In the mathematics education research literature, there is a growing body of scholarship on how mathematicians practice their craft. The purpose of this chapter is to survey some of this literature and explain how it can contribute to the philosophy of mathematical practice. We first describe how mathematics educators use empirical methodologies to investigate the behaviors of mathematicians and argue that findings from these studies can inform the philosophy of mathematical practice. We then illustrate this by summarizing research on mathematicians’ (...) understandings and mathematicians’ proof reading. (shrink)

In a 2022 paper, Hamami claimed that the orthodox view in mathematics is that a proof is rigorous if it can be translated into a derivation. Hamami then developed a descriptive account that explains how mathematicians check proofs for rigor in this sense and how they develop the capacity to do so. By exploring introductory texts in computability theory, we demonstrate that Hamami’s descriptive account does not accord with actual mathematical practice with respect to computability theory. We argue instead for (...) an alternative account in which imagination, anticipation, and interpretations of natural language play roles in establishing mathematical rigor. (shrink)

In this paper, we explore the role of syntactic representations in set theory. We highlight a common inferential scheme in set theory, which we call the Syntactic Representation Inferential Scheme, in which the set theorist infers information about a concept based on the way that concept can be represented syntactically. However, the actual syntactic representation is only indicated, not explicitly provided. We consider this phenomenon in relation to the derivation indicator position that asserts that the ordinary proofs given in mathematical (...) discourse indicate syntactic derivations in a formal logical system. In particular, we note that several of the arguments against the derivation indicator position would seem to imply that set theorists could gain no benefits from the syntactic representations of concepts indicated by their definitions, yet set theorists clearly do. (shrink)

Traditional models of mathematical proof describe proofs as sequences of assertion where each assertion is a claim about mathematical objects. However, Tanswell observed that in practice, many proofs do not follow these models. Proofs often contain imperatives, and other instructions for the reader to perform mathematical actions. The purpose of this paper is to examine the role of instructions in proofs by systematically analyzing how instructions are used in Kunen’s Set theory: An introduction to independence proofs, a widely used graduate (...) text in set theory. I use Kunen’s text to describe how instructions and constructions in proof work in mathematical practice and explore epistemic consequences of how proofs are read and understood. (shrink)

The issue of what constitutes a valid logical inference is a difficult question. At a minimum, we believe a permissible step in a proof must provide the reader with rational grounds to believe that the new step is a logically necessary consequence of previous assertions. However, this begs the question of what constitutes these rational grounds. Formalist accounts typically describe valid rules of inferences as those that can be found by applying one of the explicit rules of inference in the (...) formal system in which the proof is couched. However, philosophers of mathematics find such a description unhelpful because many inferences in the proofs that mathematicians actually produce cannot be expressed in a formal language, at least not without seriously distorting the semantic content of the inference (e.g., Larvor, 2012). In this chapter, we investigate mathematicians’ perceptions of a particular kind of inference in a particular setting. Specifically, we shed light on what types of graphical inferences mathematicians find permissible in a real analysis proof. Following Larvor (in press), we examine mathematicians’ reactions to metrical graphical inferences (i.e., inferences whose validity depends on the accuracy of the graph that was drawn and whose validity can be changed by minor deformations) and nonmetrical graphical inferences (i.e., inferences whose validity does not depend on a the accuracy of the graph and whose validity is not vulnerable to local deformations). The goal of this chapter is threefold. First, we demonstrate that most mathematicians reject metrical graphical inferences as impermissible in a real analysis proof. Second, we show that many mathematicians regard nonmetrical graphical inferences as permissible in a real analysis proofs. Third, we illustrate how mathematicians collectively disagree on the permissibility of nonmetrical inferences. (shrink)

Introduction -- Modernity, politics and Max Weber -- One-sided rationalization: Habermas on modernity, discourse and emancipation -- Critiquing Habermas: intersubjectivity, ethics and norm-free sociality -- The burden of our times: Arendt on modern oblivion and the promise of politics -- Judging Arendt: citizenship, action and the scope of politics -- The new dark age: MacIntyre on bureaucratic individualism and the hope for an ethical polity -- Engaging MacIntyre: flourishing, modernity and political struggle -- Closing reflections: ethics, politics and strategy (...) in the present. (shrink)

