In the last century, Bertrand Russell famously held that pure mathematics is part of pure logic-a theory known as "logicism". The present work is a study of Russell's logicism considered in its historical development, in its philosophical context, in relation to criticism and in comparison with other, contemporary and later, foundational theories of classical mathematics. [Volume 1 of 2.].

Bertrand Russell's contributions to last century's philosophy and, in particular, to the philosophy of mathematics cannot be overestimated.Russell, besides being, with Frege and G.E. Moore, one of the founding fathers of analytical philosophy, played a major rôle in the development of logicism, one of the oldest and most resilient1 programmes in the foundations of mathematics.Among his many achievements, we need to mention the discovery of the paradox that bears his name and the identification of its logical nature; the generalization to (...) the whole of mathematics of Frege's idea that it is not possible to draw a demarcation line between logic and arithmetic; the programme, carried out with Whitehead, of derivation of mathematics from the logical system of Principia Mathematica ; and the ramified theory of types, devised by Russell to protect the system of PM from the known paradoxes.Although there is an ample literature on these topics, it is quite important to reconsider Russell's contributions to the foundations of mathematics at a time when, as a consequence of the crisis of the classical programmes in the foundations of mathematics, new trends are beginning to develop within the philosophy of mathematics. These are trends which move in a very different direction from that of logicism, intuitionism, and Hilbert's programme.To see this we need to consider that, in spite of profound disagreements on the nature of mathematical activity, on the relationship existing between logic and mathematics, on the causes of and therapies for the paradoxes, etc., logicism, intuitionism, and Hilbert's programme share an important metaphor: the idea that mathematics is an edifice built on unshakable foundations,2 an edifice which makes possible only a cumulative growth of mathematical knowledge.Such a metaphor—which, together with more specific theses belonging to these schools of thought, remained unsupported …. (shrink)

Transhumanism and Gnosis: A Parallelism The aim of this paper is to draw a parallel between the phenomenon of gnosis and transhumanism together with its ultimate version, posthumanism. After some methodological clarifications, the paper focuses on four confrontational axes: self-recognition, cosmic and anthropological dualism, the meaning of morality, death and suffering, and finally the promise of salvation. Finally, the two doctrines are framed within the context of the Gnostic revolution, emphasizing the sense of uprootedness and post-modernity to explain the resurgence (...) of these phenomena. (shrink)

Dispositionalism is the theory of modality according to which all (metaphysical and natural) modal truths are made true by some actual irreducibly dispositional property. The relationship between Dispositionalism and time is yet to be satisfactorily explored. In this paper we contribute to this task by examining how Dispositionalism deals with ‘dated truths’: propositions involving a specific time, e.g. “It might rain at 12.30”. We examine two possible accounts: the first, 'Dated Manifestations Strategy', is the idea that powers are very fine-grained, (...) and tend towards temporally very specific manifestations. We argue that such strategy should not be adopted, for it leads to unnecessary violations of ontological parsimony; it is unable to accommodate an ontology of platonic universals; and it is incapable of offering a principled explanation of the forward-looking nature of powers. We offer an alternative account, the "Duration Strategy", which relies on an independently determined arrow of time and the existence of some “duration facts” that specify how long a power takes to bring about its manifestation. We argue that the Duration Strategy is to be preferred. We then flesh out the account by exploring the connection between powers, duration facts, and processes. (shrink)

The five-volume set Kant and Philosophy in a Cosmopolitan Sense contains the proceedings of the Eleventh International Kant Congress, which took place in Pisa in 2010. The proceedings consist of 25 plenary talks and 341 papers selected by a team of international referees from over 700 submissions. The contributions span 14 sections: Kant’s Concept of Philosophy; Theory of Cognition and Logic; Ontology and Metaphysics; Ethics; Law and Justice; Religion and Theology; Aesthetics; Anthropology and Psychology; Politics and History; Science, Mathematics, and (...) the Philosophy of Nature; Kant and the Leibnizian Tradition; Kant and the Philosophical Tradition; Kant and Schopenhauer; and Kant’s Heritage. Thanks to cooperation from the Schopenhauer Gesellschaft, the 2010 conference was the first in the history of the International Kant Congress to include a session on Kant and Schopenhauer. -/- . (shrink)

