In a fragment entitled Elementa Nova Matheseos Universalis Leibniz writes “the mathesis [...] shall deliver the method through which things that are conceivable can be exactly determined”; in another fragment he takes the mathesis to be “the science of all things that are conceivable.” Leibniz considers all mathematical disciplines as branches of the mathesis and conceives the mathesis as a general science of forms applicable not only to magnitudes but to every object that exists in our imagination, i.e. that is (...) possible at least in principle. As a general science of forms the mathesis investigates possible relations between “arbitrary objects”. It is an abstract theory of combinations and relations among objects whatsoever. In 1810 the mathematician and philosopher Bernard Bolzano published a booklet entitled Contributions to a Better-Grounded Presentation of Mathematics. There is, according to him, a certain objective connection among the truths that are germane to a certain homogeneous field of objects: some truths are the “reasons” of others, and the latter are “consequences” of the former. The reason-consequence relation seems to be the counterpart of causality at the level of a relation between true propositions. Arigorous proof is characterized in this context as a proof that shows the reason of the proposition that is to be proven. Requirements imposed on rigorous proofs seem to anticipate normalization results in current proof theory. The contributors of Mathesis Universalis, Computability and Proof, leading experts in the fields of computer science, mathematics, logic and philosophy, show the evolution of these and related ideas exploring topics in proof theory, computability theory, intuitionistic logic, constructivism and reverse mathematics, delving deeply into a contextual examination of the relationship between mathematical rigor and demands for simplification. (shrink)

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 ...

This volume will be of particular interest to researchers working in the history, and in the philosophy, of logic and mathematics, and more generally, to ...

In Subversive Spinoza , Antonio Negri spells out the philosophical credo that inspired his radical renewal of Marxism and his compelling analysis of the modern state and the global economy by means of an inspiring reading of the challenging metaphysics of the seventeenth-century Dutch-Jewish philosopher Spinoza. For Negri, Spinoza's philosophy has never been more relevant than it is today to debates over individuality and community, democracy and resistance, modernity and postmodernity.

Machine generated contents note: Prologue: Hilbert's Last Problem; 1. Introduction; Part I. Proof Systems Based on Natural Deduction: 2. Rules of proof: natural deduction; 3. Axiomatic systems; 4. Order and lattice theory; 5. Theories with existence axioms; Part II. Proof Systems Based on Sequent Calculus: 6. Rules of proof: sequent calculus; 7. Linear order; Part III. Proof Systems for Geometric Theories: 8. Geometric theories; 9. Classical and intuitionistic axiomatics; 10. Proof analysis in elementary geometry; Part IV. Proof Systems for Nonclassical (...) Logics: 11. Modal logic; 12. Quantified modal logic, provability logic, and so on; Bibliography; Index of names; Index of subjects. (shrink)

Structural proof theory is a branch of logic that studies the general structure and properties of logical and mathematical proofs. This book is both a concise introduction to the central results and methods of structural proof theory, and a work of research that will be of interest to specialists. The book is designed to be used by students of philosophy, mathematics and computer science. The book contains a wealth of results on proof-theoretical systems, including extensions of such systems from logic (...) to mathematics, and on the connection between the two main forms of structural proof theory - natural deduction and sequent calculus. The authors emphasize the computational content of logical results. A special feature of the volume is a computerized system for developing proofs interactively, downloadable from the web and regularly updated. (shrink)

Quantification is particularly seductive in times of global uncertainty. Not surprisingly, numbers, indicators, categorizations, and comparisons are central to governmental and popular response to the COVID-19 pandemic. This essay draws insights from critical data studies, sociology of quantification and decolonial thinking, with occasional excursion into the biomedical domain, to investigate the role and social consequences of counting broadly defined as a way of knowing about the virus. It takes a critical look at two domains of human activity that play a (...) central role in the fight against the virus outbreak, namely medical sciences and technological innovation. It analyzes their efforts to craft solutions for their user base and explores the unwanted social costs of these operations. The essay argues that the over-reliance of biomedical research on “whiteness” for lab testing and the techno-solutionism of the consumer infrastructure devised to curb the social costs of the pandemic are rooted in a distorted idea of a “standard human” based on a partial and exclusive vision of society and its components, which tends to overlook alterity and inequality. It contends that to design our way out of the pandemic, we ought to make space for distinct ways of being and knowing, acknowledging plurality and thinking in terms of social relations, alterity, and interdependence. (shrink)

