"Foundations of the Formal Sciences" is a series of interdisciplinary conferences in mathematics, philosophy, computer science and linguistics. The main goal is to reestablish the traditionally strong links between these areas of research that have been lost in the past decades. The second conference in the series had the subtitle "Applications of Mathematical Logic in Philosophy and Linguistics" and brought speakers from all parts of the Formal Sciences together to give a holistic view of how mathematical methods can improve our (...) philosophical and technical understanding of language and scientific discourse, ranging from the theoretical level up to applications in language recognition software. Audience: This volume is of interest to all formal philosophers and theoretical linguists. In addition to that, logicians interested in the applications of their field and logic students in mathematics, computer science, philosophy and linguistics can use the volume to broaden their knowledge of applications of logic. (shrink)

"A Survey of Ranking Theory": The paper gives an up-to-date survey of ranking theory. It carefully explains the basics. It elaborates on the ranking theoretic explication of reasons and their balance. It explains the dynamics of belief statable in ranking terms and indicates how the ranks can thereby be measured. It suggests how the theory of Bayesian nets can be carried over to ranking theory. It indicates what it might mean to objectify ranks. It discusses the formal and the philosophical (...) aspects of the tight relation and the complementarity of ranks and probabilities. It closes with comparative remarks on predecessors and other philosophical proposals as well as formal models developed in AI. (shrink)

This is the basis of the first part of the book.

Ranking theory delivers an account of iterated contraction; each ranking function induces a specific iterated contraction behavior. The paper shows how to reconstruct a ranking function from its iterated contraction behavior uniquely up to multiplicative constant and thus how to measure ranks on a ratio scale. Thereby, it also shows how to completely axiomatize that behavior. The complete set of laws of iterated contraction it specifies amend the laws hitherto discussed in the literature.

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 present a reconstruction of so-called classical, formal or Mendelian genetics using a notation which we believe is more legible than that of earlier accounts, and lends itself easily to computer implementation, for instance in PROLOG. By drawing from, and emending, earlier work of Balzer and Dawe (1986,1997), the present account presents the three most important lines of development of classical genetics: the so-called Mendel's laws, linkage genetics and gene mapping, in the form of a theory-net. This shows that the (...) set theoretic representation format used in the structuralist approach to the philosophy of science also applies to the domain of genetic theories. There construction is intended to lend more clarity to theme thodological, philosophical and didactical discussions of the foundations of genetics, and on the other hand to defend a formally, logically minded view of theories which seems to have become contested through the work of Feyerabend, Kuhn and Kitcher. (shrink)

The aim of the paper is to explicate the concept of causal independence between sets of factors and Reichenbach's screening-off-relation in probabilistic terms along the lines of Suppes' probabilistic theory of causality (1970). The probabilistic concept central to this task is that of conditional stochastic independence. The adequacy of the explication is supported by proving some theorems about the explicata which correspond to our intuitions about the explicanda.

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)

& The functional equivalence of overt movements and dynamic imagery is of fundamental importance in neuroscience. Here, we investigated the participation of the neocortical motor areas in a classic task of dynamic imagery, Shepard and Metzler's mental rotation task, by time-resolved single-trial functional Magnetic Resonance Imaging (fMRI). The subjects performed the mental-rotation task 16 times, each time with different object pairs. Functional images were acquired for each pair separately, and the onset times and..

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.

The paper argues that the standard decision theoretic account of strategies and their rationality or optimality is much too narrow, that strategies should rather condition future action to future decision situations (a point of view already developed in my Grundlagen der Entscheidungstheorie, sect. 4.4), that practical deliberation must therefore essentially rely on a relation of superiority and inferiority between possible future decision situations, that all this allows to substantially broaden the theory of practical rationality, that a long list of points (...) attended to in the literature can be subsumed under the broadened perspective (including a novel view on the iterated prisoner's dilemma and on iterated Newcomb's problem, which, however, is revised in Spohn (2003) "Dependency Equilibria and the Causal Structure of Decision and Game Situation"), and that the task to complete and systematize this list indeed forms a fruitful research programme. (shrink)

How should rational beliefs change over time? The standard Bayesian answer is: by conditionalization (a.k.a. Bayes’ Rule). But conditionalization is not an adequate rule for updating beliefs in “centred” propositions whose truth-value may itself change over time. In response, some have suggested that the objects of belief must be uncentred; others have suggested that beliefs in centred propositions are not subject to diachronic norms. Iargue that these views do not offer a satisfactory account of self-locating beliefs and their dynamics. A (...) third response is to replace conditionalization by a new norm that can deal with centred propositions. I critically survey anumber of new norms that have been proposed, and defend one particular approach. (shrink)