Paraconsistent Weak Kleene logic is the 3-valued logic with two designated values defined through the weak Kleene tables. This paper is a first attempt to investigate PWK within the perspective and methods of abstract algebraic logic. We give a Hilbert-style system for PWK and prove a normal form theorem. We examine some algebraic structures for PWK, called involutive bisemilattices, showing that they are distributive as bisemilattices and that they form a variety, \, generated by the 3-element algebra WK; we also (...) prove that every involutive bisemilattice is representable as the Płonka sum over a direct system of Boolean algebras. We then study PWK from the viewpoint of AAL. We show that \ is not the equivalent algebraic semantics of any algebraisable logic and that PWK is neither protoalgebraic nor selfextensional, not assertional, but it is truth-equational. We fully characterise the deductive filters of PWK on members of \ and the reduced matrix models of PWK. Finally, we investigate PWK with the methods of second-order AAL—we describe the class \ of PWK-algebras, algebra reducts of basic full generalised matrix models of PWK, showing that they coincide with the quasivariety generated by WK—which differs from \—and explicitly providing a quasiequational basis for it. (shrink)

Die vorliegende Arbeit zielt darauf ab, Momente der Husserlschen Phänomenologie hervorzuheben, in denen diese an ihre Grenzen stößt. Der Ausweis dieser Grenzphänomene, die in der Husserl-Literatur bisher noch nicht systematisch untersucht worden sind, steht im Zentrum der Arbeit. Der Autor hat sich systematisch mit phänomenologisch orientierten Autoren zeitgenössischer Philosophie auseinandergesetzt u. a. mit der Absicht, die Fruchtbarkeit der Husserlschen Analysen für die zeitgenössische Philosophie hervorzuheben.

Nicola Guarino is widely recognized as one of the founders of applied ontology. His deep interest in the subtlest details of theoretical analysis and his vision of ontology as the Rosetta Stone for semantic interoperability guided the development and understanding of this domain. His motivations in research stem from the conviction that all science must be for the benefit of society at large, and his motto has always been that ontologies are not just for making information systems interoperable, but – (...) more importantly – for ensuring that systems’ users understand each other. He was among the first to recognize that applied ontology must be an interdisciplinary enterprise if it is to capture the intended meaning of the terms used by an information system. (shrink)

This paper focuses on the relationship between Kant and the traditional view of dignity. I argue that some amendments to Sensen’s description of the traditional paradigm enable us to see more clearly both where Kant adheres to the latter and where his view is original. First, a consideration of Pufendorf’s use of dignity suggests (1) that, contrary to Sensen’s reconstruction, the traditional paradigm does not entail a connection between dignity and duties to oneself, and (2) that Pufendorf’s understanding of dignity (...) as a kind of esteem, as opposed to price, provides a crucial mediation between the traditional view and Kant’s view. Finally, I argue that the traditional understanding of dignity also includes a subordinate justificatory element that helps to explain Kant’s use of dignity in the Doctrine of Virtue. (shrink)

This book explores what it means to exist in virtual worlds. Chiefly drawing on the philosophical traditions of existentialism, it articulates the idea that — by means of our technical equipment and coordinated practices — human beings disclose contexts or worlds in which they can perceive, feel, act, and think. More specifically, this book discusses how virtual worlds allow human beings to take new perspectives on their values and beliefs, and explore previously unexperienced ways of being. Virtual Existentialism will be (...) useful for scholars working in the fields of philosophy, anthropology, media studies, and digital game studies. (shrink)

