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)

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)

We can measure the complexity of a logical formula by counting the number of alternations between existential and universal quantifiers. Suppose that an elementary first-order formula $\varphi $ (in $\mathcal {L}_{\omega,\omega }$ ) is equivalent to a formula of the infinitary language $\mathcal {L}_{\infty,\omega }$ with n alternations of quantifiers. We prove that $\varphi $ is equivalent to a finitary formula with n alternations of quantifiers. Thus using infinitary logic does not allow us to express a finitary formula in a (...) simpler way. (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)

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)

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)

Adorno, an important selection by Horkheimer and Adorno (from Dialectic of Enlightenment), as well as works by Walter Benjamin, Leo Lowenthal, Herbert Marcuse, Norbert Elias, and Jurgen Habermas."--BOOK JACKET.

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)

While Kant’s position concerning human freedom and divine foreknowledge is perhaps the least Molinist element of his multifaceted take on free will, Kant’s Molinism (minimally defined) is undeniable when it comes to the threat ensuing from the idea of creation. In line with incompatibilism and with careful qualifications in place, he ultimately suggests regarding free agents as uncreated. Given the limitations of our rational insight, this assumption is indispensable for granting that finite free agents can acquire their intelligible characters by (...) themselves. Nonetheless, Kant concedes that creation may, as a matter of fact, be compatible with what for Molina is the pre-volitionality of the counterfactuals of freedom. (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)