We use NF to designate the system known as Quine's New Foundations, and NF + AF to designate the same system with a suitable axiom of infinity adjoined. We use ML to designate the revised system appearing in the third printing of Quine's “Mathematical Logic”. This system ML is just the systemPproposed by Wang in [4], and essentially includes NF as a part.The pripcipal results of the present paper are:A. In NF the axiom of infinity is equivalent to the definability (...) of an ordered pair having the same type as its constituents.B. Considering the formulas of NF as having translations in the formalism of ML in the sense defined in [4], we find that a formula of NF is provable in NF if and only if its translation is provable in ML. From the fact that the axiom of infinity is provable in ML, one might be tempted to conclude that the axiom of infinity is provable in NF. It is explained why this is not a valid inference. Consequently, it would appear that there is a sense in which NF + AF is stronger than ML. (shrink)

We attempt to clarify divisions made by us in previous work (Colander et al., 2004a,b) between “orthodox, mainstream, and heterodox” in economics, following very useful remarks in Dequech (2007-08), whom we thank. We also provide specific advice for heterodox economists, namely: worry less about methodology, focus on being economists first and heterodox economists second, and prepare ideas to leave the incubator of heterodoxy to enter the mainstream economic debate.

In this era of increased polarization of opinion and contentious disagreement, CRITICAL REASONING presents a cooperative approach to critical thinking and formation of beliefs. CRITICAL REASONING emphasizes the importance of developing and applying analytical skills in real life contexts. This book is unique in providing multiple, diverse examples of everyday arguments, both textual and visual, including hard to find long argument passages from real-life sources. The book provides clear, step-by-step procedures to help you decide for yourself what to believe--to be (...) a consumer of information in our contemporary "world of experts.". (shrink)

John Burdon Sanderson Haldane was a giant among men. He made major contributions to genetics, population biology, and evolutionary theory. He was at once comfortable in mathematics, chemistry, microbiology and animal physiology. But it was his belief in education that led to his preparing his popular essays for publication. In his own words: "Many scientific workers believe that they should confine their publications to learned journals. I think that the public has a right to know what is going on inside (...) the laboratories, for some of which it pays." So begins Haldane's collection of essays, perhaps the most public intellectual communicating science before the writings of Stephen Jay Gould. The first part of the volume emphasizes the important developments in biology and natural science in the first quarter of the century. As such, it provides a benchmark for studies of the next three quarters of the century. In an unusual introduction, Price takes the readers through their paces, discussing the situation then and now in vitamins, oxygen want, disease controls, and the rewards of science as such. This is followed by Haldane's views on society, art, religion and economy as seen through the eyes of a politically alert major scientist. The editor provides readers unfamiliar with Haldane with a carefully rendered chronology of a life that began in 1892 and that spanned much of the present century. Despite ideas on race, class and politics that have seen better times, Haldane was truly exceptional in translating the science of his time into ideas that "everyman" could readily grasp. His predictions on what science would achieve were on target far more often than not. But even his failed predictions are perhaps the most interesting of all. They throw into sharp relief the truly novel and revolutionary developments in science over the past 75 years. J.B.S. Haldane held many positions and received many honors during his lifetime. But for most of the period covered in this volume, he was the William Dunn Reader in Biochemistry at Cambridge University. He simultaneously served as Fellow of New College, in Oxford University's Horticultural Institute. Carl A. Price served until 1999 as professor IIof plant molecular biology in the Waksman Institute of Microbiology at Rutgers, the State University of New Jersey. He also served as the editor of Plant Molecular Biology Reporter from 1983 until 1997. This is the first volume in a new series on the history and theory of science. (shrink)

Plato's "Politicus" (Statesman) stands, both in date and in political thought, between the "Republic" and the "Laws". It presents his thought at the point when he was chastened by disappointment with his attempts to put theory into practice at Syracuse. The dialogue reflects contemporary controversies on the method of definition; but its logical exercises and the impressive 'myth' of the two cosmic eras serve to bring out its essential political teaching. This volume contains the text in translation. In this second (...) edition, Skemp made corrections to his extensive introduction and running commentary, and added a new appendix taking into account scholarship since the first (1952) edition. (shrink)

This study investigates specific behavioral perceptual differences of ethics between practitioners and students enrolled in sales classes. Respondents were asked to indicate their beliefs to issues related to ethics in sales. A highly significant difference was found between mean responses of students and sales personnel. Managers indicated a greater concern for ethical behavior and less attention to sales than did the students. Students indicated a strong desire for success regardless of ethical constraints violated.

This paper explores a remarkable convergence of ideas and evidence, previously presented in separate places by its authors. That convergence has now become so persuasive that we believe we are working within substantially the same broad framework. Taylor's mathematical papers on neuronal systems involved in consciousness dovetail well with work by Newman and Baars on the thalamocortical system, suggesting a brain mechanism much like the global workspace architecture developed by Baars (see references below). This architecture is relational, in the sense (...) that it continuously mediates the interaction of input with memory. While our approaches overlap in a number of ways, each of us tends to focus on different areas of detail. What is most striking, and we believe significant, is the extent of consensus, which we believe to be consistent with other contemporary approaches by Weiskrantz, Gray, Crick and Koch, Edelman, Gazzaniga, Newell and colleagues, Posner, Baddeley, and a number of others. We suggest that cognitive neuroscience is moving toward a shared understanding of consciousness in the brain. (shrink)

The role of microaggressions has gained increasing philosophical attention in recent years. However, microaggressions only tell part of the story. An often-overlooked component of inequality is the uneven and unjust distribution of microaffirmations. In this paper, I give a new definition of microaffirmations as signals that a recipient belongs to some valued or high-status class. Microaffirmations can—but need not—lead individuals to gain a sense of confidence, belonging, and merit. I then explain the harms of microaffirmations, arguing that when microaffirmations are (...) distributed inequitably, they can have larger ramifications for injustice, harming some vulnerable groups more than others. In addition, microaffirmations can lead individual actors to make choices based on who gives them microaffirmations and where they receive them, and thus can have outsized influence over the direction of an individual’s life because individuals tend to migrate to where they feel valued, appreciated, and included. I then turn to solutions to the problems I raise. I argue we should attend to and attempt to rectify inequalities in microaffirmations because doing so can help ensure not just the absence of negative attention, but also that the presence of positive attention is flowing in a just and equitable way. (shrink)

Reasoning under uncertainty, that is, making judgements with only partial knowledge, is a major theme in artificial intelligence. Professor Paris provides here an introduction to the mathematical foundations of the subject. It is suited for readers with some knowledge of undergraduate mathematics but is otherwise self-contained, collecting together the key results on the subject, and formalising within a unified framework the main contemporary approaches and assumptions. The author has concentrated on giving clear mathematical formulations, analyses, justifications and consequences of the (...) main theories about uncertain reasoning, so the book can serve as a textbook for beginners or as a starting point for further basic research into the subject. It will be welcomed by graduate students and research workers in logic, philosophy, and computer science as a textbook for beginners, a starting point for further basic research into the subject, and not least, an account of how mathematics and artificial intelligence can complement and enrich each other. (shrink)