Fondée sous les auspices du père de notre modernité philosophique Descartes, puis consolidée par des penseurs aussi importants que Leibniz, Bolzano ou Husserl, la mathesis universalis paraît représenter à elle seule l'ambitieux programme du « rationalisme classique ». Des philosophes tels que Husserl, Russell, Heidegger ou Cassirer ont pu s'accorder en ce point. Le développement de la « science moderne » aurait porté ce grand « rêve dogmatique » pour mener vers son terme le destin de la métaphysique occidentale. Pourtant (...) les recherches historiques récentes ont montré que l'idée de « mathématique universelle » existait bien avant Descartes, que ce dernier ne revendiquait d'ailleurs aucune rupture sur ce point et que sa réflexion se situait même assez clairement dans l'héritage des Anciens. Comment dès lors justifier que les Anciens, avec lesquels le programme des Classiques était censé rompre, aient pu déjà se préoccuper de « mathématique universelle »? Plus simplement encore, de quoi se préoccupaient donc ces philosophes sous ce concept? Le regain d'intérêt pour la mathesis universalis à la fin du XIXe siècle n'avait-il pas conduit paradoxalement à la perte de son sens comme problème? Cette étude a pour but de suivre ces questions jusqu'à leur origine et de montrer leur importance dans le dialogue entre mathématique et philosophie. Pages de début Remerciements Introduction La constitution de la « mathématique universelle » comme problème philosophique I. Aristote II. « Mathématique universelle » et théories mathématiques : Aristote, Euclide, Epinomis III. Le moment néo-platonicien Vers la science de l'ordre et de la mesure IV. La renaissance de la mathématique universelle V. La mathesis universalis cartésienne Conclusion Annexe I. La quaestio de scientia mathematica communi Annexe II. Essai bibliographique sur la mathesis universalis chez Descartes etLeibniz Bibliographie Index nominum Pages de fin. (shrink)

In this paper, we endeavour to give a historically accurate presentation of how Leibniz understood his infinitesimals, and how he justified their use. Some authors claim that when Leibniz called them “fictions” in response to the criticisms of the calculus by Rolle and others at the turn of the century, he had in mind a different meaning of “fiction” than in his earlier work, involving a commitment to their existence as non-Archimedean elements of the continuum. Against this, we show that (...) by 1676 Leibniz had already developed an interpretation from which he never wavered, according to which infinitesimals, like infinite wholes, cannot be regarded as existing because their concepts entail contradictions, even though they may be used as if they exist under certain specified conditions—a conception he later characterized as “syncategorematic”. Thus, one cannot infer the existence of infinitesimals from their successful use. By a detailed analysis of Leibniz’s arguments in his De quadratura of 1675–1676, we show that Leibniz had already presented there two strategies for presenting infinitesimalist methods, one in which one uses finite quantities that can be made as small as necessary in order for the error to be smaller than can be assigned, and thus zero; and another “direct” method in which the infinite and infinitely small are introduced by a fiction analogous to imaginary roots in algebra, and to points at infinity in projective geometry. We then show how in his mature papers the latter strategy, now articulated as based on the Law of Continuity, is presented to critics of the calculus as being equally constitutive for the foundations of algebra and geometry and also as being provably rigorous according to the accepted standards in keeping with the Archimedean axiom. (shrink)

Descartes’ Rules for the direction of the mind presents us with a theory of knowledge in which imagination, considered as an “aid” for the intellect, plays a key role. This function of schematization, which strongly resembles key features of Proclus’ philosophy of mathematics, is in full accordance with Descartes’ mathematical practice in later works such as La Géométrie from 1637. Although due to its reliance on a form of geometric intuition, it may sound obsolete, I would like to show that (...) this has strong echoes in contemporary philosophy of mathematics, in particular in the trend of the so called “philosophy of mathematical practice”. Indeed Ken Manders’ study on the Euclidean practice, along with Reviel Netz’s historical studies on ancient Greek Geometry, indicate that mathematical imagination can play a central role in mathematical knowledge as bearing specific forms of inference. Moreover, this role can be formalized into sound logical systems. One question of general epistemology is thus to understand this mysterious role of the imagination in reasoning and to assess its relevance for other mathematical practices. Drawing from Edwin Hutchins’ study of “material anchors” in human reasoning, I would like to show that Descartes’ epistemology of mathematics may prove to be a helpful resource in the analysis of mathematical knowledge. (shrink)

