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.

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)

J. B. Schneewind's "The Invention of Autonomy" has been hailed as a major interpretation of modern moral thought. Schneewind's narrative, however, elides several serious interpretive issues, particularly in the transition from late medieval to early modern thought. This results in potentially distorted accounts of Thomas Aquinas, Hugo Grotius, and G. W. Leibniz. Since these thinkers play a crucial role in Schneewind's argument, uncertainty over their work calls into question at least some of Schneewind's larger agenda for the history of ethics.

This book has been considered by academicians and scholars of great significance and value to literature. This forms a part of the knowledge base for future generations. So that the book is never forgotten we have represented this book in a print format as the same form as it was originally first published. Hence any marks or annotations seen are left intentionally to preserve its true nature.

A supertask is a task that consists in infinitely many component steps, but which in some sense is completed in a finite amount of time. Supertasks were studied by the pre-Socratics and continue to be objects of interest to modern philosophers, logicians and physicists. The term “super-task” itself was coined by J.F. Thomson (1954). Here we begin with an overview of the analysis of supertasks and their mechanics. We then discuss the possibility of supertasks from the perspective of general relativity.

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)

A splendid edition. Schneewind's illuminating introduction succinctly situates the _Enquiry_ in its historical context, clarifying its relationship to Calvinism, to Newtonian science, and to earlier moral philosophers, and providing a persuasive account of Hume's ethical naturalism. --Martha C. Nussbaum, Brown University.

This anthology contains excerpts from some thirty-two important seventeenth- and eighteenth-century moral philosophers. Including a substantial introduction and extensive bibliographies, the anthology facilitates the study and teaching of early modern moral philosophy in its crucial formative period. As well as well-known thinkers such as Hobbes, Hume, and Kant, there are excerpts from a wide range of philosophers never previously assembled in one text, such as Grotius, Pufendorf, Nicole, Clarke, Leibniz, Malebranche, Holbach and Paley. Originally issued as a two-volume edition in (...) 1990, the anthology is now re-issued with a new foreword by Professor Schneewind, as a one-volume anthology to serve as a companion to his highly successful history of modern ethics, The Invention of Autonomy. The anthology provides many of the sources discussed in The Invention of Autonomy and taken together the two volumes will be an invaluable resource for the teaching of the history of modern moral philosophy. (shrink)