This volume examines the entire logical and philosophical production of Nikolai A. Vasil’ev, studying his life and activities as a historian and man of letters. Readers will gain a comprehensive understanding of this influential Russian logician, philosopher, psychologist, and poet. The author frames Vasil’ev’s work within its historical and cultural context. He takes into consideration both the situation of logic in Russia and the state of logic in Western Europe, from the end of the 19th century to the (...) beginning of the 20th. Following this, the book considers the attempts to develop non-Aristotelian logics or ideas that present affinities with imaginary logic. It then looks at the contribution of traditional logic in elaborating non-classical ideas. This logic allows the author to deal with incomplete objects just as imaginary logic does with contradictory ones. Both logics are objects of interesting analysis by modern researchers. (shrink)

This paper is about the ?Imaginary Logic? developed by the Russian logician Nicholas Vasil'év between about 1910 and 1913, a logic that is often claimed to be a forerunner of different sorts of modern nonclassical logics. The paper describes the content of that logic (not by trying to interpret it in modern logic, as some commentators have done, but by describing it in its own terms). It then looks at the philosophical underpinnings of the (...) class='Hi'>logic. Finally, in the light of the preceding, it discusses Vasil?év's place in the history of logic. (shrink)

Volume 40, Issue 3, August 2019, Page 298-303.

Le philosophe russe Nicolai Vasiliev est connu en tant que précurseur des logiques essentiellement non-classiques, c'est-à-dire de logiques qui diffèrent de la logique classique par l'abandon de principes qui sont corrects en logique classique. La gamme de telles logiques couvre la logique intuitionniste, la logique plurivalente, la logique paraconsistante et les logiques de la pertinence. Dans la première partie de ce texte, j'analyse brièvement les vues de Vasiliev, à savoir sa « logique imaginaire », qu'il présente comme une nouvelle logique (...) non-aristotélicienne. Dans les sections suivantes je discute l'impact des approches de Vasiliev sur la logique du consentement. Ici, les idées essentiellement non-classiques de Vasiliev seront reliées à des logiques non- essentiellement non-classiques, qui ne constituent pas une révision de la logique classique, mais étendent sa puissance expressive. (shrink)

BOOK REVIEWS: Valentin A. Bazhanov, “N.A. Vasil’ev and his Imaginary Logic”, Kanon+, Reabilitatsiia, Moscow, 2009, 240 pp., ISBN 9785883731968.

The paper investigates the system of 'Imaginary Logic' created by the Russian logician N.A. Vasil'ev (1880-1940), considered by some to be a forerunner of paraconsistent or intuitionistic logics. It is shown how he constructs a logic without the law of contradiction redefining the concept of negation. Vasil'ev singles out two levels of logic, an external one which is absolute and one depending on commitments in relation to cognizable objects which is not absolute. His reconstruction of the (...) syllogism shows the viability of his system and indicates how, indeed, he may be called an initiator of nonclassical logics. (shrink)

Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of (...) class='Hi'>imaginary worlds, and we use it to define a dynamic formal system called the Logic of Imagination Acts. We build our logic by using a possible-worlds semantics, together with a new set of static and dynamic modal operators. The role of the new dynamic operators is to call different algorithms that encode how the formal model is expanded in order to capture the different mechanisms involved in the creation and development of imaginary worlds. We provide the definitions of the language, the semantics and the algorithms, together with an example that shows how the model is expanded. By the end, we discuss some interesting features of our system, and we point out to possible lines of future work. (shrink)

A collaborative article by the Editorial Collective of Social Imaginaries. Investigations into social imaginaries have burgeoned in recent years. From ‘the capitalist imaginary’ to the ‘democratic imaginary’, from the ‘ecological imaginary’ to ‘the global imaginary’ – and beyond – the social imaginaries field has expanded across disciplines and beyond the academy. The recent debates on social imaginaries and potential new imaginaries reveal a recognisable field and paradigm-in-the-making. We argue that Castoriadis, Ricoeur, and Taylor have articulated the (...) most important theoretical frameworks for understanding social imaginaries, although the field as a whole remains heterogeneous. We further argue that the notion of social imaginaries draws on the modern understanding of the imagination as authentically creative. We contend that an elaboration of social imaginaries involves a significant, qualitative shift in the understanding of societies as collectively and politically-instituted formations that are irreducible to inter-subjectivity or systemic logics. After marking out the contours of the field and recounting a philosophical history of the imagination, the essay turns to debates on social imaginaries in more concrete contexts, specifically political-economic imaginaries, the ecological imaginary, multiple modernities and their inter-civilisational encounters. The social imaginaries field imparts powerful messages for the human sciences and wider publics. In particular, social imaginaries hold significant implications for ontological, phenomenological and philosophical anthropological questions; for the cultural, social, and political horizons of contemporary worlds; and for ecological and economic phenomena. The essay concludes with the argument that social imaginaries as a paradigm-in-the-making offers valuable means by which movements towards social change can be elucidated as well providing an open horizon for the critiques of existing social practices. (shrink)

