In this paper, we give a constructive nonstandard model of intuitionistic arithmetic (Heyting arithmetic). We present two axiomatisations of the model: one finitary and one infinitary variant. Using the model these axiomatisations are proven to be conservative over ordinary intuitionistic arithmetic. The definition of the model along with the proofs of its properties may be carried out within a constructive and predicative metatheory (such as Martin-Löf's type theory). This paper gives an illustration of the use of sheaf semantics to obtain (...) effective proof-theoretic results.The axiomatisations of nonstandard intuitionistic arithmetic (to be calledHAIandHAIωrespectively) as well as their model are based on the construction in [5] of a sheaf model for arithmetic using a site of filters. In this paper we present a “minimal” version of this model, built instead on a suitable site of provable filter bases. The construction of this site can be viewed as an extension of the well-known construction of the classifying topos for a geometric theory which uses “syntactic sites”. (Such sites can in fact be used to prove semantical completeness of first order logic in a strictly constructive framework, see [6].)We should mention that for classical nonstandard arithmetics there are several nonconstructive methods of proving conservativity over arithmetic, e.g. the compactness theorem, Mac Dowell–Specker's theorem [3]. (shrink)

In this paper, we give a constructive nonstandard model of intuitionistic arithmetic (Heyting arithmetic). We present two axiomatisations of the model: one finitary and one infinitary variant. Using the model these axiomatisations are proven to be conservative over ordinary intuitionistic arithmetic. The definition of the model along with the proofs of its properties may be carried out within a constructive and predicative metatheory (such as Martin-Löf's type theory). This paper gives an illustration of the use of sheaf semantics to obtain (...) effective proof-theoretic results.The axiomatisations of nonstandard intuitionistic arithmetic (to be calledHAIandHAIωrespectively) as well as their model are based on the construction in [5] of a sheaf model for arithmetic using a site of filters. In this paper we present a “minimal” version of this model, built instead on a suitable site of provable filter bases. The construction of this site can be viewed as an extension of the well-known construction of the classifying topos for a geometric theory which uses “syntactic sites”. (Such sites can in fact be used to prove semantical completeness of first order logic in a strictly constructive framework, see [6].)We should mention that for classical nonstandard arithmetics there are several nonconstructive methods of proving conservativity over arithmetic, e.g. the compactness theorem, Mac Dowell–Specker's theorem [3]. (shrink)

We present a solution to the problem of defining a counterpart in Algebraic Set Theory of the construction of internal sheaves in Topos Theory. Our approach is general in that we consider sheaves as determined by Lawvere-Tierney coverages, rather than by Grothendieck coverages, and assume only a weakening of the axioms for small maps originally introduced by Joyal and Moerdijk, thus subsuming the existing topos-theoretic results.

We introduce a predicative version of topos based on the notion of small maps in algebraic set theory, developed by Joyal and one of the authors. Examples of stratified pseudotoposes can be constructed in Martin-Löf type theory, which is a predicative theory. A stratified pseudotopos admits construction of the internal category of sheaves, which is again a stratified pseudotopos. We also show how to build models of Aczel-Myhill constructive set theory using this categorical structure.

This paper aims to give an informal introduction to the ways in which a topos can be viewed as an intuitionistic universe of sets. In particular, it is explained how infinitesimal real numbers and various types of ordinal numbers arise in this context.

This paper provides a partial solution to the completeness problem for Joyal's axiomatization of open and etale maps, under the additional assumption that a collection axiom holds.

