Uncertainty and affect are fundamental and interrelated aspects of the human condition. Uncertainty is often associated with negative affect, but in some circumstances it is associated with positive affect. In this paper, we review different explanations for the varying relationship between uncertainty and affect. We identify “mental simulation” as a key process that links uncertainty to affective states. We suggest that people have a propensity to simulate negative outcomes, which results in a propensity towards negative affective responses to uncertainty. We (...) also propose the existence of several important moderators of this process, including context and individual differences such as uncertainty tolerance, as well as emotion regulation strategies. Finally, we highlight important knowledge gaps and promising areas for future research, both empirical and conceptual, to further elucidate the relationship between uncertainty and affect. (shrink)

Relations between J. A. C. Chaptal, pioneer of heavy chemical industry in France, and A. L. Lavoisier, reformer of chemical theory, are examined in the light of unpublished correspondence they exchanged in the period 1784–1790. The letters, together with Chaptal's early publications, allow a reconstruction of his conversion to Lavoisier's antiphlogistic chemistry. They also reveal a series of petitions that Chaptal made to Lavoisier, in the latter's official capacity as a director of the Régie des poudres et salpêtres, for relief (...) from the controlled price of saltpetre for his acid works in Languedoc. Finally, the relationship is explored as a window on the interplay between chemical theory and industrial practice during the period of the Industrial Revolution. (shrink)

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included.

The idea of a 'logic of quantum mechanics' or quantum logic was originally suggested by Birkhoff and von Neumann in their pioneering paper [1936]. Since that time there has been much argument about whether, or in what sense, quantum 'logic' can be actually considered a true logic (see, e.g. Bell and Hallett [1982], Dummett [1976], Gardner [1971]) and, if so, how it is to be distinguished from classical logic. In this paper I put forward a simple and natural semantical (...) framework for quantum logic which reveals its difference from classical logic in a strikingly intuitive way, viz. through the fact that quantum logic admits (suitably formulated versions of) the characteristic quantum-mechanical notions of superposition and incompatibility of attributes. That is, precisely the features that distinguish quantum from classical physics also serve, within this framework, to distinguish quantum from classical logic. Some light is shed on the question of whether quantum logic is a genuine logical system by introducing a natural entailment relation for quantum-logical formulas with the implication symbol. The novelty is that, although implication behaves as it should (i.e. the 'deduction theorem' holds), the order of introduction of premises is significant. The fact that a reasonable entailment relation can be formulated for quantum logic supports the view that it is a genuine logical system and not merely an algebraic formalism. (shrink)

The strange story of the von Neumann impossibility proof is recalled, and the even stranger story of later impossibility proofs, and how the impossible was done by de Broglie and Bohm. Morals are drawn.

Summarya) Bell tries to formulate more explicitly a notion of “local causality”: correlations between physical events in different space‐time regions should be explicable in terms of physical events in the overlap of the backward light cones. It is shown that ordinary relativistic quantum field theory is not locally causal in this sense, and cannot be embedded in a locally causal theory.b) Clauser, Home and Shimony criticize several steps in Bell's argument that any theory of local “beables” is incompatible (...) with quantum mechanics. It is contended that the Clauser‐Horne derivation of a Bell‐type inequality circumvents his weak steps. The Clauser‐Horne derivation must assume that there are no undetected correlations between choices of controllable variables in two space‐like separated regions. Methodological considerations support this assumption.c) In response to criticism by Shimony, Home, and Clauser, Bell tries to clarify the argument of “The theory of local beables”, and to defend as permissible the hypothesis of free variables.d) Bell's reply to an earlier criticism by Shimony, Clauser, and Home is answered. The convergence of Bell's position towards theirs is noted. (shrink)

In this paper (a sequel to [4]) I put forward a "local" interpretation of mathematical concepts based on notions derived from category theory. The fundamental idea is to abandon the unique absolute universe of sets central to the orthodox set-theoretic account of the foundations of mathematics, replacing it by a plurality of local mathematical frameworks - elementary toposes - defined in category-theoretic terms.

