This paper deals with the modal logics associated with (possibly nonstandard) provability predicates of Peano Arithmetic. One of our goals is to present some modal systems having the fixed point property and not extending the Gödel-Löb system GL. We prove that, for every has the explicit fixed point property. Our main result states that every complete modal logic L having the Craig's interpolation property and such that , where and are suitable modal formulas, has the explicit fixed point property.

Our purpose is to present some connections between modal incompleteness andmodal logics related to the Gödel-Löb logic GL. One of our goals is to prove that for all m, n, k, l ∈ ℕ the logic K + equation image□i □jp ↔ p) → equation image□ip is incomplete and does not have the fixed point property. As a consequence we shall obtain that the Boolos logic KH does not have the fixed point property.

We characterize (both from a syntactic and an algebraic point of view) the normal K4-logics for which unification is filtering. We also give a sufficient semantic criterion for existence of most general unifiers, covering natural extensions of K4.2⁺ (i.e., of the modal system obtained from K4 by adding to it, as a further axiom schemata, the modal translation of the weak excluded middle principle).

This paper deals with Kripke-style semantics for many-valued logics. We introduce various types of Kripke semantics, and we connect them with algebraic semantics. As for modal logics, we relate the axioms of logics extending MTL to properties of the Kripke frames in which they are valid. We show that in the propositional case most logics are complete but not strongly complete with respect to the corresponding class of complete Kripke frames, whereas in the predicate case there are important many-valued logics (...) like BL, Ł and Π, which are not even complete with respect to the class of all predicate Kripke frames in which they are valid. Thus although very natural, Kripke semantics seems to be slightly less powerful than algebraic semantics. (shrink)

This note contains a correct proof of the fact that the set of all first-order formulas which are valid in all predicate Kripke frames for Hájek's many-valued logic BL is not arithmetical. The result was claimed in [5], but the proof given there was incorrect.

This volume sets out to give a philosophical "applied" account of violence, engaged with both empirical and theoretical debates in other disciplines such as cognitive science, sociology, psychiatry, anthropology, political theory, ...

This paper wishes to problematize the foundations of production governance and offer an analytical perspective on the interrelation between agents’ preferences, strategic choice, and the public sphere . The value is in the idea of preferences being social in nature and in the application both to the internal stakeholders of the organisation and its impacts on people outside. Using the concept of ‘strategic failure’ we suggest that social preferences reflected in deliberative social praxis can reduce false beliefs and increase individual (...) wellbeing. From this approach, the paper offers a taxonomy of production organisations, based on social preferences about two variables: the governance form other strategic decisions that characterize the management of a company at a more operational level, once its fundamental legal form has been chosen. Each dimension is then categorised alongside two basic preferences: towards inclusion or exclusion of ‘publics’ that have no substantial access to decision power about these variables. Our framework explains governance heterogeneity by contrasting exclusive and inclusive social preferences in cooperatives, social enterprises, as well as traditional corporations. A discussion of the evolution of social preferences and organizational forms is addressed through examples and regional experiences. (shrink)

This book aims to develop the tradition of philosophical hermeneutics, the theoretical account of interpretive (as opposed to explanatory) understanding--the account of meanings and contexts rather than causes and predictions--usually restricted to the domain of literary and textual analysis, in new directions by exploiting its potential as an instrument of critique. It refutes commonly held claims that hermeneutic analyses are necessarily relativistic, Eurocentric, or critically impotent and demonstrates how hermeneutic procedures can inform analyses of urgent current and cross-cultural issues such (...) as the biology of race, female genital excision, and the so-called "culture of poverty" thesis. Lorenzo Simpson demonstrates that a robust methodology of philosophical hermeneutics is well positioned to intervene in critical political and social issues in global ethics and justice in concert with critical theory's emancipatory aims. (shrink)

