We build a topological model, based on intuitionistic logic, for multi-agent biological systems (such as _Physarum polycephalum_, bacterial colonies or any other swarm), reacting to external nourishment stimuli. Our construction follows the topological description of brain activity, where particles (neurons) are activated by an external environment, represented by a topological space _X_ with an open cover \(\{U_i:i\in I\}\). The brain builds the model of this external space via the nerve (trace) of a topological space _X_. Here the body of _Physarum (...) polycephalum_ or a swarm made of networks of tubular structures represents a nerve (trace) of _X_ also which means that _Physarum polycephalum_ or a swarm gains orientation in the space of external stimuli even in the absence of any neural system. The logic of living organisms is based on open subsets of _X_ and thus can be represented by Heyting algebra (i.e. intuitionistically). We also consider the generalisation of the nerve construction to a categorical context, where the category is determined by the network structures of multi-agent biological system. This model can be generalised up to simulating the behaviour of any swarm by means of intuitionistic logic. (shrink)

Quantum mechanics (QM) predicts probabilities on the fundamental level which are, via Born probability law, connected to the formal randomness of infinite sequences of QM outcomes. Recently it has been shown that QM is algorithmic 1-random in the sense of Martin–Löf. We extend this result and demonstrate that QM is algorithmic $$\omega$$ -random and generic, precisely as described by the ’miniaturisation’ of the Solovay forcing to arithmetic. This is extended further to the result that QM becomes Zermelo–Fraenkel Solovay random on (...) infinite-dimensional Hilbert spaces. Moreover, it is more likely that there exists a standard transitive ZFC model M, where QM is expressed in reality, than in the universe V of sets. Then every generic quantum measurement adds to M the infinite sequence, i.e. random real $$r\in 2^{\omega }$$, and the model undergoes random forcing extensions M[r]. The entire process of forcing becomes the structural ingredient of QM and parallels similar constructions applied to spacetime in the quantum limit, therefore showing the structural resemblance of both in this limit. We discuss several questions regarding measurability and possible practical applications of the extended Solovay randomness of QM. The method applied is the formalization based on models of ZFC; however, this is particularly well-suited technique to recognising randomness questions of QM. When one works in a constant model of ZFC or in axiomatic ZFC itself, the issues considered here remain hidden to a great extent. (shrink)

In the article we are trying to answer the question why people make mistakes in their reasoning. According to the theory proposed by P. N. Johnson-Laird, reasoning is a semantic process based on mental models. Reasoners build models of the situations described in premises and then check which conclusion holds in all the models. Unfortunately, our working memory has a limited processing capacity, and so we often fail to represent all possibilities necessary to draw a valid conclusion. The more models (...) we have to build, the higher the chance of making a mistake. Due to limitations of our working memory, we tend to represent in the models only what is true, but not what is false. One of the consequences of this fact is the occurrence of certain illusions: inferences that are compelling but invalid. The existence of such illusionary inferences have been corroborated by numerous experiments. (shrink)

We use an algebraic argument to prove that there are exactly two premaximal extensions of \’s consequence. We also show that one of these extensions is the minimal structurally complete extension of the unique maximal paraconsistent extension of \. Precisely, we show that there are exactly two covers of the variety of Boolean algebras in the lattice of quasivarieties of Sugihara algebras and that there is a unique minimal paraconsistent quasivariety in that lattice. We also obtain a corollary stating that (...) the set of paraconsistent extensions of \ forms a complete sublattice of the lattice of all \’s extensions. (shrink)

It is shown that the nonlocal anomalous effective actions corresponding to the quantum breaking of the conformal symmetry can lead to observable modifications of Einstein’s equations. The fact that Einstein’s general relativity is in perfect agreement with all observations including cosmological or recently observed gravitational waves imposes strong restrictions on the field content of possible extensions of Einstein’s theory: all viable theories should have vanishing conformal anomalies. It is shown that a complete cancellation of conformal anomalies in \ for both (...) the \ invariant and the Euler invariant can only be achieved for N-extended supergravity multiplets with \. (shrink)