Abstract:Vulnerability is an important criterion to assess the ethical justification of the inclusion of participants in research trials. Currently, vulnerability is often understood as an attribute inherent to a participant by nature of a diagnosed condition. Accordingly, a common ethical concern relates to the participant’s decisionmaking capacity and ability to provide free and informed consent. We propose an expanded view of vulnerability that moves beyond a focus on consent and the intrinsic attributes of participants. We offer specific suggestions for how (...) relational aspects and the dynamic features of vulnerability could be more fully captured in current discussions and research practices. (shrink)

Various authors insist that some body of natural phenomena are legitimately describable or explainable only on one level of description, and would disqualify any description not confined to that level. None offers an acceptable definition explicitly. I extract such a definition I find implicit in the work of two such authors, J.J. Gibson and Hubert Dreyfus, and modify the result to render it more defensible philosophically. I also criticize the definition Shaw and Turvey offer, demonstrate some applications of my definition, (...) and try to forestall certain misunderstandings of those presuppositions and that definition. (shrink)

The infinitesimal methods commonly used in the 17th and 18th centuries to solve analytical problems had a great deal of elegance and intuitive appeal. But the notion of infinitesimal itself was flawed by contradictions. These arose as a result of attempting to representchange in terms ofstatic conceptions. Now, one may regard infinitesimals as the residual traces of change after the process of change has been terminated. The difficulty was that these residual traces could not logically coexist with the static quantities (...) traditionally employed by mathematics. The solution to this difficulty, as it turns out, is to regard these quantities asalso being subject to (a form of) change, for then they will have the same nature as the infinitesimals representing the residual traces of change, and will become,ipso facto, compatible with these latter.In fact, the category-theoretic models which realize the Principle of Infinitesimal Linearity may themselves be regarded as representations of a general concept of variation (cf. Bell (1986)). While the static set-theoretical models represent change or motion by making a detour through the actual (but static) infinite, the varying category-theoretic models enable such change to be representeddirectly, thus permitting the introduction of geometric infinitesimals and, as we have attempted to demonstrate in this paper, the virtually complete incorporation of the methods of the early calculus.It is surely a remarkable — even an ironic — fact that the contradiction between the flux of the objective world and the stasis of mathematical entities has found its resolution in category theory, a branch of mathematics commonly, and, as one now sees, mistakenly, regarded as the summit of gratuitous abstraction. (shrink)

This paper is an introduction to topos theory which assumes no prior knowledge of category theory. It includes a discussion of internal logic in a topos, A characterization of the category of sets, And an investigation of the notions of topology and sheaf in a topos.

A central problem in applying logical knowledge representation formalisms to traditional robotics is that the treatment of belief change is categorical in the former, while probabilistic in the latter. A typical example is the fundamental capability of localization where a robot uses its noisy sensors to situate itself in a dynamic world. Domain designers are then left with the rather unfortunate task of abstracting probabilistic sensors in terms of categorical ones, or more drastically, completely abandoning the inner workings of sensors (...) to black-box probabilistic tools and then interpreting their outputs in an abstract way. Building on a first-principles approach by Bacchus, Halpern and Levesque, and a recent continuous extension to it by Belle and Levesque, we provide an axiomatization that shows how localization can be realized wrt a basic action theory, thereby demonstrating how such capabilities can be enabled in a single logical framework. We then show how the framework can also enable localization for multiple agents, where an agent can appeal to the sensing already performed by another agent and the knowledge of their relative positions to localize itself. (shrink)

A key idea in both Frege's development of arithmetic in theGrundlagen[7] and Zermelo's 1904 proof [10] of the well-ordering theorem is that of a “type reducing” correspondence between second-level and first-level entities. In Frege's construction, the correspondence obtains betweenconceptandnumber, in Zermelo's (through the axiom of choice), betweensetandmember. In this paper, a formulation is given and a detailed investigation undertaken of a system ℱ of many-sorted first-order logic (first outlined in the Appendix to [6]) in which this notion of type reducing (...) correspondence is accorded a central role and which enables Frege's and Zermelo's constructions to be presented in such a way as to reveal their essential similarity. By adapting Bourbaki's version of Zermelo's proof of the well-ordering theorem, we show that, within ℱ, any correspondencecbetween second-level entities (here calledconcepts) and first-level ones (here calledobjects) induces a well-ordering relationW(c) in a canonical manner. We shall see that, whencis the “Fregean” correspondence between concepts and cardinal numbers,W(c) is (the well-ordering of) the ordinalω+ 1, and whencis a “Zermelian” choice function on concepts,W(c) is a well-ordering of the universal concept embracing all objects.In ℱ an important role is played by the notion ofextensionof a concept. To each conceptXwe assume there is assigned an objecte(X) in such a way that, for any conceptsX, Ysatisfying a certain predicateE, we havee(X) =e(Y) iff the same objects fall underXandY. (shrink)