Imagination has received a great deal of attention in different fields such as psychology, philosophy and the cognitive sciences, in which some works provide a detailed account of the mechanisms involved in the creation and elaboration of imaginary worlds. Although imagination has also been formalized using different logical systems, none of them captures those dynamic mechanisms. In this work, we take inspiration from the Common Frame for Imagination Acts, that identifies the different processes involved in the creation of (...) class='Hi'>imaginary worlds, and we use it to define a dynamic formal system called the Logic of Imagination Acts. We build our logic by using a possible-worlds semantics, together with a new set of static and dynamic modal operators. The role of the new dynamic operators is to call different algorithms that encode how the formal model is expanded in order to capture the different mechanisms involved in the creation and development of imaginary worlds. We provide the definitions of the language, the semantics and the algorithms, together with an example that shows how the model is expanded. By the end, we discuss some interesting features of our system, and we point out to possible lines of future work. (shrink)

Imagining is something we use everyday in our lives and in a wide variety of ways. In spite of the amount of works devoted to its study from both psychology and philosophy, there are only a few formal systems capable of modelling it; besides, almost all of those systems are static, in the sense that their models are initially predefined, and they fail to capture the dynamic process behind the creation of new imaginary scenarios. In this work, we review (...) some influential theories of imagination and use their insights to distil an algorithm describing such process. Then, we use this algorithm to define a dynamic logical system built upon on a single-agent epistemic logic that provides the necessary tools to capture how the agent voluntarily creates new imaginary worlds; in other words, our system allows the model to be expanded dynamically at any time as a result of the agent performing an act of imagination. Furthermore, we provide an axiomatization and prove that the system is sound and complete. (shrink)

The objective of this article is to characterise elimination of finite generalised imaginaries as defined in [9] in terms of group cohomology. As an application, I consider series of Zariski geometries constructed [10, 23, 24] by Hrushovski and Zilber and indicate how their nondefinability in algebraically closed fields is connected to eliminability of certain generalised imaginaries.

We characterise imaginaries (up to interdefinability) in Hilbert spaces using a Galois theory for compact unitary groups.

From Charles Taylor to Marcel Gauchet, theorists of the social imaginary have given us new ways to talk about the shared structures of meanings and practices of the West. Theorists of this group have argued against the narrow horizons of meaning that are deployed by deliberative political theories in developing their basic normative concepts and principles, providing an alternative to the oscillation between the constructivism and the realism. Theorists of the imaginary have enabled us to think about normatively (...) charged collective imaginaries as logically prior to the construction of normative principles. What theorists of the imaginary have not done is make specific connections between the ontological background of social imaginaries and the normative utterance. This lacuna has left them vulnerable to the charges of ‘normative deficit’ and vagueness that Habermas and others famously make against philosophies of ‘world disclosure’. This article develops a conception of the normative utterance that enables... (shrink)

Given an infinite Boolean algebra B, we find a natural class of equation image-definable equivalence relations equation image such that every imaginary element from Beq is interdefinable with an element from a sort determined by some equivalence relation from equation image. It follows that B together with the family of sorts determined by equation image admits elimination of imaginaries in a suitable multisorted language. The paper generalizes author's earlier results concerning definable equivalence relations and weak elimination of imaginaries for (...) Boolean algebras, obtained in 10. (shrink)

We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm {ACFG}$. This theory was introduced in [16] as a new example of $\mathrm {NSOP}_{1}$ nonsimple theory. In this paper we describe more features of $\mathrm {ACFG}$, such as imaginaries. We also study various independence relations in $\mathrm {ACFG}$, such as Kim-independence or forking independence, and describe interactions between them.

