Gegen die verbreitete Vorstellung, dass Negativität im Interesse von mehr Selbstverwirklichung, Produktivität und Positivität überwunden oder be-grenzt werden muss, eröffnet dieser Band eine andere Perspektive. Er geht den verschiedenen Formen des Negativen in Kunst, Recht und Politik nach, um zu zeigen, dass es nicht allein eine Negativität gibt, die dem Gelingen im Weg steht oder zu dessen sicher beherrschtem Mittel wird. Die Beiträge des Bandes erweisen Negativität vielmehr als eine Kraft der Befreiung, die ein Gelingen anderer Art ermöglicht.

Our perception of where touch occurs on our skin shapes our interactions with the world. Most accounts of cutaneous localisation emphasise spatial transformations from a skin-based reference frame into body-centred and external egocentric coordinates. We investigated another possible method of tactile localisation based on an intrinsic perception of ‘skin space’. The arrangement of cutaneous receptive fields (RFs) could allow one to track a stimulus as it moves across the skin, similarly to the way animals navigate using path integration. We applied (...) curved tactile motions to the hands of human volunteers. Participants identified the location midway between the start and end points of each motion path. Their bisection judgements were systematically biased towards the integrated motion path, consistent with the characteristic inward error that occurs in navigation by path integration. We thus showed that integration of continuous sensory inputs across several tactile RFs provides an intrinsic mechanism for spatial perception. (shrink)

Francesca Biagioli’s Space, Number, and Geometry from Helmholtz to Cassirer is a substantial and pathbreaking contribution to the energetic and growing field of researchers delving into the physics, physiology, psychology, and mathematics of the nineteenth and twentieth centuries. The book provides a bracing and painstakingly researched re-appreciation of the work of Hermann von Helmholtz and Ernst Cassirer, and of their place in the tradition, and is worth study for that alone. The contributions of the book go far beyond that, (...) however. It is a clear, accurate, and deep account of fascinating and philosophically momentous implications of the move to relativity theory. (shrink)

The aim of this paper is to investigate Nishida Kitarō’s way of philosophizing in the light of the concept of “transition” in order to deepen our understanding of both Nishida’s philosophy and our thinking about and in transitions, using the concept of “boundary” or “border” (Grenze) as a catalyst. For that purpose, we focus on Nishida’s essay “Place” (「場所」), passing through different parts of the text as if through successive gates on a path of transition between one place and the (...) next, until we reach the final place of “absolute nothingness.” Dwelling on this place, we turn our attention to its internal structure and try to depict it along the outlines of a boundary, following the movements taking place in Nishida’s essay. The second part proposes an interpretation of the place of nothingness as an interminable practice of boundary-crossing that doesn’t come to a halt in a final, all-encompassing place, but dynamically situates itself on countless intersecting planes. After a more or less abstract analysis of the concept of “boundary,” we will apply and concretize this approach by using the example of the skin. To this end, we expose five main features of the skin as boundary: permeability, enclosure, excessiveness, interstitiality and reciprocal self-formation. (shrink)

The global spread of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) or coronavirus disease 19 (COVID-19) has led to the imposition of severely restrictive measures by governments in the Western hemisphere. We feel a contrast between these measures and our freedom. This contrast, we argue, is a false perception. It only appears to us because we look at the issue through our contemporary moral philosophy of utilitarianism and an understanding of freedom as absence of constraints. Both these views can be (...) substituted with more sophisticated alternatives, namely an ethics of virtue and a notion of freedom of the will. These offer a fuller picture of morality and enable us to cooperate with the current restrictions by consciously choosing to adhere to them instead of perceiving them as draconian and immoral. We ask whether we should collaborate with the restrictions and argue that considerations of virtue will lead to an affirmative answer. More broadly, virtue ethics permits to deal with the practical concerns about how an individual should behave during this pandemic, given the current lockdown measures or lack thereof. -/- In section 1, we present how utilitarianism and a notion of freedom as negative liberty support the opposition to restrictive measures. In section 2, we outline an alternative based on an ethics of virtue and a more elaborated notion of free will. In the concluding section 3, we argue that considerations of virtue should guide the individual and public response to the emergency. (shrink)

