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)

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)

This volume reprints a dozen of the author’s papers, most with substantial postscripts, and adds one new one. The bulk of the material is on topics in philosophy of language, but there are also two papers on philosophy of mathematics written after the appearance of the author’s collected papers on that subject, and one on epistemology. As to the substance of Field’s contributions, limitations of space preclude doing much more below than indicating the range of issues addressed, and the general (...) orientation taken towards them. As to the style of his writing, it well exhibits the first of the two virtues, clarity and conciseness, that one looks for in philosophical prose. (shrink)

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

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)

Used as the basis of the program at the Equinox Holistic Alternative School in Toronto, The Holistic Curriculum advocates for an integrative approach to teaching and learning with a focus on developing a deep connection between mind and body.

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)

In lieu of an abstract, here is a brief excerpt of the content:John P. Anton C. P. CAVAFY'S ARS POETICA ' It is generally recognized that Constantine P. Cavafy (1863-1933) was not born a poet but became one only through persistence and labor, reaching his "first step" sometime after the midpoint of his life. In his effort to assess the quality of his earlier poetic production and sharpen his sensitivity in facing self-criticism, he decided to put in writing his (...) personal thoughts on his work sometime in 1903. The text was written in English in a personal shorthand Cavafy had devised for his own use. It was found among the papers he left to A. Sengopoulos and published for the first time in 1963 by M. Peridis, who also supplied the suitable title Ars Poetica. It falls outside the scope of this essay to discuss the antecedents of this document. Taken as a whole, the text has all the clarity and directness required of a testament designed to serve as a personal guide and handbook. The problems it discusses are limited to the needs of the poet. In this regard, the Ars Poetica has neither the range of topics nor the theoretical scope of, for instance, Aristotle's Poetics. It is quite certain that the ideas that preoccupy Cavafy in the Ars Poetica had been on his mind for a period of years. However, the Ars Poetica is his first prose piece where he gives a systematic treatment to technical and critical issues directly related to the assessment of his work and his role as a poet. In order to project here a clear image of Cavafy's struggle to reach his technical maturity which came after 1910, we need first to discuss the persistent problems he faced during this crucial decade, then to examine the attitudes and values he embodied in certain representative early poems, and finally to relate them to the guiding principles he formulated in his self-addressed poetics of 1903. A number of interrelated problems confronted Cavafy in his late twenties and throughout his thirties. They emerged one by one, to 85 86Philosophy and Literature make more pressing the demand for a consistent solution and a complete recasting of his outlook. Coming to terms with them was extremely difficult. Aside from the emotional and sexual pressures he had to face alone, there was the absence of suitable ideas and conceptual tools to provide him with even the rudiments of an intellectual framework. Whatever he borrowed from Europe and England, or resurrected from his own Hellenic heritage, proved either beyond assimilation or insufficiently digested. The lingering issues fell roughly into four areas. (i) Despite his determination to devote his life to the writing of poetry, the quality of his work was discouraging. He knew this and as a result he often expressed uncertainty about his ability to proceed. Time and again he appeared suffering from a feeling of inadequacy, but nevertheless he sought to engage a reflective mood from which to draw encouragement and hope. (ii) On the theoretical side, he identified with the long tradition which assigned a coveted cultural role to the savant-poet as discloser of truth and spokesman for humanity; this despite the prevailing climate of opinion in his immediate environment which recognized no such high position in his case. Cavafy knew that his standing with the Greek community of Alexandria had gradually dwindled with the loss of family wealth and his lowly employment, and also that his expectations to be respected in his role as a poet and leader in communal affairs were futile. This denial of personal recognition in a society dominated by commerce and finance contributed to his mood of depression. The feeling of being an outcast, despite his associations with the upper social circles of Alexandria, became a constant irritant to his sense of pride. (iii) The course of culture, the destiny of human institutions and the workings of history, became puzzles as he tried to view them through the opaque glass of disillusionment. These were the grand themes actively discussed in the writings of leading European intellectuals, but to the young poet they had a different personal urgency. His vital concern in this connection was not understanding science... (shrink)

In their target article, Nielsen Busch and Mjaaland seek to shift focus away from controversy over whether donors in protocols of controlled donation after circulatory death (cDCD) are dead. Citing...

