In a number of works, we have suggested that whereas the ordered field R of real numbers should merely be regarded as constituting an arithmetic continuum (modulo the Archimedean axiom), the ordered field No of surreal numbers may be regarded as a sort of absolute arithmetic continuum (modulo NBG). In the present chapter, as part of a more general exposition of the absolute arithmetic continuum, we will outline some of the properties of the system of surreal numbers that we believe (...) lend credence to this mathematico-philosophical thesis. We will also provide an overview of No’s rich structure as a simplicity-hierarchical (or s-hierarchical) ordered field that recursively emerges from the interplay between its structure as an ordered field and its structure as a lexicographically ordered full binary tree. Finally, we will draw attention to how properties of the system of surreal numbers considered as an s-hierarchical ordered algebraic structure can be appealed to in conjunction with classical relations between ordered algebraic and geometric systems to help resolve, for the surreal case, one of the purported difficulties that lies at the heart of attempts to bridge the gap between the domains of number and of geometrical magnitude. In particular, we will explain how it is possible that despite the fact that every surreal number, considered as a member of an s-hierarchical ordered field, differs from every other in characteristic individual properties, the absolute (Euclidean) geometrical continuum, which is modeled by the Cartesian space over the ordered field No of surreal numbers, appears as an amorphous pulp of points that display little individuality. (shrink)

In his monograph On Numbers and Games, J. H. Conway introduced a real-closed field containing the reals and the ordinals as well as a great many less familiar numbers including $-\omega, \,\omega/2, \,1/\omega, \sqrt{\omega}$ and $\omega-\pi$ to name only a few. Indeed, this particular real-closed field, which Conway calls No, is so remarkably inclusive that, subject to the proviso that numbers—construed here as members of ordered fields—be individually definable in terms of sets of NBG, it may be said to contain (...) “All Numbers Great and Small.” In this respect, No bears much the same relation to ordered fields that the system ℝ of real numbers bears to Archimedean ordered fields. In Part I of the present paper, we suggest that whereas $\mathbb{R}$should merely be regarded as constituting an arithmetic continuum, No may be regarded as a sort of absolute arithmetic continuum, and in Part II we draw attention to the unifying framework No provides not only for the reals and the ordinals but also for an array of non-Archimedean ordered number systems that have arisen in connection with the theories of non-Archimedean ordered algebraic and geometric systems, the theory of the rate of growth of real functions and nonstandard analysis. In addition to its inclusive structure as an ordered field, the system No of surreal numbers has a rich algebraico-tree-theoretic structure—a simplicity hierarchical structure—that emerges from the recursive clauses in terms of which it is defined. In the development of No outlined in the present paper, in which the surreals emerge vis-à-vis a generalization of the von Neumann ordinal construction, the simplicity hierarchical features of No are brought to the fore and play central roles in the aforementioned unification of systems of numbers great and small and in some of the more revealing characterizations of No as an absolute continuum. (shrink)

We examine the notions of negative, infinite and hotter than infinite temperatures and show how these unusual concepts gain legitimacy in quantum statistical mechanics. We ask if the existence of an infinite temperature implies the existence of an actual infinity and argue that it does not. Since one can sensibly talk about hotter than infinite temperatures, we ask if one could legitimately speak of other physical quantities, such as length and duration, in analogous terms. That is, could there be longer (...) than infinite lengths or temporal durations? We argue that the answer is surprisingly yes, and we outline the properties of a number system that could be employed to characterize such magnitudes. (shrink)

Since Euclid defined a point as “that which has no part” it has been widely assumed that points are necessarily unextended. It has also been assumed that this is equivalent to saying that points or, more properly speaking, degenerate segments, have length zero. We challenge these assumptions by providing models of Euclidean geometry where the points are extended despite the fact that the degenerate segments have null lengths, and observe that whereas the extended natures of the points are not recognizable (...) in the given models, they can be recognized and characterized by structures that are suitable expansions of the models. (shrink)