This article reports the findings of AI4People, an Atomium—EISMD initiative designed to lay the foundations for a “Good AI Society”. We introduce the core opportunities and risks of AI for society; present a synthesis of five ethical principles that should undergird its development and adoption; and offer 20 concrete recommendations—to assess, to develop, to incentivise, and to support good AI—which in some cases may be undertaken directly by national or supranational policy makers, while in others may be led by other (...) stakeholders. If adopted, these recommendations would serve as a firm foundation for the establishment of a Good AI Society. (shrink)

The paper focuses on the kind of expertise required by doctors in health communication and argues that such an expertise is twofold: both epistemological and communicative competences are necessary to achieve compliance with the patient. Firstly, we introduce the specific epistemic competences that deal with diagnosis and its problems. Secondly, we focus on the communicative competences and argue that an inappropriate strategy in communicating the reasons of diagnosis and therapy can make patient compliance unworkable. Finally, we focus on the case (...) of diabetes metaphor and propose the deliberate use of metaphors in health communication as an educational tool. On the one hand, metaphors might help doctors in explaining the disease in simpler terms and framing the experience of illness according to patient’s specific needs. On the other hand, metaphors might encourage a change in patient’s beliefs on their own experience of illness, and enable them to reach a shared decision making with doctors. (shrink)

The tenth volume of the Frontiers of Japanese Philosophy focuses on the theme of “transition,” dealing with transitory and intermediary phenomena and practices such as translation, transmission, and transformation. Written in English, German and Japanese, the contributions explore a wide range of topics, crossing disciplinary borders between phenomenology, linguistics, feminism, epistemology, aesthetics, political history, martial arts, spiritual practice and anthropology, and bringing Japanese philosophy into cross-cultural dialogue with other philosophical traditions. As exercises in “thinking in transition,” the essays reveal novel (...) modes of doing philosophy as a way of boundary crossing that takes transition not only as an object of inquiry, but also as a method of philosophical practice itself. (shrink)

The concept of adaptation is employed in many fields such as biology, psychology, cognitive sciences, robotics, social sciences, even literacy and art,1 and its meaning varies quite evidently according to the particular research context in which it is applied. We expect to find a particularly rich catalogue of meanings within evolutionary biology, where adaptation has held a particularly central role since Darwin’s The Origin of Species (1859) throughout important epistemological shifts and scientific findings that enriched and diversified the concept. Accordingly, (...) a conceptual taxonomy of adaptation in evolutionary biology may help to disambiguate it. Interdisciplinary researches focused on adaptation would benefit from such a result. In the present work we recognize and define seven different meanings of adaptation: (1) individual fitness; (2) adaptation of a population; (3) adaptation as the process of natural selection; (4) adaptive traits; (5) molecular adaptation; (6) adaptation as structural tinkering; (7) plasticity. For convenience here, we refer to them as W-, P-, NS-, T-, M-, S- and PL-ADAPTATION. We present the seven meanings in some detail, hinting at their respective origins and conceptual developments in the history of evolutionary thought (references are offered for further deepening). However, it is important to point out that evolution researchers seldom if ever refer to a single meaning purified from the others. This applies also to the authors we cite as representatives of one of the seven meanings. In Discussion and Conclusion draw from our work some future perspectives for adaptation within evolutionary biology. (shrink)

In this paper, we deal with the computation of Lie derivatives, which are required, for example, in some numerical methods for the solution of differential equations. One common way for computing them is to use symbolic computation. Computer algebra software, however, might fail if the function is complicated, and cannot be even performed if an explicit formulation of the function is not available, but we have only an algorithm for its computation. An alternative way to address the problem is to (...) use automatic differentiation. In this case, we only need the implementation of the algorithm that evaluates the function in terms of its analytic expression in a programming language, but we cannot use this if we have only a compiled version of the function. In this paper, we present a novel approach for calculating the Lie derivative of a function, even in the case where its analytical expression is not available, that is based on the In finity Computer arithmetic. A comparison with symbolic and automatic differentiation shows the potentiality of the proposed technique. (shrink)

It remains controversial whether touch is a truly spatial sense or not. Many philosophers suggest that, if touch is indeed spatial, it is only through its alliances with exploratory movement, and with proprioception. Here we develop the notion that a minimal yet important form of spatial perception may occur in purely passive touch. We do this by showing that the array of tactile receptive fields in the skin, and appropriately relayed to the cortex, may contain the same basic informational building (...) blocks that a creature navigating around its environment uses to build up a perception of space. We illustrate this point with preliminary evidence that perception of spatiotemporal patterns on the human skin shows some of the same features as spatial navigation in animals. We argue (a) that the receptor array defines a ‘tactile field’, (b) that this field exists in a minimal form in ‘skin space’, logically prior to any transformation into bodily or external spatial coordinates, and (c) that this field supports tactile perception without integration of concurrent proprioceptive or motor information. The basic cognitive elements of space perception may begin at lower levels of neural and perceptual organisation than previously thought. (shrink)

