A couple of decades ago natural phenomena began to be approached from a comprehensive and transdisciplinary point of view, as it was understood that living beings and their environments are not linear but complex. There is no doubt that this perspective of visualizing complexity and working inter-and transdisciplinarily has to be applied. The reflection on the theoretical observation (i.e. meta-observation) involved in the concept of poly-contexturality is the framework in which a theory of complex systems is possible, which in turn (...) enables an observation that oscillates (a concept of chaos theory) between modelsstructured in a hierarchical order (normally linked to a logical-deductive formalization) and models structured in hetero‐hierarchy. And this would allow this reflection to be done in a formalized language that does not follow either the principles of the Aristotelian logic or the postulates of the Kantian transcendental reflection. It is precisely this liberation from the dictates of mono-contextural logic what paves the way to an observation of complexity, in which one or the other language is used to model the states of things, such as the epistemological problems of molecular biology or the social systems. And-what is gaining relevance-it also paves the way to a true transdisciplinary meta-observation, since each discipline chooses its own contexture and only the use of poly-contexturality makesit possible to formulate transdisciplinary relationships within the framework of such meta-logic. (shrink)
Łukasiewicz’s infinite-valued logic is commonly defined as the set of formulas that take the value 1 under all evaluations in the Łukasiewicz algebra on the unit real interval. In the literature a deductive system axiomatized in a Hilbert style was associated to it, and was later shown to be semantically defined from Łukasiewicz algebra by using a “truth-preserving” scheme. This deductive system is algebraizable, non-selfextensional and does not satisfy the deduction theorem. In addition, there exists no Gentzen calculus fully adequate (...) for it. Another presentation of the same deductive system can be obtained from a substructural Gentzen calculus. In this paper we use the framework of abstract algebraic logic to study a different deductive system which uses the aforementioned algebra under a scheme of “preservation of degrees of truth”. We characterize the resulting deductive system in a natural way by using the lattice filters of Wajsberg algebras, and also by using a structural Gentzen calculus, which is shown to be fully adequate for it. This logic is an interesting example for the general theory: it is selfextensional, non-protoalgebraic, and satisfies a “graded” deduction theorem. Moreover, the Gentzen system is algebraizable. The first deductive system mentioned turns out to be the extension of the second by the rule of Modus Ponens. (shrink)
In this paper we show that, in Gentzen systems, there is a close relation between two of the main characters in algebraic logic and proof theory respectively: protoalgebraicity and the cut rule. We give certain conditions under which a Gentzen system is protoalgebraic if and only if it possesses the cut rule. To obtain this equivalence, we limit our discussion to what we call regular sequent calculi, which are those comprising some of the structural rules and some logical rules, in (...) a sense we make precise. We note that this restricted set of rules includes all the usual rules in the literature. We also stress the difference between the case of two-sided sequents and the case of many-sided sequents, in which more conditions are needed. (shrink)
ABSTRACT In this paper we study consequence relations on the set of many sided sequents over a propositional language. We deal with the consequence relations axiomatized by the sequent calculi defined in  and associated with arbitrary finite algebras. These consequence relations are examples of what we call Gentzen systems. We define a semantics for these systems and prove a Strong Completeness Theorem, which is an extension of the Completeness Theorem for provable sequents stated in . For the special case (...) of the finite linear MV-algebras, the Strong Completeness Theorem was proved in , as a consequence of McNaughton's Theorem. The main tool to prove this result for arbitrary algebras is the deduction-detachment theorem for Gentzen systems. (shrink)
When considering m-sequents, it is always possible to obtain an m-sequent calculus VL for every m-valued logic (defined from an arbitrary finite algebra L of cardinality m) following for instance the works of the Vienna Group for Multiple-valued Logics. The Gentzen relations associated with the calculi VL are always finitely equivalential but might not be algebraizable. In this paper we associate an algebraizable 2-Gentzen relation with every sequent calculus VL in a uniform way, provided the original algebra L has a (...) reduct that is a distributive lattice or a pseudocomplemented distributive lattice. We also show that the sentential logic naturally associated with the provable sequents of this algebraizable Gentzen relation is the logic that preserves degrees of truth with respect to the original algebra (in contrast with the more common logic that merely preserves truth). Finally, for some particular logics we obtain 2-sequent calculi that axiomatize the algebraizable Gentzen relations obtained so far. (shrink)
Es indudable que el inconsciente colectivo estudiado por Jung y su escuela psicoanalítica, nos ha demostrado fehacientemente que las conductas observadas y aprendidas en la infancia tanto en la familia como en la sociedad, se reproducen de manera muy similar en las generaciones jóvenes.
