Cauchy’s contribution to the foundations of analysis is often viewed through the lens of developments that occurred some decades later, namely the formalisation of analysis on the basis of the epsilon-delta doctrine in the context of an Archimedean continuum. What does one see if one refrains from viewing Cauchy as if he had read Weierstrass already? One sees, with Felix Klein, a parallel thread for the development of analysis, in the context of an infinitesimal-enriched continuum. One sees, with Emile Borel, (...) the seeds of the theory of rates of growth of functions as developed by Paul du Bois-Reymond. One sees, with E. G. Björling, an infinitesimal definition of the criterion of uniform convergence. Cauchy’s foundational stance is hereby reconsidered. (shrink)

A construction of the real number system based on almost homomorphisms of the integers $\mathbb {Z}$ was proposed by Schanuel, Arthan, and others. We combine such a construction with the ultrapower or limit ultrapower construction to construct the hyperreals out of integers. In fact, any hyperreal field, whose universe is a set, can be obtained by such a one-step construction directly out of integers. Even the maximal (i.e., On -saturated) hyperreal number system described by Kanovei and Reeken (2004) and independently (...) by Ehrlich (2012) can be obtained in this fashion, albeit not in NBG . In NBG , it can be obtained via a one-step construction by means of a definable ultrapower (modulo a suitable definable class ultrafilter). (shrink)

: Results of a search for the electroweak associated production of charginos and next-to-lightest neutralinos, pairs of charginos or pairs of tau sleptons are presented. These processes are characterised by final states with at least two hadronically decaying tau leptons, missing transverse momentum and low jet activity. The analysis is based on an integrated luminosity of 20.3 fb−1 of proton-proton collisions at recorded with the ATLAS experiment at the Large Hadron Collider. No significant excess is observed with respect to the (...) predictions from Standard Model processes. Limits are set at 95% confidence level on the masses of the lighter chargino and next-to-lightest neutralino for various hypotheses for the lightest neutralino mass in simplified models. In the scenario of direct production of chargino pairs, with each chargino decaying into the lightest neutralino via an intermediate tau slepton, chargino masses up to 345 GeV are excluded for a massless lightest neutralino. For associated production of mass-degenerate charginos and next-to-lightest neutralinos, both decaying into the lightest neutralino via an intermediate tau slepton, masses up to 410 GeV are excluded for a massless lightest neutralino.[Figure not available: see fulltext.]. (shrink)

We examine Paul Halmos’ comments on category theory, Dedekind cuts, devil worship, logic, and Robinson’s infinitesimals. Halmos’ scepticism about category theory derives from his philosophical position of naive set-theoretic realism. In the words of an MAA biography, Halmos thought that mathematics is “certainty” and “architecture” yet 20th century logic teaches us is that mathematics is full of uncertainty or more precisely incompleteness. If the term architecture meant to imply that mathematics is one great solid castle, then modern logic tends to (...) teach us the opposite lesson, namely that the castle is floating in midair. Halmos’ realism tends to color his judgment of purely scientific aspects of logic and the way it is practiced and applied. He often expressed distaste for nonstandard models, and made a sustained effort to eliminate first-order logic, the logicians’ concept of interpretation, and the syntactic vs semantic distinction. He felt that these were vague, and sought to replace them all by his polyadic algebra. Halmos claimed that Robinson’s framework is “unnecessary” but Henson and Keisler argue that Robinson’s framework allows one to dig deeper into set-theoretic resources than is common in Archimedean mathematics. This can potentially prove theorems not accessible by standard methods, undermining Halmos’ criticisms. (shrink)

This paper is an attempt to solve the following problem: given a logic, how to turn it into a paraconsistent one? In other words, given a logic in which ex falso quodlibet holds, how to convert it into a logic not satisfying this principle? We use a framework provided by category theory in order to define a category of consequence structures. Then, we propose a functor to transform a logic not able to deal with contradictions into a paraconsistent one. Moreover, (...) we study the case of paraconsistentization of propositional classical logic. (shrink)

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

This paper analyzes the problem of implication and attempts to characterize conditionals by a criterion of adequacy. A definition of implication based on the notion of limit of an infinite sequence is proposed.

