The project of this Précis de philosophie de la logique et des mathématiques (vol. 1 under the direction of F. Poggiolesi and P. Wagner, vol. 2 under the direction of A. Arana and M. Panza) aims to offer a rich, systematic and clear introduction to the main contemporary debates in the philosophy of mathematics and logic. The two volumes bring together the contributions of thirty researchers (twelve for the philosophy of logic and eighteen for the philosophy of mathematics), specialists in (...) the history or philosophy of logic or mathematics. Each volume consists of ten chapters; each chapter is about forty pages, is independent from the others and deals with a particular philosophical question about logic or mathematics. The objective is to offer to the French-speaking reader a reference book. On many of the issues addressed, this Précis offers the first clear and thorough synthesis that is available in French. -/- This book is intended for third year / master's students, but also for teachers of philosophy in secondary or higher education, for logicians and mathematicians willing to take a philosophical look at the fundamental concepts of their discipline, and for any reader interested in the basic issues discussed in the philosophy of logic and mathematics. Each chapter is self-contained, although some basic training in logic (or in mathematics, as the case may be) is required. The book should be looked at as a comprehensive framework for contemporary discussions in the philosophy of logic and mathematics, while also giving some guidance on the disciplinary content required by these discussions. -/- The first three chapters of the present volume (on the philosophy of mathematics) are devoted to the history of the philosophy of mathematics: from antiquity to the modern era, and from this period to the foundational crisis of the nineteenth century, to the twentieth century. Next, four chapters deal with the crucial questions for the philosophy of mathematics of the twentieth century: the opposition and/or comparison of set theory and category theory as foundational frameworks for mathematics; mathematical constructivism; the analysis of calculability; and Benaceraff's problem. The two following chapters are focused on the philosophy of mathematical practice, by treating the notion of ideals of proof, in particular explanation and purity, and the notion of informal proof and the use of visual artifacts in mathematical argumentation. Finally the last chapter deals with the applicability of mathematics, including the role of probability. -/- In Chapter 1, Sébastien Maronne and David Rabouin present the history of the philosophy of mathematics from antiquity to the modern era. The goal is to show that the philosophy of mathematics has a history as ancient as mathematics and philosophy itself, a history largely continuous with the latter, often by staying out of sync with respect to the former. In Chapter 2, Sébastien Gandon discusses the question of the foundations of mathematics from Kant to the end of the nineteenth century. By tying this question to Kant, he is able to show that the discussion of the foundations of mathematics that occupied a large part of these two centuries has much older roots. Accent is placed on the differences between the framework proposed by Kant for making sense of classical mathematics and the use made by Frege and then Russell of logical tools for giving a different reading of arithmetic and real analysis. The link between between these different conceptions and the evolution of mathematics itself is also underlined. -/- Chapter 3, written by Hourya Benis-Sinaceur and Mirna Džamonja, deals with the evolution of mathematics in the twentieth century, notably the structuralist turn of Dedekind, E. Noether, and Bourbaki, and certain more recent developments. They devote themselves, among other things, to explaining how these developments can be understood as responses to and extensions of questions posed during the foundational debate of the immediately preceding era. -/- In Chapter 4, Jean-Pierre Marquis and Jean-Jacques Szczeciniarz discuss the different foundational options coming from set theory and category theory. They discuss, among other things, Lawvere's program to replace ZF with an axiomatization of the category of sets, the latter judged better adapted to the needs of contemporary mathematics. Different reactions, as much philosophical as technical, raised by this program are also taken into account. -/- Constructive mathematics are the object of Chapter 5, in which Gerhard Heinzmann and Mark van Atten examine in a critical and comparative manner a variety of constructivisms, including intuitionism, constructive type theory, predicativism, and finitism. -/- In Chapter 6, Guido Gherardi and Maël Pegny present computability theory, stressing its philosophical consequences. They discuss the basic concepts of this theory, for the computability of both the natural numbers and the real numbers. They then tackle the theory of computational complexity. -/- In Chapter 7, Andrea Sereni and Fabrice Pataut present Benacerraf's problem, opposing every possible account of mathematical knowledge to the availability of a theory of truth founded on an abstract ontology of mathematical objects. They give an overview of the original problem and its reformulation by Hartry Field, and reconstruct the debate that this problem has raised, by meeting at once the major opposing positions today of the analytic affiliation of the philosophy of mathematics, as much those on the platonist side as on that of nominalism. -/- In Chapter 8, Valeria Giardino and Yacin Hamami treat certain crucial aspects of the philosophy of mathematical practice. They deal in particular with the notion of an informal proof and on the role of artifacts in mathematical reasoning. They consider how such proofs, making use of these means, can contribute to the understanding of theorems and mathematical theories, thanks also to the role of visualisation and the aid of computer tools. -/- Why do mathematics often give several proofs of the same theorem? This is the question that Andrew Arana raises in Chapter 9, introducing the notion of an epistemic ideal and discuss two such ideals, the explanatoriness and purity of proof. -/- Chapter 10 is devoted to the applicability of mathematics in the study of empirical phenomena. After summarizing the history of this question, going back to Plato and Aristotle and passing by Mill and Kant, Daniele Molinini and Marco Panza reconstruct the contemporary debate, in relation, among other things, to questions raised in the philosophy of science. -/- Two appendices complete the volume. In the first Frédéric Patras treats the French tradition in philosophy of mathematics of the 20th century. In the second, Maria Carla Galavotti discusses the notion of probability and its use in science. (shrink)