The meaning of the term “analysis” in Leibniz’s work is multifarious and it is doubtful that one could ever succeed in gathering this variety of meanings into a unified whole. However it has long been remarked that a landmass seems to detach itself from these moving waters – an island sometimes called by its inventor “The Most General Analytics of Human Thoughts”. Already sketched in the De Arte Combinatoria (1666) as a reform of the “analytical part” of Logic (pars logices (...) analytica), it rested on a very simple intuition: the possibility of developing, in parallel, three analyses, namely an analysis of thoughts (analysis notionum et veritatum), an analysis of the structure of language by which we express these thoughts (analysis linguarum or analysis grammatica) and an analysis of the symbols by which we represent them (analysis characterum). This “General Analytics” achieved, any human thought could be related to a catalog of simple notions expressed by basic characters (the so called alphabetum cogitationum humanarum) and, as a direct consequence, any truth could be expressed as a combination of these primitive symbols. (shrink)

Résumé Il est courant d’inscrire Leibniz dans une lignée qui, passant par Nicolas de Cues et Giordano Bruno, aurait marqué le triomphe de l’infini actuel dans la pensée moderne, qu’elle soit scientifique ou métaphysique. Pourtant Leibniz n’acceptait nullement un tel infini en mathématiques et s’en est expliqué à diverses reprises de manière particulièrement claire. Dans cet article, je voudrais rappeler cette position élaborée dès le début du séjour parisien (Accessio ad Arithmeticam infinitorum, fin 1672) et montrer son effectivité dans l’élaboration (...) du « fictionalisme » leibnizien en ce qui concerne les infiniment petits. Rappelant les différentes stratégies de comparaison entre les pensées de Leibniz et Nicolas de Cues, je voudrais indiquer la manière dont des textes récemment édités permettent aujourd’hui une meilleure appréciation de l’écart qui peut les séparer. (shrink)

In this paper, I pursue a dialogue initiated with the publication of Logiques des mondes on the basis of three main lines of questioning: 1. The first, most immediate one, is the meaning that should be given to the famous motto “mathematics = ontology”. Indeed, it is a different statement to claim that “mathematics is ontology”, as was promoted explicitely by Being and the event, and to say that set theory alone is ontology. It seems that there is at this (...) point an important inflection of the system, not thematized as such; is set theory a way of expressing ontology, i.e. mathematics, or is it ontology itself? 2. This leads to a broader questioning of the relationship, in mathematics, between expression and ontology, or “language” and “being”. Here I would like to point out that, contrary to what one might think, there is often an ambiguity between these two aspects not only in Badiou, but more generally in discussions of the philosophy of mathematics. If this distinction is relevant - and I will try to show why it should be - then one cannot conclude too quickly from the fact that mathematics has adopted a unified expression thanks to the language of set theory to the fact that the form of being it expresses is set-theoretic ; 3. Finally, I would like to delve into the fact that the set-theoretic language has precisely given rise to the thematization of two orientations which could be just as well coined “ontological” ; the first is anchored in the concept of number, while the other is anchored in the concept space. The fact that we have a language capable of describing them in a homogeneous fashion does not entail that we are dealing with a single domain of objects. I would like to show that this tension runs through contemporary mathematics, and consequently through Alain Badiou’s thinking more than he wants to admit. In fact, it is at the basis of various attempts proposed in mathematics to arrive at more satisfactory forms of unification than that provided by “sets” alone. (shrink)

Dans La Philosophie de l’algèbre (1962), Jules Vuillemin présente sa démarche comme une manière d’instruire « le problème, si important et si négligé aujourd’hui, de la mathesis universalis dans ses rapports à la philosophie ». Il intitule d’ailleurs la seconde partie du traité « mathématique universelle », titre qu’il reprend pour la conclusion. Présentant le projet du second tome, il avance que cette étude devait le conduire « aux questions concrètes de la mathématique universelle ». Pourtant, à aucun moment, on (...) ne voit Vuillemin expliciter la nature de ce problème. Le but de cet article sera de produire une telle explicitation en s’appuyant, en particulier, sur certains éléments avancés dans le manuscrit préparatoire du second tome. (shrink)

Cet article se propose d’étudier le concept de « mathématique universelle », apparue chez des philosophes comme Aristote, Jamblique et Proclus, dans son rapport à la mathématique. On essaye notamment de montrer qu’il ne se réduit ni à une interprétation extérieure à la donnée mathématique, ni à une pure et simple référence à une théorie, mais s’appuie sur un problème, celui de l’universalité en mathématiques, qu’il s’agit de reconstituer.

