A simple complete axiomatic system is presented for the many-valued propositional logic based on the conjunction interpreted as product, the coresponding implication (Goguen's implication) and the corresponding negation (Gödel's negation). Algebraic proof methods are used. The meaning for fuzzy logic (in the narrow sense) is shortly discussed.

Residuated fuzzy logic calculi are related to continuous t-norms, which are used as truth functions for conjunction, and their residua as truth functions for implication. In these logics, a negation is also definable from the implication and the truth constant $\overline{0}$ , namely $\neg \varphi$ is $\varphi \to \overline{0}$. However, this negation behaves quite differently depending on the t-norm. For a nilpotent t-norm (a t-norm which is isomorphic to Łukasiewicz t-norm), it turns out that $\neg$ is an involutive negation. However, (...) for t-norms without non-trivial zero divisors, $\neg$ is Gödel negation. In this paper we investigate the residuated fuzzy logics arising from continuous t-norms without non-trivial zero divisors and extended with an involutive negation. (shrink)

The works of the early Greek philosophers are not only a fundamental source for understanding archaic Greek culture and the whole of ancient philosophy, but also a perennially fresh resource that has stimulated Western thought until the present day. This nine-volume edition presents all the major fragments from the sixth to the fourth centuries BC.

The monoidal t-norm based logic MTL is obtained from Hájek''s Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...) (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

The monoidal t-norm based logic MTL is obtained from Hájek's Basic Fuzzy logic BL by dropping the divisibility condition for the strong (or monoidal) conjunction. Recently, Jenei and Montgana have shown MTL to be standard complete, i.e. complete with respect to the class of residuated lattices in the real unit interval [0,1] defined by left-continuous t-norms and their residua. Its corresponding algebraic semantics is given by pre-linear residuated lattices. In this paper we address the issue of standard and rational completeness (...) (rational completeness meaning completeness with respect to a class of algebras in the rational unit interval [0,1]) of some important axiomatic extensions of MTL corresponding to well-known parallel extensions of BL. Moreover, we investigate varieties of MTL algebras whose linearly ordered countable algebras embed into algebras whose lattice reduct is the real and/or the rational interval [0,1]. These embedding properties are used to investigate finite strong standard and/or rational completeness of the corresponding logics. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

This paper aims at being a systematic investigation of different completeness properties of first-order predicate logics with truth-constants based on a large class of left-continuous t-norms . We consider standard semantics over the real unit interval but also we explore alternative semantics based on the rational unit interval and on finite chains. We prove that expansions with truth-constants are conservative and we study their real, rational and finite chain completeness properties. Particularly interesting is the case of considering canonical real and (...) rational semantics provided by the algebras where the truth-constants are interpreted as the numbers they actually name. Finally, we study completeness properties restricted to evaluated formulae of the kind , where φ has no additional truth-constants. (shrink)

In this paper we show that the subvarieties of BL, the variety of BL-algebras, generated by single BL-chains on [0, 1], determined by continous t-norms, are finitely axiomatizable. An algorithm to check the subsethood relation between these subvarieties is provided, as well as another procedure to effectively find the equations of each subvariety. From a logical point of view, the latter corresponds to find the axiomatization of every residuated many-valued calculus defined by a continuous t-norm and its residuum. Actually, the (...) paper proves the results for a more general class than t-norm BL-chains, the so-called regular BL-chains. (shrink)

Current work in language models (LMs) helps us speed up or even skip thinking by accelerating and automating cognitive work. But can LMs help us with critical thinking -- thinking in deeper, more reflective ways which challenge assumptions, clarify ideas, and engineer new concepts? We treat philosophy as a case study in critical thinking, and interview 21 professional philosophers about how they engage in critical thinking and on their experiences with LMs. We find that philosophers do not find LMs to (...) be useful because they lack a sense of selfhood (memory, beliefs, consistency) and initiative (curiosity, proactivity). We propose the selfhood-initiative model for critical thinking tools to characterize this gap. Using the model, we formulate three roles LMs could play as critical thinking tools: the Interlocutor, the Monitor, and the Respondent. We hope that our work inspires LM researchers to further develop LMs as critical thinking tools and philosophers and other 'critical thinkers' to imagine intellectually substantive uses of LMs. (shrink)

In this paper we prove strong completeness of axiomatic extensions of first-order strict core fuzzy logics with the so-called quasi-witnessed axioms with respect to quasi-witnessed models. As a consequence we obtain strong completeness of Product Predicate Logic with respect to quasi-witnessed models, already proven by M.C. Laskowski and S. Malekpour in [19]. Finally we study similar problems for expansions with Δ, define Δ-quasi-witnessed axioms and prove that any axiomatic extension of a first-order strict core fuzzy logic, expanded with Δ, and (...) Δ-quasi-witnessed axioms are complete with respect to Δ-quasi-witnessed models. (shrink)

