This paper introduces new logical systems which axiomatize a formal representation of inconsistency (here taken to be equivalent to contradictoriness) in classical logic. We start from an intuitive semantical account of inconsistent data, fixing some basic requirements, and provide two distinct sound and complete axiomatics for such semantics, LFI1 and LFI2, as well as their first-order extensions, LFI1* and LFI2*, depending on which additional requirements are considered. These formal systems are examples of what we dub Logics of Formal Inconsistency (LFI) (...) and form part of a much larger family of similar logics. We also show that there are translations from classical and paraconsistent first-order logics into LFI1* and LFI2*, and back. Hence, despite their status as subsystems of classical logic, LFI1* and LFI2* can codify any classical or paraconsistent reasoning. (shrink)

An overcomplete logic is a logic that ‘ceases to make the difference’: According to such a logic, all inferences hold independently of the nature of the statements involved. A negation-inconsistent logic is a logic having at least one model that satisfies both some statement and its negation. A negation-incomplete logic has at least one model according to which neither some statement nor its negation are satisfied. Paraconsistent logics are negation-inconsistent yet non-overcomplete; paracomplete logics are negation-incomplete yet non-overcomplete. A paranormal logic (...) is simply a logic that is both paraconsistent and paracomplete. -/- Despite being perfectly consistent and complete with respect to classical negation, nearly every normal modal logic, in its ordinary language and interpretation, admits to some latent paranormality: It is paracomplete with respect to a negation defined as an impossibility operator, and paraconsistent with respect to a negation defined as non-necessity. In fact, as it will be shown here, even in languages without a primitive classical negation, normal modal logics can often be alternatively characterized directly by way of their paranormal negations and related operators. So, instead of talking about ‘necessity’, ‘possibility’, and so on, modal logics could be seen just as devices tailored for the study of (modal) negation. This paper shows how and to what extent this alternative characterization of modal logics can be realized. (shrink)

Motivated by Kalman residuated lattices, Nelson residuated lattices and Nelson paraconsistent residuated lattices, we provide a natural common generalization of them. Nelson conucleus algebras unify these examples and further extend them to the non-commutative setting. We study their structure, establish a representation theorem for them in terms of twist structures and conuclei that results in a categorical adjunction, and explore situations where the representation is actually an isomorphism. In the latter case, the adjunction is elevated to a categorical equivalence. By (...) applying this representation to the original motivating special cases we bring to the surface their underlying similarities. (shrink)

The Polish logician Roman Suszko has extensively pleaded in the 1970s for a restatement of the notion of many-valuedness. According to him, as he would often repeat, “there are but two logical values, true and false.” As a matter of fact, a result by W´ojcicki-Lindenbaum shows that any tarskian logic has a many-valued semantics, and results by Suszko-da Costa-Scott show that any many-valued semantics can be reduced to a two-valued one. So, why should one even consider using logics with more (...) than two values? Because, we argue, one has to decide how to deal with bivalence and settle down the tradeoff between logical 2-valuedness and truth-functionality, from a pragmatical standpoint. -/- This paper will illustrate the ups and downs of a two-valued reduction of logic. Suszko’s reductive result is quite non-constructive.We will exhibit here a way of effectively constructing the two-valued semantics of any logic that has a truth-functional finite-valued semantics and a sufficiently expressive language. From there, as we will indicate, one can easily go on to provide those logics with adequate canonical systems of sequents or tableaux. The algorithmic methods developed here can be generalized so as to apply to many non-finitely valued logics as well —or at least to those that admit of computable quasi tabular two-valued semantics, the so-called dyadic semantics. (shrink)

We say that things happen accidentally when they do indeed happen, but only by chance. In the opposite situation, an essential happening is inescapable, its inevitability being the sine qua non for its very occurrence. This paper will investigate modal logics on a language tailored to talk about essential and accidental statements. Completeness of some among the weakest and the strongest such systems is attained. The weak expressibility of the classical propositional language enriched with the non-normal modal operators of essence (...) and accident is highlighted and illustrated, both with respect to the definability of the more usual modal operators as well as with respect to the characterizability of classes of frames. Several interesting problems and directions are left open for exploration. (shrink)