It is beginning to be rather well known that Edmund Husserl, the founder of phenomenological philosophy, was originally a mathematician; he studied with Weierstrass and Kronecker in Berlin, wrote his doctoral dissertation on the calculus of variations, and was then a colleague of Cantor in Halle until he moved to the Göttingen of Hilbert and Klein in 1901. Much of Husserl’s writing prior to 1901 was about mathematics, and arguably the origin of phenomenology was in Husserl’s attempts to give philosophical (...) foundations first for analysis and later for the formal sciences in general. However, what exactly Husserl’s thoughts about mathematics were is relatively little known. Stefania Centrone’s book Logic and Philosophy of Mathematics in the Early Husserl fills this lacuna. Centrone deciphers Husserl’s early texts about mathematics and logic somewhat selectively, but also extremely accurately and carefully into lucid English and in terms we know, without however reading contemporary views into Husserl’s views. Her analysis reveals for example that Husserl’s view of logic is close to what is today taught in the standard textbooks and that he viewed abstract mathematics as a theory of structures. Her work also uncovers Husserl’s relationship to the algebraists of logic as well as to Bolzano, Frege, and Hilbert.The book is composed of three rather independent chapters. In contrast to most of the other commentaries on early Husserl, the organization of the book is thematic rather than an attempt to document the various stages in the development of Husserl’s views. The first chapter discusses Husserl’s major work on arithmetic, the second the idea of pure logic, and the last the imaginary in mathematics. (shrink)

The chemist and philosopher Michael Polanyi was one of the first twentieth-century scientists to propose a program to resolve the internal conflict of the modern Enlightenment: scientific detachment and moral nihilism with humanist values. Stefania Jha’s intellectual biography places Polanyi in the context of his time and culture, analyzes his key philosophical ideas, and explicates the application—and at times misappropriation—of his work. Polanyi’s method was not laid out in his published works, and his vocabulary tends to make his writings (...) difficult to understand. By exposing the structure of his theory of tacit knowing, and by tracing the growth of his thinking, Jha shows how the various elements of his thought are integrated. Through examination of his philosophical roots in Kant and the complexity of his evolving thought, she counteracts the popular notion that Polanyi’s philosophy stands apart from the western philosophic tradition. Jha’s deep analysis makes Polanyi’s shift of focus from science to philosophy more intelligible, his philosophy more approachable, and the causes he championed—such as the freedom of science and cultural freedom—more understandable. Applying his notion of tacit knowing in practical directions, Jha seeks to bring the study of Polanyi’s philosophy out of the specialists’ enclave and into such fields as ethics and clinical medicine. (shrink)

Discusses how cultural and economic changes around the world have caused a shift in the concepts that shape modern politics and defined the new global order.

The paper discusses inappropriate treatment by analyzing the casuistics of palliative patients in the terminal stage of illness who are hospitalized at the Department of Internal Medicine and Geriatrics of the Faculty hospital with policlinic. Our research applies the principles of palliative care in the context of bioethics. The existing clinical conditions of healthcare in Slovakia are characteristic of making a taboo of the issues of inappropriate treatment of palliative patients. Inductive-deductive and normative clinical bioethics methods of palliative care and (...) ethical strategy are applied for defining issues found in inappropriate hemodialysis treatment. An algorithm of hemodialysis treatment requires the definition of those lege artis criteria which, in the context of a patient’s autonomy and his/her decision, precondition the avoidance of the situation in which hemodialysis treatment is inappropriate. Futile treatment in a terminal condition is ethically inappropriate medical treatment that extends the suffering of patients and their relatives. Its definition is determined by the relevant legislation and the methods of bioethics. An active palliative strategy is aimed at managing the process of incurable diseases in the patient’s bio-psycho-socio-spiritual continuity in the process of special bioethics. The global bioethical objective of general bioethics for palliative care is based on the paradigm of social harmony and solidarity in the context of an authentic modus of the patient’s existence as a constitutive principle for the phenomenon of the patient’s being to finite being. (shrink)

