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..

Acknowledgements Andrea Scarantino, Nicholas Shea, Mark Sprevak, and three anonymous referees provided incisive and constructive comments, for which I am very grateful. In 2012, earlier versions of this paper were delivered in Edinburgh, at the Joint Session in Stirling, and at a workshop on natural information in Aberdeen. I thank participants for their feedback.

The discourse on climate politics so far is an expert and elitist discourse in which peoples, societies, citizens, workers, voters and their interests, views and voices are very much neglected. So, in order to turn climate change politics from its head onto its feet you have to take sociology into account. There is an important background assumption which shares in the general ignorance concerning environmental issues and, paradoxically, this is in corporated in the specialism of environmental sociology itself — this (...) is the category of ‘the environment’. If ‘the environment’ only includes everything which is not human, not social, then the concept is sociologically empty. If the concept includes human action and society, then it is scientifically mistaken and politically suicidal. (shrink)

Ulrich Meyer defends a novel theory about the nature of time, and argues against the consensus view that time and space are fundamentally alike. He presents the first comprehensive defense of a 'modal' account, which emphasizes the similarities between times and possible worlds in modal logic, and is easily reconciled with the theory of relativity.

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)