If someone claims that individuals behave as if they violate the independence axiom when making decisions over simple lotteries, it is invariably on the basis of experiments and theories that must assume the IA through the use of the random lottery incentive mechanism. We refer to someone who holds this view as a Bipolar Behaviorist, exhibiting pessimism about the axiom when it comes to characterizing how individuals directly evaluate two lotteries in a binary choice task, but optimism about the axiom (...) when it comes to characterizing how individuals evaluate multiple lotteries that make up the incentive structure for a multiple-task experiment. We reject the hypothesis about subject behavior underlying this stance: we find that preferences estimated with a model that assumes violations of the IA are significantly affected when one elicits choices with procedures that require the independence assumption, as compared to choices elicited with procedures that do not require the assumption. The upshot is that one cannot consistently estimate popular models that relax the IA using data from experiments that assume the validity of the RLIM. (shrink)

Evidence of risk aversion in laboratory settings over small stakes leads to a priori implausible levels of risk aversion over large stakes under certain assumptions. One core assumption in statements of this calibration puzzle is that small-stakes risk aversion is observed over all levels of wealth, or over a â sufficiently largeâ range of wealth. Although this assumption is viewed as self-evident from the vast experimental literature showing risk aversion over laboratory stakes, it actually requires that lab wealth be varied (...) for a given subject as one evaluates the risk attitudes of the subject. We consider evidence from a simple design that tests this assumption, and find that the assumption is strikingly rejected for a large sample of subjects from a population of college students. We conclude that the implausible predictions that flow from these assumptions do not apply to one specialized population widely used to study economic behavior in laboratory experiments. (shrink)

There is a growing consensus in Britain on the importance of character, and on the belief that the virtues that contribute to good character are part of the solution to many of the challenges facing modern society. Parents, teachers and schools understand the need to teach basic moral virtues to pupils, such as honesty, self-control, fairness, and respect, while fostering behaviour associated with such virtues today. However, until recently, the materials required to help deliver this ambition have been missing in (...) Britain. The Knightly Virtues Programme, devised by the Jubilee Centre for Character and Virtues, aims to help solve this challenge. The programme, designed for 9 to 11 year olds, draws on selected classic stories to help teach moral character in schools. This approach has proved to be popular with children and teachers, with more than 5,000 pupils from one hundred schools having participated in the programme so far. Fifty-five of these schools and 3,272 pupils were directly involved in different stages of the research. Based at the University of Birmingham, the Jubilee Centre houses leading academics dedicated to researching the various ways in which good character, which underpins the building blocks of society, can be developed. Recent research from the Centre has shown that the qualities that make up character can be learnt and taught, and suggests that we need a new emphasis on their importance in schools and in professional education. This report from the Centre into the use of classic literature within schools sets out the ways in which the Knightly Virtues Programme is able to develop the virtue literacy of school pupils, and the extent to which an understanding and awareness of good moral character can make positive changes to behaviour. The impact of the programme has been tested using several rigorous research methods, detailed in this report alongside their findings, which provide substantial empirical evidence for the effectiveness of using stories to develop virtue literacy. (shrink)

The primary responsibility for global climate change responsiveness is usually attributed to nation states. This is reflected in the United Nations’ processes aimed at enrolling governments in mitigation and adaptation programmes. Such an approach begs the question of how global climate change (GCC) responsiveness might proceed if a national government is hostile to the issue, as appears likely to be the case in the USA. This paper addresses this concern by documenting the percentage of the population of the USA who (...) are ‘covered’ by at least one of six examples of GCC responsiveness at sub-federal – state and municipality – levels. Of the population of the USA, 25.8% lives in states where all of the state-level initiatives surveyed are in effect, whereas only 4.4% are not covered by any of the six. This coverage has increased as compared to earlier surveys (Lutsey, N., and D. Sperling. 2008. “America’s Bottom-Up Climate Change Mitigation Policy.” Energy Policy 36: 673–685. doi:10.1016/j.enpol.2007.10.018). This finding suggests that there is more practical hope for GCC responsiveness than might be commonly appreciated and this also has ramifications for research in accounting. (shrink)

