We show that—unlike products of ‘transitive’ modal logics which are usually undecidable—their ‘expanding domain’ relativisations can be decidable, though not in primitive recursive time. In particular, we prove the decidability and the finite expanding product model property of bimodal logics interpreted in two-dimensional structures where one component—call it the ‘flow of time’—is • a finite linear order or a finite transitive tree and the other is composed of structures like • transitive trees/partial orders/quasi-orders/linear orders or only finite such structures expanding (...) over time. The decidability proof is based on Kruskal’s tree theorem, and the proof of non-primitive recursiveness is by reduction of the reachability problem for lossy channel systems. The result is used to show that the dynamic topological logic interpreted in topological spaces with continuous functions is decidable if the number of function iterations is assumed to be finite. (shrink)

This paper investigates (modal) extensions of Heyting-Brouwer logic, i.e., the logic which results when the dual of implication (alias coimplication) is added to the language of intuitionistic logic. We first develop matrix as well as Kripke style semantics for those logics. Then, by extending the Gö;del-embedding of intuitionistic logic into S4, it is shown that all (modal) extensions of Heyting-Brouwer logic can be embedded into tense logics (with additional modal operators). An extension of the Blok-Esakia-Theorem is proved for this embedding.

The author confronts the place of today's world in the context of human history. He focuses on such major issues of the twentieth century as human progress, fanaticism, & science.

In this influential work, first published in English in 1963, Durkheim and Mauss claim that the individual mind is capable of classification and they seek the origin of the ‘classificatory function’ in society. On the basis of an intensive examination of forms and principles of symbolic classification reported from the Australian aborigines, the Zuñi and traditional China, they try to establish a formal correspondence between social and symbolic classification. From this they argue that the mode of classification is determined by (...) the form of society and that the notions of space, time, hierarchy, number, class and other such cognitive categories are products of society. Dr Needham’s introduction assesses the validity of Durkhiem and Mauss’s argument, traces its continued influence in various disciplines, and indicates its analytical value for future researches in social anthropology. (shrink)

This paper investigates the structure of lattices of normal mono- and polymodal subframelogics, i.e., those modal logics whose frames are closed under a certain type of substructures. Nearly all basic modal logics belong to this class. The main lattice theoretic tool applied is the notion of a splitting of a complete lattice which turns out to be connected with the “geometry” and “topology” of frames, with Kripke completeness and with axiomatization problems. We investigate in detail subframe logics containing K4, those (...) containing polymodal Altn and subframe logics which are tense logics. (shrink)

Through readings of Jacques Derrida's Of Grammatology and 'The Age of Hegel', attention is given to two of the problematic types of relationships that philosophy can have with education. These engagements, alongside a reading of 'The Antinomies of the Philosophical Discipline: Letter Preface', show how Derrida’s thought can prescribe no educational programme and instead troubles educational proclamations and certainties. Throughout his life, Derrida negotiated his relationships to the educational systems and institutions to which he was responsible, these negotiations, though, were (...) not indicative of a belief in any ontologically grounded educational truth. Quite to the contrary, as I will claim, Derrida’s thought is remarkable for its deflation of the myth, stretching at least as far back to Plato’s Republic, that philosophy can discover and prescribe the practical means for its own educational good. The argument presented in this article is that Derrida’s thought is particularly fertile when it comes to educational reflection precisely because it does not close down, presuppose, or prescribe, and that these characteristics also allow for generative contradictions in Derrida's educational and philosophical thought and practice. (shrink)

Tense logics in the bimodal propositional language are investigated with respect to the Finite Model Property. In order to prove positive results techniques from investigations of modal logics above K4 are extended to tense logic. General negative results show the limits of the transfer.

Demonstrative noun phrases (e.g., that guy , this ) are of interest to philosophers of language and semanticists because they are sensitive to demonstrations or speaker intentions. The interpretation of a demonstrative therefore sheds light on the role of the context in natural language semantics. This survey reviews two types of approaches to demonstratives: Kaplan's direct reference treatment of demonstratives and other indexicals, and recent challenges to Kaplan's approach that focus on less obviously context-sensitive uses of demonstratives. The survey then (...) covers selected research on demonstratives in linguistics. This research offers new empirical puzzles and contrasting theoretical approaches to demonstratives. (shrink)

We shall describe the set of strongly meet irreducible logics in the lattice ϵLin.t of normal tense logics of weak orderings. Based on this description it is shown that all logics in ϵLin.t are independently axiomatizable. Then the description is used in order to investigate tense logics with respect to decidability, finite axiomatizability, axiomatization problems and completeness with respect to Kripke semantics. The main tool for the investigation is a translation of bimodal formulas into a language talking about partitions of (...) general frames into intervals so that relative to both Kripke frames and descriptive frames the expressive power of both languages coincides. (shrink)

It is known that even seemingly small fragments of the first-order temporal logic over the natural numbers are not recursively enumerable. In this paper we show that the monodic fragment is an exception by constructing its finite Hilbert-style axiomatization. We also show that the monodic fragment with equality is not recursively axiomatizable.