Departing from basic concepts in abstract logics, this paper introduces two concepts: conjunctive and disjunctive limits. These notions are used to formalize levels of modal operators.

Henri Bergson is primarily known for his work on time, memory, and creativity. His equally innovative interventions into politics and religion have, however, been neglected or dismissed until now. In the first book in English dedicated to Bergson as a political thinker, leading Bergson scholars illuminate his positions on core concerns within political philosophy: the significance of emotion in moral judgment, the relationship between biology and society, and the entanglement of politics and religion. Ranging across Bergson's writings but drawing mainly (...) on his last book, _The Two Sources of Morality and Religion_, the contributors consider Bergson's relevance to contemporary discussions of human rights, democratic pluralism, and environmental ethics. _Contributors._ Keith Ansell-Pearson, G. William Barnard, Claire Colebrook, Hisashi Fujita, Suzanne Guerlac, Vladimir Jankélévitch, Frédéric Keck, Leonard Lawlor, Alexandre Lefebvre, Paola Marrati, John Mullarkey, Paulina Ochoa Espejo, Carl Power, Philippe Soulez, Jim Urpeth, Melanie White, Frédéric Worms. (shrink)

Les neurosciences modernes, notamment les découvertes récentes de la recherche sur le cerveau, réclament de plus en plus un changement radical dans leurs tenants et aboutissants philosophiques, loin en particulier de l’anthropologie théologique du Christianisme qui s’appuya pendant de longs siècles sur la conception philosophique dualiste de l’union entre corps et âme. Dans cet essai, A. Ganoczy veut d’abord exposer des acquis de la recherche sur le cerveau qui entraînent, chez les uns, une conception matérialiste et, chez les autres, une (...) description non matérialiste de la personne humaine, les deux camps s’accordant à se situer dans un contexte strictement évolutionniste. S’appuyant sur les travaux et écrits de J.-P. Changeux et Gerhard Vollmer, pour les premiers, de John C. Eccles et Antonio R. Damasio, pour les seconds, A. G. examine les thèses et hypothèses de ces scientifiques qui n’hésitent pas à franchir les frontières évidentes de leurs compétences pour établir une nouvelle anthropologie, sans même une visée ouvertement et méthodiquement interdisciplinaire.Modern neuroscience, notably the recent discoveries of research on the brain, increasingly call for a radical change in their positions and philosophical conclusions, which are particularly distant from the theological anthropology of Christianity, which depended for many centuries on a duelist philosophical conception of the union between body and soul. In this essay, A. Ganoczy wishes first of all to present the results of research on the brain that result in a materialist conception for some, and for others a non-materialist description of the human person. The two camps agreed to place themselves in a strictly evolutionist context. Using the work and writings of J.-P. Changeux and Gerhard Vollmer for the first camp, John C. Eccles and Antonio R. Damasio for the second camp, A. G. examines the theses and hypotheses of these scientists who did not hesitate to go beyond the evident boundaries of their competencies to establish a new anthropology, without even having an openly, methodologically interdisciplinary outlook. (shrink)

Gilberto Freyre, the great Brazilian historian and sociologist, described Brazil as a ‘racial paradise’, a place where different races and nationalities have come to live together in a sort of ‘racial democracy’. The literature on this topic has become extensive as anthropologists, social scientists and historians felt the need to either prove or disprove such a claim. The argument that Brazil is a racial paradise or democracy is certainly romantic, even utopian; but it is true that Brazil has not experienced (...) the sort of racial friction that has been found in places such as South Africa (e.g. apartheid) or the USA (e.g. segregation laws). This article analyses interculturalism and non-formal education in Brazilian society from the perspective of Martin Buber's philosophy of dialogue and demonstrates some of the advantages interculturalism has over multiculturalism. We further suggest that the example of modern and contemporary Brazil follows Martin Buber in ‘pointing the way’ for other countries and for other societies and cultures. (shrink)