Epileptogenesis involves an increase in excitatory synaptic strength in the brain in a manner similar to synaptic potentiation. In the present study we investigated the mechanisms of short-term synaptic potentiation in patients with focal epilepsy by using 5 Hz repetitive transcranial magnetic stimulation (rTMS), a non invasive neurophysiological technique able to investigate the mechanisms of synaptic plasticity in humans. Ten patients with focal idiopathic cortical epilepsy were studied. 5 Hz-rTMS (10 stimuli-trains, 120% of motor threshold, RMT) was delivered over the (...) first dorsal interosseus (FDI) motor area of both (affected and unaffected) hemispheres. Changes in the motor evoked potential (MEP) size in the FDI muscle during the trains and the RMT were measured and compared between the hemispheres. 5 Hz-rTMS was also delivered in a group of healthy subjects over both hemispheres. 5 Hz-rTMS in patients elicited a reduced MEP facilitation compared to normal subjects. The reduced MEP amplitude was more evident in the affected hemisphere than in the unaffected hemisphere. RMT in the affected hemisphere was higher than in the unaffected hemisphere and in healthy subjects. Our findings showing a decreased response to 5 Hz-rTMS over the affected hemisphere, differently from the expected results suggest a reduced cortical excitability in epileptic patients. We hypothesize an altered balance between excitatory and inhibitory circuits in epileptic patients under chronic therapy. (shrink)

As the range of potential uses for Artificial Intelligence (AI), in particular machine learning (ML), has increased, so has awareness of the associated ethical issues. This increased awareness has led to the realisation that existing legislation and regulation provides insufficient protection to individuals, groups, society, and the environment from AI harms. In response to this realisation, there has been a proliferation of principle-based ethics codes, guidelines and frameworks. However, it has become increasingly clear that a significant gap exists between the (...) theory of AI ethics principles and the practical design of AI systems. In previous work , we analysed whether it is possible to close this gap between the ‘what’ and the ‘how’ of AI ethics through the use of tools and methods designed to help AI developers, engineers, and designers translate principles into practice. We concluded that this method of closure is currently ineffective as almost all existing translational tools and methods are either too flexible (and thus vulnerable to ethics washing) or too strict (unresponsive to context). This raised the question: if, even with technical guidance, AI ethics is challenging to embed in the process of algorithmic design, is the entire pro-ethical design endeavour rendered futile? And, if no, then how can AI ethics be made useful for AI practitioners? This is the question we seek to address here by exploring why principles and technical translational tools are still needed even if they are limited, and how these limitations can be potentially overcome by providing theoretical grounding of a concept that has been termed ‘Ethics as a Service’. (shrink)

A reconstruction of the discussion on issues of economic ethics in the Talmud, in Islamic religious, juridical and philosophical literalture, in Medieval literature, and in Reformed casuistry.

In Western societies many immigrants live in difficult social and working conditions. Together with other factors, this state of affairs represents a risk for the well being of their children. This article will consider the principle risk factors for child psychopathology and/or distress, with a distinction between temporary and permanent factors and with a peculiar attention to the interplay between risk and protective factors. Risk factors can be ordered in cultural, social, familiar/parental and individual factors. Some of these are general (...) risk factors, applying to child and adolescent psychopathology and distress independently from the status of immigrants’ offspring. Other factors are specific of migration, some of them being related to: a) different ways of immigrated families to situate themselves within the host society ; b) cultural/familiar attitudes in child’s nurture and education; c) the family role of women as well as factors specific of the pregnancy period in immigrants; d) the ability of the school system to enhance and support children’s abilities to integrate within the new society; e) the political/bureaucratic facilitation/impediment to the regularization of VISA, with the consequent effect on the sense of identity/rejection within/from the host society. In conclusion, the programs for monitoring immigrants’ living and health conditions should also include: the assessment of parental skills, the dynamic indicators of risk and protection indexes, the assessment of living conditions and social school environment, with a careful attention to those early signs of discomfort that might precede possible later onset of psychopathology and/or social distress. (shrink)