This article approaches the paradigm shift of datafication from the perspective of civil society. Looking at how individuals and groups engage with datafication, it complements the notion of “data politics” by exploring what we call the “contentious politics of data”. By contentious politics of data we indicate the bottom-up, transformative initiatives interfering with and/or hijacking dominant processes of datafication, contesting existing power relations or re-appropriating data practices and infrastructure for purposes distinct from the intended. Said contentious politics of data is (...) articulated in an array of practices of data activism taking a critical stance towards datafication. In data activism, data as mediators take a central role, both as part of an action repertoire or as objects of struggle in their own right. Leveraging social movement studies and science and technology studies, this theoretical essay argues that data activism can be mapped along two analytical dimensions: “data as stakes” vs. “data as repertoires”, and “individual practice vs. collective action”. Mapping action repertoires and tactics along these axes allows us to chart the potential emergence of a political data subject at the intersection of these two dimensions. This furthers our understanding of people’s engagement with data in relation to other forms of activism and existing work in social movement studies. It also helps us interpreting potential trajectories of contemporary social movements, as they increasingly interface with data, devices and platforms. (shrink)

Four studies show that observers and readers imagine different alternatives to reality. When participants read a story about a protagonist who chose the more difficult of two tasks and failed, their counterfactual thoughts focused on the easier, unchosen task. But when they observed the performance of an individual who chose and failed the more difficult task, participants' counterfactual thoughts focused on alternative ways to solve the chosen task, as did the thoughts of individuals who acted out the event. We conclude (...) that these role effects may occur because participants' attention is engaged when they experience or observe an event more than when they read about it. (shrink)

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The first two sections focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, (...) which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The further sections then build on this and are centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics. (shrink)

In two experiments, we investigated whether 13-month-old infants expect agents to behave in a way consistent with information to which they have been exposed. Infants watched animations in which an animal was either provided information or prevented from gathering information about the actual location of an object. The animal then searched successfully or failed to retrieve it. Infants’ looking times suggest that they expected searches to be effective when—and only when—the agent had had access to the relevant information. This result (...) supports the view that infants’ possess an incipient metarepresentational ability that permits them to attribute beliefs to agents. We discuss the viability of more conservative explanations and the relationship between this early ability and later forms of ‘theory of mind’ that appear only after children have become experienced verbal communicators. (shrink)

Stefania Tutino shows that post-Reformation Catholic culture was a rich laboratory for our current moral and hermeneutical anxieties.

"One of the most significant figures of current political thought."--New Statesman.

In the present paper, we discuss Husserl's deep account of the notions of ?calculation? and of arithmetical ?operation? which is found in the final chapter of the Philosophy of Arithmetic, arguing that Husserl is as far as we know the first scholar to reflect seriously on and to investigate the problem of circumscribing the totality of computable numerical operations. We pursue two complementary goals, namely: (i) to provide a formal reconstruction of Husserl's intuitions, and (ii) to demonstrate on the basis (...) of our reconstruction that the class of operations that Husserl has in mind turns out to be extensionally equivalent to the one that, in contemporary logic, is known as the class of partial recursive functions. (shrink)

In management literature, intellectual capital is considered the key driver of the competitive advantage of the third millennium enterprise firm; consequently, measuring, managing and reporting IC has become a critical issue. Frameworks addressed to measure and report IC have proliferated, nevertheless the adoption of these frameworks is not so widespread in practice. The strong call for critically investigating IC practices has been raised by several leading authors in the area. Doing a critical and performative IC research means empirically researching IC (...) organisational practices in specific contexts, in order to increase the understanding of the IC dynamics. By critically analysing the IC practices of ANPAS Piemonte, an Italian non-profit organisation chosen for its long-standing experience in issuing audited IC reports, the article contributes to the knowledge of how and why IC is measured and reported in a specific, outstanding NPO disclosing IC. Moreover, the case study analysis contributes to shed lights on the levers and barriers that should be faced by other managers intending to implement and effectively use an IC measurement, management and reporting system within organisation. (shrink)

Lakatos is considered to be a Popperian who adapted his Hegelian-Marxist training to critical philosophy. I claim this is too narrow and misses Lakatos' goal of understanding scientific inquiry as heuristic inquiry—something he did not find in Popper, but found in Polanyi. Archival material shows that his ‘new method' struggled to overcome what he saw as the Popperian handicap, by using Polanyi.

