Rational agents are supposed to maximize expected utility. But what are the options from which they choose? I outline some constraints on an adequate representation of an agent’s options. The options should, for example, contain no information of which the agent is unsure. But they should be sufficiently rich to distinguish all available acts from one another. These demands often come into conflict, so that there seems to be no adequate representation of the options at all. After reviewing existing proposals (...) for how to construe decision-theoretic options and finding them all wanting, I suggest that our model of rational agents should include a special domain of ‘virtual’ option propositions to serve as formal objects of deliberation and choice. (shrink)

A well-known art historian and an intimate friend of Heidegger's, Heinrich Wiegand Petzet provides a rich portrait of Heidegger that is part memoir, part biography, and part cultural history.

This book has grown out of eight years of close collaboration among its authors. From the very beginning we decided that its content should come out as the result of a truly common effort. That is, we did not "distribute" parts of the text planned to each one of us. On the contrary, we made a point that each single paragraph be the product of a common reflection. Genuine team-work is not as usual in philosophy as it is in other (...) academic disciplines. We think, however, that this is more due to the idiosyncrasy of philosophers than to the nature of their subject. Close collaboration with positive results is as rewarding as anything can be, but it may also prove to be quite difficult to implement. In our case, part of the difficulties came from purely geographic separation. This caused unsuspected delays in coordinating the work. But more than this, as time passed, the accumulation of particular results and ideas outran our ability to fit them into an organic unity. Different styles of exposition, different ways of formalization, different levels of complexity were simultaneously present in a voluminous manuscript that had become completely unmanageable. In particular, a portion of the text had been conceived in the language of category theory and employed ideas of a rather abstract nature, while another part was expounded in the more conventional set-theoretic style, stressing intui tivity and concreteness. (shrink)

Traditional logic as a part of philosophy is one of the oldest scientific disciplines. Mathematical logic, however, is a relatively young discipline and arose from the endeavors of Peano, Frege, Russell and others to create a logistic foundation for mathematics. It steadily developed during the 20th century into a broad discipline with several sub-areas and numerous applications in mathematics, informatics, linguistics and philosophy. While there are already several well-known textbooks on mathematical logic, this book is unique in that it is (...) much more concise than most others, and the material is treated in a streamlined fashion which allows the professor to cover many important topics in a one semester course. Although the book is intended for use as a graduate text, the first three chapters could be understood by undergraduates interested in mathematical logic. These initial chapters cover just the material for an introductory course on mathematical logic combined with the necessary material from set theory. This material is of a descriptive nature, providing a view towards decision problems, automated theorem proving, non-standard models and other subjects. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text. The author has provided exercises for each chapter, as well as hints to selected exercises. About the German edition: …The book can be useful to the student and lecturer who prepares a mathematical logic course at the university. What a pity that the book is not written in a universal scientific language which mankind has not yet created. - A.Nabebin, Zentralblatt. (shrink)

Gottlob Frege has exerted an enormous influence on the evolution of twentieth-century philosophy, yet the real significance of that influence is still very much a matter of debate. This book provides a completely new and systematic account of Frege's philosophy by focusing on its cornerstone: the theory of sense and reference. Two features distinguish this study from other books on Frege. First, sense and reference are placed absolutely at the core of Frege's work; the author shows that no adequate account (...) of the theory can avoid analysing the notion of thought that underpins it, or explaining how it has clarified our concept of judgement. Second, the theory is situated within the development of Frege's thought; the author reveals how the theory caused Frege to alter many of his fundamental views. In doing so the author presents a clearer picture of the problems the theory was intended to solve, and delineates more sharply the characteristic features of Frege's philosophy. (shrink)

The paper argues that Gareth Evans’ argument for transparent self-knowledge is based on a conflation of doxastic transparency with ascriptive transparency. Doxastic transparency means that belief about one’s own doxastic state, e.g., the belief that one thinks that it will rain, can be warranted by ordinary empirical observation, e.g., of the weather. In contrast, ascriptive transparency says that self-ascriptions of belief, e.g., “I believe it will rain”, can be warranted by such observation. We first show that the thesis of doxastic (...) transparency is ill-motivated and then offer a non-epistemic interpretation of ascriptive transparency by reference to the theory of explicit expressive acts: “I think it will rain” requires attendance to the weather because the utterance expresses a belief about the weather, not about ourselves. This will allow us to avoid what is often called “the puzzle of transparent self-knowledge” while remaining faithful to Evans’ linguistic observations. (shrink)

Inhalt: Vorbemerkung Kommentar Titel Vorrede Erster Teil Zweiter Teil Dritter Teil Benutzte Literatur a)Zeitgenossen und Vorläufer Fichtes b)Moderne Interpreten Sachregister zum Fichte-Text Verzeichnis der zitierten Arbeiten Fichtes.