This article addresses the ability of Parallel Distributed Processing (PDP) networks to generate stagewise cognitive development in accordance with Piaget's theory of cognitive epigenesis. We carried out a replication study of the simulation experiments by McClelland (1989) and McClelland and Jenkins (1991) in which a PDP network learns to solve balance scale problems. In objective tests motivated from catastrophe theory, a mathematical theory of transitions in epigenetical systems, no evidence for stage transitions in network performance was found. It is concluded (...) that PDP networks lack the ability to recover the positive outcomes of analogous catastrophe analyses of real cognitive developmental data. In an attempt to further characterize the learning behaviour of PDP networks, we carried out a second simulation study using the discrimination‐shift paradigm. The results thus obtained indicate that PDP learning is compatible with the learning of stimulus‐response relationships, not with the acquisition of mediating rules such as conceived in (neo‐)Piagetian theory. In closing, we speculate about the feasibility of simulating stagewise development with alternative network architectures. (shrink)

In this article, we report a study in which 109 research-active mathematicians were asked to judge the validity of a purported proof in undergraduate calculus. Significant results from our study were as follows: (a) there was substantial disagreement among mathematicians regarding whether the argument was a valid proof, (b) applied mathematicians were more likely than pure mathematicians to judge the argument valid, (c) participants who judged the argument invalid were more confident in their judgments than those who judged it valid, (...) and (d) participants who judged the argument valid usually did not change their judgment when presented with a reason raised by other mathematicians for why the proof should be judged invalid. These findings suggest that, contrary to some claims in the literature, there is not a single standard of validity among contemporary mathematicians. (shrink)

The first four chapters of Max Weber's Economy and Society presented by Talcott Parsons in 1947 as Theory of Social and Economic Organization present a coherent and complete analysis of social, economic and political structures based upon a consistent theory of social action and its understanding. Parsons did not see them this way. His lengthy introduction sought to insert them into his own “action frame of reference”, and his rearrangement of the text made it difficult for a reader to (...) understand why it was constructed the way that it is. This essay describes how Parsons came to be principal translator and editor of the text, examines the changes that he made to it, and links his editorial practice to the analytical procedures that he followed in his Structure of Social Action. ☆ This essay is developed from a paper originally presented in June 2005 at a conference on Max Weber's Basic Sociological Concepts at ZiF, Bielefeld University; an earlier version of the present paper was published as “Talcott Parsons als Übersetzer der ‘Soziologischen Grundbegriffe’ Max Webers”. Max Webers ‘Grundbegriffe’. Kategorien der kultur- und sozialwissenschaftlichen Forschung. Ed. Klaus Lichtblau. (Wiesbaden: Verlag für Sozialwissenschaften, 2006) 337–366. (shrink)

If sociology is about society must it not also be about morality? In the nineteenth and early twentieth centuries, the identification between sociology and morality was clear cut; Marx, Durkheim, Weber, Spencer, and Veblen all dealt with moral issues and one might argue that they saw themselves as engaged in a moral vocation. Now, one might argue that the connections between sociology and moral currents have become more tenuous. Moral Culture examines what it means to be moral in contemporary (...) social and cultural life. Author Keith Tester takes the highly original and revealing step of exploring how violence today, and throughout history, affects the relatively safe and secure people who live in the west and who tend to know horror only through television and cinema screens. The book raises questions about the meaning and significance of massacres in the Balkans, Rwanda and, rather more historically, the Holocaust, and the slaughter of Vietnamese peasants by American soldiers in My Lai. It also discusses how Adolf Eichmann and the men of Charlie Company might be different from or similar to us. It answers questions about whether this is a time of moral decay or more seriously, the collapse of moral Civilization. Sociologists often claim that they make a virtue of being relevant and objective, but few have attacked these issues with the urgency and originality that Keith Tester displays in this work. Each chapter provides a historically aware account of a moral problem making it especially relevant reading for students of cultural studies, sociology, political science, and moral philosophy. (shrink)