This paper studies proof systems for the logics of super-strict implication ST2–ST5, which correspond to C.I. Lewis’ systems S2–S5 freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating STn in Sn and backsimulating Sn in STn, respectively(for n=2,...,5). Next, G3-style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive of G3-style calculi, that they are sound and complete, and (...) it is shown that the proof search for G3. ST2 is terminating and therefore the logic is decidable. (shrink)

This paper introduces the logics of super-strict implications, where a super-strict implication is a strengthening of C.I. Lewis' strict implication that avoids not only the paradoxes of material implication but also those of strict implication. The semantics of super-strict implications is obtained by strengthening the (normal) relational semantics for strict implication. We consider all logics of super-strict implications that are based on relational frames for modal logics in the modal cube. it is shown that all logics of super-strict implications are (...) connexive logics in that they validate Aristotle's Theses and (weak) Boethius's Theses. A proof-theoretic characterisation of logics of super-strict implications is given by means of G3-style labelled calculi, and it is proved that the structural rules of inference are admissible in these calculi. It is also shown that validity in the S5-based logic of super-strict implications is equivalent to validity in G. Priest's negation-as-cancellation-based logic. Hence, we also give a cut-free calculus for Priest's logic. (shrink)

This paper studies proof systems for the logics of super-strict implication \(\textsf{ST2}\) – \(\textsf{ST5}\), which correspond to C.I. Lewis’ systems \(\textsf{S2}\) – \(\textsf{S5}\) freed of paradoxes of strict implication. First, Hilbert-style axiomatic systems are introduced and shown to be sound and complete by simulating \(\textsf{STn}\) in \(\textsf{Sn}\) and backsimulating \(\textsf{Sn}\) in \(\textsf{STn}\), respectively (for \({\textsf{n}} =2, \ldots, 5\) ). Next, \(\textsf{G3}\) -style labelled sequent calculi are investigated. It is shown that these calculi have the good structural properties that are distinctive (...) of \(\textsf{G3}\) -style calculi, that they are sound and complete, and it is shown that the proof search for \(\mathsf {G3.ST2}\) is terminating and therefore the logic is decidable. (shrink)

The emerging field of responsible management (RM) studies the integration of sustainability, responsibility, and ethics in managerial practices. Therefore, turning to practice theories for the study of RM appears to hold great promise of conceptual and methodological contribution. We propose a posthumanist practice approach for studying RM-as-practice. Managerial practices are conceived as the agencement of heterogeneous elements (humans, nonhumans, more-than-humans, materials, and discourses) that achieve agency in their being interconnected. Thus, RM is understood as processual, relational, emergent, and sociomaterial. We (...) contribute a framework for the empirical study of RM-as-practice on the basis of three sensitizing concepts: situatedness, sociomateriality, and textures_._ We further discuss the implications of understanding responsibility as response-ability, an engaged practice for relating to the other and the RM researcher’s role as internal to the practice agencement under study, thus, opening the debate on our own response-ability. (shrink)