Concentrating upon applications that are most relevant to modern physics, this valuable book surveys variational principles and examines their relationship to dynamics and quantum theory. Stressing the history and theory of these mathematical concepts rather than the mechanics, the authors provide many insights into the development of quantum mechanics and present much hard-to-find material in a remarkably lucid, compact form. After summarizing the historical background from Pythagoras to Francis Bacon, Professors Yourgrau and Mandelstram cover Fermat's principle of least time, the (...) principle of least action of Maupertuis, development of this principle by Euler and Lagrange, and the equations of Lagrange and Hamilton. Equipped by this thorough preparation to treat variational principles in general, they proceed to derive Hamilton's principle, the Hamilton-Jacobi equation, and Hamilton's canonical equations. An investigation of electrodynamics in Hamiltonian form covers next, followed by a resume of variational principles in classical dynamics. The authors then launch into an analysis of their most significant topics: the relation between variational principles and wave mechanics, and the principles of Feynman and Schwinger in quantum mechanics. Two concluding chapters extend the discussion to hydrodynamics and natural philosophy. Professional physicists, mathematicians, and advanced students with a strong mathematical background will find this stimulating volume invaluable reading. Extremely popular in its hardcover edition, this volume will find even wider appreciation in its first fine inexpensive paperbound edition. (shrink)

This article discusses the history of the concepts of potential infinity and actual infinity in the context of Christian theology, mathematical thinking and metaphysical reasoning. It shows that the structure of Ancient Greek rationality could not go beyond the concept of potential infinity, which is highlighted in Aristotle's metaphysics. The limitations of the metaphysical mind of ancient Greece were overcome through Christian theology and its concept of the infinite God, as formulated in Gregory of Nyssa's theology. That is how the (...) concept of actual infinity emerged. However, Gregory of Nyssa's understanding of human rationality went still further. He said that access to the infinity of God was to be found only in an asymptotic ascension, as expressed in apophatic theology, and this view endangered the rationality of theology. Deeply influenced by the apophatic tradition, Nicholas of Cusa avoided this danger by showing that infinity could be accessed by symbolic representation and asymptotic mathematical reasoning. Thus, he made an immense contribution in making infinity rationally accessible. This endeavor was finally realized by Georg Cantor. This rational accessibility revealed discernible structures of infinity, such as the continuum hypothesis, and the cardinal numbers. However, the probable logical inconsistency of Georg Cantor's all-encompassing Absolute Infinity points to an intuitive understanding of infinity that goes beyond its rational structures – as in apophatic theology. (shrink)

The interest contemporary philosophy takes in Kant's notion of apperception is restricted to his criticism of the Cartesian Ego and to his refutation of scepticism, but there is a profound lack of concern for the notion itself and for the act of spontaneity in particular which is connected with the use of the word T. Starting from a comparison of Wittgenstein's account of this use with Kant's considerations it is argued that the latter aims at a theory of formal conditions (...) of knowledge which includes the availability of the notion of the I. It is clarified what the determination of apperception as an 'act of spontaniety' amounts to (B: 132). Kant's scattered remarks on the ability of having the representation of the I, of using the word 'I', are considered in order to show that what he called 'the logical I' has something to do with the capacity of performing an act of judgment. It is argued that such an account is not to be found in contemporary discussions of 'essential indexicals', 'first-person view' and mental self-ascriptions. (shrink)