The article examines epistemological and ontological underpinnings of reasearch performed by means of magnetic resonance imaging and functional magnetic resonance imaging. It takes as its guiding line the important distinction between instruments and apparatuses drawn by Rom Harré. According to Harré, instruments such as barometers or thermometers do not cause the states they measure into existence. Apparatuses, in contradistinction, cause material states into existence to begin with, whereby theses states are subsequently processed according to suitable methods. Thus, when the objects (...) of examination are subjected to 2 or more Tesla in fMRI, a strength of magnetic field never occuring in earthly nature, technical means literally create the states to be examined. Close examination of the functioning of MRI and fMRI indicates that brain states, e.g., are not simply read, or perceived as degrees of temperature are read on scale. Hence, one does not see any mental funtion when looking at fMRI outputs, for the visible output has been semantically processed on the basis of invisible quantum mechanical processes that have undergone translations into digital data caused by the fMRI device itself. (shrink)

© 2014, The Author. A search for supersymmetry in events with large missing transverse momentum, jets, at least one hadronically decaying tau lepton and zero or one additional light leptons, has been performed using 20.3fb−1of proton-proton collision data at √ s= 8 TeV recorded with the ATLAS detector at the Large Hadron Collider. No excess above the Standard Model background expectation is observed in the various signal regions and 95% confidence level upper limits on the visible cross section for new (...) phenomena are set. The results of the analysis are interpreted in several SUSY scenarios, significantly extending previous limits obtained in the same final states. In the framework of minimal gauge-mediated SUSY breaking models, values of the SUSY breaking scale Λ below 63 TeV are excluded, independently of tan β. Exclusion limits are also derived for an mSUGRA/CMSSM model, in both the R-parity-conserving and R-parity-violating case. A further interpretation is presented in a framework of natural gauge mediation, in which the gluino is assumed to be the only light coloured sparticle and gluino masses below 1090 GeV are excluded. (shrink)

O tema do reconhecimento é central na obra de G. W. F Hegel. Classicamente, situa-se na figura da luta entre o senhor e o escravo, na Fenomenologia do Espírito. A intersubjetividade e, portanto, o reconhecimento, na obra hegeliana, colocam o seguinte problema: como é possível construir uma interpretação que supere o conceito de subjetividads moderna, positivado pela prática jusfilosófica, vindo a garantir um novo paradigma fundado na intersubjetividade e, portanto, pressupondo a teoria hegeliana do reconhecimento? Em primeiro lugar, analisa-se o (...) desejo antropológico de reconhecimento como fonte da idéia de justiça em A. Kojéve. Em seguida, apresenta-se, segundo 0 mesmo autor, a fenomenologia da justiça, que parte do princípio de que o desejo, conforme Hegel, quer o reconhecimento, sendo este a fonte última da idéia de justiça. Kojéve expõe fenomenologicamente a idéia de justiça, em três momentos: a justiça aristocrática ou a igualdade, a justiça burguesa ou a equivalência e a justiça cidadã ou a equidade. Finalmente, conclui-se que o reconhecimento intersubjetivo ocorre em vários níveis de mediação social, jurídica e política. Assim, na complexidade da sociedade mundializada, produzir uma hermenêutica jusfilosófica de cunho intersubjetivo encontra, na teoria hegeliana do reconhecimento, um fundamental pressuposto epistemológico. (shrink)

The chapters of the book do not situate Spinoza among the natural philosophical giants who opened the way to modern science. Rather they explore Spinoza's relation to the sciences in a variety of ways. Contributors: Joseph Agassi, Thomas Cook, Marjorie Grene, Hans Jonas, André Lecrivain, Genevieve Lloyd, Alexandre Matheron, Nancy Maull, Debra Nails, Michel Paty, Richard H. Popkin, David Savan, Heine Siebrand, and Joe D. Van Zandt.

