While we are commonly told that the distinctive method of mathematics is rigorous proof, and that the special topic of mathematics is abstract structure, there has been no agreement among mathematicians, logicians, or philosophers as to just what either of these assertions means. John P. Burgess clarifies the nature of mathematical rigor and of mathematical structure, and above all of the relation between the two, taking into account some of the latest developments in mathematics, including the rise of experimental (...) mathematics on the one hand and computerized formal proofs on the other hand. Along the way, a great many historical developments in mathematics, philosophy, and logic are surveyed. Yet very little in the way of background knowledge on the part of the reader is presupposed. (shrink)

Darwinism, Democracy, and Race examines the development and defence of an argument that arose at the boundary between anthropology and evolutionary biology in twentieth-century America. In its fully articulated form, this argument simultaneously discredited scientific racism and defended free human agency in Darwinian terms. The volume is timely because it gives readers a key to assessing contemporary debates about the biology of race. By working across disciplinary lines, the book's focal figures--the anthropologist Franz Boas, the cultural anthropologist Alfred Kroeber, the (...) geneticist Theodosius Dobzhansky, and the physical anthropologist Sherwood Washburn--found increasingly persuasive ways of cutting between genetic determinist and social constructionist views of race by grounding Boas's racially egalitarian, culturally relativistic, and democratically pluralistic ethic in a distinctive version of the genetic theory of natural selection. Collaborators in making and defending this argument included Ashley Montagu, Stephen Jay Gould, and Richard Lewontin. Darwinism, Democracy, and Race will appeal to advanced undergraduates, graduate students, and academics interested in subjects including Philosophy, Critical Race Theory, Sociology of Race, History of Biology and Anthropology, and Rhetoric of Science. (shrink)

This book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Saul Kripke has made fundamental contributions to a variety of areas of logic, and his name is attached to a corresponding variety of objects and results. 1 For philosophers, by far the most important examples are ‘Kripke models’, which have been adopted as the standard type of models for modal and related non-classical logics. What follows is an elementary introduction to Kripke’s contributions in this area, intended to prepare the reader to tackle more formal treatments elsewhere.2 2. WHAT IS A (...) MODEL THEORY? Traditionally, a statement is regarded as logically valid if it is an instance of a logically valid form, where a form is regarded as logically valid if every instance is true. In modern logic, forms are represented by formulas involving letters and special symbols, and logicians seek therefore to define a notion of model and a notion of a formula’s truth in a model in such a way that every instance of a form will be true if and only if a formula representing that form is true in every model. Thus the unsurveyably vast range of instances can be replaced for purposes of logical evaluation by the range of models, which may be more tractable theoretically and perhaps practically. Consideration of the familiar case of classical sentential logic should make these ideas clear. Here a formula, say (p & q) ∨ ¬p ∨ ¬q, will be valid if for all statements P.. (shrink)

In 1974, John P. "Jack" Murtha became the first Vietnam combat veteran elected to Congress. In the nearly three decades since then, Congressman Murtha has been intimately involved with governmental decisions about America's national security and foreign policy, adding his unique perspective to international affairs while faithfully representing Pennsylvania's twelfth district. _From Vietnam to 9/11 _combines personal memoir with thoughtful analysis to provide a behind-the-scenes account of the formation and conduct of U.S. foreign policy in the last quarter-century. At (...) the same time, it tells the story of a man committed to service and community. (shrink)

Prima facie it seems easy to understand what he had in mind when he spoke of accidental being and being as true. Accidental or incidental being, what the Latins would later call ens per accidens, was in fact a juxtaposition of two or more categorical beings. As such it lacked a unified essence and thus it lacked genuine being. It was being "only in name." Being as true, he told us, was in the synthesis of the intellect, that is, the (...) intellect's second operation of judgment. Apparently, it was the being of the copula "is" in a true judgment. Contrasted with this was being as false, or pseudo-being, which strictly is nonbeing, found in the copula of a false judgment. (shrink)