My chapter deals with an important part of how Wolff pursued the normative ambitions of his ethics in giving practical guidance with regard to specific moral issues. I first consider how Wolff’s ethics tackles the duties to others, which traditionally represent a difficult issue for moral perfectionism. In this regard, I argue that Wolff’s strategy combines two aspects: (a) he includes in perfection non-active aspects and (b) operates with an agent-neutral notion of perfection, in spite of important passages that might (...) suggest differently. I then focus on Wolff’s treatment of the duties concerning veracity and lying, and show how it follows that general strategy. Combining its two aspects, Wolff examines specific moral issues by adopting a non-welfarist notion of benefit and harm as the standard that can give guidance about practical cases. (shrink)

dolce, the first top-level ontology to be axiomatized, has remained stable for twenty years and today is broadly used in a variety of domains. dolce is inspired by cognitive and linguistic considerations and aims to model a commonsense view of reality, like the one human beings exploit in everyday life in areas as diverse as socio-technical systems, manufacturing, financial transactions and cultural heritage. dolce clearly lists the ontological choices it is based upon, relies on philosophical principles, is richly formalized, and (...) is built according to well-established ontological methodologies, e.g. OntoClean. Because of these features, it has inspired most of the existing top-level ontologies and has been used to develop or improve standards and public domain resources. Being a foundational ontology, dolce is not directly concerned with domain knowledge. Its purpose is to provide the general categories and relations needed to give a coherent view of reality, to integrate domain knowledge, and to mediate across domains. In these 20 years dolce has shown that applied ontologies can be stable and that interoperability across reference and domain ontologies is a reality. This paper briefly introduces the ontology and shows how to use it on a few modeling cases. (shrink)

This study explores the downsizing propensity of family and non-family firms by considering their territorial embeddedness during both periods of economic stability and financial crisis. By drawing on a panel dataset of Spanish manufacturing firms for the period 2002–2015, we show that, all things being equal, family firms have a lower propensity to downsizing than non-family firms. When considering the effect of territorial embeddedness, we found that territorially embedded family firms have an even lower propensity to downsizing than their non-family (...) counterparts. Furthermore, the concern of territorially embedded family firms for their employees’ welfare was particularly pronounced during the years of the global financial crisis. This result is explained by the existence of socially proximate relationships with the firms’ immediate surroundings, based on similarity and a sense of belonging, which push deeply rooted family firms to treat their employees as salient stakeholders during hard times. Overall, our study stresses the importance of local roots in moderating the relationship between family firms and downsizing. (shrink)

The idea of autonomy, presented as Kant’s main achievement in the Groundwork and the second Critique, is hardly present in the ethics of the “Doctrine of Virtue”. Against Pauline Kleingeld’s recent interpretation, I argue that this does not amount to a disappearance of the Principle of Autonomy, but to an important development of the notion of autonomy. I first show that Kant still advocated the Principle of Autonomy in the 1790s along with the thought of lawgiving through one’s maxims. I (...) then argue that the role of autonomy in Kant’s later ethics has a different focus than in the previous works, which requires to connect autonomy with autocracy. Conversely, in the “Doctrine of Virtue”, autocracy, which Kant had employed before as an independent notion, is construed as a new layer of autonomy. What Kant there calls subjective autonomy is thereby considered as reason’s self-government in the maxims of each rational agent. -/- . (shrink)

There is a tension between Dispositionalism––the view that all metaphysical modality is grounded in actual irreducible dispositional properties––and the possibility of time travel. This is due to the fact that Dispositionalism makes it much harder to solve a potentiality-based version of the grandfather paradox. We first present a potentiality-based version of the grandfather paradox, stating that the following theses are inconsistent: 1) time travel is possible, 2) powers fully ground modality, 3) self-defeating actions are impossible, 4) time-travellers retain their intrinsic (...) powers upon time-travelling, and 5) time-travellers are ordinary agents with basic intrinsic potentialities. We then consider a number of potential solutions, and find them wanting. We argue that the metaphysical impossibility of performing a self-defeating action acts as a necessary perfect mask––while time-travel lets us “slip” the potentiality under the mask, thus generating the contradiction. We conclude considering what are the options for the dispositionalist. (shrink)

