This paper briefly reviews the theories that seek to explain the phenomenon of corporate charitable donations and then provides a review of the empirical issues that have arisen in previous studies in this area. The findings of an analysis of charitable donations data from the entire U.K. FTSE index for the years 1985–2000 are then reported. These findings include the observation of a time-related increase in charitable donations, which is compared with an earlier study to give a 24 year history (...) of charitable donations in the U.K. The findings note little responsiveness of the monetary value of charitable donations to the economic performance of firms. An international comparison over time against U.S. trends is also reported and shows how U.S. corporations have traditionally been more generous than U.K. firms, but that the trend in the U.S. is downwards. Membership of a U.K.-based "tithing" club (the PerCent Club) is shown to be associated with higher profit performance against non-members. Members' charitable contributions against profit are shown to be higher than the FTSE mean although short of the 0.5% target figure in "cash" terms. The paper concludes with a brief discussion of these findings in relation to the theoretical positions advanced for corporate philanthropy. (shrink)

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

Many prescriptions offered in the literature for enhancing creativity and innovation in organizations raise ethical concerns, yet creativity researchers rarely discuss ethics. We identify four categories of behavior proffered as a means for fostering creativity that raise serious ethical issues: breaking rules and standard operating procedures; challenging authority and avoiding tradition; creating conflict, competition and stress; and taking risks. We discuss each category, briefly identifying research supporting these prescriptions for fostering creativity and then we delve into ethical issues associated with (...) engaging in the prescribed behavior. These four rubrics illustrate ethical issues that need to be incorporated into the creativity and innovation literature. Recommendations for how organizations can respond to the ethical issues are offered based on practices of exemplary organizations and theories of organizational ethics. A research agenda for empirically investigating the ethical impact these four categories of behavior have on organizations concludes the article. (shrink)

Whereas professional persuasion is a means to an immediate and instrumental end, ethical persuasion must rest on or serve a deeper, morally based final end. Among the moral final ends of journalism, for example, are truth and freedom. There is a very real danger that advertisers and public relations practitioners will play an increasingly dysfunctional role in the communications process if means continue to be confused with ends in professional persuasive communications. Means and ends will continue to be confused unless (...) advertisers and public relations practitioners reach some level of agreement as to the moral end toward which their efforts should be directed. In this article we advance a five-part test that defines this moral end, establishes ethical boundaries that should guide persuasive practices, and serves as a set of action-guiding principles directed toward a moral consequence in professional persuasion. The TARES Test consists of five principles: Truthfulness, Authenticity, Respect, Equity and Social Responsibility. We provide checklists to guide the practitioner in moral reflection and application of TARES Test principles. (shrink)

The psycholinguistic literature has identified two syntactic adaptation effects in language production: rapidly decaying short-term priming and long-lasting adaptation. To explain both effects, we present an ACT-R model of syntactic priming based on a wide-coverage, lexicalized syntactic theory that explains priming as facilitation of lexical access. In this model, two well-established ACT-R mechanisms, base-level learning and spreading activation, account for long-term adaptation and short-term priming, respectively. Our model simulates incremental language production and in a series of modeling studies, we show (...) that it accounts for (a) the inverse frequency interaction; (b) the absence of a decay in long-term priming; and (c) the cumulativity of long-term adaptation. The model also explains the lexical boost effect and the fact that it only applies to short-term priming. We also present corpus data that verify a prediction of the model, that is, that the lexical boost affects all lexical material, rather than just heads. (shrink)

Hume describes the sciences as "noble entertainments" that are "proper food and nourishment" for reasonable beings (EHU 1.5-6; SBN 8).1 But mathematics, in particular, is more than noble entertainment; for millennia, agriculture, building, commerce, and other sciences have depended upon applying mathematics.2 In simpler cases, applied mathematics consists in inferring one matter of fact from another, say, the area of a floor from its length and width. In more sophisticated cases, applied mathematics consists in giving scientific theory a mathematical form (...) and then explaining and predicting matters of fact by means of mathematics and the theory. Since Hume holds that, "All inferences from experience are . . . .. (shrink)

The experience of causation is a pervasive product of the human mind. Moreover, the experience of causing an event alters subjective time: actions are perceived as temporally shifted towards their effects [Haggard, P., Clark, S., & Kalogeras, J.. Voluntary action and conscious awareness. Nature Neuroscience, 5, 382-385]. This temporal shift depends partly on advance prediction of the effects of action, and partly on inferential "postdictive" explanations of sensory effects of action. We investigated whether a single factor of statistical contingency could (...) explain both these aspects of causal experience. We studied the time at which people perceived a simple manual action to occur, when statistical contingency indicated a causal relation between action and effect, and when no such relation was indicated. Both predictive and inferential "postdictive" shifts in the time of action depended on strong contingency between action and effect. The experience of agency involves a process of causal learning based on statistical contingency. (shrink)

