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..

The debate around the notions of a priori knowledge and a posteriori knowledge has proven crucial for the development of many fields in philosophy, such as metaphysics, epistemology, metametaphysics etc. We advocate that the recent debate on the two notions is also fruitful for man-made distributed computing systems and for the epistemic analysis thereof. Following a recently proposed modal and fallibilistic account of a priori knowledge, we elaborate the corresponding concept of a priori belief: We propose a rich taxonomy of (...) types of a priori beliefs and their role for the different agents that participate in the system engineering process, which match the existing view exceedingly well and are particularly promising for explaining and dealing with unexpected behaviors in fault-tolerant distributed systems. Developing such a philosophical foundation will provide a sound basis for eventually implementing our ideas in a suitable epistemic reasoning and analysis framework and, hence, constitutes a mandatory first step for developing methods and tools to cope with the various challenges that emerge in such systems. (shrink)

How can one distinguish the concept of second modernity from the concept of postmodernity? Postmodernists are interested in deconstruction without reconstruction, second modernity is about deconstruction and reconstruction. Social sciences need to construct new concepts to understand the world dynamics at the beginning of the 21st century. Modernity has not vanished, we are not post it. Radical social change has always been part of modernity. What is new is that modernity has begun to modernize its own foundations. This is what (...) it means to say modernity has become reflexive. It has become directed at itself. This causes huge new problems both in reality and in theory. There has been a pluralization of the boundaries within and between societies, between society and nature, between Us and Other, between life and death. This pluralization also changes the inherent nature of boundaries. They become not so much boundaries as a variety of attempts to draw of boundaries. Border conflicts become transformed into conflicts over the drawing of boundaries. Where postmodernism simply celebrates this multiplication of boundaries, the theory of second modernity starts with the problem this new reality poses for individual and collective decisions, and with the problem that the continued existence of such decisions poses for theory. Institutions that are capable of such conscious boundary drawing are enabled in a way that those of the first modernity were not. But this process also generates qualitatively new kinds of trouble and crises. To investigate those troubles is to unveil the emergence of the second modernity. (shrink)

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)

Ethological theory standardly attributes representational content to animal signals. In this article I first assess whether Ruth Millikan’s teleosemantic theory accounts for the content of animal signals. I conclude that it does not, because many signals do not exhibit the required sort of cooperation between signal‐producing and signal‐consuming devices. It is then argued that Kim Sterelny’s proposal, while not requiring cooperation, sometimes yields the wrong content. Finally, I outline an alternative view, according to which consumers alone are responsible for conferring (...) representational status and determining content. I suggest that consumer‐based teleosemantics reconstruct the content of both cooperative and noncooperative signals and explain how a given trait can mean different things to different consumers. †To contact the author, please write to: Department of Philosophy, King’s College London, Strand, London WC2R 2LS, U.K.; e‐mail: ulrich[email protected]. (shrink)

At the beginning of the 21st century the conditio humana cannot be understood nationally or locally but only globally. This constitutes a revolution in the social sciences. The `sociological imagination' so far has basically been a nation state imagination. The main problem is how to redefine the sociological frame of reference in the horizon of a cosmopolitan imagination. For the purpose of empirical research I distinguish between three concepts: interconnectedness , liquid modernity and cosmopolitization from within. The latter is a (...) kind of class analysis after class analysis, which takes on board globalization internalized. For the purposes of social analysis, therefore, it is necessary to distinguish systematically between the national manifestation on the one hand and cosmopolitan reality of `global flows', currents of information, symbols, money, risks, people, social inequalities, on the other. This internal involuntary and often unseen cosmopolitanization from below of the national sphere of experience is occurring, however, with the power of economic globalization. So what does inner `cosmopolitanization' mean? The key concepts and questions of a way of life, such as nourishment, production, identity, fear, memory, pleasure, fate, power and politics, can no longer be located and understood nationally, but only globally whether in the shape of globally shared collective futures, capital flows, impending ecological or economic catastrophes, global foodstuff chains, transnational power games, or the `Esperanto' of pop music. In this article I look at transformation in the understanding of space-time, of identity, of the production paradigms, as well as at the resulting consequences for key sociological concepts like class and power and, within this frame, point to certain dilemmas of cosmopolitanism. (shrink)

This article differentiates between three different axes of conflict in world risk society. The first axis is that of ecological conflicts, which are by their very essence global. The second is global financial crises, which, in a first stage, can be individualized and nationalized. And the third, which suddenly broke upon us on September 11th, is the threat of transnational terror networks, which empowers governments and states. Two sets of implications are drawn: first, there are the political dynamics of world (...) risk society. In an age where trust and faith in God, class and progress have largely disappeared, humanity's common fear has proved the last - ambivalent - resource for making new bonds. Second, the methodological nationalism that preoccupies the sociological imagination has to be overcome and a `methodological cosmopolitism' has to be created. (shrink)

The paper presents a refined method of extracting reasonable and sometimes unexpected programs from classical proofs of formulas of the form ∀x∃yB . We also generalize previously known results, since B no longer needs to be quantifier-free, but only has to belong to a strictly larger class of so-called “goal formulas”. Furthermore we allow unproven lemmas D in the proof of ∀x∃yB , where D is a so-called “definite” formula.

In this article I want to outline an argument for a New Critical Theory with a cosmopolitan intent. Its main purpose is to undermine one of the most powerful beliefs of our time concerning society and politics. This belief is the notion that “modern society” and “modern politics” are to be understood as society and politics organized around the nation‐state, equating society with the national imagination of society. There are two aspects to this body of beliefs: what I call the (...) “national perspective” of social actors, and the “methodological nationalism” of scientific observers. The distinction between these two perspectives is important because there is no logical co‐implication between them, only an interconnected genesis and history. (shrink)