We introduce the concept of partial event as a pair of disjoint sets, respectively the favorable and the unfavorable cases. Partial events can be seen as a De Morgan algebra with a single fixed point for the complement. We introduce the concept of a measure of partial probability, based on a set of axioms resembling Kolmogoroff’s. Finally we define a concept of conditional probability for partial events and apply this concept to the analysis of the two-slit experiment in quantum mechanics.

The sorites as a formal theory. The sorites paradox has been understood as a failure of classical logic and a way out can be found by choosing a non classical logic (fuzzy logic, for instance). We understand the sorites not as a problem of logic but of ontology, so we preserve classical logic and submit the premisses of the argument to a deeper analysis. As a result we obtain two theories for soritical arguments and enlighten the kind of structure requested (...) by these arguments. The former theory has a lattice theoretic flavor and is fitted for paradoxes like “the heap” and “the bald man”; the latter is group theoretic in character and can manage paradoxes based on observational predicates like “tall”, “red” and so on. In both cases the contradiction is derived from a larger set of hypotheses than in usual analysis and some of these hypotheses make assertions whose empirical meaning can be questioned. (shrink)

The sorites as a formal theory. The sorites paradox has been understood as a failure of classical logic and a way out can be found by choosing a non classical logic (fuzzy logic, for instance). We understand the sorites not as a problem of logic but of ontology, so we preserve classical logic and submit the premisses of the argument to a deeper analysis. As a result we obtain two theories for soritical arguments and enlighten the kind of structure requested (...) by these arguments. The former theory has a lattice theoretic flavor and is fitted for paradoxes like “the heap” and “the bald man”; the latter is group theoretic in character and can manage paradoxes based on observational predicates like “tall”, “red” and so on. In both cases the contradiction is derived from a larger set of hypotheses than in usual analysis and some of these hypotheses make assertions whose empirical meaning can be questioned. (shrink)

In this work we show that every structure [MATHEMATICAL SCRIPT CAPITAL A] can be expanded to a partial structure [MATHEMATICAL SCRIPT CAPITAL A]* with universal functions for the class of polynomials on [MATHEMATICAL SCRIPT CAPITAL A]*. We can embed [MATHEMATICAL SCRIPT CAPITAL A]* monomorphically in a total structure [MATHEMATICAL SCRIPT CAPITAL A]º that preserves universal functions of [MATHEMATICAL SCRIPT CAPITAL A]* and that is universal among such structures, i.e. [MATHEMATICAL SCRIPT CAPITAL A]º can be homomorphically embedded in every total structure (...) that preserves universal functions of [MATHEMATICAL SCRIPT CAPITAL A]*. Universal functions are the starting point for developing recursion theoretic tools in an [MATHEMATICAL SCRIPT CAPITAL A]* that satisfies some simple additional conditions. (shrink)

An analysis of how capitalism today produces subjectivity like any other “good,” and what would allow us to escape its hold. “Capital is a semiotic operator”: this assertion by Félix Guattari is at the heart of Maurizio Lazzarato's Signs and Machines, which asks us to leave behind the logocentrism that still informs so many critical theories. Lazzarato calls instead for a new theory capable of explaining how signs function in the economy, in power apparatuses, and in the production of (...) subjectivity. Moving beyond the dualism of signifier and signified, Signs and Machines shows how signs act as “sign-operators” that enter directly into material flows and into the functioning of machines. Money, the stock market, price differentials, algorithms, and scientific equations and formulas constitute semiotic “motors” that make capitalism's social and technical machines run, bypassing representation and consciousness to produce social subjections and semiotic enslavements. Lazzarato contrasts Deleuze and Guattari's complex semiotics with the political theories of Jacques Rancière, Antonio Negri and Michael Hardt, Paolo Virno, and Judith Butler, for whom language and the public space it opens still play a fundamental role. Lazzarato asks: What are the conditions necessary for political and existential rupture at a time when the production of subjectivity represents the primary and perhaps most important work of capitalism? What are the specific tools required to undo the industrial mass production of subjectivity undertaken by business and the state? What types of organization must we construct for a process of subjectivation that would allow us to escape the hold of social subjection and machinic enslavement? In addressing these questions, Signs and Machines takes on a task that is today more urgent than ever. (shrink)

Maurizio Lazzarato is an Italian sociologist and philosopher who lives and works in France. He collaborated on collective works with important figures like Antonio Negri and Yann Moulier-Boutang in the 1990s and has been a frequent contributor to the journal Multitudes in which the same two intellectuals were also leading voices. During the same period, he was closely involved as a theorist and activist in the long and inventive struggle of the intermittents du spectacle, French cultural workers defending (...) a social security regime that took particular account of their unstable employment and the way in which their creativity overflowed their periods of paid activity. This involvement fed into a broader... (shrink)

