The work on set theory made by A. Tarski in the years 1924-1950 is very interesting, but little know.We develope partial questions in set theory in the moment that A. Tarski intervenes and his contributionsand also influences.The principals aims in this development are:1. The axiom of choice [A.C.] and his equivalents;2. the general continuum hypothesis [G.C.H.] and the A.C.;3. the dual trichotomy principle;4. the inaccessible cardinals and his relation with the A.C. and the G.C.H.;5. the notion of finite set and (...) his relation with the A.C and the G.C.H.;6. the almost disjoint set and their relation with the G.C.H.;and finally,7. the results in Berkeley. (shrink)

This paper studies, with techniques ofAlgebraic Logic, the effects of putting a bound on the cardinality of the set of side formulas in the Deduction Theorem, viewed as a Gentzen-style rule, and of adding additional assumptions inside the formulas present in Modus Ponens, viewed as a Hilbert-style rule. As a result, a denumerable collection of new Gentzen systems and two new sentential logics have been isolated. These logics are weaker than the positive implicative logic. We have determined their algebraic models (...) and the relationships between them, and have classified them according to several standard criteria of Abstract Algebraic Logic. One of the logics is protoalgebraic but neither equivalential nor weakly algebraizable, a rare situation where very few natural examples were hitherto known. In passing we have found new, alternative presentations of positive implicative logic, both in Hilbert style and in Gentzen style, and have characterized it in terms of the restricted Deduction Theorem: it is the weakest logic satisfying Modus Ponens and the Deduction Theorem restricted to at most 2 side formulas. The algebraic part of the work has lead to the class of quasi-Hilbert algebras, a quasi-variety of implicative algebras introduced by Pla and Verdú in 1980, which is larger than the variety of Hilbert algebras. Its algebraic properties reflect those of the corresponding logics and Gentzen systems. (shrink)

No tenim temps per a res. La família, els amics, l’esport o altres dèries sempre queden en un segon pla. També el cultiu del pensament, que suposadament és una de les coses que identifica més i millor la nostra espècie, resta a l’espera. La pressa ens aclapara. En aquest context precipitat necessitem temps per descobrir el temps. Un oasi de pensament que comencem a explorar gràcies a parar atenció aquí i allà: ressenyem les observacions resultants, plantegem sengles qüestions estimulants i (...) esmolem el senderi amb l’exercici compartit d’enraonar, altrament conegut com a diàleg. No en va Ramon Llull augurava taxatiu que: “Pensar per un mateix és l’únic projecte a la vida”. (shrink)

In this paper two deductive systems associated with relevance logic are studied from an algebraic point of view. One is defined by the familiar, Hilbert-style, formalization of R; the other one is a weak version of it, called WR, which appears as the semantic entailment of the Meyer-Routley-Fine semantics, and which has already been suggested by Wójcicki for other reasons. This weaker consequence is first defined indirectly, using R, but we prove that the first one turns out to be an (...) axiomatic extension of WR. Moreover we provide WR with a natural Gentzen calculus. It is proved that both deductive systems have the same associated class of algebras but different classes of models on these algebras. The notion of model used here is an abstract logic, that is, a closure operator on an abstract algebra; the abstract logics obtained in the case of WR are also the models, in a natural sense, of the given Gentzen calculus. (shrink)

Joint activities are ubiquitous in the animal kingdom, but they differ substantially in their underlying psychological states. Humans attribute and share mental states with others in the so‐called shared intentionality. Our hypothesis is that our closest nonhuman living relatives also attribute some psychological mechanisms such as perceptions and goals to others, but, unlike humans, they are not necessarily intrinsically motivated to share those psychological states. Furthermore, it is postulated that shared intentionality is responsible for the appearance of a suite of (...) behaviors, including joint attention, declarative communication, imitative learning, and teaching, that are the basis of cultural learning and the social norms and traditions present in every human culture. (shrink)