Firstly, this contribution proposes to address synthographies – images generated through Text-to-image technologies – by deepening the epistemological shift related to the possibility of transposing the image-creation process from the analogue arts to the notational ones (or, by drawing on Nelson Goodman's terminology, from the “autographic” to the “allographic” forms of art). Secondly, the paper highlights how synthographies can be considered partly autographic and partly allographic, since the linguistic prompts constitute only the notational aspect of the generated images. Furthermore, this (...) contribution argues that the recent critiques around such images, which referenced aspects related to the absence of authorial presence and mechanicality, characterised the history of photography since its beginning. Finally, the contribution explores how the possibility to create synthographies that are almost indistinguishable from photographies easily might further separate the interaction between the detective and the depictive functions to the advantage of the latter, erasing what remains of the visual reliability and documental value of images. (shrink)

This is the first dedicated commentary to Sextus Empiricus’ treatise _Against the Arithmeticians_, dealing with crucial issues in the history of the sceptical, Platonic and Pythagorean traditions and in the ancient philosophy of mathematics.

The field of genetics has seen major advances in recent decades, particularly in research, prevention and diagnosis. One of the most recent developments, the genomic editing technique Clustered regularly interspaced short palindromic repeats (CRISPR)-Cas9, has opened the possibility for genetic therapies through genome modification. The technique marks an improvement on previous procedures but poses some serious ethical conflicts. Bioethics is the discipline geared at finding answers to ethical challenges posed by progress in medicine and biology and examining their repercussions for (...) society. It can also offer a conceptualization of these ethical dilemmas. The aim of this paper is to offer a map of the ethical dilemmas associated with this technique by way of a critical analysis of current literature. The main issues can be grouped in four areas: efficacy and security; the types of cells which can be targeted by the technique (somatic, embryonic and gametes); the goal of the therapy; and accessibility and justice. (shrink)

Equity in Early Modern Legal Scholarship takes the reader through the vast amount of legal writings on equity that were published in continental Europe in early modern times. The book offers the first comprehensive overview of the development of the legal concept of equity through the sixteenth and seventeenth century. During this time, equity scholarship broke with its medieval past and entered a lively debate on the nature and function of the concept. Lorenzo Maniscalco links these developments to the (...) early modern identification of equity with Aristotelian epieikeia, a conceptual shift that brought down the barrier that divided theological and legal writings on equity and led to its development as a tool for the interpretation and amendment of legal rules. (shrink)

Locked and unlocked strategies are at the center of this article, as ways of shedding new light on the cognitive aspects of deep learning machines. The character and the role of these cognitive strategies, which are occurring both in humans and in computational machines, is indeed strictly related to the generation of cognitive outputs, which range from weak to strong level of knowledge creativity. I maintain that these differences lead to important consequences when we analyze computational AI programs, such as (...) AlphaGo, which aim at performing various kinds of abductive hypothetical reasoning. In these cases, the programs are characterized by _locked_ abductive strategies: they deal with weak (even if sometimes amazing) kinds of hypothetical creative reasoning, because they are limited in what I call eco-cognitive openness, which instead qualifies human cognizers who are performing higher kinds of abductive creative reasoning, where cognitive strategies are instead _unlocked_. (shrink)

Lorenzo Girardi brings together themes of Europe, phenomenology and politics to reveal the relevance of Edmund Husserl and Jan Patočka’s works for contemporary political issues. Addressing the concept of crisis in Europe, this book presents an agonistic conception of liberal democracy based on Patočka’s phenomenological concept of problematicity.

Complementarity tells us we cannot know precisely the values of all the properties of a quantum object at the same time: the precise determination of one property implies that the value of some other (complementary) property is undefined. E.g. the precise knowledge of the position of a particle implies that its momentum is undefined. Here we show that a Schrödinger cat has a well defined value of a property that is complementary to its “being dead or alive” property. Then, thanks (...) to complementarity, it has an undefined value of the property “being dead or alive”. In other words, the cat paradox is explained through quantum complementarity: of its many complementary properties, any quantum system, such as a cat, can have a well defined value only of one at a time. Schrödinger’s cat has a definite value of a property which is complementary to “being dead or alive”, so it is neither dead nor alive. Figuratively one can say it is both dead and alive. While this interpretation only uses textbook concepts (the Copenhagen interpretation), apparently it has never explicitly appeared in the literature. We detail how to build an Arduino based simulation of Schrödinger’s experiment based on these concepts for science outreach events. (shrink)