This essay reevaluates the Weimar writings of Carl Schmitt and Leo Strauss, specifically, their intellectual efforts to replace the political authority of Kantian liberalism with, respectively, a ‘political theology’ and ‘Biblical atheism’ derived from the thought of early-modern state theorists like Hobbes and Spinoza. Schmitt and Strauss each insisted that post-Kantian Enlightenment rationality was unraveling into a way of thinking that violently rejected ‘form’ of any kind, fixated myopically on material things and lacked any conception of the external constraints that (...) invariably condition the possibilities of philosophy, morality and politics. They considered Kantian reason and liberal politics to pose serious threats to ‘genuine’ expressions of rationality and as dangerous obfuscations of the necessity of political order—of the brute fact that human beings stand in need of ‘being ruled,’ as such. (shrink)

Genetic changes arising in human pluripotent stem cells (hPSC) upon culture may bestow unwanted or detrimental phenotypes to cells, thus potentially impacting on the applications of hPSCs for clinical use and basic research. In the 20 years since the first report of culture‐acquired genetic aberrations in hPSCs, a characteristic spectrum of recurrent aberrations has emerged. The preponderance of such aberrations implies that they provide a selective growth advantage to hPSCs upon expansion. However, understanding the consequences of culture‐acquired variants for specific (...) applications in cell therapy or research has been more elusive. The rapid progress of hPSC‐based therapies to clinics is galvanizing the field to address this uncertainty and provide definitive ways both for risk assessment of variants and reducing their prevalence in culture. Here, we aim to provide a timely update on almost 20 years of research on this fascinating, but a still unresolved and concerning, phenomenon. (shrink)

In this paper we introduce a system S5U, formed by adding to the modal system S5 a new connective U, Up being read “probably”. A few theorems are derived in S5U, and the system is provided with a decision procedure. Several decidable extensions of S5U are discussed, and probability logic is related to plurality quantification.

One approach to the problem of differentiating a religious from a non- religious ethic would be to formulate a definition of religion that would clearly distinguish between religious and nonreligious traditions; however, a broad definition of religion would include some moral traditions, such as Marxism, commonly thought to be forms of secular humanism. A second approach would argue that some moral beliefs are independent, both in content and justification, of religious convictions; such a set of moral beliefs could be described (...) as a secular version of natural law. This approach would be rejected by those who argue that religious convictions go "all the way down." While the first can be debated by appealing to the heuristic value of various definitions of religion, the second involves familiar issues of moral epistemology. The author explores the consequences of holding a broad definition of religion and an "all the way down" epistemology. (shrink)

That the result of flipping quantifiers and negating what comes after, applied to branching-quantifier sentences, is not equivalent to the negation of the original has been known for as long as such sentences have been studied. It is here pointed out that this syntactic operation fails in the strongest possible sense to correspond to any operation on classes of models.

In this paper, I defend brain death as a criterion for determining death against objections raised by Don Marquis, Michael Nair-Collins, Doyen Nguyen, and Laura Specker Sullivan. I argue that any definition of death for beings like us relies on some sortal concept by which we are individuated and identified and that the choice of that concept in a practical context is not determined by strictly biological considerations but involves metaphysical, moral, social, and cultural considerations. This view supports acceptance of (...) a more pluralistic legal definition of death as well as acceptance of brain death as death. (shrink)

A student of Étienne Gilson and Joseph Owens, John P. Doyle taught medieval and Scholastic philosophy at Saint Louis University for forty years. Of continuing interest to Doyle has been the thought of Francisco Suárez, S.J. On this topic Doyle has published over a dozen articles and four English translations of portions of Suárez's key works. This volume celebrates the life and career of one of those rare kinds of scholars who has mastered an entire field of inquiry and (...) thought. (shrink)

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)

This chapter contains section titled: Reception of the Treatise by Francis Hutcheson and Hume's Revisions to Book 3 The Early Reviews of the Treatise and Hume's Response The Principal's Attack in 1745 and Hume's Defence in his Letter from a Gentleman Criticisms of the Treatise after Publication of the Enquiries Thomas Reid's Criticisms of Hume's Philosophy and Hume's Response Hume's Repudiation of the Treatise Conclusion Notes References Further reading.

A new axiomatization of set theory, to be called Bernays-Boolos set theory, is introduced. Its background logic is the plural logic of Boolos, and its only positive set-theoretic existence axiom is a reflection principle of Bernays. It is a very simple system of axioms sufficient to obtain the usual axioms of ZFC, plus some large cardinals, and to reduce every question of plural logic to a question of set theory.

It is correctly asserted that the intensity of the current debate over the use of animals in biomedical research is unprecedented. The extent of expressed animosity and distrust has stunned many researchers. In response, researchers have tended to take a strategic defensive posture, which involves the assertion of several abstract positions that serve to obstruct resolution of the debate. Those abstractions include the notions that the animal protection movement is trivial and purely anti-intellectual in scope, that all science is good (...) (and some especially so), and the belief that an ethical consensus can never really be reached between the parties. (shrink)

