First-order logic. The origin of modern foundational studies. Frege's system and the paradoxes. The teory of types. Zermelo-Fraenkel set theory. Hilbert's program and Godel's incompleteness theorems. The foundational systems of W.V. Quine. Categorical algebra.

This book presents and survey of the foundations of mathematics. The emphasis is on a mathematical comparison of systems rather than on any exhaustive development of analysis within a single system. Nevertheless, for most systems considered, enough details are given for the development of arithmetic, and the method of constructing the other notions of analysis is indicated. The elements of the general theory of cardinal and ordinal numbers are also furnished in the course of this work.

The late Dr. William Hatcher was renowned both as an accomplished mathematician, logician and philosopher, and as one of the world?s foremost Bahá?í scholars. To those who knew him, he was also refreshingly approachable, supportive, honest and engaging. In this small but richly insightful volume, modern mathematics and logic meet religion and philosophy in a new and stimulating way. The five essays are entitled: "Platonism and Pragmatism", "Myths, Models and Mysticism", "From Metaphysics to Logic", "A Logical Solution to (...) the Problem of Evil", and "Science and the Bahá?í Faith" With characteristic originality, Dr. Hatcher explores the interface between these disciplines now approaching each other after centuries of mutual mistrust. These valuable intellectual contributions assist the reader to bring into closer harmony the two ultimate realms expressive of essential human nature - namely that of science and of religion. (shrink)

With fascinating insight, Love, Power, and Justice explores issues of authentic morality using precepts and arguments from philosophy, science and religion, as well as the profound concepts contained in the Baha'i revelation. This work, now in its second edition, is an innovative contribution to one of the more intractable debates of our time--a time when so many different factions and individuals each claim to speak with moral authority.

This work is an essay in Peirce's epistemology, with about an equal emphasis on the "epistemology" as on the "Peirce's." In other words our intention has not been to write exclusively a piece of Peirce scholarshiJ> hence, the reader will find no elaborate tying in of Peirce's epistemology to other portions of his thought, no great emphasis on the chronology of his thought, etc. Peirce scholarship is a painstaking business. His mind was Labyrinthine, his terminology intricate, and his writings are, (...) as he himself confessed, "a snarl of twine." This book rather is intended perhaps even primarily as an essay in epistemology, taking Peirce's as the focal point. The book thus addresses a general philosophical audience and bears as much on the wider issue as on the man. I hope therefore that readers will give their critical attention to the problem of knowledge and the sugges tions we have developed around that problem and will not look here in the hope of finding an exhaustive piece of Peirce scholarship. (shrink)

This book is the result of a discontent on my part with (r) the super ficial and offhand way many determinists set forth their arguments, without the slightest hint of the difficulties which have been raised against those arguments, and (2) the fact that the chief and best argu ments of the libertarians are scattered allover the literature and are seldom if ever brought together in one package. may be taken as an effort to gather into one place Mostly this (...) work and to express as cogently as possible the arguments for freewill. So far as I know all of the arguments we treat have been made before. Only toward the end of this work do I attempt to elaborate a point not heretofore emphasized. That point is that freedom of the will is a concept intimately entangled with the human power to reason, so that if one of these powers goes, the other must also go. Moreover, both the will and the reason are intimately tied up with our moral sensitivities, so that no one of these phenomena is intelligible without the others. Hints of these ideas abound, of course, in the literature, and the degree of originality claimed is minimal. The interconnections, however, between these three basic concepts of the will, the reason, and the good, are of such great importance and are so usually ignored that I feel our short statement of the situation warrants the reader's sympathetic attention. (shrink)

Chapin reviewed this 1972 ZEITSCHRIFT paper that proves the completeness theorem for the logic of variable-binding-term operators created by Corcoran and his student John Herring in the 1971 LOGIQUE ET ANALYSE paper in which the theorem was conjectured. This leveraging proof extends completeness of ordinary first-order logic to the extension with vbtos. Newton da Costa independently proved the same theorem about the same time using a Henkin-type proof. This 1972 paper builds on the 1971 “Notes on a Semantic Analysis of (...) Variable Binding Term Operators” (Co-author John Herring), Logique et Analyse 55, 646–57. MR0307874 (46 #6989). A variable binding term operator (vbto) is a non-logical constant, say v, which combines with a variable y and a formula F containing y free to form a term (vy:F) whose free variables are exact ly those of F, excluding y. Kalish-Montague 1964 proposed using vbtos to formalize definite descriptions “the x: x+x=2”, set abstracts {x: F}, minimization in recursive function theory “the least x: x+x>2”, etc. However, they gave no semantics for vbtos. Hatcher 1968 gave a semantics but one that has flaws described in the 1971 paper and admitted by Hatcher. In 1971 we give a correct semantic analysis of vbtos. We also give axioms for using them in deductions. And we conjecture strong completeness for the deductions with respect to the semantics. The conjecture, proved in this paper with Hatcher’s help, was proved independently about the same time by Newton da Costa. (shrink)