Wie manifestierte sich die Idee der Menschenrechte im Comité sur les principes philosophiques des droits de l'homme der Unesco in den Jahren 1947/48? Die vorliegende Studie rekonstruiert die Entstehung des Komitees, zeichnet seine Arbeit nach und bestimmt seine Wirkung. Dabei werden einerseits die Faktoren erarbeitet, die auf das Komitee einwirkten und seine Diskussion der Menschenrechte beeinflussten; andererseits soll die Rückwirkung des Komitees auf die internationale Politik sichtbar gemacht werden. Die Diskussion über eine philosophische Begründung der Menschenrechte unmittelbar nach dem Ende (...) des Zweiten Weltkriegs steht dabei ebenso im Mittelpunkt wie Kooperation und Konflikt zwischen dem Komitee und dem UN-Menschenrechtsausschuss, der zur gleichen Zeit über die Allgemeinen Erklärung der Menschenrechte debattierte. Gleichzeitig ist die Studie ein Beitrag zur frühen Geschichte der Unesco und zur Funktionsstruktur internationaler Regierungsorganisationen. (shrink)

In the present paper we give a functional interpretation of Aczel's constructive set theories CZF − and CZF in systems T ∈ and T ∈ + of constructive set functionals of finite types. This interpretation is obtained by a translation × , a refinement of the ∧ -translation introduced by Diller and Nahm 49–66) which again is an extension of Gödel's Dialectica translation. The interpretation theorem gives characterizations of the definable set functions of CZF − and CZF in terms of (...) constructive set functionals. In a second part we introduce constructive set theories in all finite types. We expand the interpretation to these theories and give a characterization of the translation × . We further show that the simplest non-trivial axiom of extensionality is not interpretable by functionals of T ∈ and T ∈ + . We obtain this result by adapting Howard's notion of hereditarily majorizable functionals to set functionals. Subject of the last section is the translation ∨ that is defined in Burr for an interpretation of Kripke-Platek set theory with infinity. (shrink)

According to the transparency approach, achievement of self-knowledge is a two-stage process: first, the subject arrives at the judgment ‘p’; second, the subject proceeds to the judgment ‘I believe that p.’ The puzzle of transparency is to understand why the transition from the first to the second judgment is rationally permissible. After revisiting the debate between Byrne and Boyle on this matter, I present a novel solution according to which the transition is rationally permissible in virtue of a justifying argument (...) that begins from a premise referring to the mental utterance that is emitted in the course of judging ‘p.’. (shrink)

SummaryA simple and precise definition is offered of “term t of theory T being T‐theoretical” which can be applied to any formalized theory. The definition is in line with and emends traditional accounts of theoreticity. Its adequacy is demonstrated by application to three examples: exchange economics, classical mechanics and collision mechanics.

We define classes Φnof formulae of first-order arithmetic with the following properties:(i) Everyφϵ Φnis classically equivalent to a Πn-formula (n≠ 1, Φ1:= Σ1).(ii)(iii)IΠnandiΦn(i.e., Heyting arithmetic with induction schema restricted to Φn-formulae) prove the same Π2-formulae.We further generalize a result by Visser and Wehmeier. namely that prenex induction within intuitionistic arithmetic is rather weak: After closing Φnboth under existential and universal quantification (we call these classes Θn) the corresponding theoriesiΘnstill prove the same Π2-formulae. In a second part we consideriΔ0plus collection-principles. We (...) show that both the provably recursive functions and the provably total functions ofare polynomially bounded. Furthermore we show that the contrapositive of the collection-schema gives rise to instances of the law of excluded middle and hence. (shrink)

Many philosophical theories of self-knowledge can be understood as attempts to explain why self-ascriptions enjoy a certain kind of authority that other-ascriptions lack (the Authority Thesis). The aim of this paper is not to expand the stock of existing explanations but to ask whether the Authority Thesis can be adequately specified. To this end, I identify three requirements that must be met by any satisfactory specification. I conclude that the search for an adequate specification of the Authority Thesis leads to (...) a dilemma: it either yields an interpretation under which the thesis is philosophically interesting but false, or it produces an interpretation under which the thesis is actually true but of minor philosophical interest. (shrink)

We investigate certain statements about factors of unary functions which have connections with weak forms of the axiom of choice. We discuss more extensively the fine structure of Howard and Rubin's Form 314 from [4]. Some of our set-theoretic results have also interesting recursive versions.

