What has been the historical relationship between set theory and logic? On the one hand, Zermelo and other mathematicians developed set theory as a Hilbert-style axiomatic system. On the other hand, set theory influenced logic by suggesting to Schröder, Löwenheim and others the use of infinitely long expressions. The questions of which logic was appropriate for set theory - first-order logic, second-order logic, or an infinitary logic - culminated in a vigorous exchange between Zermelo and Gödel around 1930.

Hilbert’s unpublished 1917 lectures on logic, analyzed here, are the beginning of modern metalogic. In them he proved the consistency and Post-completeness (maximal consistency) of propositional logic -results traditionally credited to Bernays (1918) and Post (1921). These lectures contain the first formal treatment of first-order logic and form the core of Hilbert’s famous 1928 book with Ackermann. What Bernays, influenced by those lectures, did in 1918 was to change the emphasis from the consistency and Post-completeness of a logic to its (...) soundness and completeness: a sentence is provable if and only if valid. By 1917, strongly influenced by PM, Hilbert accepted the theory of types and logicism -a surprising shift. But by 1922 he abandoned the axiom of reducibility and then drew back from logicism, returning to his 1905 approach of trying to prove the consistency of number theory syntactically. (shrink)

This paper combines personal reminiscences of the philosopher John Corcoran with a discussion of certain conflicts between historians of logic and philosophers of logic. Some mistaken claims about the history of the Bolzano-Weierstrass Theorem are analyzed in detail and corrected.

What gave rise to Ernst Zermelo's axiomatization of set theory in 1908? According to the usual interpretation, Zermelo was motivated by the set-theoretic paradoxes. This paper argues that Zermelo was primarily motivated, not by the paradoxes, but by the controversy surrounding his 1904 proof that every set can be wellordered, and especially by a desire to preserve his Axiom of Choice from its numerous critics. Here Zermelo's concern for the foundations of mathematics diverged from Bertrand Russell's on the one hand (...) and from Felix Hausdorff's on the other. (shrink)

This paper explores how the Generalized Continuum Hypothesis (GCH) arose from Cantor's Continuum Hypothesis in the work of Peirce, Jourdain, Hausdorff, Tarski, and how GCH was used up to Gödel's relative consistency result.

This volume shows Russell in transition from a neo-Kantian and neo-Hegelian philosopher to an analytic philosopher of the first rank. During this period his research centred on writing The Principles of Mathematics where he drew together previously unpublished drafts. These shed light on Russell's paradox. This material will alter previous accounts of how he discovered his paradox and the related paradox of the largest cardinal. The volume also includes a previously unpublished draft of an early attempt to solve his paradox, (...) as well as the earliest known version of his generalised relation arithmetic. It contains three articles which have never previously been published in English. (shrink)

This volume of Bertrand Russell's _Collected Papers_ finds Russell focused on writing _Principia Mathematica_ during 1905–08. Eight previously unpublished papers shed light on his different versions of a substitutional theory of logic, with its elimination of classes and relations, during 1905-06. A recurring issue for him was whether a type hierarchy had to be part of a substitutional theory. In mid-1907 he began writing up the final version of _Principia_, now using a ramified theory of types, and eleven unpublished drafts (...) from 1907-08 deal with this. Numerous letters show his thoughts on the process. The volume's 80-page introduction covers the evolution of his logic from 1896 until 1909, when volume I of _Principia _went to the printer. (shrink)

The first part of the book investigates Nietzsche's knowledge and understanding of specific disciplines and the influence of particular scientists on Nietzsche ...

Peter Abelard (1079–1142 ce) was the most wide‐ranging philosopher of the twelfth century. He quickly established himself as a leading teacher of logic in and near Paris shortly after 1100. After his affair with Heloise, and his subsequent castration, Abelard became a monk, but he returned to teaching in the Paris schools until 1140, when his work was condemned by a Church Council at Sens. His logical writings were based around discussion of the “Old Logic”: Porphyry's Isagoge, aristotle'S Categories and (...) On Interpretation and boethius'S textbook on topical inference. They comprise a freestanding Dialectica (“Logic”; probably c.1116), a set of commentaries (known as the Logica [Ingredientibus], c. 1119) and a later (c. 1125) commentary on the Isagoge (Logica Nostrorum Petititoni Sociorum or Glossulae). In a work Abelard called his Theologia, issued in three main versions (between 1120 and c.1134), he attempted a logical analysis of trinitarian relations and explored the philosophical problems surrounding God's claims to omnipotence and omniscience. The Collationes (“Debates,” also known as “Dialogue between a Christian, a Philosopher and a Jew”; probably c.1130) present a rational investigation into the nature of the highest good, in which the Christian and the Philosopher (who seems to be modeled on a philosopher of pagan antiquity) are remarkably in agreement. The unfinished Scito teipsum (“Know thyself,” also known as the “Ethics”; c.1138) analyses moral action. (shrink)