We determine the computational complexity of the Hahn-Banach Extension Theorem. To do so, we investigate some basic connections between reverse mathematics and computable analysis. In particular, we use Weak König's Lemma within the framework of computable analysis to classify incomputable functions of low complexity. By defining the multivalued function Sep and a natural notion of reducibility for multivalued functions, we obtain a computational counterpart of the subsystem of second-order arithmetic WKL0. We study analogies and differences between WKL0 and the class (...) of Sep-computable multivalued functions. Extending work of Brattka, we show that a natural multivalued function associated with the Hahn-Banach Extension Theorem is Sep-complete. (shrink)

What is mathematics about? And if it is about some sort of mathematical reality, how can we have access to it? This is the problem raised by Plato, which still today is the subject of lively philosophical disputes. This book traces the history of the problem, from its origins to its contemporary treatment. It discusses the answers given by Aristotle, Proclus and Kant, through Frege's and Russell's versions of logicism, Hilbert's formalism, Gödel's platonism, up to the the current debate on (...) Benacerraf's dilemma and the indispensability argument. Through the considerations of themes in the philosophy of language, ontology, and the philosophy of science, the book aims at offering an historically-informed introduction to the philosophy of mathematics, approached through the lenses of its most fundamental problem. (shrink)

We prove a generalization of Maehara’s lemma to show that the extensions of classical and intuitionistic first-order logic with a special type of geometric axioms, called singular geometric axioms, have Craig’s interpolation property. As a corollary, we obtain a direct proof of interpolation for (classical and intuitionistic) first-order logic with identity, as well as interpolation for several mathematical theories, including the theory of equivalence relations, (strict) partial and linear orders, and various intuitionistic order theories such as apartness and positive partial (...) and linear orders. (shrink)

The classification of medical interventions as either invasive or non-invasive is commonly regarded to be morally important. On the most commonly endorsed account of invasiveness, a medical intervention is invasive if and only if it involves either breaking the skin (‘incision’) or inserting an object into the body (‘insertion’). Building on recent discussions of the concept of invasiveness, we show that this standard account fails to capture three aspects of existing usage of the concept of invasiveness in relation to medical (...) interventions—namely, (1) usage implying that invasiveness comes in degrees, (2) that the invasiveness of an intervention can depend on the characteristics of the salient alternative interventions, and (3) that medical interventions can be invasive in non-physical ways. We then offer the beginnings of a revised account that, we argue, is able to capture a wider range of existing usage. Central to our account is a distinction between two properties: basic invasiveness and threshold invasiveness. We end by assessing what the standard account gets right, and what more needs to be done to complete our schematic account. (shrink)

AI-based technologies are increasingly pervasive in a number of contexts. Our affective and emotional life makes no exception. In this article, we analyze one way in which AI-based technologies can affect them. In particular, our investigation will focus on affective artificial agents, namely AI-powered software or robotic agents designed to interact with us in affectively salient ways. We build upon the existing literature on affective artifacts with the aim of providing an original analysis of affective artificial agents and their distinctive (...) features. We argue that, unlike comparatively low-tech affective artifacts, affective artificial agents display a specific form of agency, which prevents them from being perceived by their users as extensions of their selves. In addition to this, we claim that their functioning crucially depends on the simulation of human-like emotion-driven behavior and requires a distinctive form of transparency—we call it emotional transparency—that might give rise to ethical and normative tensions. (shrink)

We investigate Turing's contributions to computability theory for real numbers and real functions presented in [22, 24, 26]. In particular, it is shown how two fundamental approaches to computable analysis, the so-called ‘Type-2 Theory of Effectivity' (TTE) and the ‘realRAM machine' model, have their foundations in Turing's work, in spite of the two incompatible notions of computability they involve. It is also shown, by contrast, how the modern conceptual tools provided by these two paradigms allow a systematic interpretation of Turing's (...) pioneering work in the subject. (shrink)

I discuss Clark’s predictive processing/extended mind hybrid, diagnosing a problem: Clark’s hybrid suggests that, when we use them, we pay attention to mind-extending external resources. This clashes with a commonly accepted necessary condition of cognitive extension; namely, that mind-extending resources must be phenomenally transparent when used. I then propose a solution to this problem claiming that the phenomenal transparency condition should be rejected. To do so, I put forth a parity argument to the effect that phenomenal transparency cannot be a (...) necessary condition on cognitive extension: roughly, since internal cognitive resources can fail to be transparent when used, by parity, external resources can fail to be phenomenally transparent too. Further, I argue that phenomenal transparency is not even a reliable indicator of cognitive extension; hence its absence should not be considered a problem for Clark’s extended mind-predictive processing hybrid. Lastly, I consider and allay a number of worries my proposal might raise, and conclude the paper. (shrink)