A disaster is an occurrence disrupting a community’s normal functioning and existence. The disruption may render it impossible to comply with principles and to respect, protect, and fulfill rights as it happens in ordinary times; it may induce an overwhelming shortage of resources and make tragic decisions unavoidable. From its very beginning, the COVID-19 pandemic evoked the scenario of disaster medicine, where triage is likely to imply not simply postponing a treatment but letting someone die. However, it is not only (...) the health care system that faces disruption risks. Lockdown measures and other restrictions were imposed to curb the pandemic, impinging upon individual freedom as well as economic activities. The proposal of mandatory vaccination implied a suspension of the principle of autonomy, which is a fundamental pillar of modern medicine. Out of the ordinary balancing efforts may be required, and two questions arise. Do such exceptional circumstances suggest reconsidering the criteria to apply, especially when essential, life-saving treatments are at stake? Who should decide? Science offers the premises to build on, but the last word does not belong to science. It remains the province of ethics and politics. (shrink)

We extend de Finetti’s No-Dutch-Book Criterion to Gödel infinite-valued propositional logic.

In the past few years, a wave of protest has spread across the world. The particularity of these uprisings lies in the way the Internet is used to support them. Scholars have analyzed these movements as being closely related to a generation that relies on the Internet as a means of organizing themselves as a force of social change. That is, the Internet is seen as a way of promoting the active participation of young people in political issues. Public opinion (...) and the mass media hail the Arab Spring revolutions as movements beneficial to the democratization of oppressive regimes. By contrast, when disobedient movements emerge in democratic countries, they are generally more cautious in evaluating these movements as enriching democracy. This cautious opinion also concerns the use of social media. In this article, the so-called Twitter revolutions are discussed in light of the theories of social psychology that analyze the relationship between disobedience and democracy. (shrink)

Autonomy is one of the central concepts of contemporary moral thought, and Kant is often credited with being the inventor of individual moral autonomy. But how and why did Kant develop this notion? The Emergence of Autonomy in Kant's Moral Philosophy is the first essay collection exclusively devoted to this topic. It traces the emergence of autonomy from Kant's earliest writings to the changes that he made to the concept in his mature works. The essays offer a close historical and (...) philosophical analysis of what prompted Kant to develop his conception of autonomy, charting the historical background which prompted his search, and thoroughly analysing different stages of his writings in order to see which element of autonomy was introduced at which point. The resulting volume will be of interest to both scholars and students of Kantian moral philosophy, as well as to anyone interested in the subject of autonomy. (shrink)

Recently, it has been argued that the use of Big Data transforms the sciences, making data-driven research possible and studying causality redundant. In this paper, I focus on the claim on causal knowledge by examining the Big Data project EXPOsOMICS, whose research is funded by the European Commission and considered capable of improving our understanding of the relation between exposure and disease. While EXPOsOMICS may seem the perfect exemplification of the data-driven view, I show how causal knowledge is necessary for (...) the project, both as a source for handling complexity and as an output for meeting the project’s goals. Consequently, I argue that data-driven claims about causality are fundamentally flawed and causal knowledge should be considered a necessary aspect of Big Data science. In addition, I present the consequences of this result on other data-driven claims, concerning the role of theoretical considerations. I argue that the importance of causal knowledge and other kinds of theoretical engagement in EXPOsOMICS undermine theory-free accounts and suggest alternative ways of framing science based on Big Data. (shrink)

For each integer n≥0, we provide an explicit functional characterization of the free n-generated BL-algebra, together with an explicit construction of the corresponding normal forms.

Cognitive reflection is recognized as an important skill, which is necessary for making advantageous decisions. Even though gender differences in the Cognitive Reflection test appear to be robust across multiple studies, little research has examined the source of the gender gap in performance. In Study 1, we tested the invariance of the scale across genders. In Study 2, we investigated the role of math anxiety, mathematical reasoning, and gender in CRT performance. The results attested the measurement equivalence of the Cognitive (...) Reflection Test – Long, when administered to male and female students. Additionally, the results of the mediation analysis showed an indirect effect of gender on CRT-L performance through mathematical reasoning and math anxiety. The direct effect of gender was no longer statistically significant after accounting for the other variables. The current findings suggest that cognitive reflection is affected by numerical skills and related feelings. (shrink)