What were Shakespeare's final thoughts on history, tragedy, and comedy? Shakespeare's Last Plays focuses much needed scholarly attention on Shakespeare's "Late Romances." The work--a collection of newly commissioned essays by leading scholars of classical political philosophy and literature--offers careful textual analysis of Pericles, Prince of Tyre, Cymbeline, The Winter's Tale, The Tempest, All is True, and The Two Noble Kinsmen. The essays reveal how Shakespeare's thought in these final works compliments, challenges, fulfills, or transforms previously held conceptions of the playwright (...) and his political-philosophical views. (shrink)

It is a fact of modern scientific thought that there is an enormous variety of logical systems - such as classical logic, intuitionist logic, temporal logic, and Hoare logic, to name but a few - which have originated in the areas of mathematical logic and computer science. In this book the author presents a systematic study of this rich harvest of logics via Tarski's well-known axiomatization of the notion of logical consequence. New and sometimes unorthodox treatments are given of the (...) underlying principles and construction of many-valued logics, the logic of inexactness, effective logics, and modal logics. Throughout, numerous historical and philosophical remarks illuminate both the development of the subject and show the motivating influences behind its development. Those with a modest acquaintance of modern formal logic will find this to be a readable and not too technical account which will demonstrate the current diversity and profusion of logics. In particular, undergraduate and postgraduate students in mathematics, philosophy, computer science, and artificial intelligence will enjoy this introductory survey of the field. (shrink)

In order to sketch an account of a moral commitment to persons as such, the essay examines empathy, sympathy, and benevolence as they arise first in special relations and then are reconstructed to include the stranger under the rubric of "extensive benevolence" or "universal love." The account, the author argues, must deal with conceptual empowerment and authorizing reasons, weakness and evil, normative conflict, and the relation of benevolence to justice.

This paper is the third of a multi-part examination of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton, AHES 61:83–145, 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies, accomplished in the construction of the System A lunar theory early in the fourth century B.C. Part II (Britton, AHES 63:357–431, 2009) examines the accomplishment of this separation by the construction of (...) a successful theory depicting the variations due to lunar anomaly in System A and its subsequent adaptation in System B. The present paper examines the introduction of the uniform zodiac, necessary for any theory depicting variations depending on the position of syzygy. It addresses three questions: (1) In light of all available evidence, what is the magnitude of the constant term in the expression Δλ* = C − 1.3828°Y, describing the difference between the Babylonian sidereal longitudes and modern tropical longitudes? (2) What considerations governed the placement of the Babylonian sidereal zodiac relative to the fixed stars? (3) When was the uniform zodiac introduced? To the first question it finds C = 3.20° ± 0.1°, scarcely different from Huber’s (Centaurus 5:192–208, 1958) estimate of 3.08°, essentially confirming Huber’s result obtained from much less data. For the second it shows that accommodating the three asterisms comprising Taurus limited the placement of the zodiac to within 3°, while the prominence of half sign multiples among the measured intervals between prominent Normal Stars led irresistibly to the choice adopted. Finally, it finds that the zodiac was introduced between −408 and −397 and probably within a very few years of −400. (shrink)

The complexity of the set of truths of arithmetic is determined for various theories of truth deriving from Kripke and from Gupta and Herzberger.

The English word 'curriculum' is derived from the Latin word curriculum meaning 'a course', 'a race' or 'a running'. This suggests a process, the idea of going through something which has a beginning, a development and an end. The secondary meaning of curriculum was 'career'. Both the primary and the secondary meanings of curriculum referred to temporal space and to non-temporal endeavours or intellectual pursuits. The expression 'curriculum vitae', then referred to both intellectual and non-intellectual pursuits. Today curriculum in the (...) educational context refers primarily, if not solely, to intellectual pursuits. Actually curriculum is related to learning in a broad sense, incorporating more than the "cognitive" aspect. This suggests that the concept curriculum is a complex notion. Various meanings have been attached to it. A careful analysis of curriculum shows that the notions of "plan", "content or subject matter", "objectives" and "method" are intimately connected to curriculum which should not be completely identified with any one of these concepts. In this short paper I propose to discuss the following question: Is the notion of subject matter inherent in that of curriculum, or, does the notion curriculum make sense without that of subject matter? Answers to this question are meant to help clarify the relationship between the curriculum and subject matter. (shrink)

My contribution to the symposium on Goedel’s philosophy of mathematics at the spring 2006 Association for Symbolic Logic meeting in Montreal. Provisional version: references remain to be added. To appear in an ASL volume of proceedings of the Goedel sessions at that meeting.