A comprehensive look at the intellectual and cultural innovations of the Weimar period During its short lifespan, the Weimar Republic witnessed an unprecedented flowering of achievements in many areas, including psychology, political theory, physics, philosophy, literary and cultural criticism, and the arts. Leading intellectuals, scholars, and critics—such as Hannah Arendt, Walter Benjamin, Ernst Bloch, Bertolt Brecht, and Martin Heidegger—emerged during this time to become the foremost thinkers of the twentieth century. Even today, the Weimar era remains a vital resource for (...) new intellectual movements. In this incomparable collection, Weimar Thought presents both the specialist and the general reader a comprehensive guide and unified portrait of the most important innovators, themes, and trends of this fascinating period. The book is divided into four thematic sections: law, politics, and society; philosophy, theology, and science; aesthetics, literature, and film; and general cultural and social themes of the Weimar period. The volume brings together established and emerging scholars from a remarkable array of fields, and each individual essay serves as an overview for a particular discipline while offering distinctive critical engagement with relevant problems and debates. Whether used as an introductory companion or advanced scholarly resource, Weimar Thought provides insight into the rich developments behind the intellectual foundations of modernity. (shrink)

BackgroundThe Public Health Service Increased Risk designation identified organ donors at increased risk of transmitting hepatitis B, hepatitis C, and human immunodeficiency virus. Despite clear data demonstrating a low absolute risk of disease transmission from these donors, patients are hesitant to consent to receiving organs from these donors. We hypothesize that patients who consent to receiving offers from these donors have decreased time to transplant and decreased waitlist mortality.MethodsWe performed a single-center retrospective review of all-comers waitlisted for liver transplant from (...) 2013 to 2019. The three competing risk events (transplant, death, and removal from transplant list) were analyzed. 1603 patients were included, of which 1244 (77.6%) consented to offers from increased risk donors.ResultsCompared to those who did not consent, those who did had 2.3 times the rate of transplant (SHR 2.29, 95% CI 1.88–2.79, p < 0.0001), with a median time to transplant of 11 months versus 14 months (p < 0.0001), as well as a 44% decrease in the rate of death on the waitlist (SHR 0.56, 95% CI 0.42–0.74, p < 0.0001). All findings remained significant after controlling for the recipient age, race, gender, blood type, and MELD. Of those who did not consent, 63/359 (17.5%) received a transplant, all of which were from standard criteria donors, and of those who did consent, 615/1244 (49.4%) received a transplant, of which 183/615 (29.8%) were from increased risk donors.ConclusionsThe findings of decreased rates of transplantation and increased risk of death on the waiting list by patients who were unwilling to accept risks of viral transmission of 1/300–1/1000 in the worst case scenarios suggests that this consent process may be harmful especially when involving “trigger” words such as HIV. The rigor of the consent process for the use of these organs was recently changed but a broader discussion about informed consent in similar situations is important. (shrink)

Numbers and other mathematical objects are exceptional in having no locations in space or time or relations of cause and effect. This makes it difficult to account for the possibility of the knowledge of such objects, leading many philosophers to embrace nominalism, the doctrine that there are no such objects, and to embark on ambitious projects for interpreting mathematics so as to preserve the subject while eliminating its objects. This book cuts through a host of technicalities that have obscured previous (...) discussions of these projects, and presents clear, concise accounts of a dozen strategies for nominalistic interpretation of mathematics, thus equipping the reader to evaluate each and to compare different ones. The authors also offer critical discussion, rare in the literature, of the aims and claims of nominalistic interpretation, suggesting that it is significant in a very different way from that usually assumed. (shrink)

Perhaps if the future existed, concretely and individually, as something that could be discerned by a better brain, the past would not be so seductive: its demands would he balanced by those of the future. Persons might then straddle the middle stretch of the seesaw when considering this or that object. It might be fun. But the future has no such reality (as the pictured past and the perceived present possess); the future is but a figure of speech, a specter (...) of thought. (shrink)

John Paul II frames the issue of disenchantment and re-enchantment in terms of “alienation” and “participation”--various works of human power recoil upon the person and inhibit full human development and participation. The neglect and distortion of human rights is one such form of alienation indicating the deeper issue concerning human flourishing. John Paul encourages a radical questioning about human progress so as to better understand the threats that accompany bureaucratic increase in power. Aspects of cultural and human development (...) offer a challenge to mankind to overcome alienation and to participate in community and social love. Through an appeal to the Spirit, and the search for truth, goodness, and beauty, John Paul seeks to open up a lived path to God by way of the person’s transcendence. (shrink)

There are schools of logicians who claim that an argument is not valid unless the conclusion is relevant to the premises. In particular, relevance logicians reject the classical theses that anything follows from a contradiction and that a logical truth follows from everything. This chapter critically evaluates several different motivations for relevance logic, and several systems of relevance logic, finding them all wanting.

One textbook may introduce the real numbers in Cantor’s way, and another in Dedekind’s, and the mathematical community as a whole will be completely indifferent to the choice between the two. This sort of phenomenon was famously called to the attention of philosophers by Paul Benacerraf. It will be argued that structuralism in philosophy of mathematics is a mistake, a generalization of Benacerraf’s observation in the wrong direction, resulting from philosophers’ preoccupation with ontology.