In 2001, the algebraico-tree-theoretic simplicity hierarchical structure of J. H. Conway’s ordered field ${\mathbf {No}}$ of surreal numbers was brought to the fore by the first author and employed to provide necessary and sufficient conditions for an ordered field to be isomorphic to an initial subfield of ${\mathbf {No}}$, i.e. a subfield of ${\mathbf {No}}$ that is an initial subtree of ${\mathbf {No}}$. In this sequel, analogous results are established for ordered exponential fields, making use of a slight generalization of (...) Schmeling’s conception of a transseries field. It is further shown that a wide range of ordered exponential fields are isomorphic to initial exponential subfields of $$. These include all models of $T$, where ${\mathbb R}_W$ is the reals expanded by a convergent Weierstrass system W. Of these, those we call trigonometric-exponential fields are given particular attention. It is shown that the exponential functions on the initial trigonometric-exponential subfields of ${\mathbf {No}}$, which includes ${\mathbf {No}}$ itself, extend to canonical exponential functions on their surcomplex counterparts. The image of the canonical map of the ordered exponential field ${\mathbb T}^{LE}$ of logarithmic-exponential transseries into ${\mathbf {No}}$ is shown to be initial, as are the ordered exponential fields ${\mathbb R})^{EL}$ and ${\mathbb R}\langle \langle \omega \rangle \rangle $. (shrink)

We suggest that, far from establishing an inconsistency in the standard theory of the geometrical linear continuum, Zeno’s Paradox of Extension merely establishes an inconsistency between the standard theory of geometrical magnitude and a misguided system of length measurement. We further suggest that our resolution of Zeno’s paradox is superior to Adolf Grünbaum’s now standard resolution based on Lebesgue measure theory.

Novel (categorical) axiomatizations of the classical arithmetic and geometric continua are provided and it is noted that by simply deleting the Archimedean condition one obtains (categorical) axiomatizations of J.H. Conway's ordered field No and its elementary n-dimensional metric Euclidean, hyperbolic and elliptic geometric counterparts. On the basis of this and related considerations it is suggested that whereas the classical arithmetic and geometric continua should merely be regarded as arithmetic and geometric continua modulo the Archimedean condition, No and its geometric counterparts (...) may be regarded as absolute arithmetic and geometric continua modulo von Neumann-Bernays-Godel set theory. (shrink)

Research on personality psychology is making important contributions to psychological science and applied psychology. This second edition of The Cambridge Handbook of Personality Psychology offers a one-stop resource for scientific personality psychology. It summarizes cutting-edge personality research in all its forms, including genetics, psychometrics, social-cognitive psychology, and real-world expressions, with informative and lively chapters that also highlight some areas of controversy. The team of renowned international authors, led by two esteemed editors, ensures a wide range of theoretical perspectives. Each research (...) area is discussed in terms of scientific foundations, main theories and findings, and future directions for research. The handbook also features advances in technology, such as molecular genetics and functional neuroimaging, as well as contemporary statistical approaches. An invaluable aid to understanding the central role played by personality in psychology, it will appeal to students, researchers, and practitioners in psychology, behavioral neuroscience, and the social sciences. (shrink)

In this chapter, we consider ethical and philosophical aspects of trust in the practice of medicine. We focus on trust within the patient-physician relationship, trust and professionalism, and trust in Western (allopathic) institutions of medicine and medical research. Philosophical approaches to trust contain important insights into medicine as an ethical and social practice. In what follows we explain several philosophical approaches and discuss their strengths and weaknesses in this context. We also highlight some relevant empirical work in the section on (...) trust in the institutions of medicine. It is hoped that the approaches discussed here can be extended to nursing and other topics in the philosophy of medicine. (shrink)

"Plato's Gift to Christianity is a book for all who seek to understand the beauty and depth of the Christian faith: for family discussions of values, virtues, and happiness; for educators who teach about the founding of Western Civilization and its basis of ethics; and especially for the Christian clergy who are not familiar with the Greek Classical and Platonic influence upon the making of Christianity. Dr. Ehrlich has presented here a most comprehensive study on the Platonic teachings adopted (...) by the New Testament and Early Church." --. (shrink)

Instead of conceiving ethical commands as divine revelations or as the discoveries of brilliant thinkers, we should see our ethical practices as evolving over tens of thousands of years, as members of our species have worked out how to live together and prosper. Here, Kitcher elaborates his radical vision of this millennia-long ethical project.