The old division of all sciences into the two equally important classes of theoretical and practical disciplines is hardly ever applied today. However, the proprium of a practical science that is aimed at what should be, can be elucidated using medicine as an example. The efforts of medicine are not limited to a mere `application' of methods and results of theoretical disciplines. Even the concepts of `illness' and `diagnosis', which are central to medicine, are defined in a normative-deontological manner. They (...) are supposed not only to help formulating and justifying assertions on facts, but also to be a means to enable and standardise action. Since every action takes place in a concrete situation, a practical science must always bridge the hiatus between the general and the particular. This requires judgement, a personal, individual capacity that cannot be operationalised without residue. In contrast to the theoretical disciplines, such a science is not the master of its own questions and problems; and is subject to the dictate of time, since all action is final and irrevocable. (shrink)

Frontmatter -- 1 Warum Institutionen wichtig sind -- 2 Das Ordnungsproblem -- 3 Harmoniemodelle -- 4 Das machtbezogene Institutionenmodell -- 5 Makromodelle -- 6 Handlungen und Ursachen -- 7 Mikromodelle -- 8 Soziale Schemata -- 9 Dynamik 1: Potentielle Institutionen -- 10 Machtbeziehungen -- 11 Formen der Macht -- 12 Soziale Institutionen -- 13 Zur Entstehung von Institutionen -- 14 Dynamik 2: Zum Wandel von Institutionen -- 15 Macht und Harmonie -- 16 Ausblicke -- Literatur -- Autoren -- Stichwörter -- (...) Verzeichnis der Symbole. (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)

Die vorgelegte Summe des Hochidealismus ersetzt - der neuen Forschungs- und Quellenlage entsprechend - die alte Konstruktion vom Dreischritt, der von Fichtes Jenaer Wissenschaftslehre ausgeht, in die Naturphilosophie Schellings ubergeht und in Hegels System vollendet aufgeht, durch die Gegenthese: Der Deutsche Idealismus ist die Begrundung der Vernunftwissenschaft im Widerstreit von drei Vollendungsanspruchen, erhoben im Identitatssystem und der positiven Philosophie Schellings, in Hegels Onto-Theo-Logik und der Ungeschriebenen Lehre Fichtes, d.i. den mundlichen Vortragszyklen nach 1800. Die eingehende Ausarbeitung dieses dreiseitigen Widerstreites hebt (...) einen Vorrang heraus. Fichtes Ungeschriebene Lehre ist die einzige der drei Vollendungsgestalten, die im Begreifen des Wahrheits- und Systemgrundes, des Absoluten, transzendentale Besinnung in absoluter Reflexion bewahrt und daher auch vorzuglich in der Lage ist, unser Zeitalter der Nichtbesinnung herauszufordern. Wolfgang Janke ist emeritierter Universitatsprofessor. Zu seinen Forschungsschwerpunkten gehort das Gebiet des Deutschen Idealismus von Kant bis Hegel. Neue Einblicke zumal in die Spatphilosophie Fichtes eroffnen seine Abhandlungen: Fichte. Sein und Reflexion, 1970. - Historische Dialektik. Von Kant bis Marx, 1977. - Vom Bilde des Absoluten, 1993. - Johann Gottlieb Fichtes Wissenschaftslehre 1805. Methodisch-systematischer und philosophiegeschichtlicher Kommentar, 1999. In der Supplementa-Reihe ist (bei Rodopi) erschienen: Entgegensetzungen. Studien zu Fichte-Konfrontationen von Rousseau bis Kierkegaard, 1994. Wolfgang Janke, dessen erster akademischer Lehrer ein Erneuerer der Kant- und Fichte-Interpretation, Heinz Heimsoeth, war und dem durch Karl-Heinz Volkmann-Schluck aus dem Heidegger-Kreis der Deutsche Idealismus in seiner problemreichen Vollendungsphase nahegebracht wurde, ist heute Ehrenprasident der Internationalen Fichte-Gesellschaft. (shrink)

It is shown that the class of reduced matrices of a logic is a 1 st order -class provided the variety associated with has the finite replacement property in the sense of [7]. This applies in particular to all 2-valued logics. For 3-valued logics the class of reduced matrices need not be 1 st order.

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)