This article sets the stage for a genealogy of the postgenomic body. It starts with the current transformative views of epigenetics and microbiomics to offer a more pluralistic history in which the ethical problem of how to live with a permeable body – that is plasticity as a form of life – is pervasive in traditions pre-dating and coexisting with modern biomedicine (particularly humoralism in its several ramifications). To challenge universalizing narratives, I draw on genealogical method to illuminate the unequal (...) distribution of plasticity across gender and ethnic groups. Finally, after analysing postgenomics as a different thought-style to genomics, I outline some of its implications for notions of plasticity. I argue that postgenomic plasticity is neither a modernistic plasticity of instrumental control of the body nor a postmodernist celebration of endless potentialities. It is instead closer to an alter-modernistic view that disrupts clear boundaries between openness and determination, individual and community. (shrink)

The Italian philosopher Maurizio Lazzarato reveals the underpinnings of contemporary subjectivity in the aesthetics and politics of mass media. This book discloses the conceptual groundwork of Lazzarato's thought as a whole for a time when his writings have become increasingly influential.

Antonio Negri wrote the two essays that comprise Time for Revolution while serving a prison sentence for alleged involvement with radical left-wing groups. Although the essays were written two decades apart, their concerns are the same: is there a place for resistance in a society utterly subsumed by capitalism? In the wake of the global crisis of capitalism heralded by the 2008 crash, the question has never been more relevant and Negri remains an insightful and passionate guide to (...) any attempt to answer it. (shrink)

Mirko Garasic (2021) argued that space travel and, by extension, the colonization of other planets could morally justify using technologies and interventions capable of profoundly modifying the characteristics of astronauts and future Martian generations. According to Garasic, however, the fact that space interventions such as human (bio)enhancement or reproductive technologies such as artificial wombs may be morally justified does not mean that they are morally acceptable technologies to be used on Earth as well. Garasic’s thesis is that we should resist (...) the temptation to establish or reinforce a continuity between the ethical standards that apply to space travel and those that apply on Earth because what applies in space (or on other planets) does not necessarily apply to our planet. Garasic argues that in space, genetic enhancement interventions are morally acceptable, as they are essential for survival. On Earth, however, we can survive even without any form of (bio)enhancement. In a previous article (2022), we presented several arguments against Garasic’s thesis regarding the exceptional morality of what is morally acceptable in space. In this article, we examine and reply to Garasic (2022), showing that he fails to defend his thesis from the objections we previously advanced. Garasic’s mistakes are: (1) assuming nature (and consequently what is “natural”) as a normative point of reference which allows establishing what is moral and what is not moral; (2) defending the choices concerning reproduction as an insufficiently demanding and therefore unsatisfactory moral principle (according to Garasic we should not bring into the world people who can have a quality of life or a condition of well-being superior to mere survival); and finally (3) of not explaining clearly what it means to defend a principle of moral exceptionalism for space travel (Garasic does not explain whether this position applies to any behavior, for which what on Earth is a virtue, in space is a vice or is not a general principle, but he makes this case only for enhancement and reproductive technologies). Through our analysis, we not only refute Garasic’s position but also show that any attempt to address space travel issues as “special” moral issues faces several difficulties and, ultimately, is doomed to failure. (shrink)

In this article, I reconstruct Hannah Arendt's theory of judgment around a number of key themes. After having distinguished two models of judgment, one based on the standpoint of the actor, the other on the standpoint of the spectator, I go on to examine their most distinctive features, in particular, the link between judgment, the imagination, and the ability to think 'representatively'. I also examine the philosophical sources of Arendt's theory of judgment, namely, Kant's theory of aesthetic judgment and its (...) criteria of validity. (shrink)

1. Costruzione e senso dell'attualismo.--2. Sviluppi e incidenza dell'attualismo.

By providing an interdisciplinary reading of advance directives regulation in international, European and domestic law, this book offers new insights into the most controversial legal issues surrounding the debate over dignity and autonomy ...

The article illustrates the different meanings of the term “logic” in Weber's work and then proceeds to discuss his approach to the explanation of historical events and in particular to counterfactual analysis. Weber's epistemology is first situated within the neo-Kantian debates of his time as well as legal positivism and historical jurisprudence. The article then focuses on this author's conception of science as a value sphere, on the aims and methods of explanation in the social and historical sciences and on (...) the key concepts of possibility judgements and adequate causation. The central role played by counterfactuals and modal logic is illustrated through the example of the battle of Marathon, which Weber himself saw as the starting point of a causal chain leading to the rise of Western rationalism. The article concludes by highlighting the pioneering role of Weber's counterfactualism for the subsequent development of possible worlds theory and its use in the causal analysis of singular historical events. (shrink)

Realitism: the postmodern attack on reality -- Realism: things that have existed since the beginning of the world -- Reconstruction: why criticism starts from reality -- Emancipation: unexamined life has no value.

In this book, renowned theorist Antonio Negri examines how Spinoza's thought constitutes a radical break with past ideas and a key tool for envisaging a form of politics beyond capitalism. His philosophy gives us new ways of looking critically at our present, revealing that power must always be seen as a question of antagonism and class struggle.