Contents/Inhalt: Preface. Vorwort. Abbreviations/Siglen. I. JASPERS ON WORLD PHILOSOPHY AND WORLD HISTORY OF PHILOSOPHY/JASPERS ÜBER WELT-PHILOSOPHIE UND WELTGESCHICHTE DER PHILOSOPHIE. Nekrolog von Karl Jaspers selbst verfaßt. Obituary by Karl Jaspers himself. Karl JASPERS: Weltgeschichte der Philosophie - Zweites Buch: Geschichte der Gehalte: Einleitung. Karl JASPERS: World History of Philosophy - Second Volume: History of the Substantive Contents of Philosophic Thought. Introduction. II. INTRODUCTION/EINLEITUNG. Leonard H. EHRLICH: Opening Remarks. Introduction of Jeanne Hersch, Honorary President of the Conference. Jeanne HERSCH: Von (...) der Wirkung einer "philosophia negativa". III. LEGACY AND TASK. VERMÄCHTNIS UND AUFGABE. Leonard H. EHRLICH: Ausblick: Vernunft, Geist, Geschichte. Sawako HANYU: the Concept of the "Encompassing" in World Philosophy. Andreas RINOFNER: Periechontologie und Weltgeschichte der Philosophie. Systematische Bemerkungen zu einem aufschlußreichen Verhältnis. Richard WISSER: Projekt und Vision einer "Weltgeschichte der Philosophie" und "Weltphilosophie" als Folgen der "Grundverfassung" von Karl Jaspers. IV. DIMENSIONS OF COMMUNICATION/RÄUME DER KOMMUNIKATION. Andreas CESANA: Grenzen der Rationalität und Kommunikation. Brenio ONETTO-BÄCHLER: Existentielle Kommunikation bei Jaspers. Czes_awa PIECUCH: Es ist gleichgültig, wer die Wahrheit ausspricht. Über die Uneigennützigkeit der existentiellen Kommunikation. Oswald O. SCHRAG: Existence, Existenz, and Social Organization. Vladimir KATASONOV: The Gadfly, Stinging the Sluggish Horse: The Socratic Mission of Jaspers's Philosophy. V. COMMUNICATIVE WORLD HISTORY OF PHILOSOPHY/KOMMUNIKATIVE WELTGESCHICHTE DER PHILOSOPHIE. Albrecht KIEL: Die Weisen des Umgreifenden, die der Mensch ist: Wege zu Jaspers' Periechontologie. Maria Luisa BASSO: K. Jaspers - N. Berdiaeff: une confrontation entre deux philosophies de l'histoire. Convergence et divergence d'affirmations. Inigo BOCKEN: Kommunikation und Mutmaßung. Versuch eines Vergleichs zwischen Jaspers' Idee einer Philosophie der Kommunikation und Nikolaus von Kues' Kunst der Mutmaßungen. Boles_aw ANDRZEJEWSKI: Jaspers' Stellung zur Romantik im Lichte seiner Sprachphilosophie. Endre KISS: Karl Jaspers' Auslegung Nietzsches als eines Metaphysikers der Immanenz. Danièle MOYAL-SHARROCK: Genie et Folie selon Jaspers. Milan UZELAC: The World and Existence. Pablo LÓPEZ-LÓPEZ: Das Studium der Philosophie als Studium der Weltgeschichte der Philosophie. VI. COMMUNICATIVE WORLD PHILOSOPHY: EAST AND WEST/KOMMUNIKATIVE WELTPHILOSOPHIE: OST UND WEST. Wonjae LEE: Karl Jaspers und das Weltproblem des interreligiösen Dialogs. Silvia MARZANO: Comunicazione mondiale, kantismo e frattura dell'essere in Karl Jaspers. Una "terza via" fra Occidente e Oriente? Indu SARIN: Jaspers's Quest for Existential Communication. Mohammed MARUF: Jaspers and Iqbal on Self, Freedom and Communication. Subhadr PANYADEEP: Ich und Nicht-Ich bei Jaspers und im Buddhismus. Kazuteru FUKUI: Das Wesen des Buddhismus und Jaspers' Philosophie. Yukio MASUBUCHI: Jaspers und Nishida. Eine Theorie des "Topos" in der Lehre von der Kommunikation. Hans SANER: Weltphilosophie und Globalkultur im interkulturellen Vergleich mit den Konzepten "Weltmusik" und "Weltkunst". Gerhard RAUCHE: The Paradox of " Das Scheitern " as a World Formula. VII. COMMUNICATIVE WORLD PHILOSOPHY: FREEDOM AND TOLERANCE/KOMMUNIKATIVE WELTPHILOSOPHIE: FREIHEIT UND TOLERANZ. Anna MASÓ-MONCLÚS: Libertad y autoridad en Hannah Arendt y Karl Jaspers. Otmar KLEIN: "Weltverabsolutierung" und Verantwortungsverlust. Kurt SALAMUN: Grenzen der Toleranz. Zum Offenheits- und Toleranzparadigma in der Philosophie von Karl Jaspers. Giorgio PENZO: Politik als Ethos und das Problem der Freiheit bei Jaspers. Gerhard KNAUSS: Von der Weimarer Republik zur Weltpolitik. Wandlungen in Jaspers' Auffassung und Wertung der Politik von der Heidelberger Frühschrift "Die geistige Situation der Zeit" bis zu den Basler Spätschriften. Hermann-Josef SEIDENECK: Freiheit und Wiedervereinigung auf dem Prüfstand. Prognose und Ergebnis unter dem Blickwinkel von existentieller Kommunikation im Welthorizont. Appendix/Anhang. (shrink)

