this article is to show that a certain, interesting set of axioms does indeed yield a completeness result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is (completely) satisfiable if (and only if) it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊧φ (if and) only if Σ⊢φ ∸2−n for all n < ω. This approximated form of strong completeness asserts that if Σ⊧φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ. -/- Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory (in a countable, recursive language) recursive? Say that a complete theory T is decidable if for every sentence φ, the value φ T is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φ T o is uniformly recursive from φ, where φ T o is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive (or even recursively enumerable) axiomatization then it is decidable. (shrink)

We present a game mechanic called pseudo-visibility for games inhabited by non-player characters (NPCs) driven by reinforcement learning (RL). NPCs are incentivized to pretend they cannot see pseudo-visible players: the training environment simulates an NPC to determine how the NPC would act if the pseudo-visible player were invisible, and penalizes the NPC for acting differently. NPCs are thereby trained to selectively ignore pseudo-visible players, except when they judge that the reaction penalty is an acceptable tradeoff (e.g., a guard might accept (...) the penalty in order to protect a treasure because losing the treasure would hurt even more). We describe an RL agent transformation which allows RL agents that would not otherwise do so to perform some limited self-reflection to learn the training environments in question. (shrink)

I introduce a mathematical account of expectation based on a qualitative criterion of coherence for qualitative comparisons between gambles (or random quantities). The qualitative comparisons may be interpreted as an agent’s comparative preference judgments over options or more directly as an agent’s comparative expectation judgments over random quantities. The criterion of coherence is reminiscent of de Finetti’s quantitative criterion of coherence for betting, yet it does not impose an Archimedean condition on an agent’s comparative judgments, it does not require the (...) binary relation reflecting an agent’s comparative judgments to be reflexive, complete or even transitive, and it applies to an absolutely arbitrary collection of gambles, free of structural conditions (e.g., closure, measurability, etc.). Moreover, unlike de Finetti’s criterion of coherence, the qualitative criterion respects the principle of weak dominance, a standard of rational decision making that obliges an agent to reject a gamble that is possibly worse and certainly no better than another gamble available for choice. Despite these weak assumptions, I establish a qualitative analogue of de Finetti’s Fundamental Theorem of Prevision, from which it follows that any coherent system of comparative expectations can be extended to a weakly ordered coherent system of comparative expectations over any collection of gambles containing the initial set of gambles of interest. The extended weakly ordered coherent system of comparative expectations satisfies familiar additivity and scale invariance postulates (i.e., independence) when the extended collection forms a linear space. In the course of these developments, I recast de Finetti’s quantitative account of coherent prevision in the qualitative framework adopted in this article. I show that comparative previsions satisfy qualitative analogues of de Finetti’s famous bookmaking theorem and his Fundamental Theorem of Prevision.The results of this article complement those of another article (Pedersen, Strictly coherent preferences, no holds barred, Manuscript, 2013). I explain how those results entail that any coherent weakly ordered system of comparative expectations over a unital linear space can be represented by an expectation function taking values in a (possibly non-Archimedean) totally ordered field extension of the system of real numbers. The ordered field extension consists of formal power series in a single infinitesimal, a natural and economical representation that provides a relief map tracing numerical non-Archimedean features to qualitative non-Archimedean features. (shrink)

A fundamental question asked in modal logic is whether a given theory is consistent. But consistent with what? A typical way to address this question identifies a choice of background knowledge axioms (say, S4, D, etc.) and then shows the assumptions codified by the theory in question to be consistent with those background axioms. But determining the specific choice and division of background axioms is, at least sometimes, little more than tradition. This paper introduces generic theories for propositional modal logic (...) to address consistency results in a more robust way. As building blocks for background knowledge, generic theories provide a standard for categorical determinations of consistency. We argue that the results and methods of this paper help to elucidate problems in epistemology and enjoy sufficient scope and power to have purchase on problems bearing on modalities in judgement, inference, and decision making. (shrink)

