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)

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)

The term ‘mutual constitution’ appears with regularity in scholarship on intersectionality, but what does it mean? We could not easily answer this question in the usual way – by reading books and articles about it – because the term has not received direct, widespread or sustained engagement in feminist theory. This led us to analyse a wide range of feminist scholarship – the entire set of 379 articles in women’s studies journals that consider both intersectionality and mutual constitution – to (...) determine whether there are patterns and commonalities in the ways this important theoretical term is used. Our analysis reveals that while there is widespread agreement that mutual constitution does not allow for an additive or binary approach, this is the only major point of shared understanding of this term. Scholars disagree over whether mutual constitution is, in fact, the same thing as intersectionality, and in practice, clusters of disciplines use the term with different norms and levels of precision. Because of the explanatory potential of this term in intersectional theory, we recommend on the basis of our analysis that social scientists reconsider the convention of asserting that entities such as race, class and gender are mutually constituted and borrow the methodological tools from feminist historians, literary critics and other humanists that would allow for a genuine determination and demonstration of when entities are mutually constituted. (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)

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)

The present "philological commentary" is directed at those who have decided to take time for reading the original text, at least in an English translation. The first volume "Textual Criticism" is intended to meet the difficulties caused by the fact that our text editions are based on manuscripts separated from the original by more than a millennium.

With the third volume, it is invited to enter the intellectual environment of Aristotle. The most relevant sources are given in full (with English translation), so that the commentary is also a reader documenting the disputationes metaphysicae of the 4th century BC. For the undeniable contradictions in the Metaphysics, a new genetic explanation is offered.

Though since Werner Jaeger's famous Studien zur Entstehungsgeschichte der Metaphysik des Aristoteles of 1912 remarkable observations were made, the topic "Composition of the Metaphysics" almost disappeared from the agenda. As, however, neglect of this philological task results in either selective reading or anachronistic systematization, the author has resumed it, extending it to the internal structure of the singular books.

Though since Werner Jaeger's famous Studien zur Entstehungsgeschichte der Metaphysik des Aristoteles of 1912 remarkable observations were made, the topic "Composition of the Metaphysics" almost disappeared from the agenda. As, however, neglect of this philological task results in either selective reading or anachronistic systematization, the author has resumed it, extendig it to the internal structure of the singular books.

The question of the relationship between ontology and theology, the main problem of the interpretation in volume 3, is also the guiding question of our last volume. The history of metaphysics is a history of the efforts towards an outlook on the world and life, which are about the meaning and connection of fundamental concepts: being, life, intellect, unity, truth, goodness. From these, the concept of divinity is derived. As in the previous volumes, a rich material of original texts and (...) interpretations is spread out. (shrink)

Der vorliegende "philologische" Kommentar beansprucht Kants Critik der reinen Vernunft aus ihren historischen Voraussetzungen zu erklären. Zu diesen gehört an erster Stelle Kants Sprache; sie ist nicht mehr die unsere, was den unvorbereiteten Leser von heute schon an der Semantik und Syntax vieler Sätze scheitern lässt. Neben einer Fülle von sprachlichen Erläuterungen und textkritischen Untersuchungen bringt der Kommentar reichliche Zitate aus den von Kant benutzten Logik- und Metaphysik-Lehrbüchern, die seine Rezeption der "dogmatischen" Philosophie Christian Wolffs und seiner Nachfolger belegen; lateinische (...) Texte werden dabei sowohl im Original als auch in deutscher Übersetzung geboten. Einzelne Motive werden ideengeschichtlich bis in die Antike zurückverfolgt; hieraus eröffnen sich Perspektiven für eine "Metakritik" von einem "vorkritischen" Standpunkt aus, die im Rahmen eines philologischen Kommentars nur angedeutet werden können. (shrink)

The first English translation of a classic work in vision science from 1936 by a leading figure in the Gestalt movement, covering topics that continue to be major issues in vision research today. This classic work in vision science, written by a leading figure in Germany's Gestalt movement in psychology and first published in 1936, addresses topics that remain of major interest to vision researchers today. Wolfgang Metzger's main argument, drawn from Gestalt theory, is that the objects we perceive (...) in visual experience are not the objects themselves but perceptual effigies of those objects constructed by our brain according to natural rules. Gestalt concepts are currently being increasingly integrated into mainstream neuroscience by researchers proposing network processing beyond the classical receptive field. Metzger's discussion of such topics as ambiguous figures, hidden forms, camouflage, shadows and depth, and three-dimensional representations in paintings will interest anyone working in the field of vision and perception, including psychologists, biologists, neurophysiologists, and researchers in computational vision—and artists, designers, and philosophers. Each chapter is accompanied by compelling visual demonstrations of the phenomena described; the book includes 194 illustrations, drawn from visual science, art, and everyday experience, that invite readers to verify Metzger's observations for themselves. Today's researchers may find themselves pondering the intriguing question of what effect Metzger's theories might have had on vision research if Laws of Seeing and its treasure trove of perceptual observations had been available to the English-speaking world at the time of its writing. (shrink)