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)

1 Choice conjecture In axiomatizing nonclassical extensions of classical sentential logic one tries to make do, if one can, with adding to classical sentential logic a finite number of axiom schemes of the simplest kind and a finite number of inference rules of the simplest kind. The simplest kind of axiom scheme in effect states of a particular formula P that for any substitution of formulas for atoms the result of its application to P is to count as an axiom. (...) The simplest kind of onepremise inference rule in effect states of a particular pair of formulas P and Q that for any substitution of formulas for atoms, if the result of its application to P is a theorem, then the result of its application to Q is to count as a theorem; similarly for many-premise rules. Such are the schemes and rules of all the best-known modal and tense logics, for instance. Sometimes it is difficult to find such simple schemes and rules. In that case one may resort to less simple schemes or less simple rules. There is no generally recognized rigorous definition of "next simplest kind" of scheme. Neither is there any generally recognized definition of "next simplest kind" of rule, and hence there is no fully rigorous enunciation of the choice conjecture, the conjecture that schemes of the next simplest kind can always be avoided in favor of rules of the next simplest kind and vice versa. Nonetheless, there are cases where intuitively one does recognize that the schemes or rules in a given axiomatization are only slightly more complex than the simplest kind, including cases where one does have a choice between adopting slightly-more-complex-than-simplest schemes and adopting slightly-more-complex-than-simplest rules. In tense logic early examples of slightly more complex rules are found in [2] and [3] : there is one example of the embarrassed use of such rules in the former, and many examples of the enthusiastic use of such rules in the latter and its sequels. Accordingly the rules in question have come to be called "Gabbay-style" rules. (shrink)

This paper is the second of a multi-part examination of the creation of the Babylonian mathematical lunar theories known as Systems A and B. Part I (Britton 2007) addressed the development of the empirical elements needed to separate the effects of lunar and solar anomaly on the intervals between syzygies. This was accomplished in the construction of the System A lunar theory by an unknown author, almost certainly in the city of Babylon and probably early in the 4th century B.C. (...) The present paper focuses mainly on System A and the likely process of its construction. The first three sections are largely descriptive – first of the basic concepts which underlie the theory; then of the component schemes comprising the theory; and finally of two distinctive texts which suggest how the theory was constructed. The crux of the paper is Sect. 4, which describes how the theory seems likely to have been constructed. Here the crucial insight in separating the effects of lunar and solar anomaly appears to have been recognizing that – of all the measurable intervals bounded by eclipses – only 235 months exhibits a variation due solely to lunar anomaly, and that by means of an elegant mathematical model the amplitudes of 223 and 12 months could be deduced from its amplitude. The rest of the section describes the likely details of the derivation of the Φ ~ Λ scheme, and the extension of the methodology to the other components of the theory. It concludes with a demonstration that Φ and its dependent schemes were anchored through the Φ ~ W scheme to the syzygy on –403 Aug 18 (GN 7391) which concluded the shortest 6-month interval in the first 24 saros cycles since –746 (and in fact in the 900 years separating Nabonassar and Ptolemy). The next three sections address a number of largely technical details and amplifications of the theory, beginning with the schemes describing the variation of lunar velocity (column F) in Sect. 5. Section 6 addresses issues concerning the interpretation of Φ and the so-call Saros Text (BM 36705), while Sect. 7 discusses System B’s corresponding treatment of the effects of lunar anomaly, illustrating both its derivative nature and mathematically less rigorous structure. Section 8 examines the accuracy of the two theories, showing that the System A theory was both remarkably accurate and superior to System B. The final section offers some brief remarks on the power and elegance of the mathematical treatment of the problem by the author of System A. (shrink)

It is striking that one of the most consequential representatives of [the] abstract scientific orientation of the seventeenth century [Thomas Hobbes] became so personalistic. This is because as a juristic thinker he wanted to grasp the reality of societal life just as much as he, as a philosopher and a natural scientist, wanted to grasp the reality of nature.... [J]uristic thought in those days had not yet become so overpowered by the natural sciences that he, in the intensity of his (...) scientific approach, should unsuspectingly have overlooked the specific reality of legal life. Carl Schmitt, Political Theology (1922)In the light of Hobbes's natural science, man and his works become a mere phantasmagoria. Through Hobbes's natural science, “the native hue” of his political science “is sicklied o'er with the pale cast” of something which is reminiscent of death but utterly lacks the majesty of death—of something which foreshadows the positivism of our day. It seems then that if we want to do justice to the life which vibrates in Hobbes's political teaching, we must understand that teaching by itself, and not in the light of his natural science. Can this be done?² Leo Strauss, “On the Basis ofHobbes's Political Philosophy” (1959). (shrink)