By utilizing new information from both clinical and experimental (lesion, electrophysiological, and gene-activation) studies with animals, the anatomy underlying anterograde amnesia has been reformulated. The distinction between temporal lobe and diencephalic amnesia is of limited value in that a common feature of anterograde amnesia is damage to part of an comprising the hippocampus, the fornix, the mamillary bodies, and the anterior thalamic nuclei. This view, which can be traced back to Delay and Brion (1969), differs from other recent models in (...) placing critical importance on the efferents from the hippocampus via the fornix to the diencephalon. These are necessary for the encoding and, hence, the effective subsequent recall of episodic memory. An additional feature of this hippocampalanterior thalamic and the perirhinal–medial dorsal thalamic systems are compromised, leading to severe deficits in both recall and recognition. (shrink)

The increasingly pervasive practice of veiling among Muslim women has stimulated a great deal of scholarly investigation and debate. This study brings empirical evidence to bear on current debates about the meaning of the veil in Islam. This article first examines the conflicting meanings of the veil among Muslim religious elites and Islamic feminists. Although the dominant gender discourse among Muslim elites strongly favors this cultural practice, an antiveiling discourse promulgated by Islamic feminists has gained ground within recent years. This (...) study then examines how these discursive disputes affect gender identity negotiation among veiled and unveiled Muslim women living in Austin, Texas. Interviews with these women highlight how their gender identities reproduce and reformulate existing Muslim gender discourses. Special attention is paid to the subjective disparities and points of congruence between both groups of respondents. This study concludes by suggesting avenues for future research on the intersection of gender, religion, and cultural difference. (shrink)

Saul Kripke has been a major influence on analytic philosophy and allied fields for a half-century and more. His early masterpiece, Naming and Necessity, reversed the pattern of two centuries of philosophizing about the necessary and the contingent. Although much of his work remains unpublished, several major essays have now appeared in print, most recently in his long-awaited collection Philosophical Troubles. In this book Kripke’s long-time colleague, the logician and philosopher John P. Burgess, offers a thorough and self-contained guide (...) to all of Kripke’s published books and his most important philosophical papers, old and new. It also provides an authoritative but non-technical account of Kripke’s influential contributions to the study of modal logic and logical paradoxes. Although Kripke has been anything but a system-builder, Burgess expertly uncovers the connections between different parts of his oeuvre. Kripke is shown grappling, often in opposition to existing traditions, with mysteries surrounding the nature of necessity, rule-following, and the conscious mind, as well as with intricate and intriguing puzzles about identity, belief and self-reference. Clearly contextualizing the full range of Kripke’s work, Burgess outlines, summarizes and surveys the issues raised by each of the philosopher’s major publications. Kripke will be essential reading for anyone interested in the work of one of analytic philosophy’s greatest living thinkers. (shrink)

Cognitive Science, Volume 46, Issue 5, May 2022.

Critics of organ donation after circulatory death (DCD) argue that, even if donors are past the point of autoresuscitation, they have not satisfied the “irreversibility” requirement in the circulatory and respiratory criteria for determining death, since their circulation and respiration could be artificially restored. Thus, removing their vital organs violates the “dead-donor” rule. I defend DCD donation against this criticism. I argue that practical medical-ethical considerations, including respect for do-not-resuscitate orders, support interpreting “irreversibility” to mean permanent cessation of circulation and (...) respiration. Assuming a consciousness-related formulation of human death, I then argue that the loss of circulation and respiration is significant, because it leads to the permanent loss of consciousness and thus to the death of the human person. The DNR request by an organ donor should thus be interpreted to mean “do not restore to consciousness.” Finally, I respond to an objection that if “irreversibility” has a medical-ethical meaning, it would entail the absurd possibility that one of two individuals in the same physical state could be alive and the other dead—an implication that some think is inconsistent with understanding death as an objective biological state of the organism. I argue that advances in medical technology have created phenomena that challenge the assumption that human death can be understood in strictly biological terms. I argue that ethical and ontological considerations about our nature bear on the definition and determination of death and thus on the permissibility of DCD. (shrink)