This paper introduces three model-theoretic constructions for generalized Epstein semantics: reducts, ultramodels and $\textsf {S}$ -sets. We apply these notions to obtain metatheoretical results. We prove connective inexpressibility by means of a reduct, compactness by an ultramodel and definability theorem which states that a set of generalized Epstein models is definable iff it is closed under ultramodels and $\textsf {S}$ -sets. Furthermore, a corollary concerning definability of a set of models by a single formula is given on the basis of (...) the main theorem and the compactness theorem. We also provide an example of a natural set of generalized Epstein models which is undefinable. Its undefinability is proven by means of an $\textsf {S}$ -set. (shrink)

The empirical slippery slope arguments are arguments of the following form: if we take a first step A, as a result of a sequence of events, step N will necessarily or very likely follow; N is clearly not acceptable; therefore we must not take step A. Such arguments are often used in the discussions concerning abortion, assisted suicide, human gene therapy, free speech, decriminalizing marijuana, gun control and other ethical or social issues. In this article, I am trying to argue (...) that although slippery slope arguments are not deductive, they need not to be considered as fallacies. There are some mechanisms that make the realization of the scenarios sketched in the slippery slope arguments much more probable than one could think. I analyze three different examples of such mechanisms. The first one originates in the psychological phenomenon of cognitive dissonance. The second is connected with the use of precedents. The third mechanism depends on so-called multi-peaked preferences which some people might have when they make their decisions. (shrink)

We present an algebraic proof of the theorem stating that there are continuum many axiomatic extensions of global consequence associated with modal system E that do not admit the local deduction detachment theorem. We also prove that all these logics lack the finite frame property and have exactly three proper axiomatic extensions, each of which admits the local deduction detachment theorem.

This paper introduces the construct of an ultravaluation inspired by the well-known ultraproduct. Basic properties and exemplary applications of this notion are shown: for compactness and definability theorems. We also use ultravaluations to check failure of compactness and undefinability.

Sixteen years ago, Prahalad and Hart introduced the possibility of both profitably serving the poor and alleviating poverty. This first iteration of the Bottom/Base of the Pyramid approach focused on selling to the poor. In 2008, after ethical criticisms leveled at it, the field moved to BoP 2.0, instead emphasizing business co-venturing. Since 2015, we have witnessed some calls for a new iteration, with the focus broadening to a more sustainable development approach to poverty alleviation. In this paper, we seek (...) to answer the question: How has the BoP approach evolved over the past 16 years, and has it delivered on its early promise? We conducted a systematic review of 276 papers published in journals in this period, utilizing a rigorous correspondence analysis method to map key trends, and then further examined the 22 empirical studies conducted on the BoP approach. Our results suggest that the field has evolved, passing through a number of trends and coming full circle—with our analysis pointing to more recent BoP literature emphasizing similar themes to those espoused in the initial BoP iteration, rather than reflecting the principles espoused in either BoP 2.0 or BoP 3.0. Our analysis also points to a lack of clear evidence that the BoP concept has delivered on its promise either to businesses or to BoP participants. (shrink)

Building on our diverse research traditions in the study of reasoning, language and communication, the Polish School of Argumentation integrates various disciplines and institutions across Poland in which scholars are dedicated to understanding the phenomenon of the force of argument. Our primary goal is to craft a methodological programme and establish organisational infrastructure: this is the first key step in facilitating and fostering our research movement, which joins people with a common research focus, complementary skills and an enthusiasm to work (...) together. This statement—the Manifesto—lays the foundations for the research programme of the Polish School of Argumentation. (shrink)