Cheating and deception are terms often used but rarely defined. They summon up unpleasant connotations; even those deeply involved with cheating and deception rationalize why they have been driven to it. Particularly for Americans and much of Western civilization, official cheating, government duplicity, cheating as policy, and conscious, contrived deception, are all unacceptable except as a last resort in response to threat of extinction. As a distasteful tool, deception is rarely used to achieve national interests, unless in relation to the (...) deployment of military force. As an area of study, it has by and large been ignored.Intrigued by attitudes toward cheating and deception, the authors decided to analyze its roots, structure, and process. They asked fundamental questions: are there categories of deception, general steps in the process of deception, and ways to evaluate its results across time and in different modes? The book that results is a typology of kinds of deception, beginning with military deception, but extending into other categories and stages.In his introduction to this new edition, Bell outlines how the book came to be written, describes the mixed emotions toward the subject displayed by govenmental and nongovernmental funding sources, and speculates about its critical and commercial reception. He discusses widespread new interest in the subject, the research that has been undertaken since this book was first published, and its limitations.This book provides a general overview of this complex subject, creating a framework for analysis of specific instances of cheating or deception. It will be of particular interest to political scientists, those interested in military affairs and strategy, and psychologists. The general reader will find the book written with a light touch, drawing examples of cheating and deception in the pursuit of love and money. The specialist reader will be intrigued by its broad-ranging examples drawn from policy and politics, wars and rumors of wars. (shrink)

Despite an abundance of research on inter-organizational trust, researchers are only beginning to understand the process of trust deterioration as an inter-organizational phenomenon. This paper presents a case study examining the deteriorating relationship between two international high-tech firms. We surveyed respondents from the supplier firm to identify major elements that reduced the supplier's trust in its customer, using the dimensions of trust identified by Mayer et al. (1995). While violations of ability, integrity, and benevolence all contributed to trust reduction, early (...) violations of trustee benevolence contributed importantly to trust deterioration. Over time, the relationship became "sensitive," and respondents reported many incidents of trust violation. Managers reported primarily integrity- and benevolence-related incidents, while no pattern emerged among operations personnel. We examine the results in light of Hosmer's (1995) ethically-based trust principles. The supplier and customer would likely differ in their opinion of whether the customer was acting "ethically." This suggests that scholars need to examine how many principles can be violated before trust is eliminated, and whether any of the principles are particularly salient in business relationships. (shrink)

We analyze Zorn's Lemma and some of its consequences for Boolean algebras in a constructive setting. We show that Zorn's Lemma is persistent in the sense that, if it holds in the underlying set theory, in a properly stated form it continues to hold in all intuitionistic type theories of a certain natural kind. (Observe that the axiom of choice cannot be persistent in this sense since it implies the law of excluded middle.) We also establish the persistence of some (...) familiar results in the theory of (complete) Boolean algebras--notably, the proposition that every complete Boolean algebra is an absolute subretract. This (almost) resolves a question of Banaschewski and Bhutani as to whether the Sikorski extension theorem for Boolean algebras is persistent. (shrink)

