Die "Paradoxien des Unendlichen" sind ein Klassiker der Philosophie der Mathematik und zugleich eine gute Einführung in das Denken des "Urgroßvaters" der analytischen Philosophie. Das Unendliche - seit jeher ein Faszinosum für die philosophische Reflexion - wurde in der Zeit nach der Grundlegung der Analysis durch Leibniz und Newton in der Mathematik zunächst als Problem betrachtet, das sich nicht vollkommen widerspruchsfrei behandeln lässt. Bernard Bolzano, der heute als "Urgroßvater der analytischen Philosophie" (Michael Dummett) gilt, zeigt in diesem klassisch gewordenen (...) Text jedoch, dass es beim Nachdenken über das Unendliche, sofern man begrifflich differenziert argumentiert und klare Definitionen zugrunde legt, keine echten Widersprüche gibt und sich die "Paradoxien des Unendlichen" auflösen lassen. Bolzano setzt sich zunächst mit den Unendlichkeitsbegriffen der Mathematik und der (idealistisch geprägten) Philosophie seiner Zeit auseinander, bevor er sich Schritt für Schritt die analytischen Grundlagen einer konsistenten Theorie des Unendlichen erarbeitet. Bereits einige Jahrzehnte vor Georg Cantors bis heute maßgeblicher mathematischer Unendlichkeitsdefinition gelingt Bolzano mit diesem Werk, dessen logische Klarheit und dessen Grad an philosophischer Durchdachtheit bis heute Beispielcharakter haben, die Rehabilitation des Unendlichen für die Philosophie der Mathematik. Die "Paradoxien des Unendlichen" wurden zuerst 1851 aus dem Nachlass herausgegeben. Diese Neuausgabe beruht auf dem der Erstausgabe zugrundeliegenden Manuskript. (shrink)

This new translation of four revised radio interviews, conducted in December 2002 at France Culture with Elie During, is the best introduction to Stiegler's Time and Technics series. This collection includes a new interview conducted specially for this volume and an interview with Artpress from 2001. In Philosophising By Accident, Stiegler introduces some of the key arguments about the technical constitution of the human and its relation to politics, aesthetics and economics. He reads philosophical texts from the perspective of his (...) controversial thesis about the three types of memory and speaks about concepts central to his later works, such as synchrony/diachrony, grammatisation and the industrial temporal object. (shrink)

Bernard Berofsky addresses that metaphysical picture directly.Nature's Challenge to Free Willoffers an original defense of Humean Compatibilism.

Reid's response to hume has traditionally been taken as begging all of hume's questions. One can, However, Find in reid an argument against hume's phenomenalistic skepticism. Reid's appeal to common sense is an attempt to call attention to the fact that we experience objects as external to us, Not as bundles of impressions. Still, Our access to these objects does arise out of sensations, Which are mental contents. Extending berkeley's idea of the "language of nature" reid suggests that language and (...) signification present apt theoretical models for explaining perception. Using this model, One can provide an answer to the argument from illusion. (shrink)

Thomas Hobbes was the first great English political philosopher. His work excited intense controversy among his contemporaries and continues to do so in our own time. In this masterly introduction to his work, Bernard Gert provides the first account of Hobbes’s political and moral philosophy that makes it clear why he is regarded as one of the best philosophers of all time in both of these fields. In a succinct and engaging analysis the book illustrates that the commonly accepted (...) view of Hobbes as holding psychological egoism is not only incompatible with his account of human nature but is also incompatible with the moral and political theories that he puts forward. It also explains why Hobbes’s contemporaries did not accept his explicit claim to be providing a natural law account of morality. Gert shows that for Hobbes, civil society is established by a free-gift of their right of nature by the citizens; it does not involve a mutual contract between citizens and sovereign. As injustice involves breaking a contract, the sovereign cannot be unjust; however, the sovereign can be guilty of ingratitude, which is immoral. This distinction between injustice and immorality is part of a sophisticated and nuanced political theory that is in stark contrast to the reading often incorrectly attributed to Hobbes that “might makes right”. It illustrates how Hobbes’s goal of avoiding civil war provides the key to understanding his moral and political philosophy. _Hobbes: Prince of Peace_ is likely to become the classic introduction to the work of Thomas Hobbes and will be a valuable resource for scholars and students seeking to understand the importance and relevance of his work today. (shrink)