This article examines the question: How do local organizations deal with competing temporal dynamics when building and implementing base/bottom of the pyramid initiatives? Time has been neglected in the BoP literature to date, yet, addressing poverty in a developing country requires a complex perspective of time. An analysis of 21 semi-structured interviews with locally based organizations implementing BoP initiatives in the Philippines revealed that the organizations had an ambitemporal perspective. In particular, we discover that they harmonize multiple temporal pacers by (...) making strategic decisions about the best mechanism of entrainment to utilize to move their community and any stakeholders to a long-term temporal horizon. We find that organizations manage this process by generating what we term a “third time” via a process of push-and-pull entrainment between the communities, the business, and the different temporal pacers. This article develops a conceptual framework for helping organizations to harmonize competing temporal dynamics to generate a bespoke “third time” for each community they work with. (shrink)

Friedrich Meinecke's Die Idee der Staatsräson (1924) is generally seen as the study in which he replaced his monistic-idealistic philosophy of history - as articulated in Weltbürgertum und Nationalstaat - by a dualistic worldview. In this article I will argue against this view. I will do so on the basis of a brief analysis of Meinecke's Staatsräson -study. I will show that Meinecke succeeded in combining his monism and his dualism within a so-called (harmonious) 'panentheistic' philosophy. Next, when discussing Meinecke's (...) position in the crisis of historicism, critics generally refer to Meinecke's Die Entstehung des Historismus (1936) or his essays from around the 1920s, but refer rarely to Die Idee der Staatsräson . Yet it is precisely this study - dealing with the theory and practice of statesmanship - that gives us a good grasp of Meinecke's reponse to the crisis of historicism, since it is in the state where idea and reality collide most brutally. Questions of ethical relativism, of the relationship between power and ethics, and of that between politics and history are nowhere more pressing than in the practice of statesmanship. It will become clear that, according to Meinecke, the statesman's (or the historian's) conscience moves him to a sphere of panentheistic harmony enabling him (and the historian) to overcome the aporias of historicism. (shrink)

The article explores the concept of infodemics during the COVID-19 pandemic, focusing on the propagation of false or inaccurate information proliferating worldwide throughout the SARS-CoV-2 health crisis. We provide an overview of disinformation, misinformation and malinformation and discuss the notion of “fake news”, and highlight the threats these phenomena bear for health policies and national and international security. We discuss the mis-/disinformation as a significant challenge to the public health, intelligence, and policymaking communities and highlight the necessity to design measures (...) enabling the prevention, interdiction, and mitigation of such threats. We then present an overview of selected opportunities for applying technology to study and combat disinformation, outlining several approaches currently being used to understand, describe, and model the phenomena of misinformation and disinformation. We focus specifically on complex networks, machine learning, data- and text-mining methods in misinformation detection, sentiment analysis, and agent-based models of misinformation spreading and the detection of misinformation sources in the network. We conclude with the set of recommendations supporting the World Health Organization’s initiative on infodemiology. We support the implementation of integrated preventive procedures and internationalization of infodemic management. We also endorse the application of the cross-disciplinary methodology of Crime Science discipline, supplemented by Big Data analysis and related information technologies to prevent, disrupt, and detect mis- and disinformation efficiently. (shrink)

This article examines the human placenta not only as a scientific, medical and biological entity but as a consumer bio-product. In the emergent placenta economy, the human placenta is exchanged and gains potentiality as food, medicine and cosmetics. Drawing on empirical research from the United States, the United Kingdom, Denmark and Japan, the authors use feminist cultural analysis and consumer theories to discuss how the placenta is exchanged and gains commodity status as a medical supplement, smoothie, pill and anti-ageing lotion. (...) Placenta preparers and new mothers cite medical properties and spirituality as reasons for eating or encapsulating the placenta, reinstating ideas of the liberated good mother. Meanwhile, the cosmetics industry situates the placenta as an extract and hence a commodity, re-naturalizing it as an anti-ageing, rejuvenating and whitening bio-product. The authors conclude that, in the emergent bio-economy, the dichotomy between the inner and the outer body is deconstructed, while the placenta gains clinical and industrial as well as affective value. (shrink)