Lorenzo Valla (1407–1457) ranks among the greatest scholars and thinkers of the Renaissance. He secured lasting fame for his brilliant critical skills, most famously in his exposure of the “Donation of Constantine,” the forged document upon which the papacy based claims to political power. Lesser known in the English-speaking world is Valla's work in the philosophy of language—the basis of his reputation as the greatest philosopher of the humanist movement. Dialectical Disputations, translated here for the first time into any (...) modern language, is his principal contribution to the philosophy of language and logic. With this savage attack on the scholastic tradition of Aristotelian logic, Valla aimed to supersede it with a new logic based on the actual historical usage of classical Latin and on a commonsense approach to semantics and argument. Valla provides a logic that could be used by lawyers, preachers, statesmen, and others who needed to succeed in public debate—one that was stylistically correct and rhetorically elegant, and thus could dispense with the technical language of the scholastics, a “tribe of Peripatetics, perverters of natural meanings.” Valla's reformed dialectic became a milestone in the development of humanist logic and contains startling anticipations of modern theories of semantics and language. Volume 1 contains Book I, in which Valla refutes Aristotle's logical works on the categories, transcendentals, and predicables, with excursions into natural and moral philosophy and theology. (shrink)

When the Canonical Ramsey’s Theorem by Erdős and Rado is applied to regressive functions, one obtains the Regressive Ramsey’s Theorem by Kanamori and McAloon. Taylor proved a “canonical” version of Hindman’s Theorem, analogous to the Canonical Ramsey’s Theorem. We introduce the restriction of Taylor’s Canonical Hindman’s Theorem to a subclass of the regressive functions, the $$\lambda $$ λ -regressive functions, relative to an adequate version of min-homogeneity and prove some results about the Reverse Mathematics of this Regressive Hindman’s Theorem and (...) of natural restrictions of it. In particular we prove that the first non-trivial restriction of the principle is equivalent to Arithmetical Comprehension. We furthermore prove that the well-ordering-preservation principle for base-$$\omega $$ ω exponentiation is reducible to this same principle by a uniform computable reduction. (shrink)

This paper attempts a reconstruction of reason’s contribution to empirical truth in connection with Kant’s definition of truth as the agreement of cognition with its object. I argue that Kant’s treatment of truth in the Transcendental Analytic gets completed in the Appendix to the Transcendental Dialectic with an often neglected but compelling argument (what I shall call the Variety Argument). This argument postulates such a variety in the appearances as to undermine any attempt at formulating empirical truths. Crucially, I argue (...) that this variety does not depict an extreme-case scenario, but our own epistemic situation without reason. Reason completes Kant’s theory of truth by allowing the understanding (i.) to form empirical concepts and (ii.) approximate to empirical truth. (shrink)

The distinction between philosophical and prophetic revelation, the separation between philosophy and theology, the theory of truth and certainty, and the passages of the KV dedicated to divine revelation all depend on signs. The Platonic etymology that combines sema and soma links the philosophical destiny of the sign to that of the body, providing the fundamental opening to the long history of dualism between body and soul. Spinoza stresses the importance of distinguishing between imagination and intellection. To think of Spinoza's (...) epistemology means to insert correctly the infinite bodies modified in infinite ways into the ontological and cosmological framework. Spinoza's definition of images lies in the physical essence of the mark. Spinoza's semiotics will then appear perhaps less anomalous than it could have seemed at a first sight, even if, for this reason, no less original. (shrink)

Philosophers have debated at length the epistemological status of scientific thought experiments. I contend that the literature on this topic still lacks a common conceptual framework, a lacuna that produces radical disagreement among the participants in this debate. To remedy this problem, I suggest focusing on the distinction between the internal and the external validity of an experiment, which is also crucial for thought experiments. I then develop an account of both kinds of validity in the context of thought experiments. (...) I show that we can naturally conceptualise internal validity in terms of games of make-believe. Then, I argue that external validity is best defined as accurate representation of a target system. Finally, I turn back to the current debate on thought experiments and show that my diarchic account provides a general framework that can be shared by the competing philosophical views, as well as a fruitful guide for their reconciliation. (shrink)