I outline some of my work and results on my matter-gravity entanglement hypothesis, according to which the entropy of a closed quantum gravitational system is equal to the system’s matter-gravity entanglement entropy. The main arguments presented are: that this hypothesis is capable of resolving what I call the second-law puzzle, i.e. the puzzle as to how the entropy increase of a closed system can be reconciled with the asssumption of unitary time-evolution; that the black hole information loss puzzle may be (...) regarded as a special case of this second law puzzle and that therefore the same resolution applies to it; that the black hole thermal atmosphere puzzle can be resolved by adopting a radically different-from-usual description of quantum black hole equilibrium states, according to which they are total pure states, entangled between matter and gravity in such a way that the partial states of matter and gravity are each approximately thermal equilibrium states ; that the Susskind–Horowitz–Polchinski string-theoretic understanding of black hole entropy as the logarithm of the degeneracy of a long string cannot be quite correct but should be replaced by a modified understanding according to which it is the entanglement entropy between a long string and its stringy atmosphere, when in a total pure equilibrium state in a suitable box, which ) goes over, at strong-coupling, to a black hole in equilibrium with its thermal atmosphere. The modified understanding in is based on a general result, which I also describe, which concerns the likely state of a quantum system when it is weakly coupled to an energy-bath and the total state is a random pure state with a given energy. This result generalizes Goldstein et al.’s ‘canonical typicality’ result to systems which are not necessarily small. (shrink)

How I became a philosopher -- To love, to love me, to love us.

Most conceptual models of the organization of the cardiovascular system begin with the premise that the nervous system regulates the metabolic and nonmetabolic reflex adjustments of the circulation. These models assume that all the neurally mediated responses of the circulation are reactive, i.e., reflexes elicited by adequate stimuli. This target article suggests that the responses of the circulation are conditional in three senses. First, as Sherrington argued, reflexes are conditional in that they never operate in a vacuum but in a (...) context together with other reflexes. Guided by functional utility, they interact rather than add. Second, as Pavlov argued, stimuli acquire meanings as a result of experience. This notion of stimulus effect plus the Sherringtonian notion of conditionality suggest that association is one of the ways stimuli eliciting cardiovascular reflexes acquire their meanings and thus their relative strengths. Finally, as Skinner and others have argued, operants are responses that act upon the environment to obtain consequences – that is, stimuli. As operants, cardiovascular responses fulfill a major biological need, functioning proactively. The cardiovascular response is an integral component of the animal's behavior regardless of whether it is an elicited reflex or the eliciting stimulus acquired its properties as a result of the genetic inheritance of the animal or through experience, or the cardiovascular response is emitted in anticipation of an environmental consequence. The main theses of this essay are: (1) behavior is an integrated set of responses and the circulation is one of the response systems comprising behavior; (2) behavior is, in part, determined by its functional significance within a context; (3) the contextual factors operative at the time of the behavior have a major role in determining which of the set of possible responses will determine the final act, that is, which behavior will be the effective response and which other behaviors will be concomitants. (shrink)

Hobbes has served for both philosophers and political scientists as the paradigm case of someone who held an egoistic view of human nature. In this article I shall attempt to show that the almost unanimous view that Hobbes held psychological egoism is mistaken, and further that Hobbes's political theory does not demand an egoistic psychology, but on the contrary is incompatible with psychological egoism. I do not maintain that Hobbes was completely consistent; in fact, I shall show that there was (...) a continuous development in Hobbes's works away from an egoistic psychology. But I do think that the main outlines of Hobbes's political theory, i.e., his account of the laws of nature, the right of nature, the obligations imposed by laws and covenants, and the rights and duties of citizen and sovereign, are essentially the same in The Elements of Law, De Cive, and Leviathan. I thus hold that even in his earliest work, The Elements, the only one where a charge of egoism is justifiable, the political theory does not depend on egoism. But the first and most important point to be established is that Hobbes did not hold an egoistic psychology. (shrink)