From a dialogic perspective between philosophy, social sciences and social reality leading to a renewed epistemology, the article intends to comprehend: the phenomenon of citizen distrust with social institutions of the Chilean State, the distrust of the citizen against the current market logics such as the commodification of the social relations, and finally, the distrust between citizens in everyday spaces. The work is framed under the studies of sociology and anthropology, from the perspective of the social imaginaries and it is (...) aimed to the deconstruction of mistrust in many central elements of social links in post-dictatorship Chile and their actual or potential relationship with discontent. Desde una perspectiva dialógica entre la filosofía, las ciencias sociales y la realidad social, que desemboca en una epistemología renovada, el artículo busca comprender: el fenómeno de la desconfianza del ciudadano con instituciones de la sociedad y del Estado chileno, la desconfianza del ciudadano frente a lógicas actuales del mercado como la mercantilización de las relaciones sociales y, por último, la desconfianza entre ciudadanos en espacios cotidianos. El trabajo es parte de los estudios de la sociología y de la antropología desde la perspectiva de los imaginarios sociales y se interesa en la deconstrucción de la desconfianza en tanto elemento característico central de los vínculos sociales en el Chile de la post-dictadura y de su relación potencial o real con el descontento. (shrink)

The paper shows elimination of imaginaries for real closed valued fields to suitable sorts. We also show that this result is in some sense optimal. The paper includes a quantifier elimination theorem for real closed valued fields in a language with sorts for the field, value group and residue field.

We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the ‘geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.

The article presents a theoretical discussion and sociological analysis about the tensions in the building of social sex/gender relationships that are at the basis of the exclusion of women within the political field. It shows contents in dispute in the production of politics, considering the weight that categories play in the relations at a global level and in the school, the attributions inside the system sex/gender, the significations in politics, and the modes in which it is subjectified, resisted and confront (...) different logics to understand life and politics, considering the conceptual distinctions between Bíos and Zoé. This discussion allows the analysis of the imaginary institution within systematic difficulties and obstacles of political and legal kind during the post dictatorship in Chile, where based on arguments about the sex/gender system, the exclusion of women from the political field is established, limiting the development of politics that valorizes cultural diversity and human rights, accentuating discrimination and social exclusion. These shape the discussion over the modes in which the political field for women is configured, recovering the possibilities of conflict as an opening of that horizon. El artículo presenta una discusión teórica y análisis sociológico acerca de las tensiones en la construcción social de las relaciones sexo/género, que fundamentan la exclusión del campo político de las mujeres. Se distinguen los contenidos en disputa en la producción de la política, considerando el peso que tienen las categorías en juego en las relaciones a nivel global y en el espacio de la escuela, las atribuciones dentro del sistema sexo/género, las significaciones de la política, y los modos en que se subjetivan, se resisten y se confrontan diferentes lógicas para entender la vida y la política, teniendo como base las distinciones conceptuales entre Bios y Zoé. Esta discusión permite analizar la institución del imaginario en el marco de las dificultades sistemáticas y obstáculos de tipo político y legal durante la post dictadura en Chile, donde sobre la base de argumentos propios del sistema sexo/género, se establece la exclusión del campo político de las mujeres, limitando el desarrollo de políticas que pongan en valor la diversidad cultural y los derechos humanos, acentuando la discriminación y la exclusión social. Estos dan forma a la discusión sobre el modo en que se configura el campo de lo político para las mujeres, recuperando las posibilidades del conflicto como apertura de este horizonte. (shrink)

This paper discusses the formation of Castoriadis’s concept of imaginary significations and relates it to his changing readings of Marx and Weber. Castoriadis’s reflections on modern capitalism took off from the Marxian understanding of its internal contradictions, but he always had reservations about the orthodox version of this idea. His writings in the late 1950s, already critical of basic assumptions in Marx’s work, located the central contradiction in the very relationship between capital and wage labour. Labour power was not (...) simply transformed into a commodity, as Marx had argued; rather, the instituted attempt to treat it as a commodity was a contradiction in itself, between the subjectivity and the objectification of labour. Castoriadis then moved on to link this claim to Weber’s analysis of the interconnections between capitalism and bureaucracy. The main contradiction of modern capitalism, whether wholly bureaucratised as in the Soviet model or increasingly bureaucratised as in the West, now seemed to be a matter of incompatible systemic imperatives: the need to control and to mobilise the workforce. Finally, difficulties with this model – and with the revolutionary expectations based on it – led to a more decisive break with classical theories and to the formulation of a bipolar image of modernity, where the vision of an autonomous society is opposed to the logic of calculation and domination, embodied in capitalist development. On both sides there is an imaginary component, irreducible to empirical givens or systemic principles. In this regard, Castoriadis remained closer to Weber than to Marx, but he also anticipated, in a distinctive way, later emphasis on the cultural dimension of modernity, and more specifi cally the notion of modernity as a new civilisation. (shrink)