Distributive bounded lattices with a dual homomorphism as unary operation, called Ockham algebras, were firstly studied by Berman (1977). The varieties of Boolean algebras, De Morgan algebras, Kleene algebras and Stone algebras are some of the well known subvarieties of Ockham algebra. In this paper, new results about the congruence lattice of Ockham algebras are given. From these results and Urquhart's representation theorem for Ockham algebras a complete characterization of the subdirectly irreducible Ockham algebras is obtained. These results are particularized (...) for a large number of subvarieties of Ockham algebras. For these subvarieties a full description of their subdirectly irreducible algebras is given as well. (shrink)

IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular, IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order to give an algebraic interpretation (...) to this construction, we generalize the concepts of perfect, bipartite and local algebra used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational axiomatizations for it. (shrink)

This collection of five articles and two interviews, compiled by the author himself as a kind of political testament, focuses on the ecological thinking he pioneered in Europe.

I defend the view that circular definitions can be useful and illuminating by focusing on the fitting-attitudes analysis of value. This definition states that an item has value if and only if it is a fitting target of attitudes. Good items are the fitting targets of positive attitudes, and bad items are the fitting targets of negative ones. I shall argue that a circular version of this definition, defended by Rabinowicz and Rønnow-Rasmussen (2006), is preferable to its non-circular counterpart and (...) upholds reasonable standards of acceptability. The standards I will be discussing come from Humberstone (1997), who claims that definitions cannot be informative as long as they are inferentially circular. (shrink)

The study of perfect, local and bipartite IMTL-algebras presented in [29] is generalized in this paper to the general non-involutive case, i.e. to MTL-algebras. To this end we describe the radical of MTL-algebras and characterize perfect MTL-algebras as those for which the quotient by the radical is isomorphic to the two-element Boolean algebra, and a special class of bipartite MTL-algebras,.

Lo psíquico, que no la psicología como ciencia, es un tema poco tratado en la filosofía de Polo. En este escrito se busca dar explicación de qué es lo psíquico y cuál es su importancia. Se defiende que lo psíquico tiene dos condiciones reduccionistas implícitas que se constituyen a partir de la crisis de la filosofía de Hegel. La primera es creer que la realidad es reductible a la percepción individual. La segunda consiste en que el pensamiento ya esté determinado (...) preconceptualmente. (shrink)

It is held by many philosophers that it is a consequence of epistemic contextualism that speakers are typically semantically blind, that is, typically unaware of the propositions semantically expressed by knowledge attributions. In his ?Contextualism, Invariantism and Semantic Blindness? (this journal, 2009), Martin Montminy argues that semantic blindness is widespread in language, and not restricted to knowledge attributions, so it should not be considered problematic. I will argue that Montminy might be right about this, but that contextualists still face a (...) serious and related problem: that it is a consequence of epistemic contextualism that subjects are typically unaware of contents conveyed by knowledge attributions, independently of whether these are semantic or non-semantic contents. Even if semantic blindness is widespread in language, it does not seem that content unawareness of this sort is. (shrink)

In a recent paper, Erasmus et al. (2021) defend the idea that the ambiguity of the term “explanation” in explainable AI (XAI) can be solved by adopting any of four different extant accounts of explanation in the philosophy of science: the Deductive Nomological, Inductive Statistical, Causal Mechanical, and New Mechanist models. In this chapter, I show that the authors’ claim that these accounts can be applied to deep neural networks as they would to any natural phenomenon is mistaken. I also (...) provide a more general argument as to why the notion of explainability as it is currently used in the XAI literature bears little resemblance to the traditional concept of scientific explanation. It would be more fruitful to use the label “understandable AI” to avoid the confusion that surrounds the goal and purposes of XAI. In the second half of the chapter, I argue for a pragmatic conception of understanding that is better suited to play the central role attributed to explanation in XAI. Following De Regt (2017) and Kuorikoski and Ylikoski (2015), the conditions of satisfaction for understanding an ML system are fleshed out in terms of an agent’s success in using the system. (shrink)

The book forms a balanced structure in which the three conceptual pillars of Spinoza's natural law theory (individuality, natural laws, and power) are first analyzed from the viewpoint of his ontology and then from the viewpoint of his ...