SummaryDuring the 1950s at the latest, Max Weber became a ‘founding father’ of sociology, chiefly on the basis of a restricted set of canonical writings and without any consideration of his wider relationships to law, economics and politics. During the last ten years of his life he was responsible for a major collaborative work, the Grundriss der Sozialökonomik—Outline of Social Economics. The title was of his own choosing; and so it might well shed new light on his work if (...) we consider how this work was organised, and how Economy and Society, written as a contribution to this handbook, was intended to form part of it. (shrink)

In contrast to political realism's equation of the `political' with domination, Hannah Arendt understood the `political' as a relation of friendship utterly opposed to the use of violence. This article offers a critique of that understanding. It becomes clear that Arendt's challenge to realism, as exemplified by Max Weber, succeeds on account of a dubious redefinition of the `political' that is the reverse image of the one-sided vision of politics she had hoped to contest. Questioning this paradoxical turn leads (...) to a critique of Arendt's separation of violence and power and, consequently, her attempt to insulate a politics of friendship from one of hostility and coercion. However, political realism is not thereby affirmed. What is required, instead, is a view of the `political' that accepts the interwoven-ness of violence and power but also emphasizes the normative ideals of moderation and care. Key Words: Hannah Arendt • enmity • friendship • moderation • the `political' • power • realism • violence • Max Weber. (shrink)

Keith Ansell-Pearson, An Introduction to Nietzsche as Political Thinker (Cambridge: Cambridge University Press, 1994) hb: 0-521-41722-8. pb: 0-521-42721-5. Paul Patton, ed., Nietzsche, Feminism and Political Theory (London: Routledge. 1993) 0-4150-8256-0. Lester M. Hunt, Nietzsche and the Origin of Virtue (London: Routledge, 1993) 0-4150-9580-8. David Owen, Maturity and Modernity. Nietzsche, Weber, Foucault and the Ambivalence of Reason (London: Routledge, 1994) 0-4150-5398-6. Peter Lassmann and Ronald Spiers, eds., Weber: Political Writings (Cambridge: Cambridge University Press. 1994) hb: 0-521 -39312-4. pb: (...) 0-521 -39719-7. Friedrich Nietzsche, On the Genealogy of Morality and Other Writings, ed. Keith Ansell-Pearson, tr. Carol Diethe (Cambridge University Press, 1994) hb: 0-521-40459-2. pb: 0-521-40610-2. (shrink)