In this essay we take stock of the shortcomings, successes, and promises of ‘biopolitics' to understand and frame global health crises such as COVID-19. We claim that rather than thinking in terms of a special relationship between Western modernity and biopolitics, it is better to look at a longer and more global histories of populations’ politics of life and health to situate present and future responses to ecological crises. Normatively, we argue for an affirmative biopolitics, that at once de-securitizes our (...) approach to our biosocial condition and expands the politics of the human estate to other molar and molecular dimensions. (shrink)

This the first of a new three-part series in which Antonio Negri, a leading political thinker of our time, explores key ideas that have animated radical thought and examines some of the social and economic forces that are shaping our world today. In this first volume Negri shows how the thinking of Marx and Foucault were brought together to create an original theoretical synthesis - particularly in the context of Italy from May ’68 onwards. At around that time, (...) the structures of industry and production began to change radically, with the emergence of new producer-subjects and new fields of capitalist value creation. New concepts and theories were developed by Foucault, Deleuze and Guattari and others to help make sense of these and related developments - concepts such as biopower and biopolitics, subjectivation and subsumption, public and common, power and potentiality. These concepts and theories are examined by Negri within the broader context of the development of European philosophical discourse in the twentieth century. Marx and Foucault provides a unique account of the development of radical thought in the late 20th and early 21st centuries and will be a key text for anyone interested in radical politics today. (shrink)

In this book, Esposito presents a historiography of organicist and holistic thought through an examination of the work of leading biologists from Britain and America. He shows how this work relates to earlier Romantic tradition and sets it within the wider context of the history and philosophy of the life sciences.

The debtor-creditor relation, which is at the heart of this book, sharpens mechanisms of exploitation and domination indiscriminately, since, in it, there is no distinction between workers and the unemployed, consumers and producers, working and non-working populations, between retirees and welfare recipients. They are all "debtors," guilty and responsible in the eyes of capital, which has become the Great, the Universal, Creditor.--from The Making of the Indebted Man Debt -- both public debt and private debt Has become a major concern (...) of economic and political leaders. In The Making of the Indebted Man, Maurizio Lazzarato shows that, far from being a threat to the capitalist economy, debt lies at the very core of the neoliberal project. Through a reading of Karl Marx's lesser-known youthful writings on John Mill, and a rereading of writings by Friedrich Nietzsche, Gilles Deleuze, Felix Guattari, and Michel Foucault, Lazzarato demonstrates that debt is above all a political construction, and that the creditor/debtor relation is the fundamental social relation of Western societies.Debt cannot be reduced to a simple economic mechanism, for it is also a technique of "public safety" through which individual and collective subjectivities are governed and controlled. Its aim is to minimize the uncertainty of the time and behavior of the governed. We are forever sinking further into debt to the State, to private insurance, and, on a more general level, to corporations. To insure that we honor our debts, we are at once encouraged and compelled to become the "entrepreneurs" of our lives, of our "human capital." In this way, our entire material, psychological, and affective horizon is upended and reconfigured. How do we extricate ourselves from this impossible situation? How do we escape the neoliberal condition of the indebted man? Lazzarato argues that we will have to recognize that there is no simple technical, economic, or financial solution. We must instead radically challenge the fundamental social relation structuring capitalism: the system of debt. (shrink)

As space travel and intentions to colonise other planets are becoming the norm in public debate and scholarship, we must also confront the technical and survival challenges that emerge from these hostile environments. This paper aims to evaluate the various arguments proposed to meet the challenges of human space travel and extraterrestrial planetary colonisation. In particular, two primary solutions have been present in the literature as the most straightforward solutions to the rigours of extraterrestrial survival and flourishing: (1) geoengineering, where (...) the environment is modified to become hospitable to its inhabitants, and (2) human (bio)enhancement where the genetic heritage of humans is modified to make them more resilient to the difficulties they may encounter as well as to permit them to thrive in non-terrestrial environments. Both positions have strong arguments supporting them but also severe philosophical and practical drawbacks when exposed to different circumstances. This paper aims to show that a principled stance where one position is accepted wholesale necessarily comes at the opportunity cost of the other where the other might be better suited, practically and morally. This paper concludes that case-by-case evaluations of the solutions to space travel and extraterrestrial colonisation are necessary to ensure moral congruency and the survival and flourishing of astronauts now and into the future. (shrink)

Using labelled formulae, a cut-free sequent calculus for intuitionistic propositional logic is presented, together with an easy cut-admissibility proof; both extend to cover, in a uniform fashion, all intermediate logics characterised by frames satisfying conditions expressible by one or more geometric implications. Each of these logics is embedded by the Gödel–McKinsey–Tarski translation into an extension of S4. Faithfulness of the embedding is proved in a simple and general way by constructive proof-theoretic methods, without appeal to semantics other than in the (...) explanation of the rules. (shrink)