We propose an extension of Aczel's constructive set theory CZF by an axiom for inductive types and a choice principle, and show that this extension has the following properties: it is interpretable in Martin-Löf's type theory. In addition, it is strong enough to prove the Set Compactness theorem and the results in formal topology which make use of this theorem. Moreover, it is stable under the standard constructions from algebraic set theory, namely exact completion, realizability models, forcing as well as (...) more general sheaf extensions. As a result, methods from our earlier work can be applied to show that this extension satisfies various derived rules, such as a derived compactness rule for Cantor space and a derived continuity rule for Baire space. Finally, we show that this extension is robust in the sense that it is also reflected by the model constructions from algebraic set theory just mentioned. (shrink)

A precise notion of ‘mathematical structure’ other than that given by model theory may prove fruitful in the philosophy of mathematics. It is shown how the language and methods of category theory provide such a notion, having developed out of a structural approach in modern mathematical practice. As an example, it is then shown how the categorical notion of a topos provides a characterization of ‘logical structure’, and an alternative to the Pregean approach to logic which is continuous with (...) the modern structural approach in mathematics. (shrink)

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces-so-called "topological semantics". The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

Using recent results in topos theory, two systems of higher-order logic are shown to be complete with respect to sheaf models over topological spaces- so -called "topological semantics." The first is classical higher-order logic, with relational quantification of finitely high type; the second system is a predicative fragment thereof with quantification over functions between types, but not over arbitrary relations. The second theorem applies to intuitionistic as well as classical logic.

Here Gellius, also the target of poems 74, 80, 89, 90, 91 and 116, is accused of incest with his mother, sister, and aunt. This accusation is coupled with the only extended mythological reference to be found in the group of short Catullan epigrams 69–116:2 not even Tethys or Oceanus can wash out Gellius' crimes. This notion that large bodies of water are unable to wash away the stain of crime is of course a topos going back to Greek (...) tragedy, but the individual naming of the two sea-deities seems to make a point—a literary point which is relevant to the invective of the poem. (shrink)

Moerdijk has introduced a topos of sheaves on a category of filters. Following his suggestion, we prove that its double negation subtopos is the topos of sheaves on the subcategory of ultrafilters - the ultrasheaves. We then use this result to establish a double negation translation of results between the topos of ultrasheaves and the topos on filters.

An investigation of the eidetic and transcendental phenomenological reductions as productive (and not merely descriptive) activities, Hence as a praxis generative of meaning. The eidetic reduction is a metaphoric system, Describing the movement from topos to tropes: the primal ontological structure is found to be that of distortion, Of a "coherent deformation," a breaking of forms, Which maintains the phenomenological horizon's openness. This founds a theory of decentered being, Ex-Centric subjectivity, And an anti-Ideologic critique.