Die Entwicklung eines philosophischen Systems ist für den Autor Folge der persönlichen Auseinandersetzung mit der Frage nach dem Lebenssinn und der Stellung des Menschen in der Welt. Die Frage nach dem Sinn des menschlichen Lebens ist die zentrale Frage des Menschen. Die zentrale Stellung bekommt diese Frage dadurch, dass der Mensch selbst - mehr unbewusst als bewusst - sie in seinem Verhalten, seinen Absichten und in seiner Lebensweise, in dem, was er vom Leben im Allgemeinen und von seinem persönlichen Leben (...) im Besonderen fordert und in ihm erreichen will, beantwortet. Diese Frage wird durch die Möglichkeit eines konkret bestimmten individuellen Lebensvollzugs gestellt und durch den Vollzug dieses individuellen, persönlichen Lebens beantwortet. Das eigentliche Problem eines jeden einzelnen Menschen ist seine Orientierung in der Welt. Den «Kompass» für die Orientierung in der Welt kann er nur in der Erkenntnis der Wirklichkeit finden. (shrink)

An esteemed philosopher discusses his theory of universal freedom, describing how even those who are members of free societies may find their liberties curtailed and includes tests of freedom including the eyeball test and the tough-luck test.

Most instructors who teach introductory courses in aesthetics or the philosophy of arts use the visual arts as their implicit reference for "art" in general, yet until now there has been no aesthetics anthology specifically orientated to the visual arts. This text stresses conceptual and theoretical issues, first examining the very notion of "the visual arts " and then investigating philosophical questions raised by various forms, from painting, the paradigmatic form, to sculpture, photography, film, dance, kitsch, and other forms on (...) the borders of the visual arts. The selections represent both classical and contemporary views and include sections by artists, art historians, and critics as well as philosophers. A singularly important text for courses in the philosophy of arts or aesthetics, this anthology is designed to enrich the philosophical and critical examination of our beliefs about the visual arts. (shrink)

Explores the confusion among physicists at the beginning of the 20th century when experimental findings kept not fitting into their mechanical view of the universe, the theoretical speculations and experimental innovations they responded with, and the new science that emerged. The mathematical details are set apart in boxes to allow nontechnical readers to engage the flow of the narrative uninterrupted. Paper edition (unseen), $29.95. Annotation copyright by Book News, Inc., Portland, OR.

In “Scientific Knowledge,” Philip Kitcher challenges arguments that deny the truth of the theoretical claims of science, and he attempts to discover reasons for endorsing the truth of such claims. He suggests that the discovery of such reasons might succeed if we ask why anyone thinks that the theoretical claims we accept are true and then look for answers that reconstruct actual belief‐generating processes. To this end, Kitcher presents the “homely argument” for scientific truth, which claims that when a (...) field of science is continually applied to yield precise predictions, then it is at least approximately true. He defends this approach and offers a supplementary account that gives more attention to detail. This account includes a historical aspect that must answer to skeptical challenges and a social aspect. (shrink)

Presents general information about meteorology, weather, and climate and includes more than thirty activities to help study these topics, including making a ...

_Idealist Alternatives to Materialist Philosophies of Science_ (ed. Philip MacEwen) presents some of the major challenges to materialist interpretations of science while also giving materialism a full hearing.

Introductory Chapter to the _Cambridge Handbook of Situated Cognition_ (CUP, 2009).