The aesthetics reflection can not carry out through the exclusive analysis of the figure produced by the artist, but demands to know the various nature factors that have intervened in the gestation of the work. For the study of the present aesthetics in the work of Michael Angel, results indispensable to know what the medieval philosophy expresses on what is beautiful. Furthermore, Michael Angel was a deep intellectual anxieties man. Therefore, the study of the theories outstanding aesthetics in his era, (...) it could give impulse to his own creativity. (shrink)
Resumen La historia ocupa un papel marginal en las teorías actuales de la globalización. Esto no deja de sorprender, pues “globalización” es, en esencia, un concepto que describe un proceso de la historia. Menos aún se habla de la filosofía de la historia, sobre todo porque ha caído en descrédito. Sin embargo, casi todas las argumentaciones emplean modelos de interpretación propios de la filosofía de la historia. Se conjetura qué tendencias generales le son inherentes a la globalización y si apuntan (...) a un “progreso” o a una “decadencia” de la civilización humana. Por último, el problema ético de la justicia global debe tomar en consideración el desarrollo de la historia acontecida. Estos temas dejan claro que el recurso a la historia con implicaciones filosóficas es imprescindible para resolver los problemas de la globalización.Contemporary theories of globalisation seldom mention history. This is surprising, because “globalisation” is essentially a term describing an historical process. There is still less mention of the philosophy of history, especially due to the discredit cast upon it. And yet nearly all of the relevant arguments operate with patterns of interpretation borrowed from the philosophy of history. The authors speculate on which general tendencies are inherent to globalisation and whether they are more indicative of the “progress” or of the “downfall” of human civilisation. Finally, the ethical problem of global justice requires us to take into account the course of history thus far. These topics underline that resorting to history with all of its philosophical implications is essential if we are to resolve the problems caused by globalisation. (shrink)
Resumen: Spinoza afirma que las decisiones, elecciones y acciones de un agente son necesarias porque están determinadas causalmente. ¿Acaso los seres humanos no son agentes morales? ¿son sólo eslabones de una cadena de causas cuyo curso no pueden controlar y que los exime de las consecuencias de sus actos, así como de premios y castigos? ¿ser un individuo libre significa aceptar pasivamente lo que ocurre y abandonar la pretensión de modificarlo? Este artículo responde a estas preguntas mediante la distinción en (...) la obra spinoziana de dos conceptos de libertad, la verdadera libertad y el libre albedrío, así como con la distinción entre la responsabilidad civil fundada en el concepto de potestas humana -y no en la verdadera libertad, aunque la posibilita-.: Spinoza sustains that the agents' decisions are necessary because they are causally determined. But then, are humans really moral agents? Is it possible that they are only passengers in a train of causes, whose course they cannot control and exempts them from the consequences of their acts, of reward or punishment? Is accepting whatever happens and quitting the aspiration of changing things the hallmark of the free man? This paper answers these questions by distinguishing two concepts of freedom, real freedom and free will, as well as two concepts of responsibility. Civil responsibility is grounded in free will, whereas moral responsibility is not grounded in true freedom, but in human power. (shrink)
The current research inspired by Foucault’s concept of panopticon, analyzes within the novel The Mister President the power relationships as a manifestation of a speech ruled by a logocentric structure of surveillance and denunciation. The work also studies the relevance of this text considering the presence of the panopticon in the represented continental reality as a coercive mechanism of control capable of normalizing the identity of the individuals and determine the political and interpersonal relationships.