Funding: Research funded by Canadian Institutes of Health Research, NNF 80045, States of Mind: Emerging Issues in Neuroethics. While there are those who object to the prospective use of propranolol to prevent or treat post-traumatic stress disorder (PTSD), most obstreperous among them the President’s Council on Bioethics, the use of propranolol can be justified for patients with severe PTSD. Propranolol, if effective, will alter the quality of certain memories in the brain. But this is not a serious threat to the (...) self understood in terms of narrative identity. A narrative identity framework acknowledges that memory is always being subtly altered or modified. For severe cases of PTSD propranolol may help victims who don’t respond to any other therapy or therapy combination regain their authentic self-narrative and engage once more in life activities. For those whose symptoms are not so severe the potential risks and side-effects of the drug may outweigh the benefits. Patients and family members should be allowed to decide, in consultation with their physician, whether this drug is appropriate in their case. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:THE EUCHARISTIC THEOLOGIES OF LAUDA SION AND THOMAS AQUINAS'S SUMMA THEOLOGIAE THOMAS J. BELL Emory University Atlanta, Georgia MANY works associated with Thomas Aquinas stand both the Office and Mass for the Feast of Corpus Christi.1 The earliest witness to this association comes from two of Thomas's Dominican brothers and younger contemporaries, Tolomeo of Lucca and William of Tocco. Around 1317 Tolomeo wrote in his Historia Ecclesiastica: " (...) Thomas composed [the Corpus Christi Office] in full, including the lessons and all the parts to be recited by day or night; the Mass, too, and whatever has to be sung on the day." 2 William, in his Historia beati Thomae completed around 1320, lists the liturgy of Corpus Christi among Thomas's works and informs us that Thomas wrote the liturgy " at the request of Pope Urban [IV]." 3 It is known that on August 11, 1264, Urban, in the bull Transiturus, declared that the Feast of Corpus Christi was to be celebrated throughout Christendom according to a "new, Roman," liturgy.4 Thomas had returned from Paris to Italy, his 1 This does not mean that Thomas created the liturgy for the feast de nova. Rather it means that Thomas selected and combined older elements from the Scriptures, the Fathers, and existing liturgies, only venturing to write from scratch those hymns and prayers necessary for expressing the theological and devotional views central to the Feast of Corpus Christi. In other words, Thomas wrote or pieced together texts " proper " to the feast and united them with the " ordinary " texts of the Mass and Office. 2 James A. Weisheipl, Friar Thomas d'Aquino: His Life, Thought and Works (Washington, D.C., 1974), p. 177. a Ibid., pp. 132, 177. 4 Ibid., pp. 179, 183. For a partial translation of the bull Transiturus see also Darwell Stone, A History of the Doctrine of the Holy Eucharist (London, 1909), vol. 1, 344-46. This "new, Roman" liturgy promulgated by Urban IV was, indeed, a new 163 164 THOMAS J. BELL homeland, five years before the bull was published. Furthermore, by 1264 he had developed a "warm friendship" with Urban, whom we know to have commissioned Thomas to write several works between 1261 and 1265.5 These facts have led most scholars since the early fourteenth century to conclude that Urban's "new" liturgy was the work of Thomas.6 In recent years, however, Cyrille Lambot has questioned whether Thomas wrote or compiled the liturgy promulgated by Urban. He has noted that Reginald of Piperno, Thomas's amanuensis and companion from 1259 to 1274, did not include the liturgy for Corpus Christi in his list of Thomas's works. Moreover, the Dominican Order, like most Orders and dioceses, did not adopt Urban's liturgy for the Feast of Corpus Christi until 1317, when John XXII required its use throughout Western Christendom.7 If Thomas had written the liturgy, argues liturgy composed for the celebration of Corpus Christi. Around 1246 a certain John, a religious of Mont-Cornillon, had compiled a liturgy for the " Body of the Lord " that was in place throughout the diocese of Liege. Being so impressed by the solemnities of the Liege eucharistic celebration, Hugh of Saint-Cher, a Dominican and the cardinal legate of Germany, declared in 1252 that the feast of Corpus Christi was to be celebrated throughout the territory under his leadership. Jacques Pantaleon, the future Urban IV, knew the solemnities of Liege from his time as the city's archdeacon. It seems that upon his election as Pope, Urban was urged by many people to establish the Feast throughout Christendom. Eventually he did this with the publication of the bull Transiturus. For more details, see Weisheipl, Friar Thomas d'Aquino, pp. 178-79. 0 Weisheipl, Friar Thomas d'Aquino, p. 147. 6 The liturgy for the Feast of Corpus Christi that is associated with Thomas is not identical with the one currently used in both the Roman rite and Dominican rite. The modern texts for the Feast reflect the liturgical reforms that have occurred since Thomas's day. Notwithstanding these reforms, the Mass for the Feast (Cibavit eos), which includes Lauda Sion, has for the most part... (shrink)

Consider the following well-known result from the theory of normed linear spaces ([2], p. 80, 4(b)): (g) the unit ball of the (continuous) dual of a normed linear space over the reals has an extreme point. The standard proof of (~) uses the axiom of choice (AG); thus the implication AC~(w) can be proved in set theory. In this paper we show that this implication can be reversed, so that (*) is actually eq7I2valent to the axiom of choice. From this (...) we derive various corollaries, for example: the conjunction of the Boolean prime ideal theorem and the Krein-Milman theorem implies the axiom of choice, and the Krein-Milman theorem is not derivable from the Boolean prime ideal theorem. (shrink)

In Culture, Genre, and Literary Vocation, Michael Davitt Bell charts the important and often overlooked connection between literary culture and authors' careers. Bell's influential essays on nineteenth-century American writers—originally written for such landmark projects as The Columbia Literary History of the United States and The Cambridge History of American Literature—are gathered here with a major new essay on Richard Wright. Throughout, Bell revisits issues of genre with an eye toward the unexpected details of authors' lives, and invites (...) us to reconsider the hidden functions that terms such as "romanticism" and "realism" served for authors and their critics. Whether tracing the demands of the market or the expectations of readers, Bell examines the intimate relationship between literary production and culture; each essay closely links the milieu in which American writers worked with the trajectory of their storied careers. (shrink)