Dans cet article, nous analysons le passage dit « mathématique » de l’Épinomis. Dans le programme de formation proposé pour les futurs membres du conseil vespéral de vigilance (990c5-991b4), certains interprètes modernes ont cru voir un témoignage capital pour l’histoire des mathématiques grecques anciennes portant sur la question de l’irrationalité. L’analyse du lexique et du mode de composition du texte – un collage maladroit d’expressions reprises aux loci mathematici platoniciens –, la confrontation avec la littérature mathématique conservée et ce que (...) l’on sait de l’histoire de cette discipline avant Euclide montrent que cette interprétation, pourtant largement répandue, est sans fon­dement. En revanche, il est possible de reconstituer une intention philosophique compréhensible et mieux à même de rendre compte de certaines particularités du passage en consultant les commentateurs anciens (Nicomaque de Gérase, Théon de Smyrne, Jamblique de Chalcis, Proclus de Lycie). En privilégiant le passage conclusif sur le « lien » des mathématiques (991d8-992a1), ils identi­fiaient une tout autre question : celle de l’unité des mathématiques, à partir de laquelle le passage mathématique prenait à leurs yeux tout son sens. (shrink)

A figura de Spinoza, com o seu sonho louco de querer desenvolver uma filosofia total “conforme a ordem da geometria”, como se esta ordem fosse intangível e fixa uma vez por todas, cristaliza particularmente bem as dúvidas que o espírito de sistema pode fazer nascer. Não somente ele representa a caricatura de uma metafísica que gostaria de se fazer passar por ciência, mas esta ciência, ela mesma, aparece como a caricatura de uma racionalidade arrogante e dobrada sobre ela mesma. Explicar (...) de que maneira pode-se, hoje, reivindicar este espírito sem cair sobre tais críticas: este será o meu principal objetivo neste artigo. (shrink)

« Et soudain, devant l'injonction à répondre, s'imposa à moi la possibilité d'une solution : tourner, comme souvent, la faiblesse en force, l'échec en programme. "Tu te souviens que Spinoza dit quelque part que les choses sont produites par Dieu avec la même nécessité qu'il résulte de l'essence d'un triangle que ses angles sont égaux à deux droits. Nous savons aujourd'hui que cette prétendue 'nécessité' découle d'un choix d'axiomes et non d'un absolu fixé une fois pour toutes. Dans la géométrie (...) de Riemann, cette mesure des angles peut même varier d'un point à l'autre, selon la courbure de l'espace. Je crois que j'aimerais pouvoir être ce genre de 'spinoziste' là : qui conserve le système, mais ne croit plus à l'essence du triangle et à l'absolue nécessité de la géométrie". Un spinoziste riemannien, en somme. » Le but de ce petit livre est de jeter les bases d'un tel programme. Il veut reprendre l'ancien rêve d'une éthique more geometrico, telle que Spinoza en a lancé le projet en plein cœur de la « révolution scientifique » et reposer avec lui la seule question qui vaille au fond : qu'est-ce que « bien vivre »? De son modèle, il retient que ce « bien » ne doit pas être pensé comme une norme extérieure au désir des hommes, mais y prend au contraire sa source, de sorte que l'éthique est inséparable d'une théorie des affects et des désirs. Mais il veut le faire dans un cadre qui n'est plus celui d'une confiance absolue dans l'usage des formalismes, ni dans la capacité de l'homme à dévoiler les « lois de la nature » ou à détenir le secret des « lois de la pensée ». « Éthique locale » ne signifie d'abord que cette provocation à penser la possibilité d'une éthique rationnelle et systématique sans accepter le point de vue de surplomb, « global », que permettait la douce assurance d'un régime transparent du monde à la raison dont les deux premières parties de l'Éthique sont profondément empreintes. Pages de début Liste des abréviations utilisées Avant-propos Incipit : Descartes en son cabinet Chapitre Premier. « À la manière des géomètres »? Chapitre II. Construire, dit-il Conclusion : en quoi ce livre est-il un livre d'éthique?Pages de fin. (shrink)

