We argue that Wittgenstein’s philosophical perspective on Gödel’s most famous theorem is even more radical than has commonly been assumed. Wittgenstein shows in detail that there is no way that the Gödelian construct of a string of signs could be assigned a useful function within (ordinary) mathematics. — The focus is on Appendix III to Part I of Remarks on the Foundations of Mathematics. The present reading highlights the exceptional importance of this particular set of remarks and, more specifically, emphasises (...) its refined composition and rigorous internal structure. (shrink)

This book is about the interrelationship between nature, semiosis, metarepresentation and (self-)consciousness, and the role played by metarepresentation in ...

The book demonstrates for the first time that transculturality – the mixed constitution of cultures – is by no means only a characteristic of the present, but has de facto determined the composition of cultures since time immemorial. This is demonstated using examples from the arts across all cultures and continents.

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)

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)

Die „Grundlage der gesamten Wissenschaftslehre“ bleibt für den, der Fichte im philosophiegeschichtlichen Zusammenhang sehen will, der wichtigste Text; dies gilt auch dann noch, wenn die Akademie-Ausgabe abgeschlossen sein wird. Der Jenaer Fichte hat nicht nur auf seine Zeitgenossen am stärksten gewirkt, er war auch seinerseits damals noch am offensten für Einflüsse. Der vorliegende Kommentar – der erste, der den gesamten deutschen Text behandelt – bietet keine Paraphrase, keine Übersetzung in eine zeitgemäßere Sprache, keine „Darstellung“, die Fichtes Disposition durch eine eigene (...) ersetzt und damit – gewollt oder ungewollt – in Konkurrenz zum Original tritt. Er will vielmehr den Leser auf seinem dornigen Pfad Satz für Satz begleiten und bei keiner Schwierigkeit im Stich lassen. Die konkrete Erforschung literarischer Bezüge und Abhängigkeiten zeigt, wie sehr der „Selbstdenker“ Fichte – unbeschadet seiner Eigenständigkeit – nicht nur in der Philosophie, sondern im ganzen Geistesleben der Epoche verwurzelt ist. Durch die ausgiebigen, mit sprachlichen Erläuterungen versehenen Zitate entlegener Quellen ist der Kommentar zugleich eine Art Lesebuch. (shrink)

Millionenjahrhaus: Zur Konzeption des Raumes der Ewigkeit im konstellativen Königtum in Sprache, Architektur und Theologie. By Stefanie Schröder. Wiesbaden: Harrassowitz Verlag, 2010. Pp. 396, plates. €84.

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 geometro-stochastic quantization of a gauge theory based on the (4,1)-de Sitter group is presented. The theory contains an intrinsic elementary length parameter R of geometric origin taken to be of a size typical for hadron physics. Use is made of a soldered Hilbert bundle ℋ over curved spacetime carrying a phase space representation of SO(4, 1) with the Lorentz subgroup related to a vierbein formulation of gravitation. The typical fiber of ℋ is a resolution kernel Hilbert space ℋ $_{\bar (...) \eta }^{(\rho )} $ constructed in terms of generalized coherent states $\bar \eta $ ρ related to the principal series of unitary irreducible representations of SO(4, 1), namely de Sitter horospherical waves for spinless particles characterized by the parameter ρ. The framework is, finally, extended to a quantum field-theoretical formalism by using bundles with Fock space fibers constructed from ℋ $_{\bar \eta }^{(\rho )} $. (shrink)

Theories of the nature of time offered by anthropology, science, and religion are not only numerous but also very different. This groundbreaking book cuts through the confusion by introducing a provocative new tripolar model of time that integrates the human, natural, and religious dimensions of time into a single, harmonious whole. Wolfgang Achtner, Stefan Kunz, and Thomas Walter begin by exploring the structures of time in anthropological terms. They discuss time phenomenologically, showing how it can be experienced in three (...) distinct ways -- the mythic-cyclic, the rational-linear, and the mystic-holistic -- and they root these experiences in the findings of modern neuroscience and trace these three forms of the perception of time within various cultures of antiquity. The second part of the book looks at time as it has been described by some of sciences most profound theories, including classical mechanics, the special and general theories of relativity, quantum mechanics, thermodynamics, and chaos theory. The authors then bring religion into the equation by surveying how time is conceived in both the Hebrew Bible and the Christian New Testament. They distinguish time concepts in wisdom and apocalyptic literature from time concepts in prophetic literature, and they demonstrate the basic eschatological orientation of the Christian view of time. "Dimensions of Time culminates by tying together the various strands of the authors' multidisciplinary, tripolar model of time. Offering a fascinating application of their unique theory, Achtner, Kunz, and Walter show how the unhealthy acceleration of life in contemporary society needs to be balanced by a rediscovery ofthe mystical experience of time, leading to a greater, deeper sense of human fulfillment. (shrink)

It is shown that the class of Kolmogorov-Loveland stochastic sequences is not closed under selecting subsequences by monotonic computable selection rules. This result gives a strong negative answer to the question whether the Kolmogorov-Loveland stochastic sequences are closed under selecting sequences by Kolmogorov-Loveland selection rules, i.e., by not necessarily monotonic, partial computable selection rules. The following previously known results are obtained as corollaries. The Mises-Wald-Church stochastic sequences are not closed under computable permutations, hence in particular they form a strict superclass (...) of the class of Kolmogorov-Loveland stochastic sequences. The Kolmogorov-Loveland selection rules are not closed under composition. (shrink)

Inhaltsverzeichnis/Table of Contents: Vorbemerkung/Preface. Dagfin FØLLESDAL: Bolzano's Legacy. Jan BERG: Bolzano, the Prescient Encyclopedist. Jan SEBESTIK: Bolzano, Exner and the Origins of Analytical Philosophy. Paul RUSNOCK: Bolzano and the Traditions of Analysis. Peter SIMONS: Bolzano on Collections. Ali BEHBOUD: Remarks on Bolzano's Collections. Mark SIEBEL: Variation, Derivability and Necessity. Edgar MORSCHER: Bolzano's Method of Variation: Three Puzzles. Rolf GEORGE: Bolzano's Programme andObjects. Mark TEXTOR: Bolzano's Sententialism. Wolfgang KÜNNE: Propositions in Bolzano and Frege. Michael DUMMETT: Comments on Wolfgang Künne's (...) Paper. Carsten Uwe GIESKE: Bolzano's Notion of Testifying. (shrink)

Kant’s theory of cognition centrally builds on his conception of self-consciousness and the transcendental use of the phrase “I think”: the ability to add the phrase “I think” to a representation is a necessary condition of the ability to cognize objects. The paper argues that “I think”, rather than denoting the content of a predicative judgement, is typically an expression of the subject’s thinking. It expresses a kind of self-consciousness that, without assertively representing the subject itself, indicates that representational contents (...) are unified in a single consciousness of a single subject. Our aim is thus to develop and defend an expressivist interpretation of Kant’s “I think”. (shrink)

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)

This series publishes outstanding monographs and edited volumes that investigate all aspects of Kant's philosophy, including its systematic relationship to other philosophical approaches, both past and present. Studies that appear in the series are distinguished by their innovative nature and ability to close lacunae in the research. In this way, the series is a venue for the latest findings in scholarship on Kant.