Entrevista concedida por Antonio Negri a Homero Santiago e Mario Marino por ocasião do lançamento da segunda edição da tradução brasileira de A anomalia selvagem: poder e potência em Espinosa.

L'articolo analizza i vari volumi di A.Negri dedicati al pensiero di Nietzsche.

Negri, a leading Marxist philosopher, has inspired anti-empire movements around the world through his writings and personal example. This work, which began as a conversation between Negri and literary critic Casarino, is the most complete review of the philosopher's work.

This study focuses on the ideas of Antonio Negri and Michael Hardt, the most influential thinkers of recent period, about the concepts of the Empire, Multitude and Biopolitical production. These concepts being at the center of contemporary political discussions problematise the ideaitonal foundations of the idea of Empire evaluated as a new form of sovereignty, the economic transformation in the contemporary capitalism and the new form of subjectivity in this age. To Negri and Hardt, Empire is seen as (...) a logic of network operating at global level and a new logic of sovereignty and governance going beyond the political boundaries of nation states as form of sovereignty. In this regard, multitude is evaluated as a collective and joint social subject against the power and command forms of empire. As for biopolitical production, it is defined as the production of life in which feelings, symbols, communication and cooperation go beyond the understanding that centers the production of tangible goods within the capitalist production and work organization. These three concepts draw an important framework in terms of understanding the economic, political transformation of the contemporary world. In this study, it was aimed at interpreting the nature of global changes brought forward by the Negri and Hardt thought within the boundaries of these three concepts. (shrink)

Essays on Husserl’s Logic and Philosophy of Mathematics sets out to fill up a lacuna in the present research on Husserl by presenting a precise account of Husserl’s work in the field of logic, of the philosophy of logic and of the philosophy of mathematics. The aim is to provide an in-depth reconstruction and analysis of the discussion between Husserl and his most important interlocutors, and to clarify pivotal ideas of Husserl’s by considering their reception and elaboration by some of (...) his disciples and followers, such as Oskar Becker and Jacob Klein, as well as their influence on some of the most significant logicians and mathematicians of the past century, such as Luitzen E. J. Brouwer, Rudolf Carnap, Kurt Gödel and Hermann Weyl. Most of the papers consider Husserl and another scholar – e.g. Leibniz, Kant, Bolzano, Brentano, Cantor, Frege – and trace out and contextualize lines of influence, points of contact, and points of disagreement. Each essay is written by an expert of the field, and the volume includes contributions both from the analytical tradition and from the phenomenological one. (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)

This study focuses on the ideas of Antonio Negri and Michael Hardt, the most influential thinkers of recent period, about the concepts of the Empire, Multitude and Biopolitical production. These concepts being at the center of contemporary political discussions problematise the ideaitonal foundations of the idea of Empire evaluated as a new form of sovereignty, the economic transformation in the contemporary capitalism and the new form of subjectivity in this age. To Negri and Hardt, Empire is seen as (...) a logic of network operating at global level and a new logic of sovereignty and governance going beyond the political boundaries of nation states as form of sovereignty. In this regard, multitude is evaluated as a collective and joint social subject against the power and command forms of empire. As for biopolitical production, it is defined as the production of life in which feelings, symbols, communication and cooperation go beyond the understanding that centers the production of tangible goods within the capitalist production and work organization. These three concepts draw an important framework in terms of understanding the economic, political transformation of the contemporary world. In this study, it was aimed at interpreting the nature of global changes brought forward by the Negri and Hardt thought within the boundaries of these three concepts. (shrink)