Aristotle's Categories can easily seem to be a statement of a naïve, pre-philosophical ontology, centered around ordinary items. Wolfgang-Rainer Mann argues that the treatise, in fact, presents a revolutionary metaphysical picture, one Aristotle arrives at by (implicitly) criticizing Plato and Plato's strange counterparts, the "Late-Learners" of the Sophist. As Mann shows, the Categories reflects Aristotle's discovery that ordinary items are things (objects with properties). Put most starkly, Mann contends that there were no things before Aristotle. The author's argument consists (...) of two main elements. First, a careful investigation of Plato which aims to make sense of the odd-sounding suggestion that things do not show up as things in his ontology. Secondly, an exposition of the theoretical apparatus Aristotle introduces in the Categories--an exposition which shows how Plato's and the Late-Learners' metaphysical pictures cannot help but seem inadequate in light of that apparatus. In doing so, Mann reveals that Aristotle's conception of things--now so engrained in Western thought as to seem a natural expression of common sense--was really a hard-won philosophical achievement. Clear, subtle, and rigorously argued, The Discovery of Things will reshape our understanding of some of Aristotle's--and Plato's--most basic ideas. (shrink)

The systems Kα of transfinite cumulative types up to α are extended to systems K∞α that include a natural infinitary inference rule, the so-called limit rule. For countable α a semantic completeness theorem for K∞α is proved by the method of reduction trees, and it is shown that every model of K∞α is equivalent to a cumulative hierarchy of sets. This is used to show that several axiomatic first-order set theories can be interpreted in K∞α, for suitable α.

I argue for the causal character of modeling in data-intensive science, contrary to widespread claims that big data is only concerned with the search for correlations. After discussing the concept of data-intensive science and introducing two examples as illustration, several algorithms are examined. It is shown how they are able to identify causal relevance on the basis of eliminative induction and a related difference-making account of causation. I then situate data-intensive modeling within a broader framework of an epistemology of scientific (...) knowledge. In particular, it is shown to lack a pronounced hierarchical, nested structure. The significance of the transition to such “horizontal” modeling is underlined by the concurrent emergence of novel inductive methodology in statistics such as non-parametric statistics. Data-intensive modeling is well equipped to deal with various aspects of causal complexity arising especially in the higher level and applied sciences. (shrink)

Sections 1, 2 and 3 contain the main result, the strong finite axiomatizability of all 2-valued matrices. Since non-strongly finitely axiomatizable 3-element matrices are easily constructed the result reveals once again the gap between 2-valued and multiple-valued logic. Sec. 2 deals with the basic cases which include the important F i from Post's classification. The procedure in Sec. 3 reduces the general problem to these cases. Sec. 4 is a study of basic algebraic properties of 2-element algebras. In particular, we (...) show that equational completeness is equivalent to the Stone-property and that each 2-element algebra generates a minimal quasivariety. The results of Sec. 4 will be applied in Sec. 5 to maximality questions and to a matrix free characterization of 2-valued consequences in the lattice of structural consequences in any language. Sec. 6 takes a look at related axiomatization. problems for finite algebras and matrices. We study the notion of a propositional consequence with equality and, among other things, present explicit axiomatizations of 2-valued consequences with equality. (shrink)

ZusammenfassungDie Mystik gilt im interreligiösen Dialog als diejenige Dimension von Religion, die gemäß dem Essentialismus den gemeinsamen Kern der Religionen darstellt. In Unterschied dazu vertritt der Kontextualismus die These, dass Mystik nur in spezifischen religiösen Kontexten entsteht und so seine unverwechselbare Eigenheit erhält. Saeed Zarrabi-Zadeh vergleicht in seiner Arbeit Meister Eckhart und Rumi methodisch so miteinander, dass er die jeweiligen Stärken des Essentialismus und des Kontextualismus nutzt und ihre Schwächen vermeidet. Auf der Grundlage dieses methodischen Neuansatzes und eines weitgefassten Mystikbegriffs, (...) der Ethik, Praxis, Spekulation und Dogmatik umfasst, kommt er zu neuen Differenzierungen im religionsphänomenologischen Vergleich und legt zugleich erhebliche Differenzen im theologischen Deutehorizont der jeweiligen Mystiker offen. Darüberhinaus arbeitet er mit seiner Interpretation der. (shrink)