This article is a discussion of Tadeusz Ślipko’s considerations concerning “the origins of human being” or, in other words, his theory of animation. One of the characteristic features of Ślipko’s Thomistic anthropology is an experimental orientation: i.e. using and referring to the data of the sciences as these relate to material, physical and biological reality. As the starting point of his position he adopts the concept of man: being composed of a material substrate, determined in his human form by the (...) immortal soul as the vital principle of his/her existence. In line with this orientation, Ślipko focuses his investigations around the idea of man conceived “as a personal being and the subject of morality as a whole, constituted in what determines his/her proper humanity.” Therefore, asking about the origins—so to say—the initial moment of human substance, Ślipko examines this issue in the context of philosophical assumptions about God as the Creator of the universe, and about man as a self-aware and self-acting being who is the cause of a series of effects. (shrink)

The aim of this paper is to show that Curry’s recent defence of the interpretivist approach to beliefs is unsuccessful. Curry tries to argue that his version of interpretivism, which is based on the model-theoretic approach to folk-psychological attributions, is well-suited to resisting the epistemological argument that is directed at interpretivism. In this paper, I argue that even if Curry’s defence is successful in this case, his theory does not have enough resources to solve the metaphysical problems of interpretivism. In (...) particular, I argue that the model-theoretic version of interpretivism that Curry espouses does not explain the claim that beliefs are constituted by the process of attribution, which is central to the interpretivist project. In the final parts of the paper, I discuss the issue of the relation between interpretivism and other forms of the broadly superficial/deflationary approach to beliefs, especially dispositionalism. I contend that if one wants to adopt a superficial/deflationary approach, it is best not to adopt interpretivism as it is an unnecessarily complex and problematic version of this broad view. (shrink)

With over three billion people currently living below the poverty line, finding better ways to lift people out of poverty is a concern of scholars from a range of disciplines. Within Management Studies, the focus is on developing market-based solutions to poverty alleviation through Bottom/Base-of-the-Pyramid initiatives. To date, these have enjoyed limited success, sometimes even exacerbating the problems they attempt to solve. As a result, there is a growing academic and practitioner push for a third iteration—BoP 3.0—that moves closer to (...) a sustainable development model of poverty alleviation. Through a grounded theory study of 21 Philippines-based organizations implementing poverty alleviation initiatives at the community level, this paper seeks to add to the existing suite of tools and guidance in the BoP field. It does so by questioning how these organizations approach the development and implementation of market-based approaches to poverty alleviation. Our results suggest that these organizations adopt a more community-centric approach, focusing on the creation of a self-reliant community before all else. We find this to be the result of a deeper understanding of the drivers of poverty in the communities they work with. Through the extrapolation of key themes and issues in our data, we propose a new conceptual model for building BoP 3.0 initiatives. This model consists of three intertwined theoretical dimensions: understanding issues as matters of concern; identifying limitations; and navigating time. These elements are linked by three active phases that allowed the organizations to move from one dimension to the next: sensemaking; entrainment; and investment. (shrink)

We give a model-theoretic treatment of the fundamental results of Kechris-Pestov-Todorčević theory in the more general context of automorphism groups of not necessarily countable structures. One of the main points is a description of the universal ambit as a certain space of types in an expanded language. Using this, we recover results of Kechris et al. (Funct Anal 15:106–189, 2005), Moore (Fund Math 220:263–280, 2013), Ngyuen Van Thé (Fund Math 222: 19–47, 2013), in the context of automorphism groups of not (...) necessarily countable structures, as well as Zucker (Trans Am Math Soc 368, 6715–6740, 2016). (shrink)

We give an almost explicit presentation of exotic functions corresponding to some exotic smooth structure on topologically trivial R4. The construction relies on the model-theoretic tools from the previous paper. We can formulate unexpected, yet direct connection between ‘‘localized’’ exotic small R4’s and some noncommutative spaces. The formalism of QM can be interpreted in terms of exotic smooth R4’s localized in spacetime. A new way of looking at the problem of decoherence is suggested. The 4-dimensional spacetime itself has built-in means (...) which may enforce a kind of decoherence. (shrink)