This paper discusses how to define logics as deductive limits of sequences of other logics. The case of da Costa's hierarchy of increasingly weaker paraconsistent calculi, known as $ \mathcal {C}$n, 1 $ \leq$ n $ \leq$ $ \omega$, is carefully studied. The calculus $ \mathcal {C}$$\scriptstyle \omega$, in particular, constitutes no more than a lower deductive bound to this hierarchy and differs considerably from its companions. A long standing problem in the literature (open for more than 35 years) is (...) to define the deductive limit to this hierarchy, that is, its greatest lower deductive bound. The calculus $ \mathcal {C}$min, stronger than $ \mathcal {C}$$\scriptstyle \omega$, is first presented as a step toward this limit. As an alternative to the bivaluation semantics of $ \mathcal {C}$min presented thereupon, possible-translations semantics are then introduced and suggested as the standard technique both to give this calculus a more reasonable semantics and to derive some interesting properties about it. Possible-translations semantics are then used to provide both a semantics and a decision procedure for $ \mathcal {C}$Lim, the real deductive limit of da Costa's hierarchy. Possible-translations semantics also make it possible to characterize a precise sense of duality: as an example, $ \mathcal {D}$min is proposed as the dual to $ \mathcal {C}$min. (shrink)

The modern world was in part born as a reaction against Aristotelianism. However, the image of Aristotle to which modern philosophers reacted was partial, to say the least. Paradoxical though it may seem, today, more than twenty-three centuries on, we may now be in the most advantageous position for understanding the Stagirite's philosophy and applying it to contemporary problems. The present book contributes to the forming of an idea of Post-modern reason inspired by a constellation of Aristotelian concepts, such as (...) prudence (phronesis), practical truth (aletheia praktike), science in act (episteme en energeiai), metaphor (metaphora), similarity (homoiosis) and the imitation-creation pair (mimesis-poiesis). They all form an interconnected network and together they make up an idea of reason that may prove suitable for the present. These concepts offer the most promising basis for undertaking a series of urgent reconciliations: of facts and values, of means and ends, of theoretical and practical reason, of intelligence and emotion. Aristotle's notions could help solve many dualisms of modern times. He offers a third way between identity and difference in ontology and politics, between algorithm and anarchism in methodology, between naïve realism and plain relativism in epistemology, between equivocity and univocity in language, between Enlightenment and Romanticism in culture... On the way, this shift facilitates the relationships between science, arts and ethics - the three parts of the sphere of culture which Modernity had separated - as well as the integration of the sphere of culture itself with the world of life. (shrink)

In many real-life applications of logic it is useful to interpret a particular sentence as true together with its negation. If we are talking about classical logic, this situation would force all other sentences to be equally interpreted as true. Paraconsistent logics are exactly those logics that escape this explosive effect of the presence of inconsistencies and allow for sensible reasoning still to take effect. To provide reasonably intuitive semantics for paraconsistent logics has traditionally proven to be a challenge. Possible-translations (...) semantics can meet that challenge by allowing for each interpretation to be composed of multiple scenarios. Using that idea, a logic with a complex semantic behavior can be understood as an appropriate combination of ingredient logics with simpler semantic behaviors into which the original logic is given a collection of translations preserving its soundness. Completeness is then achieved through the judicious choice of the admissible translating mappings. The present note provides interpretation by way of possible-translations semantics for a group of fundamental paraconsistent logics extending the positive fragment of classical propositional logic. The logics PI, Cmin, mbC, bC, mCi and Ci, among others, are all initially presented through their non-truth-functional bivaluation semantics and sequent versions and then split by way of possible-translations semantics based on 3-valued ingredients. (shrink)

In this article, I argue that there is philosophy of science since philosophy existed. Thus, the idea that the philosophy of science was born with neopositivism is historically wrong and detrimental to the development of the philosophy of science itself. Neopositivism tried to found the philosophy of science as an anti-philosophical discipline, as a field of study that came to replace simple philosophy. The attempt was maintained for thirty years, but failed. Now, this does not mean that we cannot make (...) good philosophy of science today, but that the philosophy of science has returned to the common house of philosophy, it is gradually recovering the connection that it should never have lost with the main philosophical traditions and disciplines. (shrink)