I dedicate this essay to the memory of the late Wolfgang Mommsen—the subject would have been congenial to him. It is one of a series of offshoots from a central project: a scholarly edition of Max Weber's Protestant Ethic with commentary. When I first told Prof. Mommsen of my plan in 1994 he looked me full in the face and gave a characteristic growl: “All that work!” Here was a man who knew what he was about. My thanks to (...) Ross McKibbin and Keith Tribe for reading this paper in draft. The article begins by examining Max Weber's relations with Lujo Brentano, much the most important “precursor” to Weber in the field of economics. In particular, Brentano conducted a form of parallel inquiry into the rise of ‘the spirit of capital’ in England 35 years before Weber looked for the origins of “spirit” of capitalism there, and the contrast between these two ideas casts much light both on Brentano and on Weber's Protestant Ethic. This personal history leads into a broader history of the transition in German economic thought between the 1860s – the formative decade for Brentano but also the era of Marx's Capital – and that of Weber's generation coming to maturity c.1890. Marx and Weber remain the two great canonical thinkers and original minds; but any authentic historical comparison between Marx and Weber must take in Brentano. The essence of the contrast between the generations is that between Weber's novel conception of an ethical ‘capitalism’, and the materialism and naturalism underpinning Brentano's and Marx's ‘capital’, although Weber and Brentano are alike as liberals, democrats and bourgeois. ☆ Some abbreviations for Weber: AfSS for Archiv für Sozialwissenschaft und Sozialpolitik; GARS for Gesammelte Aufsätze zur Religionssoziologie (Tübingen, 1920) vol. i; WL for Gesammelte Aufsätze zur Wissenschaftslehre (Tübingen, 1968); Grundriss for Grundriss zu den Vorlesungen über Allgemeine (“theoretische”) Nationalökonomie [1898], repr. Tübingen, 1990; MWG for Max Weber Gesamtausgabe ed. Horst Baier et al. (Tübingen, 1984); Briefe for letters by Weber in this edition; ‘Nachlaß Max Weber’ for unpublished letters from the Geheimes Staatsarchiv, Berlin-Dahlem, VI. HA Nachlaß Max Weber. Lebensbild for Marianne Weber, Max Weber: Ein Lebensbild (Tübingen, 1926); Zohn for idem, Max Weber. A Biography (New Brunswick, 1988) tr. Harry Zohn. For Brentano: Der wirtschaftende Mensch for Der wirtschaftende Mensch in der Geschichte (Leipzig, 1923); Konkrete Grundbedingungen for Konkrete Grundbedingungen der Volkswirtschaft (Leipzig, 1924); Der tätige Mensch for Der tätige Mensch und die Wissenschaft von der Wirtschaft (Marburg, 2006) ed. R. Bräu, H.G. Nutzinger. ‘Die Entwickelung der Wertlehre’ for ‘Die Entwickelung der Wertlehre’, Sitzungsberichte der Königlich Bayerischen Akademie der Wissenschaften. Philosophisch-philologische und historische Klassen. Jahrgang 1908, 3. Abhandlung (15 Feb. 1908), 1–84; ‘Theorie der Bedürfnisse’ for ‘Versuch einer Theorie der Bedürfmisse’, ibid., 10. Abhandlung (5 Dec. 1908), 1–79; ‘Die Malthussche Lehre’ for ‘Die Malthussche Lehre und die Bevölkerungsbewegung der letzten Decennien’ [1909], Abhandlungen der historischen Klasse der Königlich Bayerischen Akademie der Wissenschaften XXIV (1906–1909), 565–625, 1*–39*. (shrink)

Classical logic, beginning with the work of Aristotle, has developed into a powerful and rigorous mathematical theory with many applications in mathematics and ...

According to an attractive account of belief, our beliefs have centered content. According to an attractive account of communication, we utter sentences to express our beliefs and share them with each other. However, the two accounts are in conflict. In this paper I explore the consequences of holding on to the claim that beliefs have centered content. If we do in fact express the centered content of our beliefs, the content of the belief the hearer acquires cannot in general be (...) identical to the content the speaker expresses. I sketch an alternative account of communication, the Recentering model, that accepts this consequence and explains how expressed and acquired content are related. (shrink)

De se attitudes seem to play a special role in action and cognition. This raises a challenge to the traditional way in which mental attitudes have been understood. In this chapter, we review the case for thinking that de se attitudes require special theoretical treatment and discuss various ways in which the traditional theory can be modified to accommodate de se attitudes.

This paper considers a generalisation of the sorites paradox, in which only topological notions are employed. We argue that by increasing the level of abstraction in this way, we see the sorites paradox in a new, more revealing light—a light that forces attention on cut-off points of vague predicates. The generalised sorites paradox presented here also gives rise to a new, more tractable definition of vagueness.

Counterfactual thinking involves the imagination of non-factual alternatives to reality. We investigated the spontaneous generation of both upward counterfactuals, which improve on reality, and downward counterfactuals, which worsen reality. All subjects gained $5 playing a computer-simulated blackjack game. However, this outcome was framed to be perceived as either a win, a neutral event, or a loss. "Loss" frames produced more upward and fewer downward counterfactuals than did either "win" or "neutral" frames, but the overall prevalence of counterfactual thinking did not (...) vary with outcome valence. In addition, subjects who expected to play the game again made more upward counterfactuals and were less satisfied with the outcome than were subjects who did not expect to play again. However, once subjects saw the cards from which they could have selected had they "hit" again (two winning cards and two losing cards), all subjects generated primarily upward counterfactuals and showed a corresponding decrease in satisfaction. These results implicate both cognitive and motivational factors in the generation of counterfactuals and tell us something about the functional value of counterfactual thinking: downward counterfactuals provide comfort; upward counterfactuals prepare one for the future. (shrink)