The scholastic philosopher is interested in definition for a different reason than the lexicographer and linguist. The philosopher is trying to learn things. Fe defines, after investigating reality, in an attempt to describe reality clearly and to sum up some aspect of his understanding of reality. Hence, we find our scholastic philosophers adopting as a main feature of their method this insistence on defining, on precise and detailed explanation of their definitions, and on proving that their definitions da correctly express (...) what a nature or activity is. A dictionary of the language of scholastic philosophy fitted to the needs of beginners and of undergraduate students of the subject is not available in English. (shrink)

After more than a decade teaching ancient Greek history and philosophy at University College, Oxford, British philosopher and political theorist Bernard Bosanquet resigned from his post to spend more time writing. He was particularly interested in contemporary social theory, and was involved with the Charity Organisation Society and the London Ethical Society. He saw himself as a radical in the Liberal Party, and at a theoretical level he was a 'collectivist', considering the individual to be a part of a (...) larger social organism. He thought the state should be in harmony with the general will, and that going beyond it would lead to repression. Bosanquet's political ideas are explained in this influential work, which was published in 1899 and ran to four editions by 1923. Bosanquet begins with the theory of state, and then addresses sociological and philosophical ideas about politics before examining the idea of 'will'. (shrink)

Block's cases of superblindsight, the pneumatic drill, and the Sperling experiments do not show that P-consciousness and Aconsciousness can come apart. On certain tendentious but not implausible construals of the concepts of P- and A-consciousness, they refer to the same psychological phenomenon.

This is the text of The Lindley Lecture for 1985, given by Bernard Williams, a British philosopher.

This paper attempts to refute the familiar sceptical argument based upon the theoretical possibility of systematic transpositions of colours in different observers? colour?vision. The force of this argument lies in its apparent demonstration that cases of transposed colour?vision would be on a quite different cognitive footing from ordinary cases of colour?blindness; since colour transposition, unlike colour?blindness, could not possibly have any effect on the use of language by a person who suffered from it. It is argued (1) that this demonstration (...) works only if we assume the truth of a certain theory of the logical nature of our colour vocabulary, and (2) that this theory is false. (shrink)

The scholastic philosopher is interested in definition for a different reason than the lexicographer and linguist. The philosopher is trying to learn things. Fe defines, after investigating reality, in an attempt to describe reality clearly and to sum up some aspect of his understanding of reality. Hence, we find our scholastic philosophers adopting as a main feature of their method this insistence on defining, on precise and detailed explanation of their definitions, and on proving that their definitions da correctly express (...) what a nature or activity is. A dictionary of the language of scholastic philosophy fitted to the needs of beginners and of undergraduate students of the subject is not available in English. (shrink)

This new volume of philosophical papers by Bernard Williams is divided into three sections: the first Action, Freedom, Responsibility, the second Philosophy, Evolution and the Human Sciences; in which appears the essay which gives the collection its title; and the third Ethics, which contains essays closely related to his 1983 book Ethics and the Limits of Philosophy. Like the two earlier volumes of Williams's papers published by Cambridge University Press, Problems of the Self and Moral Luck, this volume will (...) be welcomed by all readers with a serious interest in philosophy. It is published alongside a volume of essays on Williams's work, World, Mind, and Ethics: Essays on the Ethical Philosophy of Bernard Williams, edited by J. E. J. Altham and Ross Harrison, which provides a reappraisal of his work by other distinguished thinkers in the field. (shrink)