Chimpanzees follow the gaze of conspecifics and humans — follow it past distractors and behind barriers, ‘check back’ with humans when gaze following does not yield interesting sights, use gestures appropriately depending on the visual access of their recipient, and select different pieces of food depending on whether their competitor has visual access to them. Taken together, these findings make a strong case for the hypothesis that chimpanzees have some understanding of what other individuals can and cannot see. However, chimpanzees (...) do not seem nearly so skillful in the Gesture Choice and Object Choice experimental paradigms. Neither behavioral conditioning nor theory of mind explanations can account for these results satisfactorily. Instead this chapter proposes the idea that chimpanzees have the cognitive skills to recall, represent, categorize, and reason about the behavior and perception of others, but not their intentional or mental states, because they do not know that others have such states since they cannot make a link to their own. Human beings began their own evolutionary trajectory with these same skills, but then at some point in their evolution (probably quite recently) they began to understand that their own experience could serve as some kind of model for that of other persons. This allowed for even better prediction and control of the behavior of others and better communication and cooperation with them as well, and so it was an adaptation with immediate adaptive consequences that ensured its survival. (shrink)

This essay begins with a look at the contribution made by Business Ethics and by Corporate Social Responsibility (CSR) to Business Education, and how the first two have moved to the last over time. Yet their contributions also reveal limitations that need to be taken into account in the debate on the training provided by Business Schools. This debate cannot be confined to speaking of disciplines and their cross-cutting natures but rather needs to focus directly on the kind of personal (...) profile fostered among business students. In the context of this debate on the future of Business Schools, the essay stresses the relevance of Peter-Hans Kolvenbach’s framework. He proposed an educational ideal based upon educating competent, conscious, compassionate, and committed people. This ideal took shape in the form of an educational paradigm integrating four dimensions: professional (_utilitas_), ethical-social (_iustitia_), humanist (_humanitas_) and spiritual (_fides_). The essay not only shows how each of these dimensions is in tune with some of the present proposals for renewing Business Education but also how Kolvenbach's more holistic approach can help to further integrate and spotlight the blind spots of each of them. (shrink)

The inference systems proposed for solving SAT are unsound for solving MaxSAT and MinSAT, because they preserve satisfiability but not the minimum and maximum number of clauses that can be falsified, respectively. To address this problem, we first define a clause tableau calculus for MaxSAT and prove its soundness and completeness. We then define a clause tableau calculus for MinSAT and also prove its soundness and completeness. Finally, we define a complete clause tableau calculus for solving both MaxSAT and MinSAT, (...) in that the minimum number of generated empty clauses provides an optimal MaxSAT solution and the maximum number provides an optimal MinSAT solution. (shrink)

Cuando observamos el apabullante momento histórico en que estamos viviendo, con el alto desarrollo tecnológico disponible, y nos informamos de los éxitos de la física teórica y física aplicada, los avances en la cosmología, la biología, la filosofía de la ciencia, los vuelcos que le damos a los conocimientos para ajustarlos a la circunstancias de la ciencia actual, observamos la conquista del hombre sobre el planeta y sus recursos, los cambios en la sociología mundial, los avances y prospección de avaneces (...) en medicina y "n" circunstancias conexas, nos parece que todo está "hecho ya", no alcanzamos a informamos de tanto. La simbología nos arropa... y también, a medida que analizamos términos como luz, oscuridad, espacio, tiempo, distancia, macro, micro, positivo, negativo, atractivo, repulsivo, pareciera que nos confundimos más, lo simple nos confunde. Aparentemente términos como infinito, comienzo y fin de las cosas, crean un caos en el cual se nos hace inaprehensible lo pequeño y lo muy grande.¿Qué es el tiempo esencial?, quizás sea la evocación del espacio esencial, y por ello, estamos interconectados, enmarañados en un solo ser, un solo ser universal, que contiene toda la energía universal, y que soporta toda la energía universal. ¿Y entonces? ¿Cómo es el asunto de la entropía... que comienza, crece y vuelve a comenzar?Debe haber una razón que explique la dinámica universal más allá del análisis de movimiento, que explique la síntesis y el análisis. En la búsqueda de querer objetivar la función abstracta tratamos de encontrar el esqueleto de las sombras en forma de energía y espacio exóticos. Buscamos algo que es de lo que no es. (shrink)