Peter G. Sobol - Pierre Gassendi's Philosophy and Science: Atomism for Empiricists - Journal of the History of Philosophy 45:1 Journal of the History of Philosophy 45.1 161-162 Muse Search Journals This Journal Contents Reviewed by Peter G. Sobol Mcfarland, Wisconsin Saul Fisher. Pierre Gassendi's Philosophy and Science: Atomism for Empiricists. Brill's Studies in Intellectual History 131. Leiden-Boston: Brill, 2005. Pp. xxviii + 436. Cloth, $172.50. In 1971, Richard S. Westfall described Pierre Gassendi as "the original scissors and paste man": (...) an irrepressibly eclectic compiler whose Syntagma Philosophicum was published only after his death "when the author was finally beyond the possibility of adding and patching." Westfall here echoes Voltaire and Alexandre Koyré who, as quoted in Saul Fisher's.. (shrink)

An understanding of the relationship between metaphysics and natural philosophy - or, as we might now say, between philosophy and science - is fundamental to understanding the rise of the "new science" of the seventeenth century. Twentieth-century scholarship on this relationship has been dominated by the thoughbt of Ernst Cassirer, E. A. Burtt, A. N. Whitehead, and Alexandre Koyre. These authors found a common core in the mathematization of nature, which they ascribed to a common Platonic or Pythagorean metaphysical (...) presupposition, on the part of Copernicus, Kepler, Galileo, and Descartes, that the book of nature is written in mathematical characters. Taking Burtt as its primary stalking horse, this chapter challenges this view by finding significant differences in the relations to metaphysics of major actors such as those just named. It does this in part by recognizing that, in the seventeenth century, metaphysics was an intellectual practice that one engaged in wittingly. By contrast, Burtt adopted a historiographical approach in which metaphysics consists of the nonempirical presupposition of an age (a position advanced by R. G. Collingwood). That approach, although valid within its limits, distorts or omits from consideration the witting practice of metaphysics by figures such as Kepler and Descartes. And it makes metaphysicians of Copernicus and Galileo, who are better classified as a mathematical astronomer and a mathematical natural philosopher and writer on astronomy. The chapter ends with some reflections on purportedly aphilosophical history of science. (shrink)

In lieu of an abstract, here is a brief excerpt of the content: Hypatia 14.4 (1999) 186-191 -/- [Access article in PDF] Simone De Beauvoir: a Critical Reader. Edited by Elizabeth Fallaize. London and New York: Routledge, 1998. As this special volume attests, there has been a recent resurgence of interest in Simone de Beauvoir. A number of books on her have been published in the last several years. However, Elizabeth Fallaize's book, Simone de Beauvoir: A Critical Reader (1998), occupies (...) a special niche. Many of its essays are excerpts from studies done of Beauvoir's work before this latest renaissance. Some of these studies are not in print in the United States. Some are perhaps unfamiliar to present-day readers or those from different disciplines. In addition, the articles reprinted here are otherwise not easily accessible. Fallaize has performed an important service by gathering them all in one place and by carefully editing, presenting, and, in some cases, translating them. -/- The book is divided into three sections, the first entitled "Readings of The Second Sex." Aside from Judith Okely's piece that assesses Beauvoir's chapter on myths from an anthropological standpoint, the essays mainly address the philosophical aspects of this work. Beauvoir herself of course swore that she was not a philosopher and that Jean-Paul Sartre's Being and Nothingness (1953) was the sole philosophical foundation for all her work. Some recent analyses have attempted to turn this picture on its head by arguing that Beauvoir was a central influence on, or even the origin of, the philosophical doctrines put forward in Being and Nothingness. None of the writers in this book addresses this issue. But two emphasize Beauvoir's intellectual independence from Sartre. -/- The Swedish scholar Eva Lundgren-Gothlin argues that Beauvoir turned to G. W. F. Hegel to find a satisfactory theoretical model with which to explain the subjugation of women (Lundgren-Gothlin's essay is taken from her book [End Page 186] Sex and Existence [1996]) . In opposition to other scholars, she argues that the French Hegelian Alexandre Kojève, not Sartre, influenced Beauvoir's interpretation of Hegel. Following Hegel and Kojève, Beauvoir envisioned a possible resolution to the struggle for recognition—reciprocal recognition—whereas Sartre's view of self-other relations in Being and Nothingness rules such reciprocity out. However, Lundgren-Gothlin judges, Beauvoir was not critical enough of the sexist presuppositions of Hegel's thought, citing the same pronouncements Beauvoir makes that subsequent feminists have criticized. -/- Another piece that stresses Beauvoir's philosophical originality is "Beauvoir: The Weight of Situation," taken from Sonia Kruks's book Situation and Human Existence (1990). For some time, Kruks has been doing excellent work placing Beauvoir within the wider phenomenological tradition. In this piece, she argues that, starting with the early essay Pyrrhus et Cinéas (1944) and culminating in The Second Sex (1989), Beauvoir elaborated a more nuanced position on the nature and extent of human freedom than Sartre did in Being and Nothingness. According to Beauvoir, human freedom, which Sartre dramatically proclaims is absolute, can under some conditions, notably conditions of severe oppression, "be reduced to no more than a suppressed potentiality" (Fallaize 1998, 57). In The Second Sex, Beauvoir definitively breaks with the philosophical framework of Being and Nothingness by implying that a woman's situation is a general one, not individually self-constituted, and one that she cannot transcend by an act of free choice. The phenomenology of Maurice Merleau-Ponty provides a better foundation for Beauvoir's conception of subjectivity as socially mediated and embodied than does Sartre's philosophy, Kruks suggests. -/- Another piece in this section, Judith Butler's landmark essay "Sex and Gender in Simone de Beauvoir's Second Sex" (1986), highlights Beauvoir's philosophical originality in a different way. In her introduction, Fallaize points out how this essay served as a foundation for Butler's own subsequent work on a performative theory of gender. Butler argues that Beauvoir's claim that one is not born but becomes a woman implies that gender is socially constructed and not natural, as people have insisted for centuries. But to the extent that we become women, gender is not something... (shrink)