Generality is a key value in scientific discourses and practices. Throughout history, it has received a variety of meanings and of uses. This collection of original essays aims to inquire into this diversity. Through case studies taken from the history of mathematics, physics and the life sciences, the book provides evidence of different ways of understanding the general in various contexts. It aims at showing how individuals have valued generality and how they have worked with specific types of "general" entities, (...) procedures, and arguments. (shrink)

This book, which brings together historians, philosophers and mathematicians, is a tribute to the works of Hourya Benis-Sinaceur, internationally recognized specialist of history and philosophy of mathematics.

Name der Zeitschrift: Archiv für Geschichte der Philosophie Jahrgang: 101 Heft: 3 Seiten: 345-375.

This paper consists of three main sections. In the first section, we consider how early attempts at understanding the relationship between mathematics and philosophy in Leibniz’s thought were often made within the framework of grand reconstructions guided by intellectual trends such as the search for “the ideal of system”. In the second section, we proceed to recount Leibniz’s first encounter with contemporary mathematics during his four years of study in Paris presenting some of the earliest mathematical successes which he made (...) there. In particular, we argue that recently published letters and papers reveal how his youthful mathematical reflexions were deeply intertwined with important philosophical insights that, in turn, acted as guiding ideas for his mathematical research. Finally, in the third section, we situate the central themes of the essays of the present volume within the new understanding of the interrelations between philosophy and mathematics in Leibniz’s thought briefly indicated in the opening section. (shrink)

David Hume's Enquiry concerning Human Understanding is the definitive statement of the greatest philosopher in the English language. His arguments in support of reasoning from experience, and against the "sophistry and illusion"of religiously inspired philosophical fantasies, caused controversy in the eighteenth century and are strikingly relevant today, when faith and science continue to clash. The Enquiry considers the origin and processes of human thought, reaching the stark conclusion that we can have no ultimate understanding of the physical world, or (...) indeed our own minds. In either sphere we must depend on instinctive learning from experience, recognizing our animal nature and the limits of reason. Hume's calm and open-minded skepticism thus aims to provide a new basis for science, liberating us from the "superstition" of false metaphysics and religion. His Enquiry remains one of the best introductions to the study of philosophy, and his edition places it in its historical and philosophical context. (shrink)

A leading political theorist’s groundbreaking defense of ideal conceptions of justice in political philosophy Throughout the history of political philosophy and politics, there has been continual debate about the roles of idealism versus realism. For contemporary political philosophy, this debate manifests in notions of ideal theory versus nonideal theory. Nonideal thinkers shift their focus from theorizing about full social justice, asking instead which feasible institutional and political changes would make a society more just. Ideal thinkers, on the other hand, question (...) whether full justice is a standard that any society is likely ever to satisfy. And, if social justice is unrealistic, are attempts to understand it without value or importance, and merely utopian? Utopophobia argues against thinking that justice must be realistic, or that understanding justice is only valuable if it can be realized. David Estlund does not offer a particular theory of justice, nor does he assert that justice is indeed unrealizable—only that it could be, and this possibility upsets common ways of proceeding in political thought. Estlund engages critically with important strands in traditional and contemporary political philosophy that assume a sound theory of justice has the overriding, defining task of contributing practical guidance toward greater social justice. Along the way, he counters several tempting perspectives, including the view that inquiry in political philosophy could have significant value only as a guide to practical political action, and that understanding true justice would necessarily have practical value, at least as an ideal arrangement to be approximated. Demonstrating that unrealistic standards of justice can be both sound and valuable to understand, Utopophobia stands as a trenchant defense of ideal theory in political philosophy. (shrink)