The standard notion of formal theory, in logic, is in general biased exclusively towards assertion: it commonly refers only to collections of assertions that any agent who accepts the generating axioms of the theory should also be committed to accept. In reviewing the main abstract approaches to the study of logical consequence, we point out why this notion of theory is unsatisfactory at multiple levels, and introduce a novel notion of theory that attacks the shortcomings of the received notion by (...) allowing one to take both assertions and denials on a par. This novel notion of theory is based on a bilateralist approach to consequence operators, which we hereby introduce, and whose main properties we investigate in the present paper. (shrink)

Communication campaigns often highlight environmental progress to encourage further pro-environmental behaviour. Consequently, the drop in carbon emissions caused by the COVID-19 restrictions has been framed as a positive environmental outcome of the pandemic. We conducted an experimental study with a US-representative sample (N = 500) to show that raising awareness of emissions reduction has the contrary effect: an increase in moral self-concept facilitated a negative spillover, namely, it reduced climate-friendly behavioural intentions. Normative influence was able to prevent this negative spillover (...) because activating environmental norms inhibited compensatory feelings. Besides, awareness of recent emissions reduction was less likely to increase the moral self-concept of participants with a strong environmental self-identity. Our findings demonstrate that environmental progress increases moral self-concept which, in turn, could cause a negative spillover (i.e., reduce climate-friendly low-carbon behaviour and increase climate-harmful high-carbon behaviour). Normative influences and environmental self-identity can inhibit this negative spillover. (shrink)

We study a modal language for negative operators—an intuitionistic-like negation and its paraconsistent dual—added to (bounded) distributive lattices. For each non-classical negation an extra operator is hereby adjoined in order to allow for standard logical inferences to be opportunely restored. We present abstract characterizations and exhibit the main properties of each kind of negative modality, as well as of the associated connectives that express consistency and determinedness at the object-language level. Appropriate sequent-style proof systems and adequate kripke semantics are also (...) introduced, characterizing the minimal normal logic and a few other basic logics containing such negative modalities and their companions. (shrink)

El transhumanismo es una moda intelectual que propone la transformación de los seres humanos mediante diversas tecnologías. Expondremos brevemente los rasgos más conspicuos del TH, así como las principales críticas que se le han hecho. Pero la intención de este artículo no es entrar en esta polémica; aportaremos tan solo las claves imprescindibles para poder seguir adelante. Y una de las claves más intrigantes del TH es que, por debajo de su pátina tecno-futurista, remite a ciertas ideas filosóficas tan viejas (...) como, en apariencia, incompatibles entre sí. El TH remite al naturalismo radical, tanto como al nihilismo existencialista. La tesis que aquí se defiende es que tanto el naturalismo radical como el nihilismo existencialista son producto de las diversas oleadas del dualismo: del dualismo platónico antiguo, del dualismo cartesiano moderno. Una vez que separamos, a la manera dualista, la libertad por un lado y la naturaleza por el otro, podemos contar hasta dos, como hacen los dualistas, o quedarnos solo en uno, como hacen los existencialistas, que se paran en la libertad, y los naturalistas, que solo cuentan con la naturaleza. En cualquier caso, la imagen del ser humano, que es libertad y naturaleza, sale dañada. Asoma entonces el animal aporético y enfermizo al cual hay que salvar… de sí mismo. ¿Cómo? Siguiendo el método de Procusto, pero ahora con los prefijos bio e info en lugar de sierra y martillo. Hasta que el pobre ser humano encaje en el lecho de la utopía que algunos visionarios han urdido. ¿Y no hay otra vía, otra forma de mejorar la vida humana que sea más respetuosa para con la humana envergadura? Quizá sí, mas para trazar esa tercera vía, entre el naturalismo radical que mutila y el nihilismo existencialista que descoyunta y estira, habría que negar de antemano el dualismo que a los dos engendra, y atenerse a la sensatez común, en línea con la tradición aristotélica, antes que a las ensoñaciones utópicas. En nuestra opinión, el concepto aristotélico de naturaleza humana nos habilita para juzgar las antropotecnias mejor que la normatividad extraída de las visiones futuristas propias del TH. (shrink)