This keynote takes a fresh look at Schutz’s essay on “The Stranger” of 1944. After a brief reflection on the probably universal topos of the stranger, it discerns three different kinds of strangeness in that essay: 1. the otherness of the other and the inaccessibility of the other’s experiences; 2. the strangeness vs. familiarity of elements of knowledge; and 3. the social acceptance by the in-group. Then some methodological implications of Schutz’s approach are pondered, his somewhat hidden offer of (...) an alternative sociology and the postulate of adequacy. Subsequently, two critical issues are discussed: Schutz’s handling of values and value-relations and his complete omission of affects and emotions in spite of all the hardship the immigrants at that time suffered from. An outlook on future Schutzian research concludes the paper. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Iconicity, Romance and History in the Crónica SarracinaMarina S. Brownlee (bio)Though seemingly alien discourses, romance and historiography are perennially linked. Far from offering an atemporal imaginary universe that bears no resemblance to historical specificity, romance is constructed as a response to it. Rather than simply projecting for the reader the naïve appeal of a prelapsarian escapism from the harsh realities of history, romance involves a continuous and sophisticated reinvention (...) of itself as a response to an ever-changing historico-political configuration. It is, in fact, a reciprocal relationship. We frequently see history appropriating romance paradigms explicitly, as, for example, when Bernal Díaz chooses to present Spain’s New World conquest and colonization as a continuation of the exploits of Amadís [see Gilman].Whatever form it takes, romance is committed to the celebration of a coherent system of socio-political values. This extra-textual frame of reference can take a variety of forms—from political propaganda that offers a self-aggrandizing depiction of the nobility or patron for whom the text is produced, to escapist fantasy—futuristic or archaizing. It is nostalgia for the lost world of chivalric romance which Cervantes embodies in the figure of Don Quijote, a foolish old man driven mad by his obsession with this perennial literary form. Cervantes is rightly credited with a brilliant and programmatic use of romance constructs to communicate the ongoing historical crisis of the Spanish empire. A byproduct of this romance scrutiny of history was his invention of the modern novel.Testimony to the long-standing interaction between romance and history in Spain, as elsewhere in Europe, is evident in the fact that its first romances were based on history, the so-called “romances of antiquity.” In those texts historical figures and events are evoked for the purpose of legitimating the present, vernacular poets as they celebrate the empowering myths projected by their society, as well as their own literary endeavors by invoking venerable Latin models. The well known translatio studii et imperii topos offers such allegory of empire.At the same time, the confrontation of romance and historical representation can also have a destabilizing effect, and this is programmatically explored in Pedro del Corral’s Crónica sarracina (c. 1430). His text ponders the possibilities of romance and historiography in an obsessive manner and he accomplishes his task by examining representation of the most iconic figures associated with the fall of Spain in 711, namely, La Cava and her father, Count Julián, King Rodrigo, and Pelayo, the messianic hope of the Reconquest effort which would last nearly 800 years.Of related and perhaps even broader importance, Corral’s text merits careful reading because its exploration of iconicity related to Spain’s fall offers meditations on the workings of ideology, which inevitably proposes “imaginary or formal solutions to unresolvable contradictions” [Jameson 79]. Ideology—its unmasking—is intriguingly posited by Corral in powerful ways.If we turn to Corral’s text, we find a work offering an extraordinary consideration of history and romance—their profound interaction—whose full title reads, La crónica [End Page 119] del rey don Rodrigo con la destrucción de España (The Chronicle of King Rodrigo with the Destruction of Spain). My interest in the Crónica here is primarily to consider the mechanisms by which it gestures boldly toward what Žižek has described as the project of the postmodern critique of ideology—though it is clearly a recurring cultural constant—namely to “designate the elements which point towards the system’s antagonistic character, and thus ‘estrange’ us to the self-evidence of its established identity” [Žižek 7]. A reading of the Crónica provides an extended paradigm of such estrangement.Iberia is the area of the Mediterranean which underwent the most protracted encounter between Christianity and Islam, and the events of the Moorish invasion of 711 constitute Spain’s unique foundational subject-matter—on a par with the Troy legend and with King Arthur [see Deyermond 355]. Like them, the retelling of 711 is all about forging mythic connections in order to legitimize empire in a temporally remote time-frame. What interests me in this essay is... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Going to our Happy Place: Idealism, Realism, and Nishida's Eutopia: A Response to Christian UhlChristopher S. Goto-JonesWords can be tricky things; their significance is often found in unexpected places. The word 'utopia,' for example, is usually considered to have originated in the early sixteenth century in Louvain when Thomas More fused two Greek words (ou, 'not,' and topos, 'place'). The result was a new, Greek-sounding compound, utopia, translatable (...) as 'Noplace.' Apparently, it was a small, newly discovered island where people did things differently from Europeans. By a happy coincidence, utopia was almost homophonous with another Greek compound, eutopia, which might be translated as 'Happyplace.' The word has come to be used to describe models of nonexistent societies that are imagined to be better than the ones in which we live.In his stimulating, thorough, and carefully crafted review of my recent book, Political Philosophy in Japan: Nishida, the Kyoto School, and Co-Prosperity, Christian [End Page 482] Uhl makes a great deal of my claim that Nishida's political project was utopian. He also takes issue with my characterization of Nishida as a political idealist. In the interests of clarification and in the spirit of engaged debate, I think that it is important to consider what these important (and often complicated) terms mean. In particular, the idea that 'idealist' and 'utopian' are coterminous should not be allowed to stand unchallenged. In a related way, it may be helpful to clarify what is meant by 'realist' in political thought, since Uhl claims that, far from being an idealist, Nishida was actually a realist "in a very fundamental sense of the word."Uhl is quite right to observe that I identify Nishida's political scheme as utopian in the sense that he provides a model of an ideal society as a means of demonstrating the problems in the society in which he lived.1 However, when it comes to the effectiveness of Nishida's utopian vision qua dissent in wartime Japan (or simply qua practice), the key problem slides from being utopianism itself to idealism. A utopia is an ideal society; the method required to realize that society is not necessarily part of the vision itself, although it may be implied in the structure. Consider a socialist utopia: for Marx, the road to this perfect society was paved by historical materialism; for a number of other socialists (including many Japanese socialists), the route to a broadly similar society was defined in humanist or even idealist terms. In a rather casual sense we might label the later Marx a realist and, say, Kawakami Hajime as an idealist. Nishida's utopia is no simpler,2 although it does, in fact, contain a sense of process: it is defined as a type of self-realization and it is premised upon an underlying faith in the power of the mind to transform both the self and the everyday world.I would contend that Nishida was an idealist (a thinker who works on the principle that the reality in which we live is somehow mind-correlative), although not a simple idealist, and also a political utopian. A number of his students, for example Nishitani and Kōyama, broadly shared their mentor's goals but differed in their construction of the paths to them. The quotation from Nishitani that Uhl selects reveals this clearly: he argues that if we do not "have both feet firmly grounded in the consciousness of the past as well as in the practice of the present, any idea will remain a mere concept, a utopian ideal."3 Nishitani is not taking issue with the utopia; he is challenging the process appropriate to its realization. He argues (in common with many of the other second-generation members of the Kyoto School) that an idealist philosophy that pays no attention to the significance of history can offer no blueprints for the achievement of its ideals in reality. The implied challenge to Nishida's thought here is to his understanding of the forces of historical change: idealist self-power (jiriki) is laid bare as ahistorical and inadequate as an engine for social change. Having said that, however, Nishitani does not make... (shrink)