This collection of six essays centers on Professor Koyre;'s great theme: the relative importance of metaphysics and observation, with controlled experiment a kind of marriage between the two. Professor Koyre;'s thesis might be summed up as a claim that when one is seeking to explain the scientific revolution, attention must be concentrated on the philosophical outlook of the scientist and away from speculative theories. At the time of his death, Alexandre Koyre; was a professor at the Ecole Pratique des (...) Hautes Études (Sorbonne) and a memeber of the Institute for Advanced Study in Princeton. (shrink)

Alexandre Koyré. of the fixed stars is infinite commit a contradiction in adjecto. In truth, an infinite body cannot be comprehended by thought. For the concepts of the mind concerning the infinite are either about the meaning oftheterm "infinite,"  ...

G.E. Moore, more than either Bertrand Russell or Ludwig Wittgenstein, was chiefly responsible for the rise of the analytic method in twentieth-century philosophy. This selection of his writings shows Moore at his very best. The classic essays are crucial to major philosophical debates that still resonate today. Amongst those included are: * A Defense of Common Sense * Certainty * Sense-Data * External and Internal Relations * Hume's Theory Explained * Is Existence a Predicate? * Proof of an External World (...) In addition, this collection also contains the key early papers in which Moore signals his break with idealism, and three important previously unpublished papers from his later work which illustrate his relationship with Wittgenstein. (shrink)

This is a review of Alexandre Kojève, The Religious Metaphysics of Vladimir Solovyov, translated by Ilya Merlin and Mikhail Pozdniakov, Cham: Springer International Publishing, 2018. This slim book is a translation of Kojève’s essay “La métaphysique religieuse de Vladimir Soloviev,” which was first published in two installments in the Revue d’histoire et de philosophie religieuses in 1934. The French text was itself based on Kojève’s doctoral dissertation, Die religiöse Philosophie Wladimir Solowjews, defended in Heidelberg under the direction of Karl (...) Jaspers in 1926. The translation is accompanied by an introduction from the translators discussing translation issues. In this review, I summarize Kojève’s essay and editorialize on the issue of the principal influences on Solovyov’s metaphysics. Kojève claims that most of Solovyov’s metaphysics was in fact borrowed from Schelling and perhaps also to some extent from Jakob Böhme. If that is the case, then what is usually considered the prototypical Russian metaphysics is... not Russian. (shrink)