In the last decades it has become clear that medicine must find some way to combine its scientific and humanistic sides. In other words, an adequate notion of medicine requires an integrative position that mediates between the analytic-reductionist and the normative-holistic tendencies we find therein. This is especially important as these different styles of reasoning separate “illness” (something perceived and managed by the whole individual in concert with their environment) and “disease” (a “mechanical failure” of a biological element within the (...) body). While the demand for an integrative view has typically been motivated by ethical concerns, we claim that it is also motivated, perhaps even more fundamentally, by epistemological and methodological reasons. Evidence-based bio-medicine employs experimental and statistical techniques which eliminate important differences in the ways that conscious humans evaluate, live with, and react to disease and illness. However, it is precisely these experiences that underpin the concepts and norms of bio-medicine. Humanistic disciplines, on the other hand, have the resources to investigate these experiences in an intersubjectively testable way. Medicine, therefore, cannot afford to ignore its nature as a human science; it must be concerned not only with disease and illness, but also with the ways in which patients as persons respond to malady. Insofar as attitudes and expectations influence the criteria of illness and disease, they must be studied as part of the genuine subject matter of medicine as a human science. In general, we urge that this is a necessary step to overcome today's trend to split evidence-based and clinical medicine. (shrink)

We prove that the opposite of the category of coalgebras for the Vietoris endofunctor on the category of compact Hausdorff spaces is monadic over $\mathsf {Set}$. We deliver an analogous result for the upper, lower, and convex Vietoris endofunctors acting on the category of stably compact spaces. We provide axiomatizations of the associated (infinitary) varieties. This can be seen as a version of Jónsson–Tarski duality for modal algebras beyond the zero-dimensional setting.

The paper presents and discusses the Hubble tension with respect to recent results in cosmology. I shall argue that the measurements from the James Webb Space Telescope and TRGB stars calibrations allow us to infer that the estimates of H0 with late universe methods are robust. Building on from robustness analysis, I conclude that the resolution of the tension cannot be expected to come from new systematics, but rather from new physics.

We investigated motor resonance in children using a priming paradigm. Participants were asked to judge the weight of an object shortly primed by a hand in an action-related posture or a non action-related one . The hand prime could belong to a child or to an adult. We found faster response times when the object was preceded by a grasp hand posture . More crucially, participants were faster when the prime was a child’s hand, suggesting that it could belong to (...) their body schema, particularly when the child’s hand was followed by a light object . A control experiment helped us to clarify the role of the hand prime. To our knowledge this is the first behavioral evidence of motor simulation and motor resonance in children. Implications of the results for the development of the sense of body ownership and for conceptual development are discussed. (shrink)

Munch-Jurisic’s book thoroughly describes several cases of severe distresses reported and expressed by perpetrators of tremendous acts such as mass murders. Arguing against a simplistic reading according to which these signs of distress are straightforward manifestations of some innate moral nature, and against the optimistic reading according to which they will lead to prosocial behaviors, Munch-Jursic offers compelling reasons to adopt a more complex theory of emotion. In this commentary, I aim to stress the implications of her book for the (...) debate on moral enhancement and for emotion theory in general. However, while I concur with Munch-Jurisic that emotion theory must make room for complexity and indeterminacy, I challenge her claim that motivational theories of emotion are ill-equipped to face the challenges she poses. (shrink)

(2013). Distributed intentionality: A model of intentional behavior in humans. Philosophical Psychology: Vol. 26, No. 2, pp. 267-290. doi: 10.1080/09515089.2011.641743.