We shall investigate certain set-theoretic pigeonhole principles which arise as generalizations of the usual pigeonhole principle; and we shall show that many of them are equivalent to full AC. We discuss also several restricted cases and variations of those principles and relate them to restricted choice principles. In this sense the pigeonhole principle is a rich source of weak choice principles. It is shown that certain sequences of restricted pigeonhole principles form implicational hierarchies with respect to ZF. We state also (...) several open problems in order to indicate the extent to which the whole subject of pigeonhole principles requires further exploration. (shrink)

Erstmals wird mit diesem Band in einer Wissenschaftstheorie auch umfassend die Verantwortung der Wissenschaften thematisiert. Die Wissenschaften sind für die Organisation des Zusammenlebens und der Bewältigung der Überlebensprobleme der Menschen unentbehrlich geworden. Dadurch sind für alle Wissenschaften Verantwortlichkeiten entstanden, an die hier nicht nur erinnert wird, sondern die im Einzelnen beschrieben werden. Wenn das Verantwortungsbewusstsein gegenüber dem menschlichen Gemeinwesen kaum oder gar nicht ausgebildet zu sein scheint, wird deutliche und wenn möglich konstruktive Kritik geübt. Nahezu alle Wissenschaften leiden an einer (...) mangelhaften Fundierung ihrer Grundlagen. Wenn dadurch ihre Existenzberechtigung fraglich ist, wird auf alternative Wissenschaftskonzepte hingewiesen wie etwa für die Rechtswissenschaften oder sogar ausgearbeitet wie z.B. für die Theologische Fakultät. (shrink)

Dieser Band bietet einen umfassenden Überblick über die normativen Theorien der Wissenschaft. Ende des 19. und Anfang des 20. Jhs. schien die Philosophie ihre Kompetenz in der Behandlung der Grundlagenprobleme der menschlichen Existenz an die Physik abzugeben. Einige Philosophen nutzten ihre Kenntnisse in Mathematik und Logik, um durch den Bezug auf die philosophischen Traditionen der Erkenntnistheorie mit den normativen Wissenschaftstheorien des Logische Positivismus, des Kritischen Rationalismus und des Konstruktivismus philosophisches Terrain zu erhalten. Ihr weit überzogener und nicht zu rechtfertigender Anspruch, (...) den Wissenschaftlern korrektes wissenschaftliches Arbeiten vorzuschreiben, hat trotz ihrer wissenschaftsfördernden Arbeiten wie etwa die Metrisierungstheorie oder die sprachliche Bedeutungslehre das Ansehen der Wissenschaftstheorie ruiniert. Der Band III ist darum ein Wiederbelebungsversuch einer interdisziplinären für alle Wissenschaften fruchtbaren Theorie der Wissenschaften. (shrink)

Dieser Band bietet eine umfassende Einführung in die geschichtliche Entwicklung von Wissenschaft seit der Antike. Menschen sind historische Wesen, d.h. ihr Denken und Handeln sind durch ihre historische Gewordenheit bestimmt. Dies gilt besonders für die Wissenschaft, die sich stets im Zustand der fortlaufenden Entwicklung befindet, weil das Denkvermögen des Menschen, das ihn zum wissenschaftlichen Denken befähigt, erst in einigen tausend Jahren kultureller Entwicklung entstanden ist. Beginnend mit den mythischen Bewusstseins- und Denkformen wird das Werden des begrifflichen und erkennenden Denkens nachgezeichnet (...) und das Werden der neuzeitlichen Wissenschaft in ihrer Abhängigkeit von sinnstiftenden Überzeugungen bis hin zur Quanten- und Relativitätsphysik. Wünschenswerte Weiterentwicklungen werden kurz behandelt. (shrink)

A comprehensive model for describing various forms of developments in science is defined in precise, set-theoretic terms, and in the spirit of the structuralist approach in the philosophy of science. The model emends previous accounts in centering on single systems in a homogenous way, eliminating notions which essentially refer to sets of systems. This is achieved by eliminating the distinction between theoretical and non-theoretical terms as a primitive, and by introducing the notion of intended links. The force of the model (...) is demonstrated by formally incorporating many of the important, precise meta-theoretic concepts occurring in the literature. (shrink)

This article aims to show that Williamson's anti-luminosity argument does not succeed if we presuppose a constitutive connection between the phenomenal and the doxastic. In contrast to other luminists, however, my strategy is not to critically focus on the refined safety condition in terms of degrees of confidence that anti-luminists typically use in this context. Instead, I will argue that, given a certain conception of what Chalmers calls ‘direct phenomenal concepts,’ luminosity is guaranteed even if the refined safety condition in (...) terms of degrees of confidence is taken for granted. (shrink)