The centenary of the birth of Ludwig Wittgenstein provided an opportunity for recovering some of the great Wittgensteinian subjects, for re-examining them and for discussing their implications and relevance. This volume is the result of the interchange that took place in Girona among well-known scholars of Wittgenstein's work in different countries. The eleven contributions are organized into three main subjects: on Wittgenstein's method, on knowledge and meaning, on language and use. This volume is not only the result of the different (...) and mature reflexions of its authors, but in two cases it has also unfortunately become their last contribution to the subject. (shrink)

Quins són els valors que regeixen la nostra vida? I per què vivim amb aquests valors i no amb uns altres? «Els valors van cap a on anem nosaltres perquè van amb nosaltres. ¬I mentre fem camí o mentre el busquem, els valors ens alimenten», diu el filòsof.

La tradition éthique en économie politique a été régénérée par l’Ecole de Salamanque, mais nous ne sommes pas habitués à associer le libéralisme aux scholastiques qui avaient élaboré une théorie du juste prix de validité universelle. Le marché a perdu sa dimension morale avec le rationalisme et, non dans une moindre mesure, à travers le biais religieux de la théorie de la valeur travail. Quand elle fut redécouverte en tant qu’origine véritable de la valeur, l’utilité ne recouvrit pas sa portée (...) morale, en raison du traitement mathématique qu’on lui réserva. Le rationalisme a supprimé toute conception d’évolution sociale en même temps qu’il a favorisé l’intervention. Cependant, dans cette ère de corruption, un retour à l’acception de sens commun des prix requiert, selon l’auteur, le franchissement d’une étape supplémentaire, celui de maintenir l’ancrage éthique du juste prix ou du prix du marché.The ethical tradition in political economy was regenerated by the School of Salamanca, but we are not used to associating liberalism with these Scholastics who built a theory of the just price with universal validity. The market lost its moral dimension with rationalism, not least through the religious bias of the labor theory of value. When rediscovered as the correct source of value, utility did not regain its former moral significance because of mathematical treatment. Rationalism has suppressed any concept of social evolution while promoting intervention, but, in the age of corruption, a return to the common sense of prices, the author argues, requires the further step of upholding the ethical standards of the just price or market price. (shrink)

The concept of convention has been used in different fields and from different perspectives to account for important social phenomena, and the legal sphere is no exception. Rather, reflection on whether the legal phenomenon is based on a convention and, if so, what kind of convention is involved, has become a recurring issue in contemporary legal theory. In this book, some of the foremost specialists in the field make significant contributions to this debate. In the first part, the concept of (...) convention is analysed. The second part reflects on whether the rule of recognition postulated by Hart can be understood as a convention and discusses its potential and limitations in order to explain the institutional and normative character of law. Lastly, the third part critically examines the relations between conventionalism and legal interpretation. Given the content and quality of the contributions, the book is of interest to those wanting to understand the current state of the art in legal conventionalism as well as those wanting to deepen their knowledge about these questions. (shrink)

Siguiendo la definición de Osvaldo Pessoa Jr., un “escenario contrafáctico” sería “una situación posible que no se realizó, como una posibilidad futura en algún instante del pasado”. Este concepto no es nuevo. De hecho, tiene una presencia significativa en campos como la filosofía analítica, la economía, las ciencias experimentales o la psicología. La pretensión de este texto es presentar, mediante el rigor teórico, conceptual, y el método inductivo, una reflexión no derivada de investigación. Esta reflexión es la importancia de la (...) relación entre los escenarios contrafácticos y el mundo del arte desde una perspectiva institucional. La observación inicial en la que se sustenta este texto es que, en una época en la que cualquier cosa puede ser arte y, sin embargo, no todo lo es, las razones por las que algo pudo ser arte, pero no lo fue, cobran una gran importancia para comprender la base de su valor económico y cultural y ahondar en nuestras categorías lingüísticas del presente; en este caso, la de arte. (shrink)