Various sources in the literature claim that the deduction theorem does not hold for normal modal or epistemic logic, whereas others present versions of the deduction theorem for several normal modal systems. It is shown here that the apparent problem arises from an objectionable notion of derivability from assumptions in an axiomatic system. When a traditional Hilbert-type system of axiomatic logic is generalized into a system for derivations from assumptions, the necessitation rule has to be modified in a way that (...) restricts its use to cases in which the premiss does not depend on assumptions. This restriction is entirely analogous to the restriction of the rule of universal generalization of first-order logic. A necessitation rule with this restriction permits a proof of the deduction theorem in its usual formulation. Other suggestions presented in the literature to deal with the problem are reviewed, and the present solution is argued to be preferable to the other alternatives. A contraction-and cut-free sequent calculus equivalent to the Hubert system for basic modal logic shows the standard failure argument untenable by proving the underivability of DA from A. (shrink)

Humans perceive time with millisecond precision. However, when experiencing negative or fearful events, time appears to slow down and aversive events are judged to last longer than neutral or positive events of equal duration. Feelings of control have been shown to attenuate increases in arousal triggered by anxiety-provoking events. Here, we tested whether feelings of control can go as far as influencing people’s perception of the world, by modulating the perceived duration of aversive events. Observers judged the duration of images (...) depicting positive or negative content, and we manipulated the amount of control experienced by participants. Crucially, participants never had any real control over events. All control was illusory. Results showed that when participants experienced low levels of control, negative images were judged as lasting longer than positive images. However, when participants illusorily experienced high levels of control, they no longer experienced aversive negative images as lasting longer than positive images. (shrink)

This study focuses on the ideas of Antonio Negri and Michael Hardt, the most influential thinkers of recent period, about the concepts of the Empire, Multitude and Biopolitical production. These concepts being at the center of contemporary political discussions problematise the ideaitonal foundations of the idea of Empire evaluated as a new form of sovereignty, the economic transformation in the contemporary capitalism and the new form of subjectivity in this age. To Negri and Hardt, Empire is seen as (...) a logic of network operating at global level and a new logic of sovereignty and governance going beyond the political boundaries of nation states as form of sovereignty. In this regard, multitude is evaluated as a collective and joint social subject against the power and command forms of empire. As for biopolitical production, it is defined as the production of life in which feelings, symbols, communication and cooperation go beyond the understanding that centers the production of tangible goods within the capitalist production and work organization. These three concepts draw an important framework in terms of understanding the economic, political transformation of the contemporary world. In this study, it was aimed at interpreting the nature of global changes brought forward by the Negri and Hardt thought within the boundaries of these three concepts. (shrink)

Anti-realist epistemic conceptions of truth imply what is called the knowability principle: All truths are possibly known. The principle can be formalized in a bimodal propositional logic, with an alethic modality ${\diamondsuit}$ and an epistemic modality ${\mathcal{K}}$, by the axiom scheme ${A \supset \diamondsuit \mathcal{K} A}$. The use of classical logic and minimal assumptions about the two modalities lead to the paradoxical conclusion that all truths are known, ${A \supset \mathcal{K} A}$. A Gentzen-style reconstruction of the Church–Fitch paradox is presented (...) following a labelled approach to sequent calculi. First, a cut-free system for classical bimodal logic is introduced as the logical basis for the Church–Fitch paradox and the relationships between ${\mathcal {K}}$ and ${\diamondsuit}$ are taken into account. Afterwards, by exploiting the structural properties of the system, in particular cut elimination, the semantic frame conditions that correspond to KP are determined and added in the form of a block of nonlogical inference rules. Within this new system for classical and intuitionistic “knowability logic”, it is possible to give a satisfactory cut-free reconstruction of the Church–Fitch derivation and to confirm that OP is only classically derivable, but neither intuitionistically derivable nor intuitionistically admissible. Finally, it is shown that in classical knowability logic, the Church–Fitch derivation is nothing else but a fallacy and does not represent a real threat for anti-realism. (shrink)

We describe a first experiment on whether product complexity affects competition and consumers in retail markets. We are unable to detect a significant effect of product complexity on prices, except insofar as the demand elasticity for complex products is higher. However, there is qualified evidence that complex products have the potential to induce consumers to buy more than they would otherwise. In this sense, consumer exploitability in quantities cannot be ruled out. We also find evidence for shaping effects: consumers’ preferences (...) are shaped by past experience with prices, and firms may in principle exploit this to sell more. (shrink)