This article reviews research on counterfactual, social, and temporal comparisons and proposes a Reflection and Evaluation Model (REM) as an organizing framework. At the heart of the model is the assertion that 2 psychologically distinct modes of mental simulation operate during comparative thinking: reflection, an experiential (“as if”) mode of thinking characterized by vividly simulating that information about the comparison standard is true of, or part of, the self; and evaluation, an evaluative mode of thinking characterized by the use of (...) information about the standard as a reference point against which to evaluate one’s present standing. Reflection occurs when information about the standard is included in one’s self-construal, and evaluation occurs when such information is excluded. The result of reflection is that standard–consistent cognitions about the self become highly accessible, thereby yielding affective assimilation; whereas the result of evaluation is that comparison information is used as a standard against which one’s present standing is evaluated, thereby yielding affective contrast. The resulting affect leads to either an increase or decrease in behavioral persistence as a function of the type of task with which one is engaged, and a combination of comparison-derived causal inferences and regulatory focus strategies direct one toward adopting specific future action plans. (shrink)

Locke Defines Knowledge at the beginning of Book IV of the Essay concerning Human Understanding as “the perception of the connexion and agreement, or disagreement and repugnancy of any of our Ideas” (E IV.i.2).1 So defined, knowledge varies along two dimensions. On the one hand, there are four “sorts” of knowledge: of identity or diversity; relation; co-existence or necessary connection; and real existence. On the other hand, there are three “degrees” of knowledge: intuitive knowledge, which consists in the “immediate” perception (...) of agreement or disagreement between ideas (E IV.ii.1); demonstrative knowledge, which consists in the perception of agreement or disagreement by way of intermediate (or intervening) .. (shrink)

As business and society is an inherently multi-disciplinary scholarly area, the book will draw from work in areas outside of business and management, such as psychology, sociology, philosophy, religious studies, economics and other related fields, as well as the natural sciences, education, and other professional areas of study.

Previous research has suggested that an effective strategy for debiasing judgments is to have participants "consider the opposite." The present research proposes that considering any plausible alternative outcome for an event, not just the opposite outcome, leads participants to simulate multiple alternatives, resulting in debiased judgments. Three experiments tested this hypothesis using an explanation task paradigm. Participants in all studies were asked to explain either 1 hypothetical outcome (single explanation conditions) or 2 hypothetical outcomes (multiple explanation conditions) to an event; (...) after the explanation task, participants made likelihood judgments. The results of Studies 1 and 2 indicated that debiasing occurred in all multiple explanation conditions, including those that did not involve the opposite outcome. Furthermore, the findings indicated that debiased judgments resulted from participants' spontaneous consideration of additional alternatives in making their likelihood judgments. The results of Study 3 also identified the perceived plausibility of the explained alternative as an important moderating variable in debiasing. (shrink)

Counterfactual thinking—the capacity to reflect on what would, could, or should have been if events had transpired differently—is a pervasive, yet seemingly paradoxical human tendency. On the one hand, counterfactual thoughts can be comforting and inspiring (Carroll & Shepperd, Chapter 28), but on the other they can be anxiety provoking and depressing (Zeelenberg & Pieters, Chapter 27). Likewise, such thoughts can illuminate pathways toward better future outcomes (Wong, Galinsky, & Kray, Chapter 11), yet they can also promote confusion and lead (...) us astray (Sanna, Schwarz, & Kennedy, Chapter 13). The first part of this chapter focuses on work that supports the prevailing Zeitgeist in the counterfactual thinking literature: Counterfactual thinking is beneficial. The second part of the chapter, however, strikes a more cautionary tone by reviewing work that describes some deleterious consequences of counterfactual thinking. We conclude by offering a tentative reconciliation of these conflicting perspectives and suggesting directions for future research. (shrink)