Beginning with a review the logically first stages in the project of Random Dynamics, hoping for all laws nature being emergent, we also review what can be considered a consequence of Random Dynamics, a model—by myself and Masao Ninomiya—, which in principle predicts the initial conditions in such a way as to minimize a certain functional of the history of the Universe through both past and future. This functional is indeed the imaginary part of the action, which exists (only) (...) in our model of complex action. The main point of the present is to suggest this complex action model to be also helpfull in solving some problems for quantum mechanics. Especially as our model almost makes it possible in principle to calculate the full history of the universe, it even makes it in principle calculable, which one among several measurement results in a quantum experiment will actually be realized!Our “complex action model” thus is a special case of superdeterminism—in Bells way—and does not have true causality, but rather even in some cases true backward causation. In fact we claim in our model that the SSC(Superconducting Supercollider) were stopped by the US Congress due to the backward causation from the big amounts of Higgs particles, which it would have produced, if it had been allowed to run. The noumenon (“das Ding an sich”) in our model is the Feyman path integrand or better some fundamental quantities determined from second order effects of the latter integrand. The quantum mechanics interpretation here is strongly similar to the much criticized “transactional interpretation” by John Cramer (Rev. Mod. Phys. 58:647–688, 1986), but we might respond to some of the criticism. (shrink)

In this paper we study elimination of imaginaries in some classes of pure ordered abelian groups. For the class of ordered abelian groups with bounded regular rank (equivalently with finite spines) we obtain weak elimination of imaginaries once we add sorts for the quotient groups $\Gamma /\Delta $ for each definable convex subgroup $\Delta $, and sorts for the quotient groups $\Gamma /(\Delta + \ell \Gamma )$ where $\Delta $ is a definable convex subgroup and $\ell \in \mathbb {N}_{\geq 2}$. (...) We refer to these sorts as the quotient sorts. For the dp-minimal case we obtain a complete elimination of imaginaries if we also add constants to distinguish the cosets of $\ell \Gamma $ in $\Gamma $, where $\ell \in \mathbb {N}_{\geq 2}$. (shrink)

Husserl's two notions of "definiteness" enabled him to clarify the problem of imaginary numbers. The exact meaning of these notions is a topic of much controversy. A "definite" axiom system has been interpreted as a syntactically complete theory, and also as a categorical one. I discuss whether and how far these readings manage to capture Husserl's goal of elucidating the problem of imaginary numbers, raising objections to both positions. Then, I suggest an interpretation of "absolute definiteness" as semantic (...) completeness and argue that this notion does not suffice to explain Husserl's solution to the problem of imaginary numbers. (shrink)

Shows how digital capitalism has shaped human rights practices What happens to the cultural politics of human rights when atrocities are rendered calculable, abuses are transformed into data, and victims become vectors? As human rights organisations have increasingly embraced information technologies this 'datafication' of rights has become both a reality and a pressing concern, one inextricably tangled up with questions regarding the broader political valences of human rights. Combining contemporary social and cultural theory with archival research and original ethnographic work, (...) Josh Bowsher resituates recent critiques of human rights within ongoing theoretical discussions concerning informational capitalism, digital culture and the politics of data. Critically analysing the contemporary human rights movement as an informational politics, Bowsher provides a new conceptual agenda for both exploring and overcoming the limits of human rights in an era shaped by the data flows, network infrastructures and informational logic of late capitalism. Josh Bowsher is Lecturer in Sociology at Brunel University. (shrink)