The zetetic turn in epistemology raises three questions about epistemic and zetetic norms. First, there is the relationship question: what is the relationship between epistemic and zetetic norms? Are some epistemic norms zetetic norms, or are epistemic and zetetic norms distinct? Second, there is the tension question: are traditional epistemic norms in tension with plausible zetetic norms? Third, there is the reaction question: how should theorists react to a tension between epistemic and zetetic norms? Drawing on an analogy to practical (...) philosophy, I develop a focal point view to resolve these motivating questions. On the focal point view, traditional epistemic norms and zetetic norms answer different types of normative questions. There is nevertheless a familiar type of evaluative tension between traditional epistemic norms and zetetic norms, but this tension is an unavoidable feature of the normative landscape and not a sign that traditional epistemic norms need revision. But if traditional epistemic norms are not zetetic norms, then in what sense is zetetic epistemology a project for epistemologists? I conclude by articulating a sense in which some nontraditional epistemic norms are zetetic norms, and in which zetetic epistemology is an important part of the study of theoretical rationality. (shrink)

One of the enduring concerns of moral philosophy is deciding who or what is deserving of ethical consideration. Much recent attention has been devoted to the "animal question" -- consideration of the moral status of nonhuman animals. In this book, David Gunkel takes up the "machine question": whether and to what extent intelligent and autonomous machines of our own making can be considered to have legitimate moral responsibilities and any legitimate claim to moral consideration. The machine question poses a (...) fundamental challenge to moral thinking, questioning the traditional philosophical conceptualization of technology as a tool or instrument to be used by human agents. Gunkel begins by addressing the question of machine moral agency: whether a machine might be considered a legitimate moral agent that could be held responsible for decisions and actions. He then approaches the machine question from the other side, considering whether a machine might be a moral patient due legitimate moral consideration. Finally, Gunkel considers some recent innovations in moral philosophy and critical theory that complicate the machine question, deconstructing the binary agent--patient opposition itself. Technological advances may prompt us to wonder if the science fiction of computers and robots whose actions affect their human companions could become science fact. Gunkel's argument promises to influence future considerations of ethics, ourselves, and the other entities who inhabit this world. (shrink)

This book is an attempt to get to the bottom of an acute and perennial tension between our best scientific pictures of the fundamental physical structure of the world and our everyday empirical experience of it. The trouble is about the direction of time. The situation (very briefly) is that it is a consequence of almost every one of those fundamental scientific pictures--and that it is at the same time radically at odds with our common sense--that whatever can happen can (...) just as naturally happen backwards. Albert provides an unprecedentedly clear, lively, and systematic new account--in the context of a Newtonian-Mechanical picture of the world--of the ultimate origins of the statistical regularities we see around us, of the temporal irreversibility of the Second Law of Thermodynamics, of the asymmetries in our epistemic access to the past and the future, and of our conviction that by acting now we can affect the future but not the past. Then, in the final section of the book, he generalizes the Newtonian picture to the quantum-mechanical case and (most interestingly) suggests a very deep potential connection between the problem of the direction of time and the quantum-mechanical measurement problem. The book aims to be both an original contribution to the present scientific and philosophical understanding of these matters at the most advanced level, and something in the nature of an elementary textbook on the subject accessible to interested high-school students. Table of Contents: Preface 1. Time-Reversal Invariance 2. Thermodynamics 3. Statistical Mechanics 4. The Reversibility Objections and the Past-Hypothesis 5. The Scope of Thermodynamics 6. The Asymmetries of Knowledge and Intervention 7. Quantum Mechanics Appendix: Gedankenexperiments with Heat Engines Index Reviews of this book: The foundations of statistical mechanisms are often presented in physics textbooks in a rather obscure and confused way. By challenging common ways of thinking about this subject, Time and Chance can do quite a lot to improve this situation. --Jean Bricmont, Science Albert is perfecting a style of foundational analysis that is uniquely his own...It has a surgical precision...and it is ruthless with pretensions. The foundations of thermodynamics is a topic that has accumulated a good deal of dead wood; this is a fire that will burn and burn. --Simon W. Saunders, Oxford University As usual with Albert's work, the exposition is brisk and to the point, and exceptionally clear...The book will be an extremely valuable contribution to the literature on the subject of philosophical issues in thermodynamics and statistical mechanics, a literature which has been thin on the ground but is now growing as it deserves to. --Lawrence Sklar, University of Michigan. (shrink)

By means of an example, shows the possibility of beliefs that are separately rational whilst together inconsistent.