The aim of the My Character project was to develop a better understanding of how interventions designed to develop character might enhance moral formation and futuremindedness in young people. Futuremindedness can be defined as an individual’s capacity to set goals and make plans to achieve them. Establishing goals requires considerable moral reflection, and the achievement of worthwhile aims requires character traits such as courage and the capacity to delay gratification. The research team developed two new educational interventions – a website (...) and a hard-copy journal – with the specific aim of developing future-mindedness. After development, the website and journal were piloted over a one-year period by over 1,000 11–14 year olds in six schools across England. Various research methods, including group interviews and case studies, were implemented to assess impact. In addition, a pilot RCT was conducted to assess the feasibility of using experimental methods to measure character. The main findings from the research are that: - Students benefit from opportunities in school to think about future-mindedness; this can be successfully taught through character education. - Harnessing new technology, such as the Internet, offers exciting opportunities for character education. - It is beneficial to investigate the impact of new character education resources in order to bring greater clarity about ‘what works’. The most useful approach is a mixed methods one that allows for triangulation of evidence. - It is possible to run RCTs and other experimental research in schools to assess developmental projects of this kind, but applying the method in schools and creating suitable outcome measures present challenges for researchers. - A positive indicator of the success is that five out of the six pilot schools have embedded My Character into their curriculum. In addition, many new schools, both in Britain and internationally, have started to use the website and / or journal. This report describes the research, analyses the impact of My Character and concludes with recommendations for policy makers, practitioners and researchers embarking on similar projects. These recommendations include: i) advocating that schools create space in the curriculum to teach future-mindedness through character education; ii) enhancing traditional character education teaching methods with opportunities brought by Internet technologies; iii) evaluating character education interventions using triangulated evidence drawn from a mixture of research methods. (shrink)

Appearing in English for the first time, Schelling’s 1842 lectures develop the idea that many philosophical concepts are born of religious-mythological notions.

Through clear explanation of its characteristic concepts and doctrines, and paying close attention to the published works of its philosophers, the volume ...

In CQ 45 , 547–50, S. J. Harrison and M. Winterbottom propose a series of emendations to the text of the recently discovered passage of Donatus which contains his commentary on Aen. 6.1–157. I offer some further emendations.

In CQ 45, 547–50, S. J. Harrison and M. Winterbottom propose a series of emendations to the text of the recently discovered passage of Donatus which contains his commentary on Aen. 6.1–157. I offer some further emendations.

There exist important deductive systems, such as the non-normal modal logics, that are not proper subjects of classical algebraic logic in the sense that their metatheory cannot be reduced to the equational metatheory of any particular class of algebras. Nevertheless, most of these systems are amenable to the methods of universal algebra when applied to the matrix models of the system. In the present paper we consider a wide class of deductive systems of this kind called protoalgebraic logics. These include (...) almost all (non-pathological) systems of prepositional logic that have occurred in the literature. The relationship between the metatheory of a protoalgebraic logic and its matrix models is studied. The following results are obtained for any finite matrix model U of a filter-distributive protoalgebraic logic : (I) The extension U of is finitely axiomatized (provided has only finitely many inference rules); (II) U has only finitely many extensions. (shrink)

This paper is based on Lectures 1, 2 and 4 in the series of ten lectures titled “Algebraic Structures for Logic” that Professor Blok and I presented at the Twenty Third Holiday Mathematics Symposium held at New Mexico State University in Las Cruces, New Mexico, January 8-12, 1999. These three lectures presented a new approach to the algebraization of deductive systems, and after the symposium we made plans to publish a joint paper, to be written by Blok, further developing these (...) ideas. That project was still incomplete when Blok died. In fact, there is no indication that he had prepared a draft of the paper, and we do not know what new material he intended to include. I am therefore not in a position to complete the project as he had envisioned it. So, I have settled for the more limited objective of presenting the material from the three lectures, leaving to others the task of adapting the techniques used there to more general situations. (shrink)

Modal logics are studied in their algebraic disguise of varieties of so-called modal algebras. This enables us to apply strong results of a universal algebraic nature, notably those obtained by B. Jonsson. It is shown that the degree of incompleteness with respect to Kripke semantics of any modal logic containing the axiom □ p → p or containing an axiom of the form $\square^mp \leftrightarrow\square^{m + 1}p$ for some natural number m is 2 ℵ 0 . Furthermore, we show that (...) there exists an immediate predecessor of classical logic (axiomatized by $p \leftrightarrow \square p$ ) which is not characterized by any finite algebra. The existence of modal logics having 2 ℵ 0 immediate predecessors is established. In contrast with these results we prove that the lattice of extensions of S4 behaves much better: a logic extending S4 is characterized by a finite algebra iff it has finitely many extensions and any such logic has only finitely many immediate predecessors, all of which are characterized by a finite algebra. (shrink)