We demonstrate “economies of experience” in eye-movement patterns—that is, optimization of eye-movement patterns aimed at more efficient and less costly visual processing, similar to the priming-induced formation of sparser cortical representations or reduced reaction times. Participants looked at Mooney-type, degraded stimuli that were difficult to recognize without prior experience, but easily recognizable after exposure to their undegraded versions. As predicted, eye-movement dispersion, velocity, and the number of fixations decreased with each stimulus presentation. Further analyses showed that this effect was contingent (...) on recognition, and the selection of information from the stimulus could be informed by the identity of the presented object. Finally, our study demonstrates that after exposure to the undegraded version of the stimulus, eye-movement patterns associated with its degraded and undegraded versions become more similar. This suggests that eye-movement patterns can evolve to facilitate the optimal processing of a given stimulus via experience-driven perceptual learning. (shrink)

The collection presents a variety of promising new directions in Royce scholarship from an international group of scholars, including historical reinterpretations, explorations of Royce's ethics of loyalty and religious philosophy, and contemporary applications of his ideas in psychology, the problem of reference, neo-pragmatism, and literary aesthetics.

We show that in 4-spacetime modified at very short distances due to the weakening of classical logic, the higher dimensions emerge. We analyse the case of some smooth topoi, and the case of some class of pointless topoi. The pointless topoi raise the dimensionality due to the forcing adding “string” objects and thus replacing classical points in spacetime. Turning to strings would be something fundamental and connected with set theoretical forcing. The field theory/strings dualities originate at the set theoretical level (...) of the theories. It is argued that this fundamental level can help solving some difficulties of the physical dualities. (shrink)

Porter and Kramer :78–92, 2006; Harv Bus Rev 89, 62–77, 2011) introduced ‘shared value’ as a ‘new conception of capitalism,’ claiming it is a powerful driver of economic growth and reconciliation between business and society. The idea has generated strong interest in business and academia; however, its theoretical precepts have not been rigorously assessed. In this paper, we provide a systematic and thorough analysis of shared value, focusing on its ontological and epistemological properties. Our review highlights that ‘shared value’ has (...) spread into the language of multiple disciplines, but that its current conceptualization is vague, and it presents important discrepancies in the way it is defined and operationalized, such that it is more of a buzzword than a substantive concept. It also overlaps with many other concepts and lacks empirical grounding. We offer recommendations for defining and measuring the concept, take a step toward disentangling it from related concepts, and identify relevant theories and research methods that would facilitate extending the knowledge frontier on shared value. (shrink)

This paper is devoted to the reconstruction of the implicit logic of Plato’s Par-menides. The reconstructed logic, F, makes it possible to form a new semi-intuitionistic system of logic of predicates, FN. The axioms of Peano Arithmetic (PA) and an axiom of infinity follow from FN. Therefore, FN can be seen as a new attempt at the realization of Frege’s logicist program. Some very strong systems can be seen as other variants of FN, e.g. Leśniewski’s ontology. The hypothesis from Parmenides (...) II contains proof of the existence of the two highest principles, i.e. the One and the Dyad, their mutual relationship, their relations to other things, and the reasoning regarding the mutual relationship follows some exact formal rules. Six types of Plato’s negation of a predicate are defined. The system is a first-order logic with non-classical negation of a predicate (local negation) that is non-definable by classical sentential negation. Therefore, the implicit logic of Plato’s Parmenides differs from classical syllogistics (formed in the Łukasiewicz’s style) as well as from the classical predicate calculus. (shrink)