Using Butz and Moerdijk's topological groupoid representation of a topos with enough points, a ‘syntax-semantics’ duality for geometric theories is constructed. The emphasis is on a logical presentation, starting with a description of the semantic topological groupoid of models and isomorphisms of a theory. It is then shown how to extract a theory from equivariant sheaves on a topological groupoid in such a way that the result is a contravariant adjunction between theories and groupoids, the restriction of which (...) is a duality between theories with enough models and semantic groupoids. Technically a variant of the syntax-semantics duality constructed in 1 for first-order logic, the construction here works for arbitrary geometric theories and uses a slice construction on the side of groupoids—reflecting the use of ‘indexed’ models in the representation theorem—which in several respects simplifies the construction and the characterization of semantic groupoids. (shrink)

From a logical point of view, Stone duality for Boolean algebras relates theories in classical propositional logic and their collections of models. The theories can be seen as presentations of Boolean algebras, and the collections of models can be topologized in such a way that the theory can be recovered from its space of models. The situation can be cast as a formal duality relating two categories of syntax and semantics, mediated by homming into a common dualizing object, in this (...) case 2.In the present work, we generalize the entire arrangement from propositional to first-order logic, using a representation result of Butz and Moerdijk. Boolean algebras are replaced by Boolean categories presented by theories in first-order logic, and spaces of models are replaced by topological groupoids of models and their isomorphisms. A duality between the resulting categories of syntax and semantics, expressed primarily in the form of a contravariant adjunction, is established by homming into a common dualizing object, now Sets, regarded once as a boolean category, and once as a groupoid equipped with an intrinsic topology.The overall framework of our investigation is provided by topos theory. Direct proofs of the main results are given, but the specialist will recognize toposophical ideas in the background. Indeed, the duality between syntax and semantics is really a manifestation of that between algebra and geometry in the two directions of the geometric morphisms that lurk behind our formal theory. Along the way, we give an elementary proof of Butz and Moerdijkʼs result in logical terms. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since (...) any such is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object . Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