We study modal logics in the setting of varieties of modal algebras. Any variety of modal algebras generated by a finite algebra — such, a variety is called tabular — has only finitely many subvarieties, i.e. is of finite height. The converse does not hold in general. It is shown that the converse does hold in the lattice of varieties of K4-algebras. Hence the lower part of this lattice consists of tabular varieties only. We proceed to show that there is (...) a continuum of pretabular varieties of K4-algebras — those are the non-tabular varieties all of whose proper subvarieties are tabular — in contrast with Maksimova's result that there are only five pretabular varieties of S4-algebras. (shrink)

The notion of an algebraic semantics of a deductive system was proposed in [3], and a preliminary study was begun. The focus of [3] was the definition and investigation of algebraizable deductive systems, i.e., the deductive systems that possess an equivalent algebraic semantics. The present paper explores the more general property of possessing an algebraic semantics. While a deductive system can have at most one equivalent algebraic semantics, it may have numerous different algebraic semantics. All of these give rise to (...) an algebraic completeness theorem for the deductive system, but their algebraic properties, unlike those of equivalent algebraic semantics, need not reflect the metalogical properties of the deductive system. Many deductive systems that don't have an equivalent algebraic semantics do possess an algebraic semantics; examples of these phenomena are provided. It is shown that all extensions of a deductive system that possesses an algebraic semantics themselves possess an algebraic semantics. Necessary conditions for the existence of an algebraic semantics are given, and an example of a protoalgebraic deductive system that does not have an algebraic semantics is provided. The mono-unary deductive systems possessing an algebraic semantics are characterized. Finally, weak conditions on a deductive system are formulated that guarantee the existence of an algebraic semantics. These conditions are used to show that various classes of non-algebraizable deductive systems of modal logic, relevance logic and linear logic do possess an algebraic semantics. (shrink)

The present paper is a study in abstract algebraic logic. We investigate the correspondence between the metalogical Beth property and the algebraic property of surjectivity of epimorphisms. It will be shown that this correspondence holds for the large class of equivalential logics. We apply our characterization theorem to relevance logics and many-valued logics.

A well-known result, going back to the twenties, states that, under some reasonable assumptions, any logic can be characterized as the set of formulas satisfied by a matrix 〈,F〉, whereis an algebra of the appropriate type, andFa subset of the domain of, called the set of designated elements. In particular, every quasi-classical modal logic—a set of modal formulas, containing the smallest classical modal logicE, which is closed under the inference rules of substitution and modus ponens—is characterized by such a matrix, (...) wherenow is a modal algebra, andFis a filter of. If the modal logic is in fact normal, then we can do away with the filter; we can study normal modal logics in the setting of varieties of modal algebras. This point of view was adopted already quite explicitly in McKinsey and Tarski [8]. The observation that the lattice of normal modal logics is dually isomorphic to the lattice of subvarieties of a variety of modal algebras paved the road for an algebraic study of normal modal logics. The algebraic approach made available some general results from Universal Algebra, notably those obtained by Jónsson [6], and thereby was able to contribute new insights in the realm of normal modal logics [2], [3], [4], [10].The requirement that a modal logic be normal is rather a severe one, however, and many of the systems which have been considered in the literature do not meet it. For instance, of the five celebrated modal systems, S1–S5, introduced by Lewis, S4 and S5 are the only normal ones, while only SI fails to be quasi-classical. The purpose of this paper is to generalize the algebraic approach so as to be applicable not just to normal modal logics, but to quasi-classical modal logics in general. (shrink)

Let S denote the variety of Sugihara algebras. We prove that the lattice (K) of subquasivarieties of a given quasivariety K S is finite if and only if K is generated by a finite set of finite algebras. This settles a conjecture by Tokarz [6]. We also show that the lattice (S) is not modular.

The logic RM and its basic fragments (always with implication) are considered here as entire consequence relations, rather than as sets of theorems. A new observation made here is that the disjunction of RM is definable in terms of its other positive propositional connectives, unlike that of R. The basic fragments of RM therefore fall naturally into two classes, according to whether disjunction is or is not definable. In the equivalent quasivariety semantics of these fragments, which consist of subreducts of (...) Sugihara algebras, this corresponds to a distinction between strong and weak congruence properties. The distinction is explored here. A result of Avron is used to provide a local deduction-detachment theorem for the fragments without disjunction. Together with results of Sobociski, Parks and Meyer (which concern theorems only), this leads to axiomatizations of these entire fragments — not merely their theorems. These axiomatizations then form the basis of a proof that all of the basic fragments of RM with implication are finitely axiomatized consequence relations. (shrink)

W. J. Mander presents the first ever synoptic history of British Idealism, the school of thought which dominated English-language philosophy from the 1860s to the early 20th century. He restores to its proper place this neglected period of philosophy, introducing the exponents of Idealism and explaining its distinctive concepts and doctrines.