I will be concerned with only one problem about truth which is raised by the diversity of religions which exist in the world. The problem is this: many religions claim to state truths about the nature of the universe and human destiny which are important or even necessary for human salvation and ultimate well-being. Many of these truths seem to he incompatible; yet there is no agreed method for deciding which are to he accepted; and equally intelligent, informed, virtuous and (...) holy people belong to different faiths. It seems, therefore, that a believing member of any one tradition is compelled to regard all other traditions as holding false beliefs and therefore as not leading to salvation. Since each faith forms a minority of the world's population, all religious believers thus seem committed to saying that most intelligent, virtuous and spiritually devoted people cannot know the truth or attain salvation. This is a problem, because it is in tension with the belief, held by many traditions, that the supremely real being is concerned for the salvation of all rational creatures. How can this he so if, through no fault of their own, most creatures cannot come to know the truth and thereby attain salvation? (shrink)

In the present research, the authors hypothesized that additive counterfactual thinking mind-sets, activated by adding new antecedent elements to reconstruct reality, promote an expansive processing style that broadens conceptual attention and facilitates performance on creative generation tasks, whereas subtractive counterfactual thinking mind-sets, activated by removing antecedent elements to reconstruct reality, promote a relational processing style that enhances tendencies to consider relationships and associations and facilitates performance on analytical problem-solving tasks. A reanalysis of a published data set suggested that the counterfactual (...) mind-set primes previously used in the literature tend to evoke subtractive counterfactuals. Studies 1 and 2 then demonstrated that subtractive counterfactual mind-sets enhanced performance on analytical problem-solving tasks relative to additive counterfactual mind-sets, whereas Studies 3 and 4 found that additive counterfactual mind-sets enhanced performance on creative generation tasks relative to subtractive counterfactual mind-sets. (shrink)

According to the Communicative Theory of Emotions, we experience emotions when events occur that are important for our goals and plans. A method of choice for studying these matters is the emotion diary. Emotions configure our cognitive systems and our relationships. Many of our emotions concern our relationships, and empathy is central to our experience of them. We do not always recognize our emotions or the emotions of others, but literary fiction can help improve our skills of recognition and understanding.

Effects of perceived control and close alternative outcomes were examined. Subjects played a computer-simulated "wheel-of-fortune" game with another player in which two wheels spun simultaneously. Subjects had either control over spinning the wheel or control over which wheel would determine their outcome and which would determine the other player's outcome. Results showed that (a) subjects generated counterfactuals about the aspect of the game that they controlled, (b) the direction of these counterfactuals corresponded to the close outcome associated with the aspect (...) they controlled, and (c) close counterfactuals predicted affective responses to the outcome of the wheel spin. Cognitive and motivational implications of the influence of perceived control on counterfactual generation are discussed. (shrink)

This paper deals with the "functions of intentional explanations" of actions (IEAs), i.e., explanations that refer to intentional states (beliefs, desires, etc.) of the agent. IEAs can have different formats. We consider these different formats to be instruments that enable the explainer to capture different kinds of information. We pick out two specific formats, i.e. "contrastive" and "descriptive", which will enable us to discuss the functions of IEAs. In many cases the explanation is contrastive, i.e. it makes use of one (...) or more contrasts between real intentional states and ideal intentional states (ideal from the point of view of the explainer). In many other cases IEAs have a descriptive (covering-law) format. The aim of this paper is to analyze the functions the two kinds of explanations can have. We will show that certain functions are better served by one rather than the other format. This leads to pluralism with respect to formats. We argue that both formats are necessary and that their functions are complementary. (shrink)

The present research extends previous functional accounts of counterfactual thinking by incorporating the notion of reflective and evaluative processing. Participants generated counterfactuals about their anagram performance, after which their persistence and performance on a second set of anagrams was measured. Evaluative processing of upward counterfactuals elicited a larger increase in persistence and better performance than did reflective processing of upward counterfactuals, whereas reflective processing of downward counterfactuals elicited a larger increase in persistence and better performance than did evaluative processing of (...) downward counterfactuals. Moreover, path analyses indicated that whereas the relationship between counterfactual thinking and persistence was accounted for by emotional responses following upward and downward counterfactual generation, the relationship between counterfactual thinking and performance was accounted for by enhanced persistence following reflective processing of downward counterfactuals, but was accounted for by both enhanced persistence and strategic thinking following evaluative processing of upward counterfactuals. (shrink)

