One of the greatest revolutions in mathematics occurred when Georg Cantor (1845-1918) promulgated his theory of transfinite sets.

One of the greatest revolutions in mathematics occurred when Georg Cantor promulgated his theory of transfinite sets. This revolution is the subject of Joseph Dauben's important studythe most thorough yet writtenof the philosopher and mathematician who was once called a "corrupter of youth" for an innovation that is now a vital component of elementary school curricula.Set theory has been widely adopted in mathematics and philosophy, but the controversy surrounding it at the turn of the century remains of great (...) interest. Cantor's own faith in his theory was partly theological. His religious beliefs led him to expect paradoxes in any concept of the infinite, and he always retained his belief in the utter veracity of transfinite set theory. Later in his life, he was troubled by recurring attacks of severe depression. Dauben shows that these played an integral part in his understanding and defense of set theory. (shrink)

K. T. Fann, Ludwig Wittgenstein: the man and his philosophy. New Jersey, Humanities Press; Sussex, Harvester Press: 1967. 415 pp. 10.50.Gerd Brand, The central texts of Ludwig Wittgenstein. Translated and with an introduction by Robert E. Innis. Oxford: Basil Blackwell, 1979. xxv + 182 pp. £ 10.00 /£3.95.Joseph Warren Dauben. Georg Cantor: his mathematics and philosophy of the infinite. Cambridge, Mass., and London: Harvard University Press, 1979. xiii + 404 pp., 4 plts. $25 US.S. Poggi, I sistemi (...) dell'esperienza. Psicologia, logica e teoria della scienza da Kant a Wundt. Bologna: il Mulino, 1977.679 pp., Lit. 12.000.Raymond Bradley and Norman Swartz, Possible Worlds. An introduction to logic and its philosophy. Indianapolis and New York; Hackett Publishing Company: Oxford; Blackwell: 1979. xxi + 391 pp. £15.00 /£4.95.S. Haack, Philosophy of logics. Cambridge and New York: Cambridge University Press, 1978. xiv + 276 pp. £ 13.50.F. J. Pelletier, Mass terms: some philosophicalproblems. Dordrecht, Boston and London: Reidel, 1979. xiii + 303 pp. Dfl. 70/$34.00.Theo A. F. Kuipers, Studies in inductive probability and rational expectation. Dordrecht, Holland and Boston, USA.: D. Reidel Publishing Company, 1978. xii + 145 pp. Dfl. 50/$22.50. (shrink)

I first met Ivor Grattan-Guinness and his wife Enid in the late summer of 1970. I was in England following an intensive course in German at the Goethe Institute in Prien am Chiemsee, and had arrang...

The term "fuzzy logic," as it is understood in this book, stands for all aspects of representing and manipulating knowledge based on the rejection of the most fundamental principle of classical logic---the principle of bivalence. According to this principle, each declarative sentence is required to be either true or false. In fuzzy logic, these classical truth values are not abandoned. However, additional, intermediate truth values between true and false are allowed, which are interpreted as degrees of truth. This opens a (...) new way of thinking---thinking in terms of degrees rather than absolutes. For example, it leads to the definition of a new kind of sets, referred to as fuzzy sets, in which membership is a matter of degree. The book examines the genesis and development of fuzzy logic. It surveys the prehistory of fuzzy logic and inspects circumstances that eventually lead to the emergence of fuzzy logic. The book explores in detail the development of propositional, predicate, and other calculi that admit degrees of truth, which are known as fuzzy logic in the narrow sense. Fuzzy logic in the broad sense, whose primary aim is to utilize degrees of truth for emulating common-sense human reasoning in natural language, is scrutinized as well. The book also examines principles for developing mathematics based on fuzzy logic and provides overviews of areas in which this has been done most effectively. It also presents a detailed survey of established and prospective applications of fuzzy logic in various areas of human affairs, and provides an assessment of the significance of fuzzy logic as a new paradigm. (shrink)

ABSTRACT:U.S. Organizational Sentencing Guidelines provide firms with incentives to develop formal ethics programs to promote ethical organizational cultures and thereby decrease corporate offenses. Yet critics argue such programs are cosmetic. Here we studied bank employees before and after the introduction of formal ethics training—an important component of formal ethics programs—to examine the effects of training on ethical organizational culture. Two years after a single training session, we find sustained, positive effects on indicators of an ethical organizational culture (observed unethical behavior, (...) intentions to behave ethically, perceptions of organizational efficacy in managing ethics, and the firm’s normative structure). While espoused organizational values also rose in importance post-training, the boost dissipated after the second year which suggests perceptions of values are not driving sustained behavioral improvements. This finding conflicts with past theory which asserts that enduring behavioral improvements arise from the inculcation of organizational values. Implications for future research are discussed. (shrink)