Psychologists debate whether mental attributes can be quantified or whether they admit only qualitative comparisons of more and less. Their disagreement is not merely terminological, for it bears upon the permissibility of various statistical techniques. This article contributes to the discussion in two stages. First it explains how temperature, which was originally a qualitative concept, came to occupy its position as an unquestionably quantitative concept (§§1–4). Specifically, it lays out the circumstances in which thermometers, which register quantitative (or cardinal) differences, (...) became distinguishable from thermoscopes, which register merely qualitative (or ordinal) differences. I argue that this distinction became possible thanks to the work of Joseph Black, ca. 1760. Second, the article contends that the model implicit in temperature’s quantitative status offers a better way for thinking about the quantitative status of mental attributes than models from measurement theory (§§5–6). (shrink)

Recent accounts of the role of diagrams in mathematical reasoning take a Platonic line, according to which the proof depends on the similarity between the perceived shape of the diagram and the shape of the abstract object. This approach is unable to explain proofs which share the same diagram in spite of drawing conclusions about different figures. Saccheri’s use of the bi-rectangular isosceles quadrilateral in Euclides Vindicatus provides three such proofs. By forsaking abstract objects it is possible to give a (...) natural explanation of Saccheri’s proofs as well as standard geometric proofs and even number-theoretic proofs. (shrink)

Graduate students typically first experience research ethics when they submit their masters or doctoral research projects for ethics approval. Research ethics boards in Canada review and grant ethical approval for student research projects and often have to provide additional support to these novice researchers. Previous studies have explored curriculum content, teaching approaches, and the learning environment related to research ethics for graduate students. However, research does not exist that examines students’ actual experience with the research ethics process. Qualitative description was (...) used to explore the research ethics review experience of 11 masters and doctoral students in health discipline programs. Data analysis revealed four themes: curriculum, supervisor support, the ethics application process, and students’ overall experience. The results of this research suggest ideas for enhancing curriculum, deepening students’ relationships with supervisors, and developing the role of research ethics... (shrink)

Classical logic yields counterintuitive results for numerous propositional argument forms. The usual alternatives (modal logic, relevance logic, etc.) generate counterintuitive results of their own. The counterintuitive results create problems—especially pedagogical problems—for informal logicians who wish to use formal logic to analyze ordinary argumentation. This paper presents a system, PL– (propositional logic minus the funny business), based on the idea that paradigmatic valid argument forms arise from justificatory or explanatory discourse. PL– avoids the pedagogical difficulties without sacrificing insight into argument.

Alexander’s "Infinitesimal. How a dangerous mathematical theory shaped the modern world"(London: Oneworld Publications, 2015) is right to argue that the Jesuits had a chilling effect on Italian mathematics, but I question his account of the Jesuit motivations for suppressing indivisibles. Alexander alleges that the Jesuits’ intransigent commitment to Aristotle and Euclid explains their opposition to the method of indivisibles. A different hypothesis, which Alexander doesn’t pursue, is a conflict between the method of indivisibles and the Catholic doctrine of the Eucharist. (...) This is a pity, for the conflict with the Eucharist has advantages over the Jesuit commitment to Aristotle and Euclid. The method of indivisibles was a method that developed in the course of the seventeenth century, and those who developed ‘beyond the Alps’ relied upon Aristotelian and Euclidean ideals. Alexander’s failure to recognize the importance of Aristotle and Euclid for the development of the method of indivisibles arises from an unwarranted conflation of indivisibles and infinitesimals. Once indivisibles and infinitesimals are distinguished, we observe that the development of the method of indivisibles exhibits an unmistakable sympathy for Aristotle and Euclid. Thus, it makes sense to consider an alternative explanation for the Jesuit abhorrence of indivisibles. And indeed, indivisibles but not infinitesimals conflict with the doctrine of the Eucharist, the central dogma of the Church. (shrink)

In formal logic there is a premium on clever paraphrase, for it subsumes troublesome inferences under a familiar theory. (A paradigm is Davidson's analysis 1967 of inferences like ?He buttered his toast with a knife; so, he buttered his toast?.) But the need for paraphrase in formal logic runs deeper than the odd recalcitrant inference, and thus, I shall argue, commits logicians to some interesting consequences. First, the thesis that arguments are valid in virtue of their form must be severely (...) qualified (?4). And second, it is misleading to view a formal logical theory as a standard for justifying and criticizing inference (?7). The latter point depends on the nature and role of paraphrase, which permit a range of conflicting logical theories. Conflicting logical theories arise from the conflicting goals of logical theorists and the promiscuous nature of paraphrase makes reconciliation impossible. (shrink)

The numbering in the new edition of Wittgenstein's Remarks does not in general correspond to the part and section numbers of the 1956 edition. The following concordance is useful for making cross references between the two editions.