The imposing scope and penetrating insights of German philosopher Nicolai Hartmann’s work have received renewed interest in recent years. The Neo-Kantian turned ontological realist established a philosophical approach unique among his peers, and it provides a wealth of resources for considering contemporary philosophical problems. The chapters included in this volume examine his ethics, ontology, aesthetics, philosophy of mind, and philosophy of nature. They explore his ontology of values, autonomy and human enhancement, and law; his theory of levels of reality, space-time (...) and geometry, the categories of temporality, causality, and “life,” the question of realism, and social ontology. Others take inspiration from his aesthetic theory, ideas about education,and his embrace of the Socratic pathos of wonder. They bring his philosophy into conversation with that of his contemporaries, including Roman Ingarden and Konrad Lorenz’s appropriation of Hartmann, as well as with the history of philosophy, including Plato’s theory of recollection, pre-Socratic philosophy, and that of his Russian teacher Nikolai Lossky. Those familiar with Hartmann’s wide-ranging systematic philosophy will benefit from these new engagements with his work, and those new to it will find them relevant to a number of current philosophical debates. (shrink)

As a result there is a considerable literature on the topic. I think, however, that the treatment in the literature is incomplete because there is a failure to examine the relevant emotions in significant detail, and in particular to consider their complexity and the conditions of their warrant. As a result, both defenses and critiques of the motive of duty in terms of reliability are inadequate as they stand.

Rubin and Pearl offered approaches to causal effect estimation and Lewis and Pearl offered theories of counterfactual conditionals. Arguments offered by Pearl and his collaborators support a weak form of equivalence such that notation from the rival theory can be re-purposed to express Pearl’s theory in a way that is equivalent to Pearl’s theory expressed in its native notation. Nonetheless, the many fundamental differences between the theories rule out any stronger form of equivalence. A renewed emphasis on comparative research can (...) help to guide applications, further develop each theory, and better understand their relative strengths and weaknesses. (shrink)

Three studies examined the motivational implications of thinking about how things could have been worse. It was hypothesized that when these downward counterfactuals yield negative affect, through consideration of the possibility of a negative outcome, motivation to change and improve would be increased (the wake-up call). When downward counterfactuals yield positive affect, through diminishing the impact of a potentially negative outcome, motivation to change and improve should be reduced (the Pangloss effect). Results from three studies supported these hypotheses. Studies 1 (...) and 2 showed that a manipulation of the counterfactual made about an investment influenced decisions toward that investment. Study 3 showed that students’ academic motivation was influenced by a manipulation of the type of downward counterfactual they made after an exam and that affect mediated the relationship between the counterfactual and motivation. (shrink)

ABSTRACT It has long been recognised that Adam Smith’s Wealth of Nations (1776) advances a ‘system of natural liberty’ in seeking to account for the ‘nature and causes of the wealth of nations.’ This is not however a theme that is explored or explained in the early sections of the book; in fact, not until Book IV, Ch. ix does Smith give his most expansive account of what he might mean by this term. This paper examines this chapter in detail (...) to determine the limits of his critique in that chapter of the ‘agricultural system’ (of Physiocracy), and why it might be that Smith is so parsimonious in offering a clear account of his central idea. (shrink)

Keith Graham; XIII*—Democracy, Paradox and the Real World, Proceedings of the Aristotelian Society, Volume 76, Issue 1, 1 June 1976, Pages 227–246, https://doi.

My topic is Alvin Plantinga’s ’solution’ to one of the many forms that the problem of evil takes: the modal abstract form. This form of the problem is abstract in that it does not deal with the amounts or kinds of evil which exist, but only with the fact that there is some evil or other. And it is modal in that it concerns the compossibility of the following propositions, not any evidential relation between them: God is omnipotent, omniscient, and (...) wholly goodand There is evil in the world. (shrink)