Indeterminism, understood as a notion that an event may be continued in a few alternative ways, invokes the question what a region of chanciness looks like. We concern ourselves with its topological and spatiotemporal aspects, abstracting from the nature or mechanism of chancy processes. We first argue that the question arises in Montague-Lewis-Earman conceptualization of indeterminism as well as in the branching tradition of Prior, Thomason and Belnap. As the resources of the former school are not rich enough to study (...) topological issues, we investigate the question in the framework of branching space-times of Belnap (Synthese 92:385–434, 1992). We introduce a topology on a branching model as well as a topology on a history in a branching model. We define light-cones and assume four conditions that guarantee the light-cones so defined behave like light-cones of physical space-times. From among various topological separation properties that are relevant to our question, we investigate the Hausdorff property. We prove that each history in a branching model satisfies the Hausdorff property. As for the satisfaction of the Hausdorff property in the entire branching model, we prove that it is related to the phenomenon of passive indeterminism, which we describe in detail. (shrink)

Quantum physics exhibits various non-classical and paradoxical features. Among them are non-locality and contextuality (e.g. Bell’s theorem or the Einstein-Podolsky-Rosen paradox). Since they are expected to constitute a key resource in quantum computation, several approaches have been proposed to provide high-level expressions for them. In one of these approaches, Abramsky and others use the mathematics of algebraic topology and characterize non-locality and contextuality as the same type of phenomena as M. C. Escher’s impossible figures. This article expands this topological insight (...) and demonstrates that logical paradoxes arising from circular references (of the sort formalized by Gödel’s fixed-point or diagonalization lemma) share the same topological structure as the quantum paradoxes, by reformatting the topological model of contextuality into a semantics of logical paradoxes. This topological semantics indeed provides a unifying perspective from which previous approaches of philosophers and logicians to logical paradoxes can be understood as diverse ways of fine-tuning topologies to model paradoxes. (shrink)

The theory of branching space-times is designed as a rigorous framework for modelling indeterminism in a relativistically sound way. In that framework there is room for "funny business", i.e., modal correlations such as occur through quantummechanical entanglement. This paper extends previous work by Belnap on notions of "funny business". We provide two generalized definitions of "funny business". Combinatorial funny business can be characterized as "absence of prima facie consistent scenarios", while explanatory funny business characterizes situations in which no localized explanation (...) of inconsistency can be given. These two definitions of funny business are proved to be equivalent, and we provide an example that shows them to be strictly more general than the previously available definitions of "funny business". (shrink)

In this paper we show a duality between two approaches to represent quantum structures abstractly and to model the logic and dynamics therein. One approach puts forward a “quantum dynamic frame” :2267–2282, 2005), a labelled transition system whose transition relations are intended to represent projections and unitaries on a Hilbert space. The other approach considers a “Piron lattice”, which characterizes the algebra of closed linear subspaces of a Hilbert space. We define categories of these two sorts of structures and show (...) a duality between them. This result establishes, on one direction of the duality, that quantum dynamic frames represent quantum structures correctly; on the other direction, it gives rise to a representation of dynamics on a Piron lattice. (shrink)

We define the notion of a model of higher-order modal logic in an arbitrary elementary topos E. In contrast to the well-known interpretation of higher-order logic, the type of propositions is not interpreted by the subobject classifier ΩE, but rather by a suitable complete Heyting algebra H. The canonical map relating H and ΩE both serves to interpret equality and provides a modal operator on H in the form of a comonad. Examples of such structures arise from surjective geometric morphisms (...) f : F → E, where H = f∗ΩF. The logic differs from non-modal higher-order logic in that the principles of functional and propositional extensionality are not longer valid but may be replaced by modalized versions. The usual Kripke, neighborhood, and sheaf semantics for propositional and first-order modal logic are subsumed by this notion. (shrink)

Comme son titre l’indique, cet ouvrage collectif renouvelle réflexions et analyses autour des mouvements et figures féministes du Japon dans différents domaines. L’introduction nous donne un aperçu historique et synthétique très utile pour resituer les chapitres qui suivent. Elle souligne l’apparition de figures féministes (Kishida Toshiko, Fukuda Hideko) dès le début de la construction de l’État moderne japonais. Leur combat pour accéder à l’espace politique resta minoritaire alors que le pr...

Since World War II Japanese artists have employed two seemingly contradictory ways of working, using aesthetics, materials, artistic methods technologies, and approaches that are either radically innovative and wildly experimental, or traditional/classical. Many other artists, however, in a move that seems paradoxical. have combined the two to explore the new themes of the post-atomic period. Three narrative works dealing with the effects of the World War II war effort and the atomic bombings that ended them, Yasunari Kawabata’s novel The Sound (...) of the Mountain (1952), Rio Kishida’s avant-garde play Thread Hell (1984), and the film Barefoot Gen (Hadashi no Gen), directed by Mori Masaki and written by Keiji Nakazawa (Masaki and Nakazawa 1983), exemplify this third approach. Set in the pre-War textile industry that enabled the War, during the atomic bombings, and the post-War American Occupation, all three explore the experience not only of the horrific objective effects of war but of the Japanese experience of psychic numbing, which damages the person’s sense of self and their sense of agency—their ability to act effectively in the world. All three utilize classical aesthetics to provide aesthetic experiences, for their readers/viewers, to make the experience of the work tolerable, and for their characters—to demonstrate the roles of positive aesthetic experience in making life worth while and in grounding a renewed sense of personal identity and selfhood in a self that has been shattered through trauma. (shrink)