Individualism is one of most criticized and least understood ideas in social and political thought. Is individualism the ability to act independently amidst a web of social forces? A vital element of personal liberty and a shield against conformity? Does it lead to or away from unifying individuals with communities? Individualism: A Reader provides a wealth of illuminating essays from the 17th to the early 20th centuries. In 26 selections from 25 writers individualism is explained and defended, often from unusual (...) perspectives. This anthology includes not only selections from well-known writers, but also many lesser-known pieces--reprinted here for the first time--by philosophers, social theorists, and economists who have been overlooked in standard accounts of individualism. The depth and complexity of ideas about individualism are reflected in the six sections in this collection. The first examines individuality generally, with the following five detailing social, moral, political, religious, and economic individualism. Throughout, individualism is analyzed and defended through the lenses of classical liberalism, free-market libertarianism, individual anarchism, voluntary socialism, religious individualism, abolitionism, free thought, and radical feminism. Both richly historical and sharply contemporary, Individualism: A Reader provides a multitude of perspectives and insights on personal liberty and the history of freedom. (shrink)

Offers a critical evaluation of the foundational assumptions and claims, scriptural, theological and philosophical, of John Hick's theocentric critique of the Christian affirmation of Jesus' uniqueness.

While experience often affords important knowledge and insight that is difficult to garner through observation or testimony alone, it also has the potential to generate conflicts of interest and unrepresentative perspectives. We call this tension the paradox of experience. In this paper, we first outline appeals to experience made in debates about access to unproven medical products and disability bioethics, as examples of how experience claims arise in bioethics and some of the challenges raised by these claims. We then motivate (...) the idea that experience can be an asset by appealing to themes in feminist and moral epistemology, distinguishing between epistemic and justice-based appeals. Next, we explain the concern that experience may be a liability by appealing to empirical work on cognitive biases and theoretical work about the problem of partial representation. We conclude with preliminary recommendations for addressing the paradox and offer several questions for future discussion. (shrink)

Elite U.S.-based global law firms concentrate in the costliest districts of superstar cities, especially two neighborhoods in Manhattan. This pattern has persisted despite both the dispersal of Biglaw clients across less-dense, lower-cost U.S. geographies and the development of telework capacity. It suggests a puzzle: law is among the occupations most conducive to remote work, yet Biglaw prior to the coronavirus pandemic required in-person work in the priciest places—meaning it paid a premium on both of its biggest expenses, wages and real (...) estate. How might this equilibrium be explained, and what might lead it to change? This Article contends that Biglaw clustering reflects a management preference for the exploitation of proven strategies over the exploration of novel and uncertain ones—but that the pandemic telework experience is eroding this dichotomy. This analysis has direct implications for private international law practice, where large-scale transactions and disputes are handled by Biglaw firms and involve significant international travel. This Article contributes to a growing literature on telework’s impacts on cities, labor markets, and industries, and is the first to extend that focus to Biglaw and PIL. A post-pandemic Biglaw embrace of dispersal via telework would destabilize standard accounts of collaboration in agglomeration economies. While the Article expresses skepticism about that outcome, it identifies a mechanism by which it might plausibly come about. Crucially, this mechanism—the replacement of an exploit vs. explore choice with two different exploit options—posits as the key driver not technology but management learning and innovation that quickened during the pandemic. (shrink)

Prior to the end of the Cold War, the word 'democracy' was rarely used by international lawyers. Few international organisations supported democratic governance, and the criteria for recognition of governments took little account of whether regimes enjoyed a popular mandate. But the events of 1989–1991 profoundly shook old assumptions. Democratic Governance and International Law attempts to assess international law's new-found interest in fostering transitions to democracy. Is an entitlement to democratic government now emerging in international law? If so, what are (...) its normative foundations? How have global and regional organisations encouraged transitions to democracy, and are their efforts consistent with their constitutional frameworks? How should international law react to elections in which profoundly anti-democratic parties win the vote? In this volume, leading legal scholars grapple with these and other questions to assess the future of international law on this most domestic of questions. (shrink)

Starting with the Apollonian Greek theory of techne, Means Without End presents a history of transformations of ideas about technology, viewed within their broader philosophical, theological, and scientific contexts. Critically focusing on the ideological genealogy of technology without limits and finding its cultural roots in Christian theology, it details ideological developments in the Renaissance, Enlightenment, and 19th century which prepared the way for a theory of autonomous technology and for postmodern technoculture in the 20th century.