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

I modify Grice's theory of conversational implicature so as to accommodate acts of implicating propositions by asking questions, acts of implicating questions by asserting propositions, and acts of implicating questions by asking questions. I describe the relations between a declarative sentence's semantic content (the proposition it semantically expresses), on the one hand, and the propositions that a speaker locutes, asserts, and implicates by uttering that sentence, on the other. I discuss analogous relations between an interrogative sentence's semantic content (the question (...) it semantically expresses), and the questions that a speaker locutes, asks, and implicates by uttering that sentence. (shrink)

Consider the following two (hypothetical) generic causal claims: “Living in a neighborhood with many families with children increases purchases of bicycles” and “living in an affluent neighborhood with many families with children increases purchases of bicycles.” These claims not only differ in what they suggest about how bicycle ownership is distributed across different neighborhoods (i.e., “the data”), but also have the potential to communicate something about the speakers’ values: namely, the prominence they accord to affluence in representing and making decisions (...) about the social world. Here, we examine the relationship between the level of granularity with which a cause is described in a generic causal claim (e.g., neighborhood vs. affluent neighborhood) and the value of the information contained in the causal model that generates that claim. We argue that listeners who know any two of the following can make reliable inferences about the third: 1) the level of granularity at which a speaker makes a generic causal claim, 2) the speaker’s values, and 3) the data available to the speaker. We present results of four experiments (N=1,323) in the domain of social categories that provide evidence in keeping with these predictions. (shrink)

I attempt to get as clear as possible on the chain of reasoning by which irreversible macrodynamics is derivable from time-reversible microphysics, and in particular to clarify just what kinds of assumptions about the initial state of the universe, and about the nature of the microdynamics, are needed in these derivations. I conclude that while a “Past Hypothesis” about the early Universe does seem necessary to carry out such derivations, that Hypothesis is not correctly understood as a constraint on the (...) early Universe’s entropy. (shrink)

Understanding Animal Welfare, 2nd Edition is revised and expanded to incorporate new research and developments in animal welfare. Updated with greater accessibility in mind, the reader is guided through animal welfare in its cultural and historical context, methods of study, and applications in practice and policy. Drawing examples from farm, companion, laboratory and zoo animals, the text provides an up-to-date overview of research and its applications, while also tracing how concepts and methods have evolved over time. Originally intended for scientists (...) and professionals, Understanding Animal Welfare has also found a home in undergraduate classrooms. It is now the essential text for students, practitioners, veterinarians, and researchers in animal welfare and related fields. (shrink)

We start by presenting three different views that jointly imply that every person has many conscious beings in their immediate vicinity, and that the number greatly varies from person to person. We then present and assess an argument to the conclusion that how confident someone should be in these views should sensitively depend on how massive they happen to be. According to the argument, sometimes irreducibly de se observations can be powerful evidence for or against believing in metaphysical theories.

Worries about mental causation are prominent in contemporary discussions of the mind and human agency. Originally, the problem of mental causation was that of understanding how a mental substance (thought to be immaterial) could interact with a material substance, a body. Most philosophers nowadays repudiate immaterial minds, but the problem of mental causation has not gone away. Instead, focus has shifted to mental properties. How could mental properties be causally relevant to bodily behavior? How could something mental qua mental cause (...) what it does? After looking at the traditional Problem of Interaction, we survey various versions of the property-based problem and look at proposed solutions to them. (shrink)

Unprecedented advances in medicine, genetic engineering, and demographic forecasting raise new questions that strain the categories and assumptions of traditional ethical theories. Heyd's approach resolves many paradoxes in intergenerational justice, while offering a major test case for the profound problems of the limits of ethics and the nature of value. This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and (...) impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992. (shrink)

In this paper we show that axiomatic extensions of H. Wansing’s connexive logic $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) are algebraizable (in the sense of J.W. Blok and D. Pigozzi) with respect to sub-varieties of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras. We develop the structure theory of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ )-algebras, and we prove their representability in terms of twist-like constructions over implicative lattices (Heyting algebras). As a consequence, we further clarify the relationship between the aforementioned classes. Finally, taking advantage of (...) the above machinery, we provide some preliminary remarks on the lattice of axiomatic extensions of $$\textsf{C}$$ ( $$\textsf{C}^{\perp }$$ ) as well as on some properties of their equivalent algebraic semantics. (shrink)