Rendre hommage à un auteur, ce n'est pas seulement célébrer ce qu'il fut mais c'est aussi alerter sur ce que son oeuvre apporte au présent et à l'avenir de la connaissance. C'est bien le sens donné à cet hommage à André-Jean Arnaud. Repenser le droit, c'était pou r cet auteur érudit : repenser les lieux, les conditions et les façons de l'étudier en dépassant les frontières géographiques en même temps que les frontières disciplinaires. En montrant en quoi André-Jean Arnaud fut, (...) hors des sentiers battus et des orthodoxies de la production et de la transmission des savoirs en la matière, un exceptionnel précurseur et l'infatigable artisan d'un nouveau régime de connaissance sur le droit, le présent ouvrage s'adresse à toutes celles et à tous ceux, enseignants, chercheurs, étudiants ou simples citoyens, pou r qui l'étude du droit permet de mieux comprendre ce que sont et ce que sont susceptibles de devenir nos sociétés. (shrink)

In this paper we carry out an algebraic investigation of the weak nilpotent minimum logic and its t-norm based axiomatic extensions. We consider the algebraic counterpart of WNM, the variety of WNM-algebras and prove that it is locally finite, so all its subvarieties are generated by finite chains. We give criteria to compare varieties generated by finite families of WNM-chains, in particular varieties generated by standard WNM-chains, or equivalently t-norm based axiomatic extensions of WNM, and we study their standard completeness (...) properties. We also characterize the generic WNM-chains, i. e. those that generate the variety [MATHEMATICAL DOUBLE-STRUCK CAPITAL W]ℕ[MATHEMATICAL DOUBLE-STRUCK CAPITAL M], and we give finite axiomatizations for some t-norm based extensions of WNM. (shrink)

The philosophy problem of identity and the related problem of change go back to the ancient Greek philosophers and fascinated later figures including Leibniz, Locke and Hume. Heraclitus argued that one could not swim in the same river twice because new waters were ever flowing in. When is a river not the same river? If one removes one plank at a time when is a ship no longer a ship? What is the basic nature of identity and persistence? This book (...) introduces and asseses the philosophical puzzles posed by things persisting through time. Beginning with essential historical background to the problem it explores the following key topics and debates: mereology and identity, including 'Leibniz's Law' the constitution view of identity the 'relative identity' argument concerning identity temporary identity four-dimensionalism, counterpart and mulitiple counterpart theory supervenience the problem of temporary intrinsics the necessity of identity presentism ontological and epistemological criteria for persistence and the difference between them. Including chapter summaries, annotated further reading and a glossary this book is essential reading for anyone seeking a clear and informative introduction to and assessement of the metaphysics of identity. (shrink)

Se presenta la hipótesis de que la mirada más allá de la modernidad puede descubrir la nueva sociedad que ha estado surgiendo en el vientre de la vieja. La insurrección de saberes subyugados e imaginaciones reprimidas, que caracteriza la transición, estaría definiendo una nueva perspectiva e interpretación del mundo, que serían expresión de la resistencia a la destrucción aún vinculada al viejo orden social y de los empeños de construcción del nuevo.

Trata-se de capítulo de um livro sobre a noção de "substância" na história da filosofia e contém uma discussão sobre a noção ordinária de "corpo" do ponto de vista da filosofia analítica.

Los movimientos sociales contemporáneos se hacen antisistémicos en su propia dinámica, cuando profundizan sus empeños y descubren la naturaleza e interconexiones de los obstáculos que enfrentan. Empieza a generalizarse la intuición, anticipada por pensadores radicales del último medio siglo, de que estamos al fin de una era. A partir de las experiencias de la Asamblea Popular de los Pueblos de Oaxaca, reflexiono en este trabajo sobre la necesidad de limpiar nuestras miradas –contaminadas aún por la era que termina- al concebir (...) las luchas actuales y emprender esfuerzos de transformación. Serían desgaste estéril si están atrapados en elementos de la víspera. La nueva sociedad no puede ser mera extrapolación de la antigua. Al plantear la necesidad de preparar el funeral de la sociedad económica (capitalismo y socialismo), del imperio estadounidense y del régimen político mexicano, sugiero también caminos para acotar con mayor precisión los rumbos y maneras de la lucha anticapitalista actual. (shrink)

In nine essays, each related to a different time frame, author analyzes diverse aspects of Venezuelans' cultural behavior in regard to what the author considers 'taste.' Witty and amusing, often sarcastic and colloquial, book does not lose perspective of the historical context. A curious x-ray of Venezuelan idiosyncrasies"--Handbook of Latin American Studies, v. 58.