We systematically study the completion of choice problems in the Weihrauch lattice. Choice problems play a pivotal rôle in Weihrauch complexity. For one, they can be used as landmarks that characterize important equivalences classes in the Weihrauch lattice. On the other hand, choice problems also characterize several natural classes of computable problems, such as finite mind change computable problems, non-deterministically computable problems, Las Vegas computable problems and effectively Borel measurable functions. The closure operator of completion generates the concept of total (...) Weihrauch reducibility, which is a variant of Weihrauch reducibility with total realizers. Logically speaking, the completion of a problem is a version of the problem that is independent of its premise. Hence, studying the completion of choice problems allows us to study simultaneously choice problems in the total Weihrauch lattice, as well as the question which choice problems can be made independent of their premises in the usual Weihrauch lattice. The outcome shows that many important choice problems that are related to compact spaces are complete, whereas choice problems for unbounded spaces or closed sets of positive measure are typically not complete. (shrink)

Many approaches to quantum gravity -the theory that should account for quantum and gravitational phenomena under the same theoretical umbrella- seem to point at some form of spacetime emergence, i.e., the fact that spacetime is not a fundamental entity of our physical world. This tenet has sparked many philosophical discussions: from the so-called empirical incoherence problem to different accounts of emergence and mechanisms thereof. In this contribution, I focus on the partial order relation of causal set theory and argue that (...) causation can be characterized as an a-temporal constraint over the kinematic space defined by the theory. The relation constrains the growth of a new element/event with respect to the other elements/events of a given set. Therefrom, the flow of time emerges from the collection of the possible growths of the given set, where each possibility is characterized by a classical probability assigned by the dynamics of the theory. (shrink)

Der profilierte Marx-Forscher Marco Iorio liefert eine kundige Einführung für jeden, der unvoreingenommen wissen will, was Karl Marx denn nun wirklich zu sagen hat. In dieser kritischen und konstruktiven Gesamtinterpretation kommen alle wichtigen Themen zur Sprache: von Geschichtsphilosophie und Gesellschaftstheorie über ökonomischer und politischer Theorie bis hin zu revolutionstheoretischen und moralphilosophischen Problemstellungen. Die berücksichtigte Sekundärliteratur deckt sämtliche aktuell relevanten Strömungen ab, darunter analytischer Marxismus, Postkolonialismus, Poststrukturalismus, Post- bzw. Neomarxismus. Damit eignet sich die Einführung auch hervorragend als Kursbuch für Lehrveranstaltungen (...) und als studienbegleitende Lektüre. (shrink)

The modern world was in part born as a reaction against Aristotelianism. However, the image of Aristotle to which modern philosophers reacted was partial, to say the least. Paradoxical though it may seem, today, more than twenty-three centuries on, we may now be in the most advantageous position for understanding the Stagirite's philosophy and applying it to contemporary problems. The present book contributes to the forming of an idea of Post-modern reason inspired by a constellation of Aristotelian concepts, such as (...) prudence (phronesis), practical truth (aletheia praktike), science in act (episteme en energeiai), metaphor (metaphora), similarity (homoiosis) and the imitation-creation pair (mimesis-poiesis). They all form an interconnected network and together they make up an idea of reason that may prove suitable for the present. These concepts offer the most promising basis for undertaking a series of urgent reconciliations: of facts and values, of means and ends, of theoretical and practical reason, of intelligence and emotion. Aristotle's notions could help solve many dualisms of modern times. He offers a third way between identity and difference in ontology and politics, between algorithm and anarchism in methodology, between naïve realism and plain relativism in epistemology, between equivocity and univocity in language, between Enlightenment and Romanticism in culture... On the way, this shift facilitates the relationships between science, arts and ethics - the three parts of the sphere of culture which Modernity had separated - as well as the integration of the sphere of culture itself with the world of life. (shrink)

Sartre maintains that “all consciousness is consciousness of something.” Idiosyncratically, he also understands this “intentionality principle” to entail that what consciousness is “of” is necessarily distinct from it (or “outside of” it, or “transcendent to” it). Nonetheless, he also maintains that all consciousness is necessarily conscious of—or rather, “(of)”—itself in a non‐intentional (in his terms: “non‐positional/non‐thetic”) manner. Given that this non‐positional/thetic self‐consciousness is not intentional, it is evidently immune to the “difference” principle, but this is less clear with respect to (...) self‐reflection (which Sartre simply calls “reflection”). It seems impossible for reflection to be “intentional” because intentionality entails difference—yet it also seems problematic to consider reflection “non‐intentional” because it then becomes difficult to distinguish reflection from non‐positional/thetic self‐consciousness as such (which is inherently “unreflective”). This can be called Sartre's “dilemma of reflection.” While Sartre seems to alternate between portraying reflection as intentional and as non‐intentional (it generally appears like the former), this paper argues that it should be conceived as both according to different respects. By piecing together various passages of Sartre's texts and drawing out their implications, Sartre can be shown to have the resources for an answer to his own dilemma. (shrink)