This paper introduces Basic Intuitionistic Set Theory BIST, and investigates it as a first-order set theory extending the internal logic of elementary toposes. Given an elementary topos, together with the extra structure of a directed structural system of inclusions on the topos, a forcing-style interpretation of the language of first-order set theory in the topos is given, which conservatively extends the internal logic of the topos. This forcing interpretation applies to an arbitrary elementary topos, since (...) any such is equivalent to one carrying a dssi. We prove that the set theory BIST+Coll is sound and complete relative to forcing interpretations in toposes with natural numbers object. Furthermore, in the case that the structural system of inclusions is superdirected, the full Separation schema is modelled. We show that all cocomplete and realizability toposes can be endowed with such superdirected systems of inclusions.A large part of the paper is devoted to an alternative notion of category-theoretic model for BIST, which, following the general approach of Joyal and Moerdijkʼs Algebraic Set Theory, axiomatizes the structure possessed by categories of classes compatible with BIST. We prove soundness and completeness results for BIST relative to the class-category semantics. Furthermore, BIST+Coll is complete relative to the restricted collection of categories of classes given by categories of ideals over elementary toposes with nno and dssi. It is via this result that the completeness of the original forcing interpretation is obtained, since the internal logic of categories of ideals coincides with the forcing interpretation. (shrink)

We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé’s construction in Model Theory, with applications to homogeneous models and countably categorical theories.

In this article, I elucidate the significance of Heidegger’s ‘question of being’ from a topological point of view by explaining the relationship between his thought of place and language. After exploring various hermeneutic strategies of reading Heidegger’s oeuvre, I turn to Richard Capobianco’s interpretation of Heidegger and critically engage with his idea of the experience of being itself as the ‘luminous self-showing of logos’. In doing so, I explain the later turn from ‘truth’ to ‘place’ and articulate why logos needs (...) to be conceived as the gathering site of the presencing of being. In arguing against the primacy of passive receptivity and active projection, I put forward the primacy of language as the topos and logos of being. In returning to the Capobianco-Sheehan debate, I conclude by explaining why Heidegger’s place-related notions cannot be thought metaphorically. (shrink)

In 1991, Ukrainian independence opened an important theoretical channel for debating the status of its women. The people's collective memory of an ancient matriarchy generated a neo-matriarchal mythology which has been transformed into a delusional ideology that legitimizes female subordination, in the name of her alleged empowerment. Fieldwork in Ukraine – annual visits, including travel from one end of the country to another in official capacities, and many extended stays in Ukraine, as a scholar, researcher, educator and participant in key (...) events, provided opportunities for exchanging views with countless people from many walks of life throughout the country. Participation in a host of programs – television ‘specials’ on gender, seminars, retreats, workshops and conferences, designed to raise the consciousness of women and men alike – provided an array of opportunities to observe at first hand the way that today's women construct individual identity. Extensive research in the press (many runs of daily newspapers, including Den’, in Kyiv, and Vysoky Zamok in Lviv, and women's journals such as the widely read Zhinka, among others) added further insights. Television viewing, popular publications collected habitually during my numerous visits to Ukraine, copies of documents contributed by my Ukrainian friends and colleagues, outdoor advertising, posters and intimate gatherings at the homes of likeminded women, all played a part in the formation of my impressions of Ukrainian women's inferior status. In this paper I use my findings to explore the conflicting discourses on women's alleged empowerment, and the essentialist constraints on their self-realization, together with measures adopted to date on changing gender stereotypes and promoting equal rights and opportunities. (shrink)