In Western societies many immigrants live in difficult social and working conditions. Together with other factors, this state of affairs represents a risk for the well being of their children. This article will consider the principle risk factors for child psychopathology and/or distress, with a distinction between temporary and permanent factors and with a peculiar attention to the interplay between risk and protective factors. Risk factors can be ordered in cultural, social, familiar/parental and individual factors. Some of these are general (...) risk factors, applying to child and adolescent psychopathology and distress independently from the status of immigrants’ offspring. Other factors are specific of migration, some of them being related to: a) different ways of immigrated families to situate themselves within the host society ; b) cultural/familiar attitudes in child’s nurture and education; c) the family role of women as well as factors specific of the pregnancy period in immigrants; d) the ability of the school system to enhance and support children’s abilities to integrate within the new society; e) the political/bureaucratic facilitation/impediment to the regularization of VISA, with the consequent effect on the sense of identity/rejection within/from the host society. In conclusion, the programs for monitoring immigrants’ living and health conditions should also include: the assessment of parental skills, the dynamic indicators of risk and protection indexes, the assessment of living conditions and social school environment, with a careful attention to those early signs of discomfort that might precede possible later onset of psychopathology and/or social distress. (shrink)

As the range of potential uses for Artificial Intelligence, in particular machine learning, has increased, so has awareness of the associated ethical issues. This increased awareness has led to the realisation that existing legislation and regulation provides insufficient protection to individuals, groups, society, and the environment from AI harms. In response to this realisation, there has been a proliferation of principle-based ethics codes, guidelines and frameworks. However, it has become increasingly clear that a significant gap exists between the theory of (...) AI ethics principles and the practical design of AI systems. In previous work, we analysed whether it is possible to close this gap between the ‘what’ and the ‘how’ of AI ethics through the use of tools and methods designed to help AI developers, engineers, and designers translate principles into practice. We concluded that this method of closure is currently ineffective as almost all existing translational tools and methods are either too flexible or too strict. This raised the question: if, even with technical guidance, AI ethics is challenging to embed in the process of algorithmic design, is the entire pro-ethical design endeavour rendered futile? And, if no, then how can AI ethics be made useful for AI practitioners? This is the question we seek to address here by exploring why principles and technical translational tools are still needed even if they are limited, and how these limitations can be potentially overcome by providing theoretical grounding of a concept that has been termed ‘Ethics as a Service.’. (shrink)

Comments on a session organized by the William James Society at the 2010 APA. Talks included: Paul J. Croce (Stetson), Presidential Address: “The Predisciplinary James.” Ramón del Castillo (Madrid), “The Comic Mind of William James;” Loren Goldman (Chicago), “The Ideological James: Radical Appropriations of a Liberal Philosoper;” and Emma Sutton (Wellcome Institute), “James and the Politics of Psychotherapy.”.

This paper suggests that James’s account of the self developed in tandem with his social vision. The Jamesian self promoted social transformation and the creation of a strong and virtuous citizenry that could participate in political action and initiate effective social change in a pluralistic, democratic society. The paper also argues that James’s account of the self represented an attempt to rethink the relationship between individual and society in a way that would allow both for pluralism and for community.

The Ethics of Energy. William James’s Moral Philosophy in Focus... brings to completion [Sergio] Franzese’s reinterpretation of James’s work, as a “philosophical anthropology,” which Franzese began articulating in several essays and in his first book on James, L’uomo indeterminato. Saggio su William James (Rome: Anselmo, 2001). James’s diverse philosophical and psychological work, Franzese argued, aimed to outline a philosophical “science of man.” This philosophical anthropology, as James once wrote about philosophy, would be erected on the building blocks provided by the (...) “special sciences.” It would not only seek to answer the central question of philosophy (the question of “the place of Man in nature”), but also to provide people with intellectual and practical tools that they could deploy in order to find the meaning of human life and better act and react within their multiple environments. (shrink)

In abstract argumentation, each argument is regarded as atomic. There is no internal structure to an argument. Also, there is no specification of what is an argument or an attack. They are assumed to be given. This abstract perspective provides many advantages for studying the nature of argumentation, but it does not cover all our needs for understanding argumentation or for building tools for supporting or undertaking argumentation. If we want a more detailed formalization of arguments than is available with (...) abstract argumentation, we can turn to structured argumentation, which is the topic of this special issue of Argument and Computation. In structured argumentation, we assume a formal language for representing knowledge and specifying how arguments and counterarguments can be constructed from that knowledge. An argument is then said to be structured in the sense that normally, the premises and claim of the argument are made explicit, and the relationship between the premises and claim is formally defined (for instance, using logical entailment). In this introduction, we provide a brief overview of the approaches covered in this special issue on structured argumentation. (shrink)