: In this commentary we engage with Paul’s Transformative Experience as it relates to decision making. We consider why deciding whether to undergo a transformative experiences can feel so agonizing yet also be so fun, whether people have any preferences to decide over in the first place, and who people even think they are. Keywords: Transformative Experience; Big Decisions; Preference Construction; Theory of Self; Mental Effort Decisioni trasformative e relative insoddisfazioni Riassunto: In questo commento ci concentreremo su come il volume (...) di L.A. Paul Transformative Experience affronta i processi decisionali. Esamineremo perché la decisione se intraprendere un’esperienza trasformativa possa risultare così struggente ed essere altresì divertente; se le persone abbiano in assoluto qualche preferenza nel prendere decisioni definitive e chi le persone persone ritengono di essere. Parole chiave: Esperienza trasformativa; Grandi decisioni; Costruzione delle preferenze; Teoria del sé; Sforzo mentale. (shrink)

As the expansion of the Internet and the digital formatting of all kinds of creative works move us further into the information age, intellectual property issues have become paramount. Computer programs costing thousands of research dollars are now copied in an instant. People who would recoil at the thought of stealing cars, computers, or VCRs regularly steal software or copy their favorite music from a friend's CD. Since the Web has no national boundaries, these issues are international concerns. The contributors-philosophers, (...) legal theorists, and business scholars, among others-address questions such as: Can abstract ideas be owned? How does the violation of intellectual property rights compare to the violation of physical property rights? Can computer software and other digital information be protected? And how should legal systems accommodate the ownership of intellectual property in an information age? Intellectual Property is a lively examination of these and other issues, and an invaluable resource for librarians, lawyers, businesspeople, and scholars. (shrink)

Introduction A brief look at the competing present-day interpretations of Hume's philosophy will leave the uninitiated reader completely baffled. On the one hand , Hume is seen as a philosopher who attempted to analyse concepts with ...

In this original work of psychoanalytic theory, John Muller explores the formative power of signs and their impact on the mind, the body and subjectivity, giving special attention to work of the French psychoanalyst Jacques Lacan and the American philosopher Charles Sanders Peirce. Muller explores how Lacan's way of understanding experience through three dimensions--the real, the imaginary and the symbolic--can be useful both for thinking about cultural phenomena and for understanding the complexities involved in treating psychotic patients. Muller develops (...) Lacan's perspective gradually, presenting it as distinctive approaches to data from a variety of sources, such as cognitive, social and developmental psychology, literature, history, art, and psychoanalytic treatment. The book's first four chapters present Muller's reading of selected data from child development research, psychology and linguistics, approximating a semiotic model of "normal" development. The following three chapters examine in a Lacanian framework the structural basis of psychotic stages as indicative of massive semiotic failure in development. The final chapters on human narcissism suggest reasons that "normal" development may be impossible. (shrink)

David Lewis in the short monograph Parts of Classes (PC) undertakes a fundamental re‐examination of the relationship between mereology, the general theory of parts, and set theory, the general theory of collections. Given Lewis's theses, to be an element of a set or member of class is just to have a singleton that is a part thereof. Lewis in PC adds a claim of kind of ontological innocence, comparable to that of first‐order logic, for mereology. The only substantive assumption of (...) plethynticology is that for any condition there are some things such that they are precisely the things for which the conditions hold. All the alternatives, making do with a single domain of individuals, have in common that they involve the axiom of choice. Restated in Hazen's terminology rather than Frege's, the fallback assumption is that there are no more small species than individuals. (shrink)