In this paper, we analyze the astronomical tables in al-Zīj al-Muqtabis by Ibn al-Kammād (early twelfth century, Córdoba), based on the Latin and Hebrew versions of the lost Arabic original, each of which is extant in a unique manuscript. We present excerpts of many tables and pay careful attention to their structure and underlying parameters. The main focus, however, is on the impact al-Muqtabis had on the astronomy that developed in the Iberian Peninsula and the Maghrib and, more generally, on (...) the transmission and diffusion of Indian astronomy in the West after the arrival of al-Khwārizmī’s astronomical tables in al-Andalus (Muslim Spain) in the tenth century. This tradition of Indian origin competed with the Greek tradition represented by al-Battānī’s astronomical tables and was much more alive in the Iberian Peninsula and the Maghrib than previously thought. From Spain, the Indian tradition entered mainstream European astronomy, where we find echoes of it in all versions of the Alfonsine Tables, both in manuscript and in the printed editions (beginning in 1483), as well as in Copernicus’s De Revolutionibus, published in 1543. (shrink)

D’un point de vue patrimonial, le célèbre texte des Éléments de géométrie de Clairaut, publié la première fois en 1741, est traditionnellement considéré comme le début d’une riche histoire plutôt que son aboutissement, en raison notamment du succès considérable qu’il a eu dès sa parution et de la manière dont Clairaut en a défendu le projet, en rupture apparente avec le modèle euclidien. Nous proposons ici une image un peu différente qui s’appuie sur la nature très particulière de la production (...) géométrique foisonnante dans laquelle le traité de Clairaut s’insère et doit être compris. Nous présentons tout d’abord le côté paradoxal de l’ouvrage, qui revendique non seulement une grande originalité mais aussi une non moins grande conformité au genre des « éléments » de géométrie spéculative. Nous indiquons ensuite cinq raisons majeures qui montrent que le texte était en effet largement conforme aux attendus de l’époque, y compris dans sa revendication d’accessibilité et de rupture vis-à-vis du modèle euclidien. Nous dégageons deux originalités de l’ouvrage : le fait de confondre les caractéristiques des géométries spéculatives et pratiques dans un seul et même ouvrage ; et le fait d’écrire un ouvrage de géométrie suivant un « ordre analytique », mais sans algèbre. (shrink)

We provide a suitable theoretical foundation for the notion of the quantum coherent state which describes the electrostatic field due to a static external macroscopic charge distribution introduced by the author in 1998 and use it to rederive the formulae obtained in 1998 for the inner product of a pair of such states. (We also correct an incorrect factor of 4π\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$4\pi$$\end{document} in some of those formulae.) Contrary to what one might expect, (...) this inner product is usually non-zero whenever the total charges of the two charge distributions are equal, even if the charge distributions themselves are different. We actually display two different frameworks that lead to the same inner-product formulae, in the second of which Gauss’s law only holds in expectation value. We propose an experiment capable of ruling out the latter framework. We then address the problem of finding a product picture for QED—i.e. a reformulation in which it has a total Hamiltonian, arising as a sum of a free electromagnetic Hamiltonian, a free charged-matter Hamiltonian and an interaction term, acting on a Hilbert space which is a subspace (the physical subspace) of the full tensor product of a charged-matter Hilbert space and an electromagnetic-field Hilbert space. (The traditional Coulomb gauge formulation of QED isn’t a product picture in this sense because, in it, the longitudinal part of the electric field is a function of the charged matter operators.) Motivated by the first framework for our coherent-state construction, we find such a product picture and exhibit its equivalence with Coulomb gauge QED both for a charged Dirac field and also for a system of non-relativistic charged balls. For each of these systems, in all states in the physical subspace (including the vacuum in the case of the Dirac field) the charged matter is entangled with longitudinal photons and Gauss’s law holds as an operator equation; albeit the electric field operator (and therefore also the full Hamiltonian) while self-adjoint on the physical subspace, fails to be self-adjoint on the full tensor-product Hilbert space. The inner products of our electrostatic coherent states and the product picture for QED are relevant as analogues to quantities that play a rôle in the author’s matter-gravity entanglement hypothesis. Also, the product picture provides a temporal gauge quantization of QED which appears to be free from the difficulties which plagued previous approaches to temporal-gauge quantization. (shrink)