Professor Grünbaum's much-discussed refutation of Zeno's metrical paradox turns out to be ad hoc upon close examination of the relevant portion of measure theory. Although the modern theory of measure is able to defuse Zeno's reasoning, it is not capable of refuting Zeno in the sense of showing his error. I explain why the paradox is not refutable and argue that it is consequently more than a mere sophism.

Mathematics used to be portrayed as a deductive science. Stemming from Polya, however, is a philosophical movement which broadens the concept of mathematical reasoning to include inductive or quasi-empirical methods. Interest in inductive methods is a welcome turn from foundationalism toward a philosophy grounded in mathematical practice. Regrettably, though, the conception of mathematical reasoning embraced by quasi-empiricists is still too narrow to include the sort of thought-experiment which Mueller describes as traditional mathematical proof and which Lakatos examines in Proofs and (...) refutations. This paper extends the concept of mathematical reasoning along two further dimensions to accommodate thought-experiment.Keywords: Thought-experiment; Informal proof; Mathematical reasoning. (shrink)

This editorial, introducing the Journal for Theoretical & Marginal Mathematics Education, is historically situated in a moment when the field of mathematics education research is on the precipice of acknowledging that the old world is dying. That is to say, the way research has been done before is no longer adequate for operating within the White, Colonial, cis-hetero Patriarchal, Abled Capitalist dystopia we find ourselves. This inadequacy is, however, not a reason for despair but instead for celebration. Instead of directing (...) our resources towards reifying existing norms and structures, towards adopting exhausted methods and theories—as is the way of the old world—we can instead foster a ‘new aesthetics’ of mathematics education research, wherein we remake the very material that constitutes mathematics education research itself. In doing so, we engage with the politics of the margins of mathematics education research. We discuss the critical, philosophical, and psychoanalytic as three potential, but non-exhaustive, departures from mathematics education research as it has been. Each of these marginal approaches, in their own way, points to the ways that presuming a fixed mathematics education research enacts exclusionary politics and precludes change. Let this be our manifesto, written from the margins, for a more root-grasping, more self-reflective, and freer mathematics education research. (shrink)

Morality can help guide behavior and facilitate relationships. Although moral judgments by autistic people are similar to neurotypical individuals, many researchers argue that subtle differences signify deficits in autistic individuals. Moral foundation theory describes moral judgments in terms of differences rather than deficits. The current research, aimed at assessing autistic individuals’ moral inclinations using Haidt’s framework, was co-designed with autistic community members. Our aim was to describe autistic moral thinking from a strengths-based perspective while acknowledging differences that may pose interpersonal (...) challenges among autistic youth. We assessed 25 autistic and 23 neurotypical children’s moral judgments using the Moral Foundations Questionnaire for Kids. We used semi-structured interviews and qualitative analysis with a subset of participants to describe children’s moral reasoning. Analyses suggested that autistic and neurotypical children make similar judgments about moral transgressions across all five moral foundations. General linear mixed modeling showed that the greatest predictor of recommending punishment was how bad children deemed moral transgressions to be. We also found a trend that autistic children were more likely to recommend punishment for harmless norms violations than were neurotypical children. Future research could use longitudinal methods to understand the development of moral judgments among autistic and neurotypical children. (shrink)

In a ground-breaking essay Nagel contended that the controversy over impossible numbers influenced the development of modern logic. I maintain that Nagel was correct in outline only. He overlooked the fact that the controversy engendered a new account of reasoning, one in which the concept of a well-made language played a decisive role. Focusing on the new account of reasoning changes the story considerably and reveals important but unnoticed similarities between the development of algebraic logic and quantificational logic.

A plausible and popular rule governing the scope of truth-functional logic is shown to be indequate. The argument appeals to the existence of truth-functional paraphrases which are logically independent of their natural language counterparts. A more adequate rule is proposed.