What is the fundamental insight behind truth-functionality ? When is a logic interpretable by way of a truth-functional semantics? To address such questions in a satisfactory way, a formal definition of truth-functionality from the point of view of abstract logics is clearly called for. As a matter of fact, such a definition has been available at least since the 70s, though to this day it still remains not very widely well-known. A clear distinction can be drawn between logics characterizable through: (...) (1) genuinely finite-valued truth-tabular semantics; (2) no finite-valued but only an infinite-valued truthtabular semantics; (3) no truth-tabular semantics at all. Any of those logics, however, can in principle be characterized through non-truth-functional valuation semantics, at least as soon as their associated consequence relations respect the usual tarskian postulates. So, paradoxical as that might seem at first, it turns out that truth-functional logics may be adequately characterized by non-truth-functional semantics . Now, what feature of a given logic would guarantee it to dwell in class (1) or in class (2), irrespective of its circumstantial semantic characterization? (shrink)

La sostenibilidad, por sí misma, no es un criterio útil para evaluar la adecuación y moralidad de un acto, dado que se trata de un concepto abierto, necesitado de conexión con diversos elementos heterogéneos. Por su parte, el concepto de desarrollo sostenible carece de concreción, pues se define en términos de necesidades futuras de muy difícil predicción. Como guía de nuestras acciones será más útil el concepto de desarrollo humano sostenible, formulado en términos de capacidades, fundamentado filosóficamente en un enfoque (...) aristotélico. Dicho enfoque nos permite definir una teoría política del bien común, centrada en la persona, con toda su integridad y complejidad. (shrink)

Non-classical negations may fail to be contradictory-forming operators in more than one way, and they often fail also to respect fundamental meta-logical properties such as the replacement property. Such drawbacks are witnessed by intricate semantics and proof systems, whose philosophical interpretations and computational properties are found wanting. In this paper we investigate congruential non-classical negations that live inside very natural systems of normal modal logics over complete distributive lattices; these logics are further enriched by adjustment connectives that may be used (...) for handling reasoning under uncertainty caused by inconsistency or undeterminedness. Using such straightforward semantics, we study the classes of frames characterized by seriality, reflexivity, functionality, symmetry, transitivity, and some combinations thereof, and discuss what they reveal about sub-classical properties of negation. To the logics thereby characterized we apply a general mechanism that allows one to endow them with analytic ordinary sequent systems, most of which are even cut-free. We also investigate the exact circumstances that allow for classical negation to be explicitly defined inside our logics. (shrink)

Besides the better-known Nelson logic and paraconsistent Nelson logic, in 1959 David Nelson introduced, with motivations of realizability and constructibility, a logic called $\mathcal{S}$. The logic $\mathcal{S}$ was originally presented by means of a calculus with infinitely many rule schemata and no semantics. We look here at the propositional fragment of $\mathcal{S}$, showing that it is algebraizable, in the sense of Blok and Pigozzi, with respect to a variety of three-potent involutive residuated lattices. We thus introduce the first known algebraic (...) semantics for $\mathcal{S}$ as well as a finite Hilbert-style calculus equivalent to Nelson’s presentation; this also allows us to clarify the relation between $\mathcal{S}$ and the other two Nelson logics $\mathcal{N}3$ and $\mathcal{N}4$. (shrink)

Libertarianism deals with what the law should be. In this article, we focus on what the appropriate law to punish criminals should be in a libertarian society; that is, one that respects the Non-Aggression Principle and property rights. We examine various theories of punishment and explain why some are incompatible with libertarianism. We contribute to the latest libertarian theory of punishment suggesting the necessity to take time preference into consideration. We conclude stating a limit and a limitation to libertarian punishment (...) theories. (shrink)