The discussion paper synthesises the insights shared during a keynote panel at the 26th International Philosophy of Nursing Conference, themed “Reimagining a nursing ecosystem in an uncertain world.” It delves into the substantial impact uncertainty has on nursing, offering innovative strategies for reconceptualization. Through a critical examination of evidence‐based practice, the tendency to homogenise nursing is discussed, prompting advocacy for a Nietzschean political framework as a form of resistance and emancipation. Drawing inspiration from Donna Haraway, a transition from individualistic to (...) relational approaches is needed, especially amidst social and economic instability. Furthermore, the integration of caritas and Indigenous epistemologies underscore the significance of cultural sensitivity in nursing. Meanwhile, Ubuntu philosophy champions empathy and collective values, while a convergence of Eastern and Western philosophical traditions promises to enrich nursing practice. Ultimately, the panellists advocate for overcoming rigid ideologies in favour of a pluralistic approaches, ontologies, epistemologies and ethics to address contemporary challenges, and signal for a philosophical reorientation to engage uncertainty and reshape nursing roles in an ever‐evolving and world. (shrink)

Like most goods‐producing sectors in the West, modern health‐care systems have been profoundly changed by globalization and the neoliberal policies that attend it. Since the 1970s, the role of the welfare state has been considerably reduced; funding and management of health systems have been subjected to wave upon wave of reorganization and assimilated to the private sector. At the same time, neoliberal policy has imposed the notion of patient empowerment, thus turning patients into consumers of health. The literature on nursing (...) has accordingly reported on the significant repercussions on all aspects of the profession, from delivery of care and treatment, through training for new nurses, to legislated policy reforms regarding the role and responsibilities of modern nurses. In light of these developments, this paper analyses and theorizes about the way the injection of neoliberal policy is linked to and affects the practice of nursing. Drawing on a number of Nietzschean arguments, we begin with an exploration of the complex effects of neoliberalism, bureaucratization, and technocratization on the health system and the practice of nursing. Our main theoretical point here is that neoliberal policy engenders and promotes a neoliberal tide, which results in the conversion of the values that drive modern nursing practice. We then examine this tide in the light of Nietzsche's concepts. Starting with an analysis based on the ontology of the will to power, we show that nurses are dominated by neoliberal values embedded in technocratic and bureaucratic ideologies. Finally, we argue that the application of neoliberal policy constitutes a form of domestication from which one might potentially be freed through the Nietzschean concept of transvaluation of values. This transvaluation, as its freeing from some of the neoliberal tide, may be accomplished in accordance with a hierarchy of specific life‐affirming values for nursing culture and practice. (shrink)

To understand globalization, one needs to examine its provenance within the metaphysical tradition and, in particular, in relation to the ways in which power tends to operate in modernity. While its operations are necessary for shaping relations, the pervasiveness with which power invests beings tends to obscure the event, and in particular, temporality and historicity, which mark the possibility of undoing power's formative influence on beings and relations. The event becomes the site of a specific tension between power and the (...) power-free, between changes intrinsic to power's intensification and a transformation indicative of a letting-go of power. In the face of our (post)modern tradition of increasingly intense macro and microflows of power, the power-free calls into question the metaphysical tradition of power that has underwritten the development of modernity. This transformation is neither a destruction nor an abandonment of modernity, but indicates an alternative to the prevalent and pervasive practices of power. (shrink)

We consider consciousness attributed to systems in space-time which can be purely physical without biological background and focus on the mathematical understanding of the phenomenon. It is shown that the set theory based on sets in the foundations of mathematics, when switched to set theory based on ZFC models, is a very promising mathematical tool in explaining the brain/mind complex and the emergence of consciousness in natural and artificial systems. We formalise consciousness-supporting systems in physical space-time, but this is localised (...) in open domains of spatial regions and the result of this process is a family of different ZFC models. Random forcing, as in set theory, corresponds precisely to the random influence on the system of external stimuli, and the principles of reflection of set theory explain the conscious internal reaction of the system. We also develop the conscious Turing machines which have their external ZFC environment and the dynamics is encoded in the random forcing changing models of ZFC in which Turing machines with oracles are formulated. The construction is applied to cooperating families of conscious agents which, due to the reflection principle, can be reduced to the implementation of certain concurrent games with different levels of self-reflection. (shrink)