This article aims to justify the positive role in the empirical investigation of nature that Kant attributes to the idea of God in the Critique of Pure Reason. In particular, I propose to read the Transcendental Ideal section and the Appendix to the Transcendental Dialectic together to see whether they can reciprocally illuminate each other. I argue that it is only by looking at the transcendental deduction of the ideas of reason and the resulting analogical conception of God that a (...) fully legitimate positive use of the idea of God can be vindicated. (shrink)

In today's world, the corporate image of the largest companies is closely linked to their performance in the field of corporate social responsibility and the disclosure of information on that topic, specifically, on climate change. Since the Board of Directors is the body responsible for this process, the aim of this article is to show the role that companies' Boards of Directors play in the accountability process vis-à-vis stakeholders in relation to one specific aspect which has enormous significance in environmental (...) information: practices used to monitor greenhouse gas emissions. In order to achieve this, we shall verify certain business characteristics, in addition to the size and activity of the Board of Directors, and we shall take different dependence models into consideration. These models will include variables related to the level of independence and diversity of the Board of Directors, which interact with dummy variables representing the company's litigation risks regarding environmental behavior and the institutional macro-context of the organization's country of origin. The results make it clear that Boards of Directors are basically focused on the traditional responsibility of creating economic value, instead of dealing with today's broader business world concepts, which include social responsibility. This focus, therefore, does not favor the accountability process before other stakeholders, if this makes it more difficult to protect the interests of shareholders. (shrink)

Firstly, this contribution proposes to address synthographies – images generated through Text-to-image technologies – by deepening the epistemological shift related to the possibility of transposing the image-creation process from the analogue arts to the notational ones (or, by drawing on Nelson Goodman's terminology, from the “autographic” to the “allographic” forms of art). Secondly, the paper highlights how synthographies can be considered partly autographic and partly allographic, since the linguistic prompts constitute only the notational aspect of the generated images. Furthermore, this (...) contribution argues that the recent critiques around such images, which referenced aspects related to the absence of authorial presence and mechanicality, characterised the history of photography since its beginning. Finally, the contribution explores how the possibility to create synthographies that are almost indistinguishable from photographies easily might further separate the interaction between the detective and the depictive functions to the advantage of the latter, erasing what remains of the visual reliability and documental value of images. (shrink)

Es un estudio en profundidad de la teología filosófica desarrollada en el ámbito de la filosofía analítica, en la cual se ha sometido a examen el concepto mismo de Dios, con vistas a probar si era lógicamente defendible; de no serlo, tendríase una prueba de la inexistencia de Dios. El autor acude a una lógica no clásica (contradictorial y gradualista) para articular el concepto de Dios de manera que, a pesar de tales contradicciones, es lógicamente defendible.

Illustrating the knowledge and ideas of thinkers such as Mandeville, Hume, Montesquieu and Smith, this book fully investigates the entire panorama of social sciences as well as providing a clear and concise analysis of the history of the social sciences from the point at which evolutionary theory entered the field. Examining the history of culture and humanity, Lorenzo Infantino discusses the 'discovery of society, ' when people stopped seeing behind every social phenomenon the direct action of human and/or divine (...) will, and how the subsequent void was filled by the unintended creation of language, habits, customs, laws and public power. Focussing on the idea that the object of social sciences should be the study of unintended consequences, Infantino also expertly reviews the approach of 'methodological individualism'. Forward-thinking, the book highlights the need for a rule of law in cultural evolution to prevent harm to others and allow a greater freedom of choice when deciding future actions. Providing an in-depth explanation of why the social sciences are needed and highlighting the task of a social scientist, this book will be invaluable for researchers in the fields of politics, economics and sociology. (shrink)