As a literary genre and practice, philosophical and political epistolography seems to have been alive and well in the fourth-century Roman empire. We have fragments of twenty letters of the late third- and early fourth-centuryc.e. Platonist philosopher Iamblichus of Chalcis to former students and other contemporaries, some of whom appear to have been imperial officeholders ; theEpistle to Himeriusof Sopater the Younger to his brother Himerius on the latter's assumption of an unknown governorship in the East, probably sometime in the (...) 340s or 350s ; the Emperor Julian'sEpistle to Themistius, which was likely written and publishedc.December 361/early 362; and theEpistle to Julianof the Aristotelian philosopher Themistius on proper rule, which seems to have been a response, in part, to Julian'sEpistle to Themistiusand perhaps was written to the emperor when both men likely resided in Constantinople at the same time. These philosophical and political letters are but a few examples from this period. All four authors mentioned above, who are representative of intellectual life in the East during the fourth century, produced epistles which reflect Greek political theory in a Roman imperial context. (shrink)

El presente artículo tiene por objeto desarrollar la ética del dolor que se nos presenta en el pensamiento de Miguel de Unamuno. Para este quehacer, basándonos en sus escritos fundamentales, nos adentramos en el impacto que tiene la muerte y el dolor en la conducta vital del ser humano, además de sumergirnos en su concepción del amor como consuelo sanador del sentimiento trágico de la vida. Por último, se analiza la influencia directa de Blaise Pascal en la ética del dolor (...) unamuniana. De esta suerte, al descubrir el valor del sufrimiento en la vida, concluimos que el dolor mismo nos garantiza la existencia, y la existencia sufriente nos garantiza tanto el amor como la esperanza en la inmortalidad del alma humana. (shrink)

La razón emancipadora, posible allí donde se descubre la opresión, es un primer paso hacia una razón liberadora, posible cuando se des-oculta el eurocentrismo de la Razón excluyente, esa fabricación del proceso de modernización como devenir del Occidente privilegiado. La razón no desaparece, sino que se abre hasta dejar espacio a la existencia de diferentes tipos de saberes o racionalidades. Esta descentralización de la Razón excluyente, que corre desiderativamente paralela a una descentralización del sujeto, alumbra heterotopías plurales hacia una superación (...) de la ontología fundamental. El no-Ser se constituye así, consciente de su positividad, como alteridad insospechada que interpela directamente al Ser desde una exterioridad que no reclama sino un carácter de instancia decisiva en las transformaciones pendientes hacia una pluriversidad. Para ello es preciso pensar el mundo desde una ontología que no sea la mera reafirmación del Ser. (shrink)

El ser humano precisa de la técnica para vivir y desarrollarse en todas sus dimensiones, biológicas, sociales y espirituales. La técnica, por su parte, cobra sentido cuando es puesta precisamente al servicio del desarrollo humano. Pero lo técnico ha ido desplegándose a lo largo de la historia en diversas modalidades: de la simple técnica hemos pasado a la tecnología, después a la tecnociencia, de ahí a la biotecnología y, en última instancia, a la antropotecnia. En los últimos años algunos pensadores (...) han propuesto emplear lo técnico sobre el propio ser humano, para transformarlo en un ser posthumano. Tanto Husserl como la escuela de Frankfurt habían denunciado ya la pérdida del sentido provocada por la absolutización de la razón instrumental. Nosotros detectamos que el riesgo del sinsentido se intensifica cuando lo técnico se aplica sin criterio, sin otra razón que la puramente instrumental, sobre el propio ser humano. Argumentamos que, si este proyecto antropotécnico se cumpliese, probablemente lo técnico mismo perdería su sentido y vería posiblemente debilitado su propio crecimiento. Entendemos que la respuesta, con todo, no ha de ir en la línea neoludita, sino en la línea de la actitud que Heidegger denominó serenidad. (shrink)