Patients suffering from the Cotard syndrome can deny being alive, having guts, thinking or even existing. They can also complain that the world or time have ceased to exist. In this article, I argue that even though the leading neurocognitive accounts have difficulties meeting that task, we should, and we can, make sense of these bizarre delusions. To that effect, I draw on the close connection between the Cotard syndrome and a more common condition known as depersonalisation. Even though they (...) are not delusional, depersonalised patients seem to have experiences that are quite similar to those of Cotard patients. I argue that these experiences are essentially characterised by a lack of subjective character and of two other structural features of experience, which I call ‘the present character’ and ‘the actual character’. Cotard's nihilistic delusions simply consist in taking these anomalous experiences at face value. (shrink)

(2013). Does consciousness entail subjectivity? The puzzle of thought insertion. Philosophical Psychology: Vol. 26, No. 2, pp. 291-314. doi: 10.1080/09515089.2011.625117.

This chapter addresses the claim that, as new types of neurointervention get developed allowing us to enhance various aspects of our mental functioning, we should work to prevent the use of such interventions from ever becoming the “new normal,” that is, a practice expected—even if not directly required—by employers. The author’s response to that claim is that, unlike compulsion or most cases of direct coercion, indirect coercion to use such neurointerventions is, per se, no more problematic than the pressure people (...) all find themselves under to use modern technological devices like computers or mobile phones. Few people seem to believe that special protections should be introduced to protect contemporary Neo-Luddites from such pressures. That being said, the author acknowledges that separate factors, when present, can indeed render indirect coercion to enhance problematic. The factors in question include lack of safety, fostering adaptation to oppressive circumstances, and having negative side effects that go beyond health. Nonetheless, the chapter stresses that these factors do not seem to be necessary correlates of neuroenhancement. (shrink)

Descartes was certain that he was thinking and he was accordingly certain that he existed. Like Descartes, we seem to be more certain of our thoughts and our existence than of anything else. What is less clear is the reason why we are thus certain. Philosophers throughout history have provided different interpretations of the cogito, disagreeing both on the kind of thoughts it characterizes and on the reasons for its cogency. According to what we may call the empiricist interpretation of (...) the cogito, I can only claim to be certain of having experiences, and this certainty, as well as that of my own existence, stems from their phenomenal and subjective character. According to rationalist interpretations, on the other hand, I am certain of having some self-reflexive propositional attitudes, and this certainty derives from their rational features. Psychiatric patients suffering from acute forms of depersonalization or of the Cotard syndrome often doubt that they think and exist, and might even believe that they don't. I argue that their study allows us to favor the empiricist interpretation of the cogito. (shrink)

One objection to enhancement technologies is that they might lead us to live inauthentic lives. Memory modification technologies (MMTs) raise this worry in a particularly acute manner. In this paper I describe four scenarios where the use of MMTs might be said to lead to an inauthentic life. I then undertake to justify that judgment. I review the main existing accounts of authenticity, and present my own version of what I call a “true self” account (intended as a complement, rather (...) than a substitute, to existing accounts). I briefly describe current and prospective MMTs, distinguishing between memory enhancement and memory editing . Moving then to an assessment of the initial scenarios in the light of the accounts previously described, I argue that memory enhancement does not, by its very nature, raise serious concerns about authenticity. The main threat to authenticity posed by MMTs comes, I suggest, from memory editing. Rejecting as inadequate the worries about identity raised by the President’s Council on Bioethics in Beyond Therapy , I argue instead that memory editing can cause us to live an inauthentic life in two main ways: first, by threatening its truthfulness, and secondly, by interfering with our disposition to respond in certain ways to some past events, when we have reasons to respond in such ways. This consideration allows us to justify the charge of inauthenticity in cases where existing accounts fail. It also gives us a significant moral reason not to use MMTs in ways that would lead to such an outcome. (shrink)

In this paper, we put forward a new account of emergence called “transformational emergence”. Such an account captures a variety of emergence that can be considered as being diachronic and weakly ontological. The fact that transformational emergence actually constitutes a genuine form of emergence is motivated. Besides, the account is free of traditional problems surrounding more usual, synchronic versions of emergence, and it can find a strong empirical support in a specific physical phenomenon, the fractional quantum Hall effect, which has (...) long been touted as a paradigmatic case of emergence. (shrink)