To find more information on Rowman & Littlefield titles, please visit us at www.rowmanlittlefield.com.

Singularity Hypotheses: A Scientific and Philosophical Assessment offers authoritative, jargon-free essays and critical commentaries on accelerating technological progress and the notion of technological singularity. It focuses on conjectures about the intelligence explosion, transhumanism, and whole brain emulation. Recent years have seen a plethora of forecasts about the profound, disruptive impact that is likely to result from further progress in these areas. Many commentators however doubt the scientific rigor of these forecasts, rejecting them as speculative and unfounded. We therefore invited prominent (...) computer scientists, physicists, philosophers, biologists, economists and other thinkers to assess the singularity hypotheses. Their contributions go beyond speculation, providing deep insights into the main issues and a balanced picture of the debate. (shrink)

Volume 20, Issue 2, February 2020, Page 66-68.

Hastings Center Report, Volume 52, Issue 1, Page 42-50, January/February 2022.

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:The Cambridge Companion to Bertrand RussellPeter H. DentonNicholas Griffin, editor. The Cambridge Companion to Bertrand Russell. New York: Cambridge University Press, 2003. Pp. xvii + 550. Cloth, $75.00. Paper, $26.00.It is a daunting task to conceive of a single companion to Bertrand Russell, who in life as in thought was never content with a single anything. Nicholas Griffin has brought his customary expertise to the project, and in (...) snaring fourteen other contributors to this volume, has produced a welcome addition to an academic's library of Russell materials.The shape of the volume, its contents and its presentation, however, unfortunately reflect the lopsided nature of current Russell studies. One hopes for a companion volume that has the breadth of the earlier volume edited fifty years ago by Paul Schilpp, but in vain. This book is overwhelmingly about Russell before 1918, almost entirely about philosophy of mathematics, epistemology and logic, and several of the pieces easily could have been included in a festschrift for Frege instead.What is included is well done, but to call it "the most convenient and accessible guide to Russell available" is to speak in comparative terms. To be fair, it sets out to focus on a narrow definition of Russell's contributions to modern philosophy, and the contributors accomplish this task. Ian Grattan-Guinness writes on "Mathematics in and behind Russell's Logicism, and its Reception," a subject that continues into "Bertrand Russell's Logicism" by Martin Godwyn and Andrew D. Irvine. The roots of analytic philosophy are of primary concern in this volume, so Richard L. Cartwright explores "Russell and Moore, 1898-1905" and Michael Beaney relates "Russell and Frege." "The Theory of Descriptions" by Peter Hylton sets up two pieces on "Russell's Substitutional Theory" (Gregory Landini) and "The Theory of Types" (Alasdair Urquhart), while Paul Hager's "Russell's Method of Analysis" leads into "Russell's Neutral Monism" (R.E.Tully) and "The Metaphysics of Logical Atomism" (Bernard Linsky).The next portion of the book expands the intellectual focus somewhat, with "Russell's Structuralism and the Absolute Description of the World" by William Demopoulos—perhaps [End Page 349] the best in a series of good papers—and "From Knowledge by Acquaintance to Knowledge by Causation" by Thomas Baldwin. Approaching the end of the book, Anthony Grayling's essay on "Russell, Experience, and the Roots of Science" remains firmly planted in the pre-1918 milieu, though his tentative commentary on Human Knowledge at least glimmers the extension of Russell's intellectual life into the post-Great War period.Effectively the entire second half of Russell's life is left to the final contributor, Charles Pidgen, for commentary. Author of Russell on Ethics, much of Pigden's short essay here ("Bertrand Russell: Moral Philosopher or Unphilosophical Moralist?") somewhat plaintively directs the reader to his book for an elaboration of why Russell is worth reading after 1918, at least on the subject of ethics. Of the other authors, only Hager (317) observes the extent to which Russell's post-War work mistakenly has been ignored.The book concludes with a selective bibliography. The audience, for the most part, is a specialist one, with only some essays accessible to the general reader. On that score, Griffin's introduction and his own essay, "Russell's Philosophical Background," are easily the most readable. At the risk of quibbling, I was disturbed by the uneven production of the book, as each author set his own standard for footnotes, endnotes and bibliography (creating a jumble of styles). Even within individual contributions, there are a number of inconsistencies in notation as well as typographical errors.By the end, I was left hoping there might be a second companion volume for Bertrand Russell, one that reflects what he spent the last fifty years of his life thinking, writing, and doing. In the absence of such material (which is of far greater popular interest today just as it was in Russell's lifetime), this book by itself is more of a companion to current Russell studies than to Bertrand Russell himself.Peter H. DentonThe University of WinnipegCopyright © 2004 Journal of the History of Philosophy, Inc.... (shrink)