This is a contribution to the discussion on the role of truth degrees in manyvalued logics from the perspective of abstract algebraic logic. It starts with some thoughts on the so-called Suszko’s Thesis (that every logic is two-valued) and on the conception of semantics that underlies it, which includes the truth-preserving notion of consequence. The alternative usage of truth values in order to define logics that preserve degrees of truth is presented and discussed. Some recent works studying these in the (...) particular cases of Łukasiewicz’s many-valued logics and of logics associated with varieties of residuated lattices are also presented. Finally the extension of this paradigm to other, more general situations is discussed, highlighting the need for philosophical or applied motivations in the selection of the truth degrees, due both to the interpretation of the idea of truth degree and to some mathematical difficulties. (shrink)

Chimpanzees follow the gaze of conspecifics and humans — follow it past distractors and behind barriers, ‘check back’ with humans when gaze following does not yield interesting sights, use gestures appropriately depending on the visual access of their recipient, and select different pieces of food depending on whether their competitor has visual access to them. Taken together, these findings make a strong case for the hypothesis that chimpanzees have some understanding of what other individuals can and cannot see. However, chimpanzees (...) do not seem nearly so skillful in the Gesture Choice and Object Choice experimental paradigms. Neither behavioral conditioning nor theory of mind explanations can account for these results satisfactorily. Instead this chapter proposes the idea that chimpanzees have the cognitive skills to recall, represent, categorize, and reason about the behavior and perception of others, but not their intentional or mental states, because they do not know that others have such states since they cannot make a link to their own. Human beings began their own evolutionary trajectory with these same skills, but then at some point in their evolution (probably quite recently) they began to understand that their own experience could serve as some kind of model for that of other persons. This allowed for even better prediction and control of the behavior of others and better communication and cooperation with them as well, and so it was an adaptation with immediate adaptive consequences that ensured its survival. (shrink)

In recent years, scholars have increasingly dedicated their attention to analyse and reflect on the topic of leadership. However, the debate has often focused on the figure of the leader, as if being a leader were a self-sufficient function in itself, understood without finalities or independent of them. I would argue that leadership is not a position that can be assumed, but, rather, a relationship that is constructed. Similarly, the question of leaders has often given rise to a deconstruction of (...) its components, without any insight as to how the reality is put together. Leadership cannot be understood solely from a technical or instrumental perspective. It is not a mere relational skill that simply requires developing competencies. The exercise of leadership always includes—explicitly or implicitly—a connection with values. Therefore, developing leadership is impossible without a personal process that develops the person’s capacity for perception, learning, interiorisation, explicit sense-making and constructing meaning. These issues are truly important at a time in which the debate on business education and its contribution is completely open, targeting the very core of business education’s reason for being. Though open, the debate can only become a truly dynamic discussion if there is a real dialogue between the different positions and traditions. For this reason, this paper proposes an anthropological and non-denominational reading of some of the fundamental meditations found in the Spiritual Exercises of Saint Ignatius which could be used as a heuristic in the debate regarding what business schools propose. This paper represents an initial step in this direction, exploring some of the potentialities of the Spiritual Exercises for business schools that do not claim any religious tradition. (shrink)

En aquesta arrencada del segle XXI, en què la tecnologia ens afalaga i alhora ens domina, ens calen humanistes que ens ajudin a interpretar la realitat i a tenir criteris per a abordar-la. Josep Maria Puigjaner, l'autor d'aquest llibre, s'ha proposat apropar al lector, a través de la narració d'alguns retalls -reals o imaginaris- de les seves vides, la personalitat de vuit humanistes que ens transmeteren, durant el segle XX, la seva manera d'entendre la vida i l'home. Són escriptors (...) que mereixen el qualificatiu de clàssics, és a dir que parlen des d'una perspectiva interior, profunda i arrelada en el coneixement i en l'experiència del significat de la naturalesa humana i els seus ideals de futur. (shrink)