Recent attempts to develop and apply digital ethics principles to address the challenges of the digital transformation leave organisations with an operationalisation gap. To successfully implement such guidance, they must find ways to translate high-level ethics frameworks into practical methods and tools that match their specific workflows and needs. Here, we describe the development of a standardised risk assessment tool, the Principle-at-Risk Analysis (PaRA), as a means to close this operationalisation gap for a key level of the ethics infrastructure at (...) many organisations – the work of an interdisciplinary ethics panel. The PaRA tool serves to guide and harmonise the work of the Digital Ethics Advisory Panel at the multinational science and technology company Merck KGaA in alignment with the principles outlined in the company’s Code of Digital Ethics. We examine how such a tool can be used as part of a multifaceted approach to operationalise high-level principles at an organisational level and provide general requirements for its implementation. We showcase its application in an example case dealing with the comprehensibility of consent forms in a data-sharing context at Syntropy, a collaborative technology platform for clinical research. (shrink)

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and Δ-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics–namely the class of algebras defined over the real unit (...) interval, the rational unit interval, the hyperreals , the strict hyperreals and finite chains, respectively–and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. (shrink)

Mit seiner Theorie der vernünftigen Übereinkunft liefert André Olbrich die Grundlegung eines Kriteriums für moralische Urteile über richtig und falsch: Im Anschluss an klassische und moderne Vertragstheoretiker wird die Akzeptanz eines Urteils durch die Betroffenen zum obersten Rechtfertigungsmaßstab erhoben. Das vertragstheoretische Denken wird weiterentwickelt und konsequent als umfassende normative Theorie ausformuliert. Die Leserinnen und Leser erfahren, von welchem Standpunkt aus sich die Regeln unseres sozialen Miteinanders einer Kritik unterziehen lassen und auf welchen moralischen Grundlagen Recht und Politik aufbauen.

André Tosel, décédé en mars 2017, était un philosophe engagé, attaché tout au long de son existence à faire vivre un marxisme critique puisant notamment dans le meilleur de la tradition italienne de ce courant de pensée ; il fut l'un des rares français à introduire et discuter les oeuvres majeures d'A. Labriola et surtout d'A. Gramsci, ainsi par ailleurs que celles de Vico dont il fut un fin connaisseur. Il consacra sa thèse de doctorat d'état aux rapports entre religion, (...) politique et philosophie chez Spinoza et contribua de façon décisive à de nouvelles lectures du philosophe en le mettant en miroir de Marx. Professeur de philosophie des universités de Besançon, Franche Comté, de Paris 1 Panthéon-Sorbonne et de Nice Sophia-Antipolis, dans lesquelles il occupa de nombreuses fonctions de directions administratives et scientifiques, il était un homme de collectif attaché à faire vivre le savoir, s'engageant dans la vie universitaire et politique, contribuant également de manière décisive au lancement et à l'animation de la revue Actuel Marx. Passionné par l'évolution des pensées contemporaines, il intervenait régulièrement dans des débats d'actualité, sous la forme de contributions dans L'Humanité ou dans des ouvrages destinés à un public large, tout particulièrement dans la dernière période sur les questions de sécularisation, de laïcité et de religion. Cet ouvrage entend lui rendre hommage en abordant les différentes facettes de son oeuvre, traversant un demi-siècle de vie intellectuelle. (shrink)

El uso de sistemas de machine learning en los procesos de selección laboral ha sido de gran utilidad para agilizarlos y volverlos más eficientes, pero al mismo tiempo ha generado problemas en términos de equidad, confiabilidad y transparencia. En este artículo comenzamos explicando los diferentes usos de la Inteligencia Artificial en los procesos de selección laboral en Estados Unidos. Presentamos los sesgos sexuales y raciales que han sido detectados en algunos de ellos y explicamos los obstáculos jurídicos y prácticos para (...) su detección y análisis. Un posible remedio jurídico a la discriminación algorítmica es el régimen de impacto diferencial sistémico utilizado en Estados Unidos. Usamos algunas características de este régimen para señalar los vacíos jurídicos frente a la discriminación en el acceso al empleo en el ámbito del derecho laboral colombiano, y ofrecemos algunas características generales que podría tener un régimen de esa naturaleza. (shrink)

Hegelians normally consider Hegel's philosophical system from two perspectives: metaphysics, interpreting this discipline as the central one to understand the work of the German philosopher, or non-metaphysics, being more relevant alternative interpretations that avoid it. This article presents a study on the senses of reflection. These senses can be extrinsic or absolute. These two senses are the backbones of the Hegelian system. Therefore, by means of a study of whether extrinsic and absolute reflection are notions that guide us towards metaphysical (...) or non-metaphysical readings, we try to give an answer to the debate between the possible interpretations of Hegel. (shrink)