In the wake of the global financial crisis of 2008, the greatest economic disaster since the Great Depression, the cover story of the July 18th 2009 issue of The Economist, entitled “What went wrong with economics,” opened with an unequivocally incriminating statement: “Of all the economic bubbles that have been pricked, few have burst more spectacularly than the reputation of economics itself.” In the months surrounding this indictment, many influential economists, including several Nobel laureates, were drawn to the same embarrassing (...) conclusion. Despite the existence of a handful of Cassandras, economists, as a group, had failed to foresee the crash. This short essay reviews the criticisms addressed to modern economic theory in the immediate aftermath of the crash. Overall, the main issues raised by critics were that (a) economists versed in the dominant models in macroeconomics and finance have been blinded to the possibility that we live in an uncertain and complex world; and (b) that the content of current economics education has sidelined many of the relevant insights to be found in the history of the discipline. This has led the critics to call for changes in the institutional structure of discipline, with a particular emphasis on the promotion of interdisciplinarity, and theoretical and methodological pluralism. (shrink)

This article is the introductory chapter to a festschrift in honour of Geoff Hodgson. In work spanning four decades, Geoff Hodgson has made many path-breaking contributions to institutional economics, evolutionary economics, economic methodology, the history of economic thought and social theory more broadly. Hodgson’s reputation as a prolific and important writer, whose work transcends traditional disciplinary boundaries, is matched by his credentials as an academic entrepreneur, whose involvement in the formation of two international scholarly societies and the foundation of the (...) Journal of Institutional Economics has expanded the opportunities for constructive dialogue among social scientists. To celebrate Hodgon’s fantastic career, this volume brings together 19 original contributions by world-leading scholars in specific areas that have played a significant role in influencing Hodgson’s thinking or represent key debates to which he has contributed. The chapter introduces these contributions, and summarizes a conversation with Hodgson that is also included in the volume. (shrink)

[Multiple authors] In this paper, we propose a general architecture that is based on fast/slow solvers and a metacognitive component. We then present experimental results on the behavior of an instance of this architecture, for AI systems that make decisions about navigating in a constrained environment. We show how combining the fast and slow decision modalities allows the system to evolve over time and gradually pass from slow to fast thinking with enough experience, and that this greatly helps in decision (...) quality, resource consumption, and efficiency. (shrink)

New algorithms for the numerical solution of Ordinary Differential Equations (ODEs) with initial condition are proposed. They are designed for work on a new kind of a supercomputer – the Infinity Computer, – that is able to deal numerically with finite, infinite and infinitesimal numbers. Due to this fact, the Infinity Computer allows one to calculate the exact derivatives of functions using infinitesimal values of the stepsize. As a consequence, the new methods described in this paper are able to work (...) with the exact values of the derivatives, instead of their approximations. (shrink)

Alberto Giubilini and Francesca Minerva's controversial article ‘After-Birth Abortion: Why Should the Baby Live?’ has received a lot of criticism since its publishing. Part of the recent criticism has been made by pro-life philosopher Christopher Kaczor, who argues against infanticide in his updated book ‘Ethics of Abortion’. Kaczor makes four arguments to show where Giubilini and Minerva's argument for permitting infanticide goes wrong. In this article I argue that Kaczor's arguments, and some similar arguments presented by other philosophers, are (...) mistaken and cannot show Giubilini and Minerva's view to be flawed. I claim that if one wants to reject the permissibility of infanticide, one must find better arguments for doing so. (shrink)

The Renaissance architect, moral philosopher, cryptographer, mathematician, Papal adviser, painter, city planner and land surveyor Leon Battista Alberti provided the theoretical foundations of modern perspective geometry. Alberti’s work on perspective exerted a powerful influence on painters of the stature of Albrecht Dürer, Leonardo da Vinci and Piero della Francesca. But his Della pittura of 1435–36 contains also a hitherto unrecognized ontology of pictorial projection. We sketch this ontology, and show how it can be generalized to apply to representative devices (...) in general, including maps and spatial and non-spatial databases. (shrink)

