In this note, we show that a partition of a cake is Pareto optimal if and only if it maximizes some convex combination of the measures used by those who receive the resulting pieces of cake. Also, given any sequence of positive real numbers that sum to one (which may be thought of as representing the players' relative entitlements), we show that there exists a partition in which each player receives either more than, less than, or exactly his or her (...) entitlement (according to his or her measure), in any desired combination, provided that the measures are not all equal. (shrink)

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time's arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory's ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine's version or in Bohm's version, does (...) not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

Plato and Platonism reviews the natures and limits of Platonic interpretation. Students, academics and researchers will find that Moravcsik's careful and rigorous analysis offers an understanding of what Platonism in our times would have been like. The book leads us to an appreciation of genuine Platonism, rarely discussed today.

Die wirtschaftliche und soziale Bedeutung der Juden im Mittelalter.--John Spencer's Erklärung der biblischen Gesetze in ihrer Beziehung zu Maimonides.--Max Webers Soziologie des antiken Judentums.--Zu Gabirols allegorischer Deutung der Erzählung vom Paradies.--Das Problem der Willensfreiheit bei Ḥasdai Crescas und den islamschen Aristotelikern.--Religion und Wissenschaft im mittelalterlichen und im modernen Denken.--Zur Kritik der Offenbarungsreligion in der islamischen und jüdischen Philosophie.--[Le-ḥeḳer ha-meḳorot shel Sefer ha-ʻiḳarim].--Die Akademie für die Wissenschaft des Judentums.--Die religiösen Motive in der Philosophie des Maimonides.--Das Problem der Kontingenz in der Philosophie (...) des Maimonides.--Die Normierung des Glaubensinhalts im Judentum.--Hermann Cohens Ethik. (shrink)

The aim of this paper is to analyze time-asymmetric quantum mechanics with respect to the problems of irreversibility and of time’s arrow. We begin with arguing that both problems are conceptually different. Then, we show that, contrary to a common opinion, the theory’s ability to describe irreversible quantum processes is not a consequence of the semigroup evolution laws expressing the non-time-reversal invariance of the theory. Finally, we argue that time-asymmetric quantum mechanics, either in Prigogine’s version or in Bohm’s version, does (...) not solve the problem of the arrow of time because it does not supply a substantial and theoretically founded criterion for distinguishing between the two directions of time. (shrink)

In the Phaedrus scientific psychology is an integral part of Plato's outline of scientific rhetoric. An accomplished rhetorician must know all types of human souls , he must know what kind of soul is affected by what kind of speech, and he must be able to apply this theoretical knowledge in front of an audience, so as to achieve the intended persuasion with unfailing certainty. This knowledge is an essential qualification of a philosopher; it enables him to choose a soul (...) of the right type and plant in it words of wisdom. His words, that is the authentic logos, acquire new life in the soul of the recipient, who in his turn sows their progeny in other suitable souls . In the dialogue, Socrates implants the words of wisdom in the soul of Phaedrus, and wishes that Phaedrus may similarly influence Lysias . Socrates’ work on Phaedrus permeates the whole dialogue, giving it its dramatic unity, and yet interpreters disagree on it. The late dating of the dialogue, which has been accepted as axiomatic throughout this century, stands in the way of seeing it clearly. Phaedrus in the Protagoras and in the Symposium does not appear like a man who would appropriate the exalted ideal raised before him in the Phaedrus. The majority of modern interpreters therefore cannot see Phaedrus’ conversion to philosophy in the Phaedrus as anything but ironic. I shall argue that Plato in the dialogue does enact his Phaedran ideal of the authentic communication of philosophy, and that this precludes the ironical reading of the dialogue. (shrink)

In the Phaedrus scientific psychology is an integral part of Plato's outline of scientific rhetoric. An accomplished rhetorician must know all types of human souls, he must know what kind of soul is affected by what kind of speech, and he must be able to apply this theoretical knowledge in front of an audience, so as to achieve the intended persuasion with unfailing certainty. This knowledge is an essential qualification of a philosopher; it enables him to choose a soul of (...) the right type and plant in it words of wisdom. His words, that is the authentic logos, acquire new life in the soul of the recipient, who in his turn sows their progeny in other suitable souls. In the dialogue, Socrates implants the words of wisdom in the soul of Phaedrus, and wishes that Phaedrus may similarly influence Lysias. Socrates’ work on Phaedrus permeates the whole dialogue, giving it its dramatic unity, and yet interpreters disagree on it. The late dating of the dialogue, which has been accepted as axiomatic throughout this century, stands in the way of seeing it clearly. Phaedrus in the Protagoras and in the Symposium does not appear like a man who would appropriate the exalted ideal raised before him in the Phaedrus. The majority of modern interpreters therefore cannot see Phaedrus’ conversion to philosophy in the Phaedrus as anything but ironic. I shall argue that Plato in the dialogue does enact his Phaedran ideal of the authentic communication of philosophy, and that this precludes the ironical reading of the dialogue. (shrink)

By moving away from the traditional reductionist reading of the quantum theory of atoms in molecules, in this paper we analyze the role played by QTAIM in the relationship between molecular chemistry and quantum mechanics from an emergentist perspective. In particular, we show that such a relationship involves two steps: an intra-domain emergence and an inter-domain emergence. Intra-domain emergence, internal to quantum mechanics, results from the fact that the electron density, from which all the other QTAIM’s concepts are defined, arises (...) from the wavefunction as a coarse-grained magnitude. Inter-domain emergence involves an analogical link, a mapping, between QTAIM’s entities, such as topological atoms and bond paths, and the entities that populate the molecular-chemistry domain, such as chemical atoms and chemical bonds. (shrink)