The present work depicts the content and functions of very specific carriers of collective memory, namely the epigraphic transmissions. The rich tradition of using epigraphic objects, their durability and communicative seriousness, make them consistently attractive forms of transferring memory also in small local communities of towns, villages, parishes, schools and working commu-nities. Those seen as particularly interesting ones are epigraphic objects, whose task is to “commemorate the origins”. The use of the “topos of origins” creates an initiation moment on (...) the line of collective memory of a given local community. The observations presented in the work relate to the epigraphic resource, created in the last half century within the spatial framework of the borderland of Silesia and Lesser Poland. (shrink)

This dissertation is concerned with one of the central but most perplexing theories in Plotinus's metaphysics, namely the nature and origin of time. In contrast to those interpretations of Neoplatonism that treat time as an imperfect image and passive product of eternity, I argue for a much more subtle and multifaceted concept that makes the human observer central to Plotinus's account of how time is actualized and thus passes. His emphasis on mystical experience and the individual soul's journey toward the (...) One and the realm of eternity strengthens this account. By reading the treatise On Eternity and Time in this light, I demonstrate the importance of embodied human consciousness for the Plotinian theory of time. ;This emphasis invites comparison with the one contemporary Continental thinker who devoted countless pages in both his published work and his manuscripts to the relationship between time and consciousness. In the second part of the dissertation I argue that the Husserlian and Plotinian subjects have analogous characteristics, in accordance with their parallel roles as sources of time, and that the Husserlian notion of omnitemporality offers the best way of understanding the internal connection between Plotinus's notion of eternity and his notion of actualization through human experience. At the same time, Plotinus challenges a phenomenological account by giving the eternal ontological priority over the human realm of temporality. Nevertheless, these intriguing affinities and oppositions suggest that Plotinus's theory of time and eternity can best be understood and even expanded by uncovering its phenomenological underpinnings. (shrink)

: In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ‘‘from the Created to the Creating’’ (tsukuru mono kara tsukurareta mono e) through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ‘‘Space of Transparency’’ put forth (...) by Ufan Lee, the leader of Monoha, is the principal example. This essay investigates Nishida’s notion of shintai and its influence on Lee’s theory of art. (shrink)

In his philosophy of nothingness, Kitar Nishida illuminates the matrix of transformation of the world ''from the Created to the Creating'' through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The ''Space of Transparency'' put forth by Ufan Lee, the leader of Monoha, (...) is the principal example. This essay investigates Nishida's notion of shintai and its influence on Lee's theory of art. (shrink)

The concept of topos has received considerable attention from both argumentation and discourse studies, although its usage and meaning remain obscure. In this article, I argue that the rediscovery of Aristotelian thought might provide a comprehensible explication of topos. Despite the discourse historical approach’s emphasis on topos, its context is found to be limited and this exposes the argumentation strategies of the DHA to criticism. To overcome any shortcomings and provide a better understanding of topos, a (...) classical approach to the concept is suggested, derived from Aristotle’s rhetoric and dialectic. By focusing on Greek media discourses on ‘Islamist terrorism’, I seek to illustrate the synthesis between the DHA’s argumentation strategies and Aristotelian topos as a fruitful analytical and theoretical tool. (shrink)

Terminologically, the “topos of mu” and the “predicative self” originated in the Kyoto School and are traceable to the work of its founder NISHIDA Kitarō. The full phrase was coined by NAKAMURA Yūjirō. Conceptually, the topos of mu or place of nothingness is Nishida’s development of the Buddhist notion of anatta or no self and radiating out from that locus of emptiness is a self constituted by its predicates or the things to which it is connected by an (...) existential copula. Deeply ingrained in Western languages, metaphysics, and religion is the subjective self, in both the linguistic and psychological senses of “subjective.” That Buddhism, as reworked by the Kyota School, or Daoism, or any other non-Western tradition of thought, will catch on in the West was a puerile fantasy of some members of the first generation of environmental philosophers. There is a good chance, however, that the Western worldview may evolve toward a similar conception of the self—as ecological, relational, or systems thinking becomes ever more ingrained. We in the West may come to understand that we are constituted by our social and environmental relationships, in which we are deeply embedded and on which we are utterly dependent, such that world care is the essence of self-help. (shrink)