The focus of this paper is the incomputability of some topological functions using the tools of Borel computability theory, as introduced by V. Brattka in [3] and [4]. First, we analyze some basic topological functions on closed subsets of ℝn, like closure, border, intersection, and derivative, and we prove for such functions results of Σ02-completeness and Σ03-completeness in the effective Borel hierarchy. Then, following [13], we re-consider two well-known topological results: the lemmas of Urysohn and Urysohn-Tietze for generic metric spaces (...) . Both lemmas define Σ02-computable functions which in some cases are even Σ02-complete. (shrink)

The essay analyses utopia as a key concept to investigate modern politics. It argues that looking at the works of Machiavelli and More in order to retrace the utopia-realism nexus permits to develop a valuable analytical tool to interpret the outset of political modernity.

Nel suo pionieristico lavoro Conditions in Königsberg and the Making of Kant's Philosophy, Giorgio Tonelli lamentava l'assenza di un'indagine approfondita sul contesto intellettuale di Königsberg e sull'eventuale influenza che esso esercitò su alcuni aspetti del pensiero di Kant. Questo libro vuole colmare questa lacuna prestando particolare attenzione alla tradizione aristotelica, alla Schulphilosophie, e alla corrente dell'eclettismo, che dominarono l'ambiente regiomontano sino all'avvento della filosofia critica kantiana. Il lavoro mostra come dai fallimenti dei progetti logici e metafisici precritici, legati alle influenze (...) ricevute dall'ambiente di Königsberg, Kant abbia tratto le idee e gli spunti per la stesura della Kritik der reinen Vernunft. (shrink)

In this paper we study a new approach to classify mathematical theorems according to their computational content. Basically, we are asking the question which theorems can be continuously or computably transferred into each other? For this purpose theorems are considered via their realizers which are operations with certain input and output data. The technical tool to express continuous or computable relations between such operations is Weihrauch reducibility and the partially ordered degree structure induced by it. We have identified certain choice (...) principles such as co-finite choice, discrete choice, interval choice, compact choice and closed choice, which are cornerstones among Weihrauch degrees and it turns out that certain core theorems in analysis can be classified naturally in this structure. In particular, we study theorems such as the Intermediate Value Theorem, the Baire Category Theorem, the Banach Inverse Mapping Theorem, the Closed Graph Theorem and the Uniform Boundedness Theorem. We also explore how existing classifications of the Hahn—Banach Theorem and Weak Kőnig's Lemma fit into this picture. Well-known omniscience principles from constructive mathematics such as LPO and LLPO can also naturally be considered as Weihrauch degrees and they play an important role in our classification. Based on this we compare the results of our classification with existing classifications in constructive and reverse mathematics and we claim that in a certain sense our classification is finer and sheds some new light on the computational content of the respective theorems. Our classification scheme does not require any particular logical framework or axiomatic setting, but it can be carried out in the framework of classical mathematics using tools of topology, computability theory and computable analysis. We develop a number of separation techniques based on a new parallelization principle, on certain invariance properties of Weihrauch reducibility, on the Low Basis Theorem of Jockusch and Soare and based on the Baire Category Theorem. Finally, we present a number of metatheorems that allow to derive upper bounds for the classification of the Weihrauch degree of many theorems and we discuss the Brouwer Fixed Point Theorem as an example. (shrink)

This chapter focuses on one of the common fallacies in Western philosophy, 'legalistic mistake'. The use of “legal‐like” terms abounds outside the legal domain. But sometimes the users of these terms commit the fallacy Joel Feinberg called the legalistic mistake. On widening the use of such legal‐like terms, we must be cautious, for we might find ourselves guilty of making inferential mistakes or even proffering pure nonsense. The error, according to Feinberg, is committed by “one who, in stating a moral (...) question using a legal‐like term, uncritically imports the precision of that term in its strict legal sense, while excluding appeal to the kinds of criteria which alone can decide its use”. In “On Being 'Morally Speaking a Murderer’” Feinberg introduced the idea that, sometimes, using legal notions outside legal contexts may lead to a peculiar kind of fallacy he called the legalistic mistake. (shrink)

Dr. Marco Forgione (University of Milan), COSMOS team member, interviewed Prof. Peter Galison (Harvard University) in occasion of the event “Photographs from Outer Space”.