La sobre-tecnificación inhumana ha promovido una visión reduc- cionista que afecta la forma en que se ejerce la medicina, dañando gravemente la relación médico-paciente. La carencia de formación en competencias humanísticas determina una visión utilitarista y sociobiologista. La deficiencia en la comprensión con respecto a las emociones individuales y ajenas es determinante en las habilidades sociales que, como médicos, debemos promover en las próximas generaciones, de modo que logremos recentrar la atención médica y científica en una visión antropocentrista. La Inteligencia (...) Emocional (IE) es definida como la habilidad para percibir e identificar las emociones ajenas y propias, para discriminar entre ellas y utilizar dicha información para guiar el pensamiento, actuando en consecuencia. Es necesario estructurar la educación médica de las competencias humanísticas en beneficio del ejercicio profesional, fundado en habilidades de comunicación que reflejen una visión integral del ser humano. Se llevó a cabo una revisión de 83 artículos, con la finalidad de identificar la relación existente entre la Inteligencia Emocional y la relación médicop-paciente, presentando un panorama integral sobre la relevancia que la enseñanza de dichas competencias tiene en la educación médica del siglo XXI. (shrink)

The reading that we propose of Freud's work here allows to join the issue of subjectivity and telling the truth from the perspective of confession such as can be differentiated and related to the question of Christian confession. Without being confused with a spiritual exercise, psychoanalysis, in reviving the ambition of bringing into being a subject freed from what haunts and persecutes him, the modern name of this being the "unconscious", does not erase its Western origin. Nevertheless, psychoanalysis modifies the (...) ancient way of understanding the link between speech and desire. (shrink)

We follow the ideas given by Chen and Grätzer to represent Stone algebras and adapt them for the case of Stonean residuated lattices. Given a Stonean residuated lattice, we consider the triple formed by its Boolean skeleton, its algebra of dense elements and a connecting map. We define a category whose objects are these triples and suitably defined morphisms, and prove that we have a categorical equivalence between this category and that of Stonean residuated lattices. We compare our results with (...) other works and show some applications of the equivalence. (shrink)

Soberanía y obediencia fueron dos nociones clave en las discusiones que se dieron en los albores de la modernidad. Parte de los debates se centró en la cuestión de la legitimidad del poder político y, en consecuencia, en por qué debemos obedecer, qué beneficios trae la obediencia y cuáles son sus límites. En todos estos casos, la noción de violencia aparece con diferentes rostros, y principalmente con la fisonomía de la guerra —punto de máxima expresión de la violencia explícita—, problema (...) que la autoridad política viene, de alguna manera, a resolver. El Estado soberano, sin embargo, lejos está de ser la representación del irenismo, se convierte en monopolio legítimo de la violencia. Este trabajo pretende abordar tales cuestiones desde las teorías de Hobbes y Harrington. Ambos justificaron la obligación de los súbditos a acatar la ley que se impone y que garantiza, por sobre todas las cosas, su vida. (shrink)

In the original publication, the corresponding author was indicated incorrectly. The correct corresponding author of the article should be Ori Lahav. The original article has been updated accordingly.

This article provides a discussion of the concepts of politics, sovereignty and man in the thinking of CARL SCHMITT and THOMAS HOBBES, clarifying certain similarities and differences between the two authors. It attempts to understand the well-known theory of the German author concerning that which is political, as drawn from the struggle and distinction between friend/foe in light of the threat posed by the Hobbesian state of nature and the meaning of war. These ideas call for a State that does (...) not arise as the result of a contract, but from unity based on exclusions, according to SCHMITT. The Acerca de los conceptos de política Dolores Marcos y soberanía en Carl Schmitt y Thomas Hobbes need for an absolute power that can protect and coerce connects with certain features of HOBBES´ Leviathan. Finally, the conflictive dimension of man is understood as essential for the political realm, which is based, precisely, on egotistical and dange rous features in human beings. Understanding this sphere turns out to be essential for developing an approach to the resolution of conflicts. (shrink)

To repoliticize the body is to assert that human beings do not have bodies, but they are bodies. The human being is a living body. This idea frames a fundamental ethical question—“which human lives are worth living?”—in different terms: “which bodies are apt or conformable to become human?”. To address this question, which this article intends to, is to engage in transformative philosophy. Two contemporary currents of thought dive into this vital issue: cyborg feminism and queer feminism. From a decolonial (...) standpoint, a focus on the bodies that suffer and an orientation towards possible futures, where life might not be the privilege of some particular kinds of corporality, will prove fruitful to begin unraveling the answer. (shrink)