Both dilation and non-conglomerability have been alleged to conflict with a fundamental principle of Bayesian methodology that we call \textit{Good's Principle}: one should always delay making a terminal decision between alternative courses of action if given the opportunity to first learn, at zero cost, the outcome of an experiment relevant to the decision. In particular, both dilation and non-conglomerability have been alleged to permit or even mandate choosing to make a terminal decision in deliberate ignorance of relevant, cost-free information. Although (...) dilation and non-conglomerability share some similarities, some authors maintain that there are important differences between the two that warrant endorsing different normative positions regarding dilation and non-conglomerability. This article reassesses the grounds for treating dilation and non-conglomerability differently. Our analysis exploits a new and general characterization result for dilation to draw a closer connection between dilation and non-conglomerability. (shrink)

A characterization result of dilation in terms of positive and negative association admits an extremal counterexample, which we present together with a minor repair of the result. Dilation may be asymmetric whereas covariation itself is symmetric. Dilation is still characterized in terms of positive and negative covariation, however, once the event to be dilated has been specified.

In an essay recently published in this journal, Branden Fitelson argues that a variant of Miller’s argument for the language dependence of the accuracy of predictions can be applied to Joyce’s notion of accuracy of credences formulated in terms of scoring rules, resulting in a general potential problem for Joyce’s argument for probabilism. We argue that no relevant problem of the sort Fitelson supposes arises since his main theorem and his supporting arguments presuppose the validity of nonlinear transformations of credence (...) functions that Joyce’s theory, charitably construed, would identify as invalid on the basis of the principle of simple dominance. (shrink)

This article elaborates on foundational issues in the social sciences and their impact on the contemporary theory of belief revision. Recent work in the foundations of economics has focused on the role external social norms play in choice. Amartya Sen has argued in [Sen93] that the traditional rationalizability approach used in the theory of rational choice has serious problems accommodating the role of social norms. Sen's more recent work [Sen96, Sen97] proposes how one might represent social norms in the theory (...) of choice, and in a very recent article [BS07] Walter Bossert and Kotaro Suzumura develop Sen's proposal, offering an extension of the classical theory of choice that is capable of dealing with social norms. The first part of this article offers an alternative functional characterization of the extended notion of rationality employed by Bossert and Suzumura in [BS07]. This characterization, unlike the one offered in [BS07], represents a norm-sensitive notion of rationality in terms of a pure functional constraint unmediated by a notion of revealed preference (something that is crucial for the application developed in the second part of this article). This functional characterization is formulated for general domains (as is Bossert and Suzumura's characterization) and is therefore empirically more applicable than usual characterizations of rationality. Interestingly, the functional constraint we propose is a variant of a condition first entertained in [AGM85] by Carlos Alchourrón, Peter Gärdenfors and David Makinson in the area of belief change. The second part of this article applies the theory developed in the first part to the realm of belief change. We first point out that social norms can be invoked to concoct counterexamples against some postulates of belief change (like postulate (*7)) that are necessary for belief change to be relational. These examples constitute the epistemological counterpart of Sen's counterexamples against condition α in rational choice (as a matter of fact, Rott has showed in [Rot01] that condition and postulate (*7) are mutually mappable). These examples are variants of examples Rott has recently presented in [Rot04]. One of our main goals in this article consists in applying the theory developed in the first part to develop a theory of norm-inclusive belief change that circumvents the counterexamples. We offer a new axiomatization for belief change and we furnish correspondence results relating constraints of rational choice to postulates of belief change. (shrink)