In this paper we study a reducibility that has been introduced by Klaus Weihrauch or, more precisely, a natural extension for multi-valued functions on represented spaces. We call the corresponding equivalence classes Weihrauch degrees and we show that the corresponding partial order induces a lower semi-lattice. It turns out that parallelization is a closure operator for this semi-lattice and that the parallelized Weihrauch degrees even form a lattice into which the Medvedev lattice and the Turing degrees can be embedded. The (...) importance of Weihrauch degrees is based on the fact that multi-valued functions on represented spaces can be considered as realizers of mathematical theorems in a very natural way and studying the Weihrauch reductions between theorems in this sense means to ask which theorems can be transformed continuously or computably into each other. As crucial corner points of this classification scheme the limited principle of omniscience LPO, the lesser limited principle of omniscience LLPO and their parallelizations are studied. It is proved that parallelized LLPO is equivalent to Weak Kőnig's Lemma and hence to the Hahn—Banach Theorem in this new and very strong sense. We call a multi-valued function weakly computable if it is reducible to the Weihrauch degree of parallelized LLPO and we present a new proof, based on a computational version of Kleene's ternary logic, that the class of weakly computable operations is closed under composition. Moreover, weakly computable operations on computable metric spaces are characterized as operations that admit upper semi-computable compact-valued selectors and it is proved that any single-valued weakly computable operation is already computable in the ordinary sense. (shrink)

This book fills a major gap in the ever-increasing secondary literature on Hannah Arendt's political thought by providing a dedicated and coherent treatment of the many, various and interesting things which Arendt had to say about law. Often obscured by more pressing or more controversial aspects of her work, Arendt nonetheless had interesting insights into Greek and Roman concepts of law, human rights, constitutional design, legislation, sovereignty, international tribunals, judicial review and much more. This book retrieves these aspects of her (...) legal philosophy for the attention of both Arendt scholars and lawyers alike. The book brings together lawyers as well as Arendt scholars drawn from a range of disciplines (philosophy, political science, international relations), who have engaged in an internal debate the dynamism of which is captured in print. Following the editors' introduction, the book is split into four Parts: Part I explores the concept of law in Arendt's thought; Part II explores legal aspects of Arendt's constitutional thought: first locating Arendt in the wider tradition of republican constitutionalism, before turning attention to the role of courts and the role of parliament in her constitutional design. In Part III Arendt's thought on international law is explored from a variety of perspectives, covering international institutions and international criminal law, as well as the theoretical foundations of international law. Part IV debates the foundations, content and meaning of Arendt's famous and influential claim that the 'right to have rights' is the one true human right. (shrink)

Emoticons and facial emojis are ubiquitous in contemporary digital communication, where it has been proposed that they make up for the lack of social information from real faces. In this paper, I construe them as cultural artifacts that exploit the neurocognitive mechanisms for face perception. Building on a step-by-step comparison of psychological evidence on the perception of faces vis-à-vis the perception of emoticons/emojis, I assess to what extent they do effectively vicariate real faces with respect to the following four domains: (...) (1) the expression of emotions, (2) the cultural norms for expressing emotions, (3) conveying non-affective social information, and (4) attention prioritization. (shrink)

In the substitutional framework, validity is truth under all substitutions of the nonlogical vocabulary. I develop a theory where □ is interpreted as substitutional validity. I show how to prove soundness and completeness for common modal calculi using this definition.

In this contribution, I explore the possibility of characterizing the emergence of time in causal set theory (CST) in terms of the growing block universe (GBU) metaphysics. I show that although GBU seems to be the most intuitive time metaphysics for CST, it leaves us with a number of interpretation problems, independently of which dynamics we choose to favor for the theory —here I shall consider the Classical Sequential Growth and the Covariant model. Discrete general covariance of the CSG dynamics (...) does not allow us to individuate a single history of the universe (defined by a causal history of different causal sets), thereby making the claim that ‘the past exists’ at best problematic. In addition, because the evolution of the universe in CSG dynamics leads to an outward branching causal tree, it becomes impossible to determine a proper ‘line of becoming’, thereby blurring the presentists’ claim that only the present exists. Similarly, the covariant approach runs into the same, if not even more severe problems, since each configuration of the universe would amount to a set of possible causal sets, thereby making the individuation of a single configuration of the universe —and thus the physical interpretation of the theory— implausible. (shrink)