In this paper we give a strong normalization proof for a set of reduction rules for classical logic. These reductions, more general than the ones usually considered in literature, are inspired to the reductions of Felleisen's lambda calculus with continuations.

The meaning of a formula built out of proof-functional connectives depends in an essential way upon the intensional aspect of the proofs of the component subformulas. We study three such connectives, strong equivalence (where the two directions of the equivalence are established by mutually inverse maps), strong conjunction (where the two components of the conjunction are established by the same proof) and relevant implication (where the implication is established by an identity map). For each of these connectives we give a (...) type assignment system, a realizability semantics, and a completeness theorem. This form of completeness implies the semantic completeness of the type assignment system. (shrink)

This paper presents a constructive interpretation for the proofs in classical logic of $\Sigma^0_1$ -sentences and for a witness extraction procedure based on Prawitz's reduction rules.

We live in an age of impotence. Stuck between global war and global finance, between identity and capital, we seem to be incapable of producing the radical change that is so desperately needed. Is there still a way to disentangle ourselves from a global order that shapes our politics as well as our imagination? In his most systematic book to date, renowned Italian theorist Franco Berardi tackles this question through a solid yet visionary analysis of the three fundamental concepts (...) of Possibility, Potency, and Power. Characterizing Possibility as the content, Potency as the energy, and Power as the form, Berardi suggests that the road to emancipation unravels from the awareness that the field of the possible is only limited, and not created, by the power structures that implement it. Other futures and other worlds are always already inscribed within the present, despite power's attempt at keeping them invisible. Overcoming any temptation of giving in to despair or nostalgia, Berardi proposes the notion of 'futurability' as a way to remind us that even within the darkness of our current crisis lies dormant the horizon of possibility. (shrink)

A wide-ranging exploration of the present, and the future, of the Unconscious. The Unconscious knows no time, it has no before-and-after, it does not have a history of its own. Yet, it is not always the same. As it emerges in the life of people and societies, the Unconscious is shaped by ever-changing historical conditions: its form depends on the unique 'psychosphere' of each historical age. In the early twentieth century, Freud characterised the Unconscious as the dark side of the (...) well-ordered framework of Progress and Reason. At the end of the past century, Deleuze and Guattari described it as a laboratory: the magmatic force that ceaselessly brings about new possibilities of imagination. Today, at a time of viral pandemics and in the midst of the catastrophic collapse of capitalism, the Unconscious has begun to emerge in yet another form. In this book, Franco 'Bifo' Berardi vividly illustrates the form in which the Unconscious will make itself manifest for decades to come, and the challenges that it will pose to our possibilities of political action, poetic imagination, and therapy."--Publisher's description. (shrink)

Une théorie de la politique n'existe pas dans la pensée libertine intéressée à l'élaboration d'un modèle moral concentré sur la dimension de la vie privée. Pourtant à l'intérieur de cette tradition dans la deuxième moitié du VIIe siècle en France, s'amorce un filon à cheval entre utopie et roman d'aventure dans lequel apparaissent des formes d'organisation sociétales modelées selon les principes de la liberté, égalité, tolérance qui constitueront les mots d'ordres des philosophes des lumières.

An Innovating approach to Plato’s philosophy Through a careful survey of several significant Platonic texts, mainly focussing on the nature of knowledge, Essays on Plato’s Epistemology offers the reader a fresh and promising approach to Plato’s philosophy as a whole. From the very earliest reception of Plato’s philosophy, there has been a conflict between a dogmatic and a sceptical interpretation of his work and thought. Moreover, the two sides are often associated, respectively, with a metaphysical and an anti-metaphysical approach. This (...) book, continuing a line of thought that is nowadays strongly present in the secondary literature – and also followed by the author in over thirty years of research –, maintains that a third way of thinking is required. Against the widespread view that an anti-dogmatic philosophy must go together with an anti-metaphysical stance, Trabattoni shows that for Plato, on the contrary, a sober and reasonable assessment of both the powers and limits of human reason relies on a proper metaphysical outlook. (shrink)

Concatenation, conjunction, and connection -- The sensitive infosphere -- Global skin : a trans-identitarian patchwork -- The aesthetic genealogy of globalization -- Language, limit, excess -- Avatars of the general intellect -- The swarm effect -- Social morphogenesis and neuroplasticity -- The transhuman -- The horizon of mutation -- Consciousness and evolution -- The end.