In response to a drying climate, an integrated property planning tool was developed over three years to help landowners make better use of available rainfall. A sequence was identified which indicated how parts of each property are affected by soil moisture limitations. The sequence was combined with soil properties to indicate targeted strategies for each location aimed to improve soil moisture availability, biomass utilisation, and long-term viability of the farm or ranching enterprise. As a result of training of land owners (...) and operators in use of this tool, 97% of participants indicated that they have begun or intend to make changes in land management; 78% are intending to make three or more substantial changes; and 91% felt better prepared for the impacts of climate change. The key to the success of this technique is that it identifies critical sustainable production drivers in a simple plan format and offers tailored management options which can address more variable climate conditions. The integrated planning tool has application as a driver of climate change adaptation in agricultural regions where farm units contain substantial landscape variation and seasonal rainfall is frequently limiting to production. (shrink)

An important application of cognitive architectures is to provide human performance models that capture psychological mechanisms in a form that can be “programmed” to predict task performance of human–machine system designs. Although many aspects of human performance have been successfully modeled in this approach, accounting for multitalker speech task performance is a novel problem. This article presents a model for performance in a two-talker task that incorporates concepts from psychoacoustics, in particular, masking effects and stream formation.

Introduction: What is the critical spirit?--Utopianism, ancient and modern, by M.I. Finley.--Primitive society in its many dimensions, by S. Diamond.--Manicheanism in the Enlightenment, by R.H. Popkin.--Schopenhauer today, by M. Horkheimer.--Beginning in Hegel and today, by K.H. Wolff.--The social history of ideas: Ernst Cassirer and after, by P. Gay.--Policies of violence, from Montesquieu to the Terrorist, by E.V. Walter.--Thirty-nine articles: toward a theory of social theory, by J.R. Seeley.--History as private enterprise, by H. Zinn.--From Socrates to Plato, by H. Meyerhoff.--Rational society (...) and irrational art, by H. Read.--The quest for the Grail; Wagner and Morris, by C.E. Schorske.--Valéry; Monsieur Teste, by L. Goldmann.--History and existentialism in Sartre, by L. Krieger.--German popular biographies; culture's bargain counter, by L. Lowenthal.--The Rechtsstaat as magic wall, by O. Kirchheimer. (shrink)

Bibliographical footnotes. Introduction: What is the critical spirit?--Utopianism, ancient and modern, by M.I. Finley.--Primitive society in its many dimensions, by S. Diamond.--Manicheanism in the Enlightenment, by R.H. Popkin.--Schopenhauer today, by M. Horkheimer.--Beginning in Hegel and today, by K.H. Wolff.--The social history of ideas: Ernst Cassirer and after, by P. Gay.--Policies of violence, from Montesquieu to the Terrorist, by E.V. Walter.--Thirty-nine articles: toward a theory of social theory, by J.R. Seeley.--History as private enterprise, by H. Zinn.--From Socrates to Plato, by H. (...) Meyerhoff.--Rational society and irrational art, by H. Read.--The quest for the Grail; Wagner and Morris, by C.E. Schorske.--ValeÌ ry; Monsieur Teste, by L. Goldmann.--History and existentialism in Sartre, by L. Krieger.--German popular biographies; culture's bargain counter, by L. Lowenthal.--The Rechtsstaat as magic wall, by O. Kirchheimer. Revolution from above: some notes on the decision to collectivize Soviet agriculture, by E.H. Carr.--Winston Churchill, power politician and counter revolutionary, by A.J. Mayer.--Brahmins and business, 1870-1914; a hypothesis on the social basis of success in American history, by G. Kolko.--On the limits of professional thought, by M.R. Stein.--The limits of integration, by P. Mattick.--The society nobody wants; a look beyond Marxism and liberalism.--Marcuse as teacher, by W. Leiss, J.D. Ober and E. Sherover.--Marcuse bibliography, by W. Leiss, J.D. Ober and E. Sherover (p. 427-433). (shrink)