Gerd Gigerenzer and Thomas Sturm have recently proposed a modest form of what they describe as a normative, ecological and limited naturalism. The basic move in their argument is to infer that certain heuristics we tend to use should be used in the right ecological setting. To address this argument, we first consider the case of a concrete heuristic called Take the Best (TTB). There are at least two variants of the heuristic which we study by making explicit the choice (...) functions they induce, extending these variants of TTB beyond binary choice. We argue that the naturalistic argument can be applied to only one of the two variants of the heuristic; we also argue that the argument for the extension requires paying attention to other “rational” virtues of heuristics aside from efficacy, speed, and frugality. This notwithstanding, we show that there is a way of extending the right variant of TTB to obtain a very well behaved heuristic that could be used to offer a stronger case for the naturalistic argument (in the sense that if this heuristic is used, it is also a heuristic that we should use). The second part of the article considers attempts to extending the naturalistic argument from algorithms dealing with inference to heuristics dealing with choice. Our focus is the so-called Priority Heuristic, which we extend from risk to uncertainty. In this setting, the naturalist argument seems more difficult to formulate, if it remains feasible at all. Normativity seems in this case extrinsic to the heuristic, whose main virtue seems to be its ability to describe actual patterns of choice. But it seems that a new version of the naturalistic argument used with partial success in the case of inference is unavailable to solve the normative problem of whether we should exhibit the patterns of choice that we actually display. (shrink)

There are many cases of conduct for which responsibility can plausibly be ascribed to a group, in addition to any responsibility ascribable to the group's constituent members. It is important to be able to make such ascriptions because without them we are unable to assign responsibilities for many sorts of humanly-caused harms for which responsibility cannot reasonably be ascribed to individuals alone. Two recent theories of collective responsibility advance our understanding of why it is important to be able to hold (...) groups accountable, but they apply only to a limited spectrum of groups, and rely on the plausibility of importing unnecessary individualistic assumptions into discussions of collective responsibility. ;I argue that we can justify ascription of collective responsibility without engaging in difficult metaphysical or ontological disputes. In particular, in order legitimately to ascribe collective responsibility we need not demonstrate that groups are capable of exhibiting intentions, or that groups can be considered 'moral persons'. We may reasonably consider organized groups to take action, and we may justly blame or praise them, when their members engage in what I call 'joint purposive behavior', as when an automobile manufacturer knowingly markets faulty vehicles. I argue, further, that certain unorganized groups, or 'random collectivities', can justly be blamed for promoting values and attitudes conducive to harmful behavior, as when a hate group advocates violent actions against minorities, or praised as groups for promoting values that encourage laudable behavior. ;I argue that most objections to collective responsibility rely on various misunderstandings of what it means for a group to be collectively responsible, notably, the belief that if a group is responsible its members cannot also be individually responsible, and the belief that collective responsibility 'distributes' among the individuals in the responsible group. In addition, I argue that large-scale environmental problems such as global warming lend themselves to a collectivist analysis, and that a view of collective responsibility that balances the harm-prevention and fault-finding purposes of responsibility ascription may help us to resolve such problems. (shrink)

Continuous first-order logic has found interest among model theorists who wish to extend the classical analysis of “algebraic” structures to various natural classes of complete metric structures. With research in continuous first-order logic preoccupied with studying the model theory of this framework, we find a natural question calls for attention. Is there an interesting set of axioms yielding a completeness result?The primary purpose of this article is to show that a certain, interesting set of axioms does indeed yield a completeness (...) result for continuous first-order logic. In particular, we show that in continuous first-order logic a set of formulae is satisfiable if it is consistent. From this result it follows that continuous first-order logic also satisfies an approximated form of strong completeness, whereby Σ⊨φ only if Σ⊢φ∸ 2-n for all n < ω. This approximated form of strong completeness asserts that if Σ⊨φ, then proofs from Σ, being finite, can provide arbitrarily better approximations of the truth of φ.Additionally, we consider a different kind of question traditionally arising in model theory—that of decidability. When is the set of all consequences of a theory recursive? Say that a complete theory T is decidable if for every sentence φ, the value φT is a recursive real, and moreover, uniformly computable from φ. If T is incomplete, we say it is decidable if for every sentence φ the real number φT∘ is uniformly recursive from φ, where φT∘is the maximal value of φ consistent with T. As in classical first-order logic, it follows from the completeness theorem of continuous first-order logic that if a complete theory admits a recursive axiomatization then it is decidable. (shrink)

This volume is one of the most significant documents on the thought of the giant of the twentieth-century philosophy. Russell's 'Reply to Criticisms, ' supplemented by a 1971 'Addendum, ' displays his unrivalled clarity, perceptiveness, and scalpel-like wit, on topics ranging from mathematical logic to political philosophy, from epistemology to philosophy of history.