In this paper we investigate first order common knowledge logics; i.e., modal epistemic logics based on first order logic with common knowledge operators. It is shown that even rather weak fragments of first order common knowledge logics are not recursively axiomatizable. This applies, for example, to fragments which allow to reason about names only; that is to say, fragments the first order part of which is based on constant symbols and the equality symbol only. Then formal properties of "quantifying into" (...) epistemic contexts are investigated. The results are illustrated by means of epistemic representations of Nash Equilibria for finite games with mixed strategies. (shrink)

In this influential work, first published in English in 1963, Durkheim and Mauss claim that the individual mind is capable of classification and they seek the origin of the ‘classificatory function’ in society. On the basis of an intensive examination of forms and principles of symbolic classification reported from the Australian aborigines, the Zuñi and traditional China, they try to establish a formal correspondence between social and symbolic classification. From this they argue that the mode of classification is determined by (...) the form of society and that the notions of space, time, hierarchy, number, class and other such cognitive categories are products of society. Dr Needham’s introduction assesses the validity of Durkhiem and Mauss’s argument, traces its continued influence in various disciplines, and indicates its analytical value for future researches in social anthropology. (shrink)

Tense logics formulated in the bimodal propositional language are investigated with respect to Kripke-completeness (completeness) and decidability. It is proved that all minimal tense extensions of modal logics of finite width (in the sense of K. Kine) as well as all minimal tense extensions of cofinal subframe logics (in the sense of M. Zakharyaschev) are complete. The decidability of all finitely axiomatizable minimal tense extensions of cofinal subframe logics is shown. A number of variations and extensions of these results are (...) also presented. (shrink)

This paper briefly summarizes Durkheim’s theory of the dual nature of man suggested earlier in his Elementary Forms of Religious Life. It is characteristic of human beings that two opposite principles confront each other within them: soul and body, concept and sensation, moral activity and sensory appetites. Although this inherent inconsistency of man has been long recognized by philosophical thought, no doctrine explanation to it has been provided to date. While empiricist monism has proved to be unable to explain how (...) concepts emerge from sensations and disinterestedness develops from self-interest, absolute idealism, on the contrary, cannot deduce sensations from concepts. Although theories suggested by Plato and Kant do not bypass the problem of dualism, they only rephrase it and make no progress in solving it. According to Durkheim, dualism of human nature stems from the fact that all religions are founded on dividing all things into the sacred and the profane. This division, in turn, is explained by coexistence of collective and individual origins in the human being. Sacred things arise out of the collective origin that enables individual consciousnesses to fuse into communion. Collective origin does not act with constant strength, but intensifies during the periods of effervescence, when it subdues the individual origin. Since the importance of the social aspect of man increases over time, there is no reason to believe that complete consent between individual and society is possible that would endow man with internal harmony. (shrink)

We investigate computational properties of propositional logics for dynamical systems. First, we consider logics for dynamic topological systems (W.f), fi, where W is a topological space and f a homeomorphism on W. The logics come with ‘modal’ operators interpreted by the topological closure and interior, and temporal operators interpreted along the orbits {w, f(w), f2 (w), ˙˙˙} of points w ε W. We show that for various classes of topological spaces the resulting logics are not recursively enumerable (and so not (...) recursively axiomatisable). This gives a ‘negative’ solution to a conjecture of Kremer and Mints. Second, we consider logics for dynamical systems (W, f), where W is a metric space and f and isometric function. The operators for topological interior/closure are replaced by distance operators of the form ‘everywhere/somewhere in the ball of radius a, ‘for a ε Q +. In contrast to the topological case, the resulting logic turns out to be decidable, but not in time bounded by any elementary function. (shrink)

Based on the results of [11] this paper delivers uniform algorithms for deciding whether a finitely axiomatizable tense logic has the finite model property, is complete with respect to Kripke semantics, is strongly complete with respect to Kripke semantics, is d-persistent, is r-persistent.It is also proved that a tense logic is strongly complete iff the corresponding variety of bimodal algebras is complex, and that a tense logic is d-persistent iff it is complete and its Kripke frames form a first order (...) definable class. From this we obtain many natural non-d-persistent tense logics whose corresponding varieties of bimodal algebras are complex. (shrink)