A philosophical examination of the treatment of logic and God in Lacan's later psychoanalytic theory. In The Not-Two, Lorenzo Chiesa examines the treatment of logic and God in Lacan's later work. Chiesa draws for the most part from Lacan's Seminars of the early 1970s, as they revolve around the axiom “There is no sexual relationship.” Chiesa provides both a close reading of Lacan's effort to formalize sexual difference as incompleteness and an assessment of its broader implications for philosophical realism (...) and materialism. Chiesa argues that “There is no sexual relationship” is for Lacan empirically and historically circumscribed by psychoanalysis, yet self-evident in our everyday lives. Lacan believed that we have sex because we love, and that love is a desire to be One in face of the absence of the sexual relationship. Love presupposes a real “not-two.” The not-two condenses the idea that our love and sex lives are dictated by the impossibility of fusing man's contradictory being with the heteros of woman as a fundamentally uncountable Other. Sexual liaisons are sustained by a transcendental logic, the so-called phallic function that attempts to overcome this impossibility. Chiesa also focuses on Lacan's critical dialogue with modern science and formal logic, as well as his dismantling of sexuality as considered by mainstream biological discourse. Developing a new logic of sexuation based on incompleteness requires the relinquishing of any alleged logos of life and any teleological evolution. For Lacan, the truth of incompleteness as approached psychoanalytically through sexuality would allow us to go further in debunking traditional onto-theology and replace it with a “para-ontology” yet to be developed. Given the truth of incompleteness, Chiesa asks, can we think such a truth in itself without turning incompleteness into another truth about truth, that is, into yet another figure of God as absolute being? (shrink)

In this paper, I offer a systematic account of Kant’s view on ‘phenomenal substance’. Several studies have recently analyzed Kant’s notion of substance. However, I submit that more needs to be said about how this notion is reconceptualized within the critical framework to vindicate a genuine and legitimate sense of substance in the phenomenal realm. More specifically, I show that Kant’s transcendental idealism does not commit him to a rejection of substantiality in phenomena. Rather, Kant isolates a general notion of (...) substance (as ultimate subject) and argues that (i) the relationality of phenomena is compatible with this notion; and that (ii) matter and all its parts are the ultimate subjects of everything existing in space (as what is independently movable in space). I suggest that vindicating a genuine and legitimate notion of phenomenal substance has far-ranging consequences for the interpretation of Kant’s empirical realism. (shrink)

Dispositionalism, perhaps the most popular variant of non-Humean metaphysics, submits that dispositions, powers, or capacities, are part of the furniture of the world. In this book I advance an original approach to dispositionalism revolving around the notion of Dispositional Reality; the novelty lies in the fact that the account, unlike most alternatives on the market, does not require the reification of objects, facts, properties, nor their dispositional essences – and is in fact compatible with a far more deflationary approach to (...) dispositions, while still being true to the non-Humean spirit of the proposal. This power metaphysics without powers allows one to dispel several puzzles in recent literature, or recast them under a new light. Albeit with its own peculiarities, this proposal constitutes a variant of explanatory dispositionalism, according to which realism about dispositions ought not to be understood as an ontological inflation, but as an explanatory inversion within the nomic and modal family. Some of these explanations are hereby attempted, and a study of various types of non-causal explanation will be provided. (shrink)

This book is an attempt to save "the sexual" from the oblivion to which certain strands in queer theory tend to condemn it, and at the same time to limit the risks of anti-politics and solipsism contained in what has been termed antisocial queer theory. It takes a journey from Sigmund Freud to Mario Mieli and Guy Hocquenghem, from Michel Foucault and Judith Butler to Teresa de Lauretis, Leo Bersani, Lee Edelman, and Tim Dean, and from all of these thinkers (...) back to Immanuel Kant and Thomas Hobbes. At the end, through readings of Bruce LaBruce's movies on gay zombies, the elitism of antisocial queer theory is brought into contact with popular culture. The living dead come to represent a dispossessed form of subjectivity, whose monstrous drives are counterposed to predatory desires of liberal individuals. The reader is thus lead into the interstitial spaces of the Queer Apocalypses, where the past and the future collapse onto the present, and sexual minorities resurrect to the chance of a non-heroic political agency. (shrink)