In three studies, factors influencing the incidence of fraudulent financial reporting were assessed. We examined (1) the effects of personal values and (2) codes of corporate conduct, on whether managers misrepresented financial reports. In these studies, executives and controllers were asked to respond to hypothetical situations involving fraudulent financial reporting procedures. The occurrence of fraudulent reporting was found to be high; however, neither personal values, codes of conduct, nor the interaction of the two factors played a significant role in fraudulent (...) financial reporting. (shrink)

The first volume of the Library of Living Philosophers (LLP) appeared in 1939, the brainchild of the late Professor Paul A. Schilpp. Schilpp saw that it would help to eliminate confusion and endless sterile disputes over interpretation if great philosophers could be confronted by their capable philosophical peers and asked to reply. As well as a number of critical essays with the chosen philosopher's replies to each essay, each volume would include an intellectual autobiography and an up-to-date bibliography The (...) LLP series has exceeded even Schilpp's expectations, enabling great philosophers to do more than clarify by extending and elaborating their thoughts. A volume in the Library of Living Philosophers is not merely a commentary on a philosopher's work; it is a critical part of that work. (shrink)

Written by the man considered the "Person of the Century" by Time magazine, this is not a glimpse into Einstein's personal life, but an extension and elaboration into his thinking on science. Two of the great theories of the physical world were created in the early 20th century: the theory of relativity and quantum mechanics. Einstein created the theory of relativity and was also one of the founders of quantum theory. Here, Einstein describes the failure of classical mechanics and the (...) rise of the electromagnetic field, the theory of relativity, and of the quanta. Written in German by Einstein himself, the book is faced, page-by-page, with a translation by the noted Professor of Philosophy Paul Arthur Schilpp. (shrink)

During the Italian campaigns of the French Revolutionary Wars (1796–1801), several epidemic outbreaks sparked acrimonious aetiological debates: were the fevers spread by soldiers and prisoners of war, or produced by environmental factors? This debate was not only a scientific issue, but also a political one, for causation was linked to accountability. Looking at a series of medical investigations written by French military practitioners, this paper argues that theories of contagion were used by civilians to accuse the army of spreading disease, (...) in what I describe as an “aetiology of blame.” Likewise, military officials attempted to absolve themselves of responsibility for the spread of disease by focusing on unwholesome environments, depicting diseases as unavoidable fatalities. Military doctors thus supported French imperial endeavours by obscuring the army's responsibility for the spread of diseases, putting forward aetiologies of fate and blaming individual behaviour. Even when they did not radically dismiss contagionist perspectives, military practitioners insisted on a wide range of pathogenic causes. Their discourses were in line with medical theories of the time, but they downplayed the responsibility of the army for the spread of diseases, which they depicted as a factor among others. Military doctors were thus not always involved in the direct and deliberate production of ignorance, but they did sustain controversies and uncertainty. (shrink)

The format of this Library of Living Philosophers volume differs from that of its fifteen predecessors. Because of Sartre's failing eyesight, it was not possible for him either to read the critical essays or to respond in the usual way to his critics. Nor did he feel able to prepare an autobiography. Thus, in order to collect the material needed for the volume, it was necessary to conduct personal taped interviews with Sartre and then to have those interviews translated, edited, (...) and arranged in an order that would approximate as closely as possible the customary format of the volumes in the Library of Living Philosophers series. Skillfully and conscientiously conducted, the interviews themselves resulted in a unique and valuable document. At the time they occurred, Sartre was in good health except for his near-blindness, and he answered questions in a lively and easy manner. Although he seemed most comfortable when talking autobiographically, he nevertheless responded to many of the philosophical questions raised by the contributors to this volume. (shrink)

--Moore's autobiography.--Descriptive and critical essays on the philosophy of G. E. Moore.--The philosopher replies.--Bibliography of the writings of G. E. Moore (to July, 1952) compiled by Emerson Buchanan and G. E. Moore (p. [689]-699).