Positive ignorance is the putting in to question of, and sometimes moving on from, the knowledge we think we have, and asking where it might be just or helpful to do so. Drawing primarily on the work of Barbara Johnson, this article shows how the notion of positive ignorance might be offered as a tool in the context of education and educational research. Partly a critical development of Richard Smith's argument in ‘The Virtues of Unknowing’, I attempt to understand ‘unknowing’ (...) as an active rather than passive form of ‘not knowing’, in a manner that challenges some aspects of ‘the virtues of unknowing’ and its concomitant epistemological and ethical positions, not least those tied to Smith's advocacy for what he calls the ‘well-stocked mind’. Unknowing, in my reading, is not a dispositional acceptance of the desirability of nonknowledge, instead, unknowing is a means of epistemological resistance, especially against that which, often with very real social and political consequences, is presented as self-evident. (shrink)

Thomas Williams has developed a radical interpretation of Duns Scotus’s voluntarism using an earlier interpretation of my own as a foil. He argues that the goodness of creatures and the rightness of actions are wholly dependent on the divine will, apart from any reference to the divine intellect, human nature, or any principle other than God’s own arbitrary will. I explain how his interpretation fails to account for the roles that essential goodness and divine justice play in divine volition. The (...) unmitigated voluntarism that Williams develops does not conform to the full range of authentic Scotistic texts. Despite the interest Williams’s voluntarism may have if taken as a theoretical position, it does not do justice to the nuance and speculative depth of Scotus’s actual understanding of the divine will, whose creative artistry is repugnant to arbitrary volition. I am grateful to Williams for the provocation to develop further the richness of Scotus’s volutarism. (shrink)

This paper does not present an advocacy of a passive education as opposed to an active education nor does it propose that passive education is in any way ‘better’ or more important than active education. Through readings of Maurice Blanchot, Jacques Derrida and B.S. Johnson, and gentle critiques of Jacques Rancière and John Dewey, passive education is instead described and outlined as an education which occurs whether we attempt it or not. As such, the object of critique for this essay (...) are forms of educational thought which, through fate or design, exclude the passive dimension, either within or outside of formal educational settings. An underlying component of this argument is therefore also that education does occur outside of formal educational settings and that, contra Gert Biesta and his critique of ‘learnification’, we may gain rather than lose something by attending to it as education. (shrink)

In this paper, we introduce a new fragment of the first-order temporal language, called the monodic fragment, in which all formulas beginning with a temporal operator have at most one free variable. We show that the satisfiability problem for monodic formulas in various linear time structures can be reduced to the satisfiability problem for a certain fragment of classical first-order logic. This reduction is then used to single out a number of decidable fragments of first-order temporal logics and of two-sorted (...) first-order logics in which one sort is intended for temporal reasoning. Besides standard first-order time structures, we consider also those that have only finite first-order domains, and extend the results mentioned above to temporal logics of finite domains. We prove decidability in three different ways: using decidability of monadic second-order logic over the intended flows of time, by an explicit analysis of structures with natural numbers time, and by a composition method that builds a model from pieces in finitely many steps. (shrink)

Questions religieuses.--La vérité et la vie.--Morale et religion.--L'au-dela intérieur.--Pascal et le temps présent.--La idée de liberté en France et en Allemagne.--Après la guerre.--Morale et démocratie.--L'idéalisme franc̜ais et le temps présent.

LA PHILOSOPHIE A L'ECOLE NATIONALE AVANT 1960 : LOUIS ALTHUSSER. Louis Althusser (1918-1990) : psychologie. Louis Althusser (1918-1990) : philosophie politique. LA PHILOSOPHIE A L'ECOLE NATIONALE AVANT 1960 : JEAN HYPPOLITE. Jean Hyppolite (1907-1968) : Aristote, Spinoza, Hume. Jean Hyppolite (1907-1968) : Aristote, Spinoza, Hume, Comte. Jean Hyppolite (1907-1968) : Descartes, Hume, Hegel, Comte, Marx, Husserl, Heidegger, psychanalyse. AUTRES REPERES DE L'EPOQUE 1960-2000. Le dossier Althusser cinquante ans après. L'aventure de la philosophie française depuis les années 1960. EXPLORATION DE DIVERS (...) TYPES DIALECTIQUES. Alain lecteur et admirateur de Hegel et de Marx. L'encyclopédisme dialectique dans la psychologie d'Henri Wallon. Le style dialectique dans les travaux de Germaine Wallon. (shrink)

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