This book argues against the view that mathematical knowledge is a priori,contending that mathematics is an empirical science and develops historically,just as ...

Examines what is necessary for a group to constitute an agent that can display akrasia, and what steps such a group might take to establish self‐control. The topic has some interest in itself, and the discussion suggests some lessons about how we should think of akrasia in the individual as well as in the collective case. Under the image that the lessons support, akrasia is a sort of constitutional disorder: a failure to achieve a unity projected in the avowal of (...) agency. This image fits well with the constitutional model of the soul in Plato's Republic. (shrink)

There has recently been a revival of interest in panpsychism as a theory of consciousness. The hope of the contemporary proponents of panpsychism is that the view enables us to integrate consciousness into our overall theory of reality in a way that avoids the deep difficulties that plague the more conventional options of physicalism on the one hand and dualism on the other. However, panpsychism comes in two forms — strong and weak emergentist — and there are arguments that seem (...) to show that weak emergentist panpsychism faces problems analogous to those of physicalism whilst strong emergentist panpsychism faces problems analogous to those of dualism. In this paper, I will develop a new hybrid of the strong and weak emergentist forms of panpsychism, a view according to which subjects of experience are strongly emergent but their phenomenal properties are weakly emergent. I will argue that this hybrid view manages to avoid the challenges facing both physicalism and dualism, and the analogues of those challenges that seem to undermine standard forms of panpsychism. (shrink)

This chapter outlines three programs that aim to use biological insights in support of philosophical positions in ethics: Aristotelian approaches found, for example, in Thomas Hurka and Philippa Foot; Humean approaches found in Simon Blackburn and Allan Gibbard; and biologically grounded approaches found in of Elliott Sober and Brian Skyrms. The first two approaches begin with a philosophical view, and seek support for it in biology. The third approach begins with biology, and uses it to illuminate the status of morality. (...) This chapter pursues a version of the third program. A major accomplishment of evolutionary biology has been the explanation of biological altruism, which opens the door to a similar explanation of psychological altruism, or “fellow-feeling.” The chapter conjectures that humans have evolved a capacity for normative governance by socially shared rules. A process of cultural evolution led to the social rules with which we are familiar. This genealogical story poses a challenge, for the idea of moral truth plays no role in it. The story therefore lends support to non-cognitivism or anti-realist expressivism. The chapter concludes by exploring the implications of the genealogical story for moral knowledge, moral objectivity, and the idea of moral authority. (shrink)

This paper explores the role of moral uncertainty in explaining the morally disruptive character of new technologies. We argue that existing accounts of technomoral change do not fully explain its disruptiveness. This explanatory gap can be bridged by examining the epistemic dimensions of technomoral change, focusing on moral uncertainty and inquiry. To develop this account, we examine three historical cases: the introduction of the early pregnancy test, the contraception pill, and brain death. The resulting account highlights what we call “differential (...) disruption” and provides a resource for fields such as technology assessment, ethics of technology, and responsible innovation. (shrink)

A person presented with adequate but not conclusive evidence for a proposition is in a position voluntarily to acquire a belief in that proposition, or to suspend judgment about it. The availability of doxastic options in such cases grounds a moderate form of doxastic voluntarism not based on practical motives, and therefore distinct from pragmatism. In such cases, belief-acquisition or suspension of judgment meets standard conditions on willing: it can express stable character traits of the agent, it can be responsive (...) to reasons, and it is compatible with a subjective awareness of the available options. (shrink)

Can groups be rational agents over and above their individual members? We argue that group agents are distinguished by their capacity to mimic the way in which individual agents act and that this capacity must “supervene” on the group members' contributions. But what is the nature of this supervenience relation? Focusing on group judgments, we argue that, for a group to be rational, its judgment on a particular proposition cannot generally be a function of the members' individual judgments on that (...) proposition. Rather, it must be a function of their individual sets of judgments across many propositions. So knowing what the group members individually think about some proposition does not generally tell us how the group collectively adjudicates that proposition: the supervenience relation must be “setwise,” not “proposition‐wise.” Our account preserves the individualistic view that group agency is nothing mysterious but also suggests that a group agent may hold judgments that are not directly continuous with its members' corresponding individual judgments. (shrink)

This is a book about the aesthetics of wonder, about wonder as it figures in our relation to the visual world and to rare or new experiences.