In his philosophy of nothingness, Kitarō Nishida illuminates the matrix of transformation of the world "from the Created to the Creating" (tsukuru mono kara tsukurareta mono e) through shintai, or the body. In this matrix, shintai enters into the stage of an action-sensation continuum and emerges as the immaculate iconic tool of nothingness to create new figures as extended self. This idea of shintai has resonance with the development of postwar art in Japan. The "Space of Transparency" put forth by (...) Ufan Lee, the leader of Monoha, is the principal example. This essay investigates Nishida's notion of shintai and its influence on Lee's theory of art. (shrink)

The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory (...) of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples. (shrink)

We extend the topos-theoretic treatment given in previous papers of assigning values to quantities in quantum theory. In those papers, the main idea was to assign a sieve as a partial and contextual truth-value to a proposition that the value of a quantity lies in a certain set D of real numbers. Here we relate such sieve-valued valuations to valuations that assign to quantities subsets, rather than single elements, of their spectrum (we call these interval valuations). There are two (...) main results. First, there is a natural correspondence between these two kinds of valuation, which uses the notion of a state's support for a quantity (Section 3). Second, if one starts with a more general notion of interval valuation, one sees that our interval valuations based on the notion of support (and correspondingly, our sieve-valued valuations) are a simple way to secure certain natural properties of valuations, such as monotonicity (Section 4). (shrink)

We give a formal interpretation of Martin-Löf's Constructive Theory of Types in Elementary Topos Theory which is presented as a formalised theory with intensional equality of objects. Types are interpreted as arrows and variables as sections of their types. This is necessary to model correctly the working of the assumption x ∈ A. Then intensional equality interprets equality of types. The normal form theorem which asserts that the interpretation of a type is intensional equal to the pullback of its (...) “alignment” along some “base” arrow relates this interpretation to categorical semantic of types. (shrink)

The concept of love has emerged as a central topic for philosophical and theoretical discussion over the past few years. Whereas the dominant ideology of love in contemporary culture insists that love be understood as a discovery of my long lost second half with whom I merge and finally recreate a whole, contemporary philosophers and theorists have stressed the need to reconsider the concept of love within an ethical framework that can sustain the idea of the other as forever different (...) and separate. Taking as a starting point two different taxi scenes offered by Foucault and Woolf respectively, the article outlines and discusses those two contemporary love grammars, focusing on the concepts of lack and fantasy. Whereas Woolf’s taxi scene is reminiscent of a notion of love as a fantasy of unification, Foucault’s notion of love not only observes the need to maintain the other’s specificity and separateness, but also considers lack and fantasy to be primary and fundamental parts of love as lived experience. While Foucault insists on pleasure and action he also observes the central and unavoidable power of imagination that is attributed the name and function of recollection. The article finally addresses the question of if and how we might be responsible for our daydreams and fantasies. (shrink)

Byzantine authors frequently used the well-known topos of modesty in the opening lines of their literary works. This common introduction, usually served two purposes: The authors expressed a genuine, or, perhaps, feigned concern about their ability to deal adequately with their subject both in terms of form and substance, and they preemptively tried to thwart any possible criticism on the part of the audience for any shortcomings in their work by beginning with this sort of captatio benevolentiae. Typical examples (...) of this topos are not only numerous among hagiographers throughout the Byzantine millennium, but even in such writers as Theophanes Confessor, as one can see from the preamble to his Chronography. It is only after the 11th century that “we sometimes encounter the author's frank appraisal of his talent, for example in Psellos and Tzetzes.” As early an author as John of Damascus, however, also displayed his self-appreciation for his talent and this will be the subject of this short article. Here, I shall examine John of Damascus' own personal stance to the topos of modesty/humility and, in one particular case, his rather interesting variation on it. (shrink)