We aim to show from a new perspective that Quine’s ontological relativity, based largely on his so-called “proxy-function argument”, falls short of being a rigorously coherent philosophical conception, as it exhibits significant formal defects. This new perspective enables exposing the shortcomings of Quine's position and suggests a possible reformulation of the original position. Moreover, we argue that his ontological relativity is inconsistent with the empirical data associated with some of our best physical theories, such as quantum mechanics. We refer to (...) fundamental concepts of philosophy and the foundations of mathematics in order to clarify our critique of Quine’s position concerning the relation between formalized theories and both what we can know about the real world and how we come to know it. (shrink)

The aim of the text is to consider Gianni Vattimo's claim that hermeneutics needs to be more rational due to its criticised relativism and aestheticism. From this perspective, the author considers the projects proposed by Bartosz Brożek and Chrysostomos Mantzavinos, based on the assumption that the cognitive phenomena underlying the understanding of human behaviour and the resulting artefacts can be described using naturalistic methods. Finally, the question is considered whether these attempts, coming from outside the hermeneutic movement, offer hope for (...) eliminating the flaws of hermeneutics mentioned by Vattimo, and what the prospects are for further research on this issue. (shrink)

S'opposant à la clôture hégélienne de la négativité, c'est-à-dire à l'esclavage intériorisé et affirmé par l'homme posthistorique, Bataille définit l'homme en tant que l'être ontologiquement déchiré, constitué par le conflit incontournable pouvant être enlevé non par un moment quelconque de l'histoire, mais uniquement par la mort. Contrairement à la prise de position hégélienne mystifiée l'homme n'est pas, selon Bataille, exclusivement une conscience tout à fait temporalisée, mais aussi un corps et une impulsion ou bien une emanation personifiée de l'énergie cosmique (...) et solaire. En tant que tel il est une négativité par excellence, une tension notoire entre l'interdit et le projet d'une part et la transgression et le dépense anarchique de l'autre, donc un être convulsif orienté non vers la plénitude positivement défini, mais vers la perte. Plus que par les avantages de la culture rejetant la violence et diminuant une existence devenant plus en plus utilisée et fonctionnalisée, l'homme est instigué, selon Bataille, par le sacré qui détermine originairement la dynamique de la vie. Attiré par le sacré en tant que le revers de l'homogénéité de la culture l'homme se dirige vers l'existence tragique souveraine, aspire à l'impossible. Aux système, savoir, possibilités, histoire et vie miasmatique excluant l'extase qui pour la raison n'est rien ou est par elle au moins tout à fait instrumentalisée dans la stratégie de sa ruse, Bataille oppose l'impossible athéologique et asystématique ou bien le non-savoir en tant que régions où se manifeste la souveraineté de l'homme. La souveraineté paradoxale du point de vue des codes pragmatiques, parce que fondée non sur le choix assidu et avare de l'accumulation et de la durée, mais sur le choix excessif de la perte, rudimentaire pour la vie traitée comme une explosion dionysiaque ou solaire. (shrink)

A general duality connecting the level of a formal theory and of a metatheory is proposed. Because of the role of natural numbers in a metatheory the existence of a dual theory is conjectured, in which the natural numbers become formal in the theory but in formalizing non-formal natural numbers taken from the dual metatheory these numbers become nonstandard. For any formal theory there may be in principle a dual theory. The dual shape of the lattice of projections over separable (...) Hilbert space is exhibited. The crucial ingredient of this dual theory is set-theoretical (Cohen) forcing. Then, some attempts have been made to exhibit the dual shape of the exotic smooth (small) structures on topological ℝ4. There are striking similarities of both pictures. Nonstandard solutions of the equations of motion of 10-dimensional superstring of IIB type are described as a model theoretic extension of standard ones. Based on Brans conjecture one can predict the existence of sources of gravity in 4 dimensions. By their dual origins they carry quantum information as well. The generalized Maldacena conjecture appears naturally, which sheds light on a definition of background independent string theory. (shrink)