The Nordic countries aim to have a unique place within the European and global health data economy. They have extensive nationally maintained and centralized health data records, as well as numerous biobanks where data from individuals can be connected based on personal identification numbers. Much of this phenomenon can be attributed to the emergence and development of the Nordic welfare state, where Nordic countries sought to systematically collect large amounts of population data to guide decision making and improve the health (...) and living conditions of the population. Recently, however, the so-called Nordic gold mine of data is being re-imagined in a wholly other context, where data and its ever-increasing logic of accumulation is seen as a driver for economic growth and private business development. This article explores the development of policies and strategies for health data economy in Denmark and Finland. We ask how nation states try to adjust and benefit from new pressures and opportunities to utilize their data resources in data markets. This raises questions of social sustainability in terms of states being producers, providers, and consumers of data. The data imaginaries related to emerging health data markets also provide insight into how a broad range of different data sources, ranging from hospital records and pharmacy prescriptions to biobank sample data, are brought together to enable “full-scale utilization” of health and welfare data. (shrink)

Recent models in quantum cosmology make use of the concept of imaginary time. These models all conjecture a join between regions of imaginary time and regions of real time. We examine the model of James Hartle and Stephen Hawking to argue that the various no-boundary attempts to interpret the transition from imaginary to real time in a logically consistent and physically significant way all fail. We believe this conclusion also applies to quantum tunneling models, such as that (...) proposed by Alexander Vilenkin. We conclude, therefore, that the notion of emerging from imaginary time is incoherent. A consequence of this conclusion seems to be that the whole class of cosmological models appealing to imaginary time is thereby refuted. (shrink)

We give a complete characterization of Boolean algebras admitting weak elimination of imaginaries in terms of elementary invariants.

According to the logical positivists, signs (words and pictures) of imaginary beings have no referent (Goodman). The semiotic theory behind this assumption is dualistic and Cartesian: signs vs. nonsigns as well as the mental vs. the material world are in fundamental opposition. Peirce’s semiotics is based on the premise of the sign as a mediator between such opposites: signs do not refer to referents, they represent objects to a mind, but the object of a sign can be existent or (...) nonexistent, a feeling or an idea, something merely imaginary or even something false. The paper examines the nature of imaginary, nonexistent, and nonfigurative objects, such as unicorns, phoenixes, or nonrepresentative paintings, and shows why verbal or visual representations of imaginary beings and even nonfigurative paintings, which seem to represent nothing, are fully developed signs with a variety of objects determining their representation. (shrink)

We consider the theory P of pairs F (...) is generically free. (shrink)

Topology is integral to a shift in socio-cultural theory from a linguistic to a mathematical paradigm. This has enabled in Badiou and Žižek a critique of the symbolic register, understood in terms of pure conceptual abstraction. Drawing on topology, this article understands it instead in terms of the figure. The break with the symbolic and language necessitates a break with form, but topologically still preserves a logic of the figure. This becomes a process of figuration, indeed a process of (...) `deformation'. Badiou/Žižek will then presume a break with the symbolic for `the real'. But topology entails the centrality of not the real but the imaginary. With Castoriadis, this imaginary is understood as productive and social, and with Sloterdijk as spatial. In our times this is a self-organizing socio-technical imaginary. For Niklas Luhmann these socio-technical systems engage in coupling. They structurally couple with other social imaginaries. Their self-organization, going beyond pure functionality, operates through semantic excess: an excess that organizes the system and is their structure. Such structural coupling entails semantic exchange, consisting of not just information but also of images. (shrink)

The vision of integrating artificial intelligence in education is part of an ongoing push for harnessing digital solutions to improve teaching and learning. Drawing from Jasanoff and Hasse, this paper deliberates on how sociotechnical imaginaries are interrelated to the implications of new technologies, such as AI, in education. Complicating Hasses’s call for the development of Socratic ignorance to consider our predispositions about new technologies and open new prospects of thought, this paper revisits postphenomenology and Feenberg’s critical constructivist theories. While embracing (...) the notion of Socratic ignorance, this paper stresses the importance of developing a nuanced understanding of technology that realizes its lack of neutrality and supports the creation of a deeper understanding of how knowledge is produced, deployed, and interpreted in the digital age. Thus, this paper argues that an amalgam of Hasse’s call for advancing Socratic ignorance combined with postphenomenology and critical constructivism can support students in developing a critical understanding of technology and opening new landscapes of imaginaries. (shrink)