This succinct introduction to modern theories of literature and the arts demonstrates how each theory is built and what it can accomplish. Represents a wide variety of theories, including phenomenological theory, hermeneutical theory, gestalt theory, reception theory, semiotic theory, Marxist theory, deconstruction, anthropological theory, and feminist theory. Uses classic literary texts, such as Keats’s Ode on a Grecian Urn, Spenser’s The Shephearde’s Calender and T. S. Eliot’s The Waste Land to illustrate his explanations. Includes key statements by the major proponents (...) of each theory. Presents the different theories objectively, allowing students to decide which if any, they subscribe to. Gives students a sense of the potential of theory. Includes a glossary of technical terms. (shrink)

Der eigentümliche Ausdruck, der heute meist für Welt steht, der Ausdruck Umwelt, scheint ein Welt-Verhältnis auszudrücken, das den Akzent nicht aufs Objekt, sondern aufs Subjekt verlegt hat, auf die den Weltmittelpunkt einnehmende Monade. Diese scheint die Welt nicht mehr als gegebene, sondern als Ensemble von Varietäten zu verstehen, auf die sie zugreifen kann, dem Flaneur auf den Supermärkten dieser Welt vergleichbar. Der Form nach hält sie an einem Eigentumsbegriff fest, der als substantiell, als statisch auslegt, was in Wirklichkeit dynamisch ist (...) in einer Welt, die seit Generationen keinerlei festes Eigentum mehr gelten lassen konnte. Es ist der permanente Zugriff, der verrät, daß er dem in Wahrheit Rechnung trägt. Das >Eigentum sieht sich auf den permanenten Gestus der Aneignung angewiesen. Ein perverseres System ist geschichtlich wahrscheinlich niemals beobachtet worden. Nicht das viel gescholtene Konkurrenzprinzip, ein weit virulenteres Movens treibt es an. Denn das Aneignungsprinzip. (shrink)

Die Frage, wie ein Anfang im Denken zu machen sei, oder wie der Anfang von Denken zu denken sei, war Gegenstand der philosophischen Reflexion des Klassischen Deutschen Idealismus. Die Autoren dieses Bandes thematisieren nun für philosophische Konzepte aus der Zeit vor und nach dem Klassischen Idealismus, wie in ihnen das Problem des Anfangs gedacht wird. Betrachtete Autoren sind: Marsilius Ficino, Johannes Scotus Eriugena, Giordano Bruno, Christoph Scheibler, Husserl, Meister Eckhard, Nishida und Davidson.

Recent claims, mainly from computer scientists, concerning a largely automated and model-free data-intensive science have been countered by critical reactions from a number of philosophers of science. The debate suffers from a lack of detail in two respects, regarding the actual methods used in data-intensive science and the specific ways in which these methods presuppose theoretical assumptions. I examine two widely-used algorithms, classificatory trees and non-parametric regression, and argue that these are theory-laden in an external sense, regarding the framing of (...) research questions, but not in an internal sense concerning the causal structure of the examined phenomenon. With respect to the novelty of data-intensive science, I draw an analogy to exploratory as opposed to theory-directed experimentation. (shrink)

Many spiritual traditions employ certain mental techniques (meditation) which consist in inhibiting mental activity whilst nonetheless remaining fully conscious, which is supposed to lead to a realisation of one’s own true nature prior to habitual self-substantialisation. In this paper I propose that this practice can be understood as a special means of becoming aware of consciousness itself as such. To explain this claim I conduct some phenomenologically oriented considerations about the nature of consciousness qua presence and the problem of self-presence (...) of this presence. (shrink)

Every domain-specific ontology must use as a framework some upper-level ontology which describes the most general, domain-independent categories of reality. In the present paper we sketch a new type of upper-level ontology, which is intended to be the basis of a knowledge modelling language GOL (for: 'General Ontological Language'). It turns out that the upper- level ontology underlying standard modelling languages such as KIF, F-Logic and CycL is restricted to the ontology of sets. Set theory has considerable mathematical power and (...) great flexibility as a framework for modelling different sorts of structures. At the same time it has the disadvantage that sets are abstract entities (entities existing outside the realm of time, space and causality), and thus a set-theoretical framework should be supplemented by some other machinery if it is to support applications in the ripe, messy world of concrete objects. In the present paper we partition the entities of the real world into sets and urelements, and then we introduce several new ontological relations between these urelements. In contrast to standard modelling and representation formalisms, the concepts of GOL provide a machinery for representing and analysing such ontologically basic relations. (shrink)