Essays and documents in support of the works of Gaialight - DOCUMENTS: The Passion of Jeanne d’Art (2007) - Letter to Gaia (2007) - “Art as Such”: This is Not Pop ... (2008) - Writing Toward Darkness (2009) - Scarlett Words: Light America (2009) - The Darklight Elaboration (2010) - The Darklight Elaboration: Zeitgeist or Episteme? (2010) - Cam Girls (2011) - Brooklyn Buzz (2011) - Brooklyn Buzz: The Semi-divine Metropolis (2011) - Reconnaissance: Light War, Mass Surveillance, Video Games (2011) (...) - First Cause (2011) - Met Ladies (2011) - When Cam Girls Met Ladies (2011) / OUTTAKES (2007): 15 Questions About Editioned Art Photography (2007) - A Few Awkward Questions for Francesca Woodman (2007) - October Revolution (2007) . (shrink)

Michael Hauskeller (“Reflections from a Troubled Stream: Giubliani and Minerva on ‘After-Birth Abortion’) has recently suggested that we should resist rationalist tendencies in moral discourse: “[I]s not all morality ultimately irrational? Even the most strongly held moral convictions can be shown to lack a rational basis.” (Hauskeller 2012, p. 18) Hauskeller was responding to Alberto Giubliani and Francesca Minverva’s (2012) recent defense of the permissibility of killing infants, but his anti-rationality arguments have wide-reaching implications. Yet pace Hauskeller, rationality is (...) indeed of crucial importance to any ethical argument. We should not abandon rationality for the sake of refuting one discomforting hypothesis; instead, rationality must be rigorously employed, here and elsewhere, in the search for the truth. (shrink)

Dans un texte désormais célèbre, Ferdinand de Saussure insiste sur l’arbitraire du signe dont il vante les qualités. Toutefois il s’avère que le symbole, signe non arbitraire, dans la mesure où il existe un rapport entre ce qui représente et ce qui est représenté, joue un rôle fondamental dans la plupart des activités humaines, qu’elles soient scientifiques, artistiques ou religieuses. C’est cette dimension symbolique, sa portée, son fonctionnement et sa signification dans des domaines aussi variés que la chimie, la théologie, (...) les mathématiques, le code de la route et bien d’autres qui est l’objet du livre La Pointure du symbole. -/- Jean-Yves Béziau, franco-suisse, est docteur en logique mathématique et docteur en philosophie. Il a poursuivi des recherches en France, au Brésil, en Suisse, aux États-Unis (UCLA et Stanford), en Pologne et développé la logique universelle. Éditeur-en-chef de la revue Logica Universalis et de la collection Studies in Universal Logic (Springer), il est actuellement professeur à l’Université Fédérale de Rio de Janeiro et membre de l’Académie brésilienne de Philosophie. SOMMAIRE -/- PRÉFACE L’arbitraire du signe face à la puissance du symbole Jean-Yves BÉZIAU La logique et la théorie de la notation (sémiotique) de Peirce (Traduit de l’anglais par Jean-Marie Chevalier) Irving H. ANELLIS Langage symbolique de Genèse 2-3 Lytta BASSET -/- Mécanique quantique : quelle réalité derrière les symboles ? Hans BECK -/- Quels langages et images pour représenter le corps humain ? Sarah CARVALLO Des jeux symboliques aux rituels collectifs. Quelques apports de la psychologie du développement à l’étude du symbolisme Fabrice CLÉMENT Les panneaux de signalisation (Traduit de l’anglais par Fabien Shang) Robert DEWAR Remarques sur l’émergence des activités symboliques Jean LASSÈGUE Les illustrations du "Songe de Poliphile" (1499). Notule sur les hiéroglyphes de Francesca Colonna Pierre-Alain MARIAUX Signes de vie Jeremy NARBY Visualising relations in society and economics. Otto Neuraths Isotype-method against the background of his economic thought Elisabeth NEMETH Algèbre et logique symboliques : arbitraire du signe et langage formel Marie-José DURAND – Amirouche MOKTEFI Les symboles mathématiques, signes du Ciel Jean-Claude PONT La mathématique : un langage mathématique ? Alain M. ROBERT. (shrink)

my goal here is to provide a detailed analysis of the methods of inference that are employed in De prospectiva pingendi. For this purpose, a method of natural deduction is proposed. the treatise by Piero della Francesca is a manifestation of a union between the ne arts and the mathematical sciences of arithmetic and geometry. He de nes painting as a part of perspective and, speaking precisely, as a branch of geometry, which is why we nd advanced geometrical exercises (...) here. (shrink)