Film is an art form with a language and an aesthetic all its own. Since 1979, David Bordwell and Kristin Thompson's Film Art has been the best-selling and widely respected introduction to the analysis of cinema. Taking a skills-centered approach supported by a wide range of examples from various periods and countries, the authors strive to help students develop a core set of analytical skills that will deepen their understanding of any film, in any genre. Frame enlargements throughout the (...) text enable students to view images taken directly from completed films, while an optional, text-specific tutorial CD-ROM helps clarify and reinforce specific concepts addressed in the text with the use of film clips. Building on these strengths, the ninth edition adds coverage of new technologies, updated examples, and references to the authors' acclaimed weblog to provide unparalleled currency and connect students with the world of cinema today. (shrink)

In a spirit of collegial support, this paper argues that Beckett and Hager’s theoretical justification and empirical exemplifications do not do full justice to the complexity of group or team learning. We firstly reaffirm our support for the theoretical argument Becket and Hager make, though expressing some reservations about Complexity Theory, to explain the taken-for-granted assumptions that learning by an individual is the paradigm case of learning and that context plays a minimal role in this process. Drawing on our joint (...) and separate work, we demonstrate that Becket and Hager’s argument is less radical than it may initially seem because it is predicated on: (i) cognitive-bounded rather than “distributed” or “extended” conception of mind; (ii) material rather than a “immaterial” conception of activity; and (iii) co-present rather than a “fractional” or “connective” conception of ontology. Despite making this critique, we conclude by making the case that we are adding further substance to Becket and Hager’s overarching argument and, in doing so, encouraging them to be more radical about how they conceptualise the complexity of learning. (shrink)

Our aim in this entry is to articulate the state of the art in the moral psychology of personal identity. We begin by discussing the major philosophical theories of personal identity, including their shortcomings. We then turn to recent psychological work on personal identity and the self, investigations that often illuminate our person-related normative concerns. We conclude by discussing the implications of this psychological work for some contemporary philosophical theories and suggesting fruitful areas for future work on personal identity.

Dark matter is a fundamental component of the standard cosmological model, but in spite of four decades of increasingly sensitive searches, no-one has yet detected a single dark-matter particle in the laboratory. An alternative cosmological paradigm exists: MOND (Modified Newtonian Dynamics). Observations explained in the standard model by postulating dark matter are explained in MOND by proposing a modification of Newton's laws of motion. Both MOND and the standard model have had successes and failures – but only MOND has repeatedly (...) predicted observational facts in advance of their discovery. In this volume, David Merritt outlines why such predictions are considered by many philosophers of science to be the 'gold standard' when it comes to judging a theory's validity. In a world where the standard model receives most attention, the author applies criteria from the philosophy of science to assess, in a systematic way, the viability of this alternative cosmological paradigm. (shrink)

Perceptualists say that having a pain in a body part consists in perceiving the part as instantiating some property. I argue that perceptualism makes better sense of the connections between pain location and the experiences undergone by people in pain than three alternative accounts that dispense with perception. Turning to fellow perceptualists, I also reject ways in which David Armstrong and Michael Tye understand and motivate perceptualism, and I propose an alternative interpretation, one that vitiates a pair of objections—due (...) to John Hyman—concerning the meaning of ‘Amy has a pain in her foot’ and the idea of bodily sensitivity. Perceptualism, I conclude, remains our best account of the location of pains. (shrink)

Epistemic Evaluation aims to explore and apply a particular methodology in epistemology. The methodology is to consider the point or purpose of our epistemic evaluations, and to pursue epistemological theory in light of such matters. Call this purposeful epistemology. The idea is that considerations about the point and purpose of epistemic evaluation might fruitfully constrain epistemological theory and yield insights for epistemological reflection. Several contributions to this volume explicitly address this general methodology, or some version of it. Others focus on (...) advancing some application of the methodology rather than on theorizing about it. The papers go on to explore the idea that purposes allow one to understand the conceptual demands on knowing, examine how purposeful epistemology might shed light on the debate between internalist and externalist epistemologies, and further develop the idea of purposeful epistemology. (shrink)