The ideas of Franz Rosenzweig have had relatively little impact outside of the circle of contemporary liberal Jewish thinkers. It is even more unlikely that his name would be found in any of the countless volumes an ethical theory. I argue that the ethical theory implied in his primary philosophical work, The Star of Redemption, is compelling and worth sustained and serious study by a wider audience. ;Rosenzweig rejects an Hegelian totalitarian ontological framework for ethics, in favor of a relational (...) ethics that is based on the immediate demands of a concretely contingent other. I construct the epistemological foundations for such an ethics out of his work, by drawing on an analogy from the new science of chaos and Rosenzweig's avowed reliance on Hermann Cohen's differential calculus of infinitesimals. ;In addition to considering the mathematical symbolic logic that serves to structure his epistemology, I consider how aesthetics plays a role in his ethical theory. I contrast essential elements of Rosenzweig's philosophy with those of Martin Heidegger's in order to specify why these two contemporaries have been so closely associated and why they should be more clearly distinguished from each other. Besides the obvious cultural parameters, what makes them similar is not only their univocal departure from a Western metaphysics of substance, but also a common concern to locate human beings in the vitally relational way that we exist in the world. Their differences are most clearly defined in how each respectively appropriates language and aesthetics in that locative process. ;For Heidegger, art as the way of language par excellence becomes the medium by which a human being becomes aware of his/her own solitary and finite existence through bringing one face-to-face with the ultimate nature of one's own death. For Rosenzweig, that same awareness is countered by his introduction of the revelatory experience of responsible love of one human being for an other, and which he analogically models on a dialogical encounter with God. I argue that the ultimate difference between these two thinkers, then, is that with Rosenzweig we are provided with the tools to develop an ethical theory that has contemporary relevance for responsible relationships, while with Heidegger, who openly rejects ethics as the context for a discourse on human authenticity, we are left with next to nothing. (shrink)

Despite of its formal precision and its great many applications, Shannon’s theory still offers an active terrain of debate when the interpretation of its main concepts is the task at issue. In this article we try to analyze certain points that still remain obscure or matter of discussion, and whose elucidation contribute to the assessment of the different interpretative proposals about the concept of information. In particular, we argue for a pluralist position, according to which the different views about information (...) are no longer rival, but different interpretations of a single formal concept. (shrink)

Morality is often thought of as non-rational or sub-rational. In Moral Notions, first published in 1967, Julius Kovesi argues that the rationality of morality is built into the way we construct moral concepts. In showing this he also resolves the old Humean conundrum of the relation between 'facts' and 'values'. And he puts forward a method of reasoning that might make 'applied ethics' (at present largely a hodge-podge of opinions) into a constructive discipline. Kovesi's general theory of concepts - (...) important in its own right - is indebted to his interpretation of Plato, and his three papers on Plato, first published here, explain this debt. This new edition of Moral Notions also includes a foreward by Philippa Foot, a biography of the author, and a substantial afterword in which the editors, Robert Ewin and Alan Tapper, explain the signficance of Kovesi's work. (shrink)

Aristotle did not see a sharp contrast between the psychological and the physical. He viewed the physical as just the natural, and treats the psychological as part of the physical. This essay attempts to explain why this is so, and presents observations about Aristotle’s framework. It explores the relation of hylomorphism to functionalism, and argues against funtionalist interpretations of Aristotle due to the belief that Aristotle was confronting a different set of concerns and issues.

Introduction.--The literary form and philosophical content of the Platonic dialogue.--Plato's method of dialectic.

Enactivists often defend the following two claims: Successful interactions are not driven and explained by the interactors’ ability to mindread. And the mechanisms enabling 2nd personal social cognition and those enabling 3rd personal social cognition are distinct. In this paper, I argue that both of these claims are false. With regard to I argue that enactivists fail to provide a plausible alternative to traditional accounts of social cognition in interaction. I examine and reject Hanne De Jaegher’s view according to which (...) interaction is “constitutive” for social interaction. Furthermore, I critically discuss Shaun Gallagher’s and Daniel Hutto’s views according to which social interactions are exclusively driven by low level cognitive mechanisms such as “gaze following” and “emotion detection”. Concerning, I rely on data from so called “spontaneous response” false belief tasks to show that interactive and observational paradigms require the same “social-cognitive” interpretation. (shrink)

In the present paper we address the problem of optical isomerism embodied in the socalled “Hund’s paradox”, which points to the difficulty to account for chirality by means of quantum mechanics. In particular, we explain the answer to the problem proposed by the theory of decoherence. The purpose of this article is to challenge this answer on the basis of a conceptual analysis of the phenomenon of decoherence, that reveals the limitations of the theory of decoherence to solve the difficulties (...) posed by optical isomerism and, in general, by quantum measurement. (shrink)

In Plato's Theaetetus Socrates is portrayed as a midwife of the intellect. The comparison of Socratic questioning to midwifery had until recently been commonly attributed to Socrates himself. In 1977 M. F. Burnyeat published Socratic Midwifery, Platonic Inspiration, which transformed the way in which the dialogue has since been perceived. The author maintains that the midwife comparison is in no sense to be attributed to the historical Socrates.

The main aim of this work is to contribute tothe elucidation of the concept of informationby comparing three different views about thismatter: the view of Fred Dretske's semantictheory of information, the perspective adoptedby Peter Kosso in his interaction-informationaccount of scientific observation, and thesyntactic approach of Thomas Cover and JoyThomas. We will see that these views involvevery different concepts of information, eachone useful in its own field of application. This comparison will allow us to argue in favorof a terminological `cleansing': it (...) is necessaryto make a terminological distinction among thedifferent concepts of information, in order toavoid conceptual confusions when the word`information' is used to elucidate relatedconcepts as knowledge, observation orentropy. (shrink)