Today, we believe that the map is a copy of the Earth, without realizing that the opposite is true: in our culture the Earth has assumed the form of a map. In Blinding Polyphemus, Franco Farinelli elucidates the philosophical correlation between cultural evolution and shifting cartographies of modern society, giving readers an interdisciplinary study that attempts to understand and redefine the fundamental structures of cartography, architecture, and the notion of "space." Following the lessons of nineteenth-century critical German geography, this (...) is a manual of geography without any map. To indicate where things are means already responding, in implicit and unreflective ways, to prior questions about their nature. Blinding Polyphemus not only takes account of the present state of the Earth and of human geography, it redefines the principal models we possess for the description of the world: the map, above all, as well as the landscape, subject, place, city, and space. (shrink)

In this book, Franco Berardi guides the reader through a wry, dark, disconcerting but also brilliant and invigorating journey through the recent upheavals that we have witnessed. He argues that if our world is dead, then the space is open for another to appear - a world where apocalypse can shake us out of our contemporary zombie-like existence.

Any living organism interacts with and responds specifically to environmental molecules by expressing specific olfactory receptors. In this paper, this specificity will be first examined in causal terms with particular emphasis on the mechanisms controlling olfactory gene expression, cell-to-cell interactions and odor-decoding processes. However, this type of explanation does not entirely justify the role olfactory receptors have played during evolution, since they are also expressed ectopically in different organs and/or tissues. Homologous olfactory genes have in fact been found in such (...) diverse cells and/or organs as spermatozoa, testis and kidney where they are assumed to act as chemotactic sensors or renin modulators. To justify their functional diversity, homologous olfactory receptors are assumed to share the same basic role: that of conferring a self-identity to cells or tissues under varying environmental conditions. By adopting this standpoint, the functional attribution as olfactory or chemotactic sensors to these receptors should not be seen either as a cause conditioning receptor gene expression, or as a final effect resulting from genetically predetermined programs, but as a direct consequence of the environmental conditions olfactory receptor genes have explored during evolution. The association of odorant patterns with specific environmental or contextual situations makes their relationship semiotically triadic, due to the emergence of an interpretant capable of perceiving odorants as meaningful signs out of a noisy background. This perspective highlights the importance of odorant-receptor relationships as respect to the properties of the interacting partners. It is our contention that only when taken together can these different explanatory strategies provide a realistic account of how olfactory receptor genes have been structurally and functionally modified during evolution. (shrink)

If we can and do have some self‐knowledge, how do we acquire it? By examining the ways in which we acquire self‐knowledge—by introspection—we can try shedding some light onto the nature and the breadth of self‐knowledge, as others have tried to do with other forms of knowledge. My aim is to show that introspection involves multiple (that is, at least two) distinct processes, a view I call “pluralism about introspection”. One of the virtues of pluralism is that it explains how (...) we can have such a wide variety of self‐knowledge despite our cognitive limitations. (shrink)

In Rousseau, Nietzsche, and the Image of the Human Paul Franco explores the relationship between Nietzsche and Rousseau and their critique of modern life. Franco begins by arguing that "among philosophers, Jean-Jacques Rousseau and Friedrich Nietzsche are perhaps the two most influential explorers and shapers of the moral and cultural imagination of late modernity." And yet Nietzsche was often highly critical of Rousseau. Indeed, their critiques of modern life differ in important respects. Rousseau focused on the growing political (...) and economic inequality in modern society and proposed a more egalitarian politics. Nietzsche decried the inability of society to take account of the exceptional individual and found Rousseau's political ideas wrong-headed. It is Franco's objective to explore their critiques of the modern life they observed--in the mid 18th century of the French Enlightenment and the late 19th century of industrializing and increasingly secular and scientific Europe--and show how they differed and how the earlier thinker formed the basis of much of the later thinkers' ideas. (shrink)

A study of what Descartes calls émotions in his Passions of the Soul suggests that, rather than just a theory of passions—as Descartes himself explicitly claims to be proposing—he was in practice putting forward a more comprehensive theory of passions-émotions, a unified theory which would be closer to what today should properly be called Descartes’ theory of emotions. I try here to make explicit the grounds of this unity by showing that émotions both fit within the functional account Descartes attributes (...) to what he calls passions; and complement the intentionality of passions by expanding it to new objects. In order to show this I offer also a tentative distinction, functionally and intentionally, between passions and émotions in general, on one hand, and, on the other, between the two apparent types of émotions Descartes refers to in the treatise—interior or internal [intérieure] and intellectual [intellectuelle] émotions. (shrink)

ABSTRACTThis paper analyses the discourses produced on their websites by the two organisations that conducted the official ‘leave’ and ‘remain’ campaigns in the Brexit referendum. The analysis, whi...