C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom → ) → . This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper , 201-208).

A four-valued matrix is presented which validates all theorems of the implicational fragment, IF, of the classical sentential calculus in which at most two distinct sentence letters occur. The Wajsberg/Diamond-McKinsley Theorem for IF follows as a corollary: every complete set of axioms (with substitution and detachment as rules) must include at least one containing occurrences of three or more distinct sentence letters. Additionally, the matrix validates all IF theses built from nine or fewer occurrences of connectives and letters. So the (...) classic result of Jagkovski for the full sentential calculus -that every complete axiom set must contain either two axioms of length at least nine or else one of length at least eleven-can be improved in the implicational case: every complete axiom set for IF must contain at least one axiom eleven or more characters long. Both results are "best possible", and both apply as well to most subsystems of IF, e.g., the implicational fragments of the standard relevance logics, modal logics, the relatives of implicational intutionism, and logics in the Lukasiewicz family. (shrink)

detail a question that, for a quarter of a century, remained open despite intense study by various researchers. Is the formula XC B = e(x e(e(e( ) e( )) z)) a single axiom for the classical equivalential calculus when the rules of inference consist..

In this new book, Ulrich Beck develops his now widely used concepts of second modernity, risk society and reflexive sociology into a radical new sociological ...

The notion of societal boundaries aims to enhance the debate on planetary boundaries. The focus is on capitalist societies as a heuristic for discussing the expansionary dynamics, power relations, and lock-ins of modern societies that impel highly unsustainable societal relations with nature. While formulating societal boundaries implies a controversial process – based on normative judgments, ethical concerns, and socio-political struggles – it has the potential to offer guidelines for a just, social-ecological transformation.

Morality and economic rationality: integrative economic ethics as the rational ethics of economic activity; Part II. Reflections on the Foundations of Economic ...

Ulrich Beck's best selling Risk Society established risk on the sociological agenda. It brought together a wide range of issues centering on environmental, health and personal risk, provided a rallying ground for researchers and activists in a variety of social movements and acted as a reference point for state and local policies in risk management. The Risk Society and Beyond charts the progress of Beck's ideas and traces their evolution. It demonstrates why the issues raised by Beck reverberate widely (...) throughout social theory and covers the new risks that Beck did not foresee, associated with the emergence of new technologies, genetic and cybernetic. The book is unique because it offers both an introduction to the main arguments in Risk Society and develops a range of critical discussions of aspects of this and other works of Beck. (shrink)

The aim of the paper is this: Instead of presenting a provisional and necessarily insufficient characterization of what mathematical physics is, I will ask the reader to take it just as that, what he or she thinks or believes it is, yet to be prepared to revise his opinion in the light of what I am going to tell. Because this is precisely, what I intend to do. I will challenge some of the received or standard views about mathematical physics (...) and replace them by a more sophisticated picture, which takes into account the methodological and philosophical roots of mathematical physics in Göttingen. (shrink)

Toen Ulrich Libbrecht vanaf de jaren 1970 Vlaanderen en Nederland inspireerde met ‘oosterse wijsheid voor de westerse mens’ was dit pionierswerk. Ondertussen heeft de globalisering zich verder voltrokken, is boeddhisme en meditatie geen exotisme meer en is China dichterbij gekomen. Hoe kijkt de filosoof nu tegen deze ontwikkelingen aan? Dit boek is ontstaan uit gesprekken waarin Libbrecht op een meesterlijke wijze oosterse en westerse inzichten integreert tot een nieuw antwoord op actuele vragen en universele thema’s. Hierin benadrukt hij de (...) waarde van natuur, wetenschap en religieus bewustzijn in de betekenis van re-ligare: herverbinden. In dit boek zet hij geen theorie uiteen, maar neemt de lezer mee op de boeiende weg van het denken, doortrokken van ontroering en een rijke levenservaring. (shrink)

In recent years the works of Friedman, Howard and many others have made obvious what perhaps was always self-evident. Namely, that the philosophy of the logical empiricists was shaped primarily by Einstein and his invention of the theory of relativity, whereas Hilbert and his axiomatic approach to the exact sciences had comparatively little impact on the logical empiricists and their understanding of science — if they had any effect at all. This is in one respect quite astonishing, insofar as Einstein (...) himself confessed 1921 in his famous lecture before the Prussian Academy of Science that “without it [the axiomatic point of view] it would have been impossible for me to propound the theory of relativity”.2 Hence the simple question arises: why didn’t the logical empiricists pay more attention to Hilbert and his axiomatic point of view, than they in fact did? It is an aim of this paper to answer this question and in part to correct this one-sided view in the hypothetical or contra-factual sense that the logical empiricists would have done better, if they had paid somewhat more attention to Hilbert and his axiomatic approach to science. (shrink)

This article investigates the prospect of giving de dicto- and de re-necessity a uniform treatment. The historical starting point is a puzzle raised by Aristotle's claim, advanced in one of the modal chapters of his Prior Analytics, that universally privative apodeictic premises simply convert. As regards the Prior and the Posterior Analytics, the data suggest a representation of propositions of the type in question by doubly modally qualified formulae of modal predicate logic that display a necessity operator in two distinct (...) positions. Can the N-operator occurring in these positions be given a unified semantical treatment (which would justify dispensing with a notational differentiation)? A positive answer, based on a suitably shaped truth condition for N-formulae, is given, and is supported in the final section with an alternative proof theoretically based conception of a property's essential belonging to an individual. (shrink)

By assembling authors with a wide range of different disciplinary backgrounds, from philosophy, literature, political science, sociology to medical anthropology ...