Deviendrai-je le héros de ma propre vie ou ce rôle sera-t-il tenu par un autre? Cette question, inspirée de la littérature, nous interpelle : tout être humain doit trouver sa propre voie, sa manière personnelle de participer à l’aventure humaine. Or, aucun de nous n’est vraiment préparé à se lancer dans un tel périple. Nous n’avons pas choisi notre milieu familial et culturel. Notre corps est fragile, notre pensée faillible. Puis, la route sera parsemée d’embûches de toutes sortes : précipitation, (...) erreur de calcul, malentendu, abandon, chagrin d’amour, injustice, ressentiment, maladie, conflit. Pourtant, nous espérons tous et toutes vivre en paix et avec un minimum de liberté. Pour y parvenir, nous suivrons les chemins qui nous semblent les meilleurs. Comment les choisir? Quelle sera notre boussole? Cet ouvrage porte sur notre quête philosophique d’unité ou d’harmonie. L’auteur y ouvre dix fenêtres sur diverses expériences de vie, de notre premier à notre dernier souffle. (shrink)

Diversität ist eines der zentralen Themen unserer Zeit. Sie durchdringt alle Lebensbereiche unserer Gesellschaften. Das Nachdenken über Diversität reicht von den Naturwissenschaften über die Geschichtswissenschaften, die Gesellschaftswissenschaften, die Philosophie bis zu den Künsten. Diversität ist zudem politisch und emotional beladen. Man denke an gesellschaftliche Minderheiten und ihre Rechte oder an das massive Artensterben unserer Tage. In diesem Buch wird nicht nur über Einzelaspekte von Diversität berichtet, es wird auch eine Synthese versucht. Drei einleitende Kapitel der HerausgeberInnen führen verständlich in komplexe (...) interdisziplinäre Problemzusammenhänge ein. Der Band versammelt 17 Beiträge namhafter Autorinnen und Autoren aus den Bereichen Kunst-, Kultur- und Wissenschaftsgeschichte, Medizin und Gesellschaftstheorie.00. (shrink)

El pluralismo religioso trata de presentar lugares comunes en los que establecer diálogos entre diferentes religiones sin intención de persuadir. En esta investigación se aborda el pluralismo religioso en los periodos de Tubinga y Berna de Hegel. Esto es, en la filosofía del joven Hegel, periodo en el que se dedicó especialmente a la reflexión sobre la política y la religión. En este periodo, menos estudiado por la academia que su madurez, encontramos que hay al menos tres lugares comunes que (...) pueden facilitar el diálogo interreligioso: el sentimiento, la universalidad ética y la libertad. En esta investigación se presenta estos tres tópicos que Hegel descubre para el diálogo entre diferentes religiones para, finalmente, conectarlos con la discusión cronológicamente posterior sobre el pluralismo religioso. (shrink)

Pourquoi Averroès? Pourquoi Averroès juriste? Parce que dans le cadre du débat avec ceux qui soutiennent le caractère indubitable du texte sacré, Averroès affirme la primauté de la raison. Il a ainsi mis en avant le questionnement, le doute dans la recherche de la vérité. Ce doute toléré dans le cercle restreint des philosophes était inacceptable en droit (la charia) qui s'applique à tous les membres de la communauté des musulmans. D'où sa condamnation et son exil. La redécouverte de la (...) pensée d'Averroès pourrait permettre au monde arabo-musulman de s'extraire du chaos. (shrink)

On présente trop souvent Spinoza comme le créateur de l'un des systèmes conceptuels les plus arides de l'histoire de la pensée. Loin d'être un système de plus, il s'agit en fait d'un itinéraire existentiel, de l'effort d'un homme pour se libérer du malheur, de l'ignorance, de la souffrance, lot de tout homme venant en ce monde. Pour sortir de ce bourbier où la vie s'enlise, il faut prendre la décision ferme d'y voir enfin clair sur la nature des biens que (...) nous aimons et auxquels nou nous attachons car il y va de notre bonheur et de notre malheux. Pour y parvenir, 'il convient d'abord de trouver un moyen de guérir l'entendement' et de se consacrer entièrement à la mise en œuvre de cette guérison de soi. Ces pages, nées d'une libre méditation, ont pour seul but d'attirer l'attention sur un aspect de l'œuvre et de la vie d'un homme qui fut un Sage, et don't la voix demeure aussi vivante qu'au jour où elle s'éleva pour la première fois"--Page 4 of cover. (shrink)