Apostoli and Brown have shown that the class of formulae valid with respect to the class of -ary relational frames is completely axiomatized by Kn: an n-place aggregative system which adjoins [RM], [RN], and a complete axiomatization of propositional logic, with [Kn]:□α1 ∧...∧□αn+1 → □2/ is the disjunction of all pairwise conjunctions αi∧αj )).Their proof exploits the chromatic indices of n-uncolourable hypergraphs, or n-traces. Here, we use the notion of the χ-product of a family of sets to formulate an alternative (...) definition of an n-trace, which in turn enables a new and simpler completeness proof. (shrink)

: Aristotle struggles with two basic tensions in his understanding of reality or substance that have parallels in Indian metaphysical speculation. The first of these tensions, between the understanding of reality as the underlying substrate (to hupokeimenon) and as the individual "this" (tode ti), finds a parallel in the concept of dravya in Patañjali's Mahābhāsa. The second tension, between the understanding of reality as the individual this and as the intelligible essence of the individual this (to ti ēn einai), corresponds (...) to an ambiguity in the concept of vastu in Kumārila's Ślokavārttika. (shrink)

A Transition to Proof: An Introduction to Advanced Mathematics describes writing proofs as a creative process. There is a lot that goes into creating a mathematical proof before writing it. Ample discussion of how to figure out the "nuts and bolts'" of the proof takes place: thought processes, scratch work and ways to attack problems. Readers will learn not just how to write mathematics but also how to do mathematics. They will then learn to communicate mathematics effectively. The text emphasizes (...) the creativity, intuition, and correct mathematical exposition as it prepares students for courses beyond the calculus sequence. The author urges readers to work to define their mathematical voices. This is done with style tips and strict "mathematical do’s and don’ts", which are presented in eye-catching "text-boxes" throughout the text. The end result enables readers to fully understand the fundamentals of proof. Features: The text is aimed at transition courses preparing students to take analysis Promotes creativity, intuition, and accuracy in exposition The language of proof is established in the first two chapters, which cover logic and set theory Includes chapters on cardinality and introductory topology. (shrink)

Genomic research—including whole genome sequencing and whole exome sequencing—has a growing presence in contemporary biomedical investigation. The capacity of sequencing techniques to generate results that go beyond the primary aims of the research—historically referred to as “incidental findings”—has generated considerable discussion as to how this information should be handled—that is, whether incidental results should be returned, and if so, which ones.Federal regulations governing most human subjects research in the United States require the disclosure of “the procedures to be followed” in (...) the research as part of the informed consent process. It seems reasonable to assume—and indeed, many commentators have concluded—that genomic investigators will be expected to inform participants about, among other procedures, the prospect that incidental findings will become available and the mechanisms for dealing with them. Investigators, most of whom will not have dealt with these issues before, will face considerable challenges in framing meaningful disclosures for research participants.To help in this task, we undertook to identify the elements that should be included in the informed consent process related to incidental findings. We did this by surveying a large number of genomic researchers (n = 241) and by conducting in‐depth interviews with a smaller number of researchers (n = 28) and genomic research participants (n = 20). Based on these findings, it seems clear to us that routine approaches to informed consent are not likely to be effective in genomic research in which the prospect of incidental findings exists. Ensuring that participants’ decisions are informed and meaningful will require innovative approaches to dealing with the consent issue. We have identified four prototypical models of a consent process for return of incidental findings. (shrink)

Two experiments examined the typicality structure of contrasting political categories. In Experiment 1, two separate groups of participants rated the typicality of 15 individuals, including political figures and media personalities, with respect to the categories Democrat or Republican. The relation between the two sets of ratings was negative, linear, and extremely strong, r = −.9957. Essentially, one category was treated as a mirror image of the other. Experiment 2 replicated this result, showing some boundary conditions, and extending the result to (...) liberal and conservative categories. The same method was applied to two other pairs of contrasting categories, healthy and junk foods, and male and female jobs. For those categories, the relation between contrasting pairs was weaker and there was less of a direct trade-off between typicality in one category versus typicality in its opposite. The results are discussed in terms of implications for political decision making and reasoning, and conceptual representation. (shrink)