While perhaps best known for his Lives, Plutarch also wrote philosophical dialogues that constitute a major intellectual legacy from the first century A.D. This collection presents two important short works from his writings in moral philosophy. They reveal Plutarch at his best--informative, sympathetic, rich in narrative--and are accompanied by an extensive commentary that situates Plutarch and his views on marriage in their historical context.

Experiential acquaintance is an alleged relation between ourselves and our experiences that has sometimes been hypothesised as necessary for knowledge of our experiences. This paper begins with a clarification of ‘acquaintance’ and an explanation of ‘experience’ that focuses attention on a famous, but flawed, argument by G. E. Moore. It goes on to critically examine several recent arguments concerning experiential acquaintance and to show how internalist foundationalism can respond to a famous Sellarsian dilemma without appeal to a relation of acquaintance (...) with our experiences. It concludes that we can dispense with experiential acquaintance. (shrink)

The logical properties of the 'if-then' connective of ordinary English differ markedly from the logical properties of the material conditional of classical, two-valued logic. This becomes apparent upon examination of arguments in conversational English which involve (noncounterfactual) usages of if-then'. A nonclassical system of propositional logic is presented, whose conditional connective has logical properties approximating those of 'if-then'. This proposed system reduces, in a sense, to the classical logic. Moreover, because it is equivalent to a certain nonstandard three-valued logic, its (...) decision procedure is almost as efficient as that of the classical logic. It therefore provides a rational and convenient system in which to formalize English arguments. (shrink)

The formal systems of logic have ordinarily been regarded as independent of biology, but recent developments in evolutionary theory suggest that biology and logic may be intimately interrelated. In this book, William Cooper outlines a theory of rationality in which logical law emerges as an intrinsic aspect of evolutionary biology. This biological perspective on logic, though at present unorthodox, could change traditional ideas about the reasoning process. Cooper examines the connections between logic and evolutionary biology and illustrates how logical (...) rules are derived directly from evolutionary principles, and therefore have no independent status of their own. Laws of decision theory, utility theory, induction, and deduction are reinterpreted as natural consequences of evolutionary processes. Cooper's connection of logical law to evolutionary theory ultimately results in a unified foundation for an evolutionary science of reason. It will be of interest to professionals and students of philosophy of science, logic, evolutionary theory, and cognitive science. (shrink)

Critics of SRI have said little about the integrity of corporate representations resulting in screening inclusion or exclusion. This is surprising given social and environmental accounting research that finds corporate posturing and deception in the absence of external verification, and a parallel body of literature describing corporate "greenwashing" and other forms of corporate disinformation. In this paper I argue that the problems and challenges of ensuring fair and accurate corporate social reporting mirror those accompanying corporate compliance with law. Similarities and (...) points of convergence between social reporting and corporate compliance are discussed, along with proposals for reform. (shrink)

This paper traces the intellectual development of the workplace privacy construct in the course of American thinking. The role of technological development in this process is examined, particularly in regard to the information gathering/dissemination dilemmas faced by employers and employees alike. The paper concludes with some preliminary considerations toward a theory of workplace privacy.

Plato's Sophist provides a careful translation of the Sophist, one of Plato's most complex and difficult dialogues, and includes materials designed to facilitate its usefulness as a text in college courses. The translation employs a minimum of interpretative paraphrasing while being presented in clear, readable English. Special attention has been given to consistency in translating key Greek terms. The book presents a special list of these terms and discusses them in the endnotes. The result is a translation that enables the (...) reader who lacks a knowledge of Greek to get much closer than usual to the original text. Cobb's introduction contains a detailed summary of the entire dialogue, clarifying the main themes and the general structure. He offers a fresh interpretation of the dialogue that shows how each theme contributes to the exploration of the nature of, and the relation between, philosophy and sophistry. The introduction is particularly useful to first readers of the Sophist. (shrink)

In the interval between the time of the Reformation and today, large numbers of Christians seem quietly to have shifted their allegiance from one God to another, leaving themselves with the doctrine of the Trinity but no longer retaining the God whom it adumbrates.