_Ideology and Utopia_ argues that ideologies are mental fictions whose function is to veil the true nature of a given society. They originate unconsciously in the minds of those who seek to stabilise a social order. Utopias are wish dreams that inspire the collective action of opposition groups which aim at the entire transformation of society. Mannheim shows these two opposing elements to dominate not only our social thought but even unexpectedly to penetrate into the most scientific theories in philosophy, (...) history and the social sciences. This new edition contains a new preface by Bryan S. Turner which describes Mannheim's work and critically assesses its relevance to modern sociology. The book is published with a comprehensive bibliography of Mannheim's major works. (shrink)

Biographical material.--Descriptive and critical essays on the philosophy of Ernst Cassirer.--The philosopher speaks for himself.--Bibliography of the writings of Ernst Cassirer.

Alfred North Whitehead has made an enormous impact upon philosophical thinking. His work continues to fascinate, and occasionally to exasperate, Whitehead's 'Principia Mathematica' is crucial to an understanding of recent philosophy of logic and of mathematics. Whitehead's metaphysics has proved formidably difficult yet stimulating. With his ideas on God he fathered a major school of modern theology.

Over 90% of the organs transplanted in China before 2010 were procured from prisoners. Although Chinese officials announced in December 2014 that the country would completely cease using organs harvested from prisoners, no regulatory adjustments or changes in China’s organ donation laws followed. As a result, the use of prisoner organs remains legal in China if consent is obtained. We have collected and analysed available evidence on human rights violations in the organ procurement practice in China. We demonstrate that the (...) practice not only violates international ethics standards, it is also associated with a large scale neglect of fundamental human rights. This includes organ procurement without consent from prisoners or their families as well as procurement of organs from incompletely executed, still-living prisoners. The human rights critique of these practices will also address the specific situatedness of prisoners, often conditioned and traumatized by a cascade of human rights abuses in judicial structures. To end the unethical practice and the abuse associated with it, we suggest to inextricably bind the use of human organs procured in the Chinese transplant system to enacting Chinese legislation prohibiting the use of organs from executed prisoners and making explicit rules for law enforcement. Other than that, the international community must cease to abet the continuation of the present system by demanding an authoritative ban on the use of organs from executed Chinese prisoners. (shrink)

In the contemporary discussion of hidden variable interpretations of quantum mechanics, much attention has been paid to the “no hidden variable” proof contained in an important paper of Kochen and Specker. It is a little noticed fact that Bell published a proof of the same result the preceding year, in his well-known 1966 article, where it is modestly described as a corollary to Gleason's theorem. We want to bring out the great simplicity of Bell's formulation of this result and to (...) show how it can be extended in certain respects. (shrink)

The molecular mechanism of temperature‐dependent sex determination (TSD) is a long‐standing mystery. How is the thermal signal sensed, captured and transduced to regulate key sex genes? Although there is compelling evidence for pathways via which cells capture the temperature signal, there is no known mechanism by which cells transduce those thermal signals to affect gene expression. Here we propose a novel hypothesis we call 3D‐TSD (the three dimensions of thermolabile sex determination). We postulate that the genome has capacity to remodel (...) in response to temperature by changing 3D chromatin conformation, perhaps via temperature‐sensitive transcriptional condensates. This could rewire enhancer–promoter interactions to alter the expression of key sex‐determining genes. This hypothesis can accommodate monogenic or multigenic thermolabile sex‐determining systems, and could be combined with upstream thermal sensing and transduction to the epigenome to commit gonadal fate. (shrink)