In his latest book, Eric Scerri presents a completely original account of the nature of scientific progress. It consists of a holistic and unified approach in which science is seen as a living and evolving single organism. Instead of scientific revolutions featuring exceptionally gifted individuals, Scerri argues that the "little people" contribute as much as the "heroes" of science. To do this he examines seven case studies of virtually unknown chemists and physicists in the early 20th century quest to discover (...) the structure of the atom. They include the amateur scientist Anton van den Broek who pioneered the notion of atomic number as well as Edmund Stoner a then physics graduate student who provided the seed for Pauli's Exclusion Principle. Another case is the physicist John Nicholson who is virtually unknown and yet was the first to propose the notion of quantization of angular momentum that was soon put to good use by Niels Bohr. Instead of focusing on the logic and rationality of science, Scerri elevates the role of trial and error and multiple discovery and moves beyond the notion of scientific developments being right or wrong. While criticizing Thomas Kuhn's notion of scientific revolutions he agrees with Kuhn that science is not drawn towards an external truth but is rather driven from within. The book will enliven the long-standing debate on the nature of science, which has increasingly shied away from the big question of "what is science?". (shrink)

This chapter argues that scientific and philosophical progress in our understanding of the living world requires that we abandon a metaphysics of things in favour of one centred on processes. We identify three main empirical motivations for adopting a process ontology in biology: metabolic turnover, life cycles, and ecological interdependence. We show how taking a processual stance in the philosophy of biology enables us to ground existing critiques of essentialism, reductionism, and mechanicism, all of which have traditionally been associated with (...) substance ontology. We illustrate the consequences of embracing an ontology of processes in biology by considering some of its implications for physiology, genetics, evolution, and medicine. And we attempt to locate the subsequent chapters of the book in relation to the position we defend. (shrink)

This article explores the substitution and complementary effects between political and social strategies on firm performance in the context of an emerging market (EM). Using in‐depth, historical case‐study approach, the article investigates how companies integrate political and social resources in this market. Corporate performance includes traditional measures, such as accounting performance and nonfinancial measures like the ease of doing business. The study finds that social strategies are stronger enablers of firm long‐term performance than political strategies. The latter have a short‐term (...) impact on performance, but their success over time is limited. The main drawback of reliance on political resources in EMs is the lack of political stability, fragmented polity, and weak political coalitions. We identify rather limited evidence of firms using these two strategies as complements. Thus, we suggest that firms should employ both these strategies in the EM. (shrink)

Reason and Value collects 15 new papers by leading contemporary philosophers on themes from the work of Joseph Raz. Raz has made major contributions in a wide range of areas, including jurisprudence, political philosophy, and the theory of practical reason; but all of his work displays a deep engagement with central themes in moral philosophy. The subtlety and power of Raz's reflections on ethical topics make his writings a fertile source for anyone working in this area. Especially significant are his (...) explorations of the connections between practical reason and the theory of value, which constitute a sustained and penetrating treatment of a set of issues at the very center of moral philosophy as it is practiced today. The contributors to the volume acknowledge the importance of Raz's contributions by engaging critically with his positions and offering independent perspectives on the topics that he has addressed. The volume aims both to honour Raz's accomplishments in the area of ethical theorizing, and to contribute to an enhanced appreciation of the significance of his work for the subject. (shrink)

This book offers a reassessment of the political philosophy of the British Idealists, a group of once influential and now neglected nineteenth-century Hegelian philosophers, whose work has been much misunderstood. Peter Nicholson focuses on F. H. Bradley's idea of morality and moral philosophy; T. H. Green's theory of the Common Good, of the social nature of rights, of freedom, and of state interference; and Bernard Bosanquet's notorious theory of the General Will. By examining the arguments offered by the Idealists (...) and by their critics the author is able to penetrate the deep layers of hostile comment laid down by several generations of later writers and to show that these ideas, once properly understood, are not only defensible but interesting and important. (shrink)

Describes how the author became an on-call substitute teacher in pursuit of the realities of American public education, describing his complex difficulties with helping educate today's students in spite of flawed curriculums and interpersonal challenges.

This essay is a response to comments made by Shane Fhelan, Cheshire Calhoun, and Naomi Scheman on my book The Play of Reason: From the Modern to the Postmodern. I reiterate my belief that we best approach the issue of consensus and dissension in second’ Order justifications of social and political claims not philosophically but sociologically, politically, historically. I suggest similar approaches for dealing with the question of meaning. This mow signals an endorsement not of indifference but rather of commitment (...) and humility. (shrink)