ABSTRACT:U.S. Organizational Sentencing Guidelines provide firms with incentives to develop formal ethics programs to promote ethical organizational cultures and thereby decrease corporate offenses. Yet critics argue such programs are cosmetic. Here we studied bank employees before and after the introduction of formal ethics training—an important component of formal ethics programs—to examine the effects of training on ethical organizational culture. Two years after a single training session, we find sustained, positive effects on indicators of an ethical organizational culture (observed unethical behavior, (...) intentions to behave ethically, perceptions of organizational efficacy in managing ethics, and the firm’s normative structure). While espoused organizational values also rose in importance post-training, the boost dissipated after the second year which suggests perceptions of values are not driving sustained behavioral improvements. This finding conflicts with past theory which asserts that enduring behavioral improvements arise from the inculcation of organizational values. Implications for future research are discussed. (shrink)

Charles Sanders Peirce: A Life. Joseph Brent; The Promise of Pragmatism: Modernism and the Crisis of Knowledge and Authority. John Patrick Diggins; Charles S. Peirce's Evolutionary Philosophy. Carl R. Hausman; Charles S. Peirce and the Philosophy of Science: Papers from the Harvard Sesquicentennial Congress. Edward C. Moore; Reasoning and the Logic of Things: The Cambridge Conferences Lectures of 1898. Charles Sanders Peirce, Kenneth Laine Ketner; Writings of Charles S. Peirce: A Chronological Edition. Volume 5: 1884-1886. Charles Sanders Peirce, Christian (...) J. W. Kloesel. (shrink)

In December and January of 1983–1984, archaeologists excavating the tomb of an ancient Chinese provincial bureaucrat at a Western Han Dynasty site near Zhangjiashan, in Jiangling county, Hubei Province, discovered a number of books on bamboo strips, including inter alia works on legal statutes, military practice, and medicine. Among these was a previously unknown mathematical work on some 200 bamboo strips, the Suan shu shu, or Book of Numbers and Computations. Based upon other works found in the tomb, especially a (...) copy of the Er nian lü ling (Laws and Decrees of the Second Year (of the reign of empress Lü, i.e. Lü Hou)), archaeologists have dated the tomb to ca. 186 BCE (Lü Hou’s regency lasted from 188 to 180 BCE). The Suan shu shu, as the earliest yet discovered work devoted specifically to mathematics from ancient China, has stirred considerable interest among Chinese historians of science. The translation and commentary offered here draw extensively on the works cited in Sect. 3 below. Several appendixes devoted to specific issues related to translating the Suan shu shu, including its title and the problem of determining English equivalents for various commodities that arise in the text, may be found in Appendix II. (shrink)

This article describes the mystery of a long lost codex of Archimedes that resurfaced briefly at the turn of the last century by Johan Ludwig Heiberg. Long enough for the Danish historian of mathematics Heiberg to identify, photograph and eventually transcribe “The Method” and several other works by Archimedes of considerable mathematical interest. In 1879 Heiberg completed his dissertation, Quaestiones Archimedeae, devoted to Archimedes’ life, works, and transmission of his texts.Este artículo describe el misterio de un códice de Arquímedes perdido (...) hace mucho tiempo que reapareció brevemente a principios del siglo pasado de la mano de Johan Ludwig Heiberg. Tiempo suficiente para que el historiador danés de las matemáticas Heiberg pudiese identificar, fotografiar y, finalmente, transcribir “El Método” y varias otras obras de Arquímedes de interés matemático considerable. En 1879 Heiberg completó su tesis doctoral, Quaestiones Archimedeae, dedicado a la vida de Arquímedes, las obras, y la transmisión de sus textos. (shrink)

I. Bernard Cohen (1914–2003), the first American to receive a Ph.D. in history of science, was a Harvard undergraduate ('37) and then a Ph.D. student and protégé of George Sarton, founder of Isis and the History of Science Society. He went on to succeed Sarton as editor of Isis (1952–1958) and, later, president of the Society (1961–1962); he was also a president of the International Union of the History and Philosophy of Science. Cohen was an internationally recognized Newton scholar; his (...) interests were encyclopedic, ranging from science and public policy to the history of computers, with several decades as a special consultant for history of computing with IBM. Among his hundreds of publications were such major books as Franklin and Newton (1956), The Birth of a New Physics (1959; rpt., 1985), The Newtonian Revolution (1980), Revolution in Science (1985), Science and the Founding Fathers (1995), Howard Aiken: Portrait of a Computer Pioneer (1999), and his last book, The Triumph of Numbers (2005), not to mention two jointly authored contributions, the variorum edition and new English translation of Newton's Principia, which will surely still be read a century from now. (shrink)

ABSTRACT:While tone at the top is widely regarded as an important predictor of ethical behavior in organizations, we argue that recent research overlooks the various conflicting ethical tones present in many multi-organizational work settings. Further, we propose that the resolution processes promulgated in many firms and professional associations to reconcile this conflict reinforce the tone at the bottom or a tone at the top of the employee’s organization, and that both of these approaches can conflict with the tone at the (...) top of other important organizations such as professional and regulatory organizations. Here we adapt Integrative Social Contract Theory’s priority rules to propose a multi-tone reconciliation process which prioritizes conflicting ethical tones based upon features of the organization and the effects on society. Using three contextualizations, we demonstrate the effectiveness of the multi-tone reconciliation process over current processes. We conclude with recommendations for future research and implications for practice. (shrink)