A contra-classical logic is a logic that, over the same language as that of classical logic, validates arguments that are not classically valid. In this paper I investigate whether there is a single, non-trivial logic that exhibits many features of already known contra-classical logics. I show that Mortensen’s three-valued connexive logic _M3V_ is one such logic and, furthermore, that following the example in building _M3V_, that is, putting a suitable conditional on top of the \(\{\sim, \wedge, \vee \}\) -fragment of (...) _LP_, one can get a logic exhibiting even more contra-classical features. (shrink)

Seen from the point of view of evaluation conditions, a usual way to obtain a connexive logic is to take a well-known negation, for example, Boolean negation or de Morgan negation, and then assign special properties to the conditional to validate Aristotle’s and Boethius’ Theses. Nonetheless, another theoretical possibility is to have the extensional or the material conditional and then assign special properties to the negation to validate the theses. In this paper we examine that possibility, not sufficiently explored in (...) the connexive literature yet.We offer a characterization of connexive negation disentangled from the cancellation account of negation, a previous attempt to define connexivity on top of a distinctive negation. We also discuss an ancient view on connexive logics, according to which a valid implication is one where the negation of the consequent is incompatible with the antecedent, and discuss the role of our idea of connexive negation for this kind of view. (shrink)

Francez has suggested that connexivity can be predicated of connectives other than the conditional, in particular conjunction and disjunction. Since connexivity is not any connection between antecedents and consequents—there might be other connections among them, such as relevance—, my question here is whether Francez’s conjunction and disjunction can properly be called ‘connexive’. I analyze three ways in which those connectives may somehow inherit connexivity from the conditional by standing in certain relations to it. I will show that Francez’s connectives fail (...) all these three ways, and that even other connectives obtained by following more closely Wansing’s method to get a connexive conditional, fail to be connexive as well. (shrink)

In this paper we discuss whether the relation between formulas in the relating model can be directly introduced into the language of relating logic, and present some stances on that problem. Other questions in the vicinity, such as what kind of functor would be the incorporated relation, or whether the direct incorporation of the relation into the language of relating logic is really needed, will also be addressed.

In this paper I probe the idea that neither possibilism nor trivialism could be ruled out on a purely logical basis. I use the apparatus of relational structures used in the semantics for modal logics to engineer some models of possibilism and trivialism and I discuss a philosophical stance about logic, truth values and the meaning of connectives underlying such analysis.

Alberic of Paris put forward an argument, ‘the most embarrassing of all twelfth-century arguments’ according to Christopher Martin, which shows that the connexive principles contradict some other logical principles that have become deeply entrenched in our most widely accepted logical theories. Building upon some of Everett Nelson’s ideas, we will show that the steps in Alberic of Paris’ argument that should be rejected are precisely the ones that presuppose the validity of schemas that are nowadays taken as some of the (...) most trivial logical truths: (A∧B) → A and (A∧B) → B, i.e. Simplification. (shrink)

However broad or vague the notion of connexivity may be, it seems to be similar to the notion of relevance even when relevance and connexive logics have been shown to be incompatible to one another. Relevance logics can be examined by suggesting syntactic relevance principles and inspecting if the theorems of a logic abide to them. In this paper we want to suggest that a similar strategy can be employed with connexive logics. To do so, we will suggest some properties (...) that seem to be hinted at in Nelson’s work. Following this strategy will ideally shed some light over the notion of content and will also help make a clear comparison between relevance and connexive logics. (shrink)

In this paper we show that, when analyzed with contemporary tools in logic—such as Dunn-style semantics, Reichenbach’s three-valued logic exhibits many interesting features, and even new responses to some of the old objections to it can be attempted. Also, we establish some connections between Reichenbach’s three-valued logic and some contra-classical logics.

It has been claimed that contracting connectivesContracting connective are conditionalsConditional. Our modest aim here is to show that the conditional-like features of a contracting connectiveContracting connective depend on the defining features of the conditionalConditional in a particular logic, yes, but they also depend on the underlying notion of logical consequence and the structure of the collection of truth values. More concretely, we will show that under P-consequenceP-consequence and suitable satisfiability conditions for the conditionalConditional, conjunctionsConjunction are contracting connectivesContracting connective for some (...) logics without thereby being conditional-ish. (shrink)

Mortensen studies dual intuitionistic logic by dualizing topos internal logic, but he did not study a sequent calculus. In this paper I present a sequent calculus for complement-topos logic, which throws some light on the problem of giving a dualization for LJ.

Here we study two connexive logics based on one of the conditionals introduced by Church in [4] and on some negations defined through falsity constants in the sense of Ackermann in [1].

According to logical non-necessitarianism, every inference may fail in some situation. In his defense of logical monism, Graham Priest has put forward an argument against non-necessitarianism based on the meaning of connectives. According to him, as long as the meanings of connectives are fixed, some inferences have to hold in all situations. Hence, in order to accept the non-necessitarianist thesis one would have to dispose arbitrarily of those meanings. I want to show here that non-necessitarianism can stand, without disposing arbitrarily (...) of the meanings of connectives, based on a minimalist view on the meanings of connectives. (shrink)

. In this paper we present a proposal that (i) could validate more relations in the square than those allowed by classical logic (ii) without a modification of canonical notation neither of current symbolization of categorical statements though (iii) with a different but reliable semantics.

Logic is an excellent tool for reasoning about most philosophical topics, including logical issues themselves. Discussions about the validity or otherwise of certain principles have been widespread throughout the history of logic. This chapter exemplifies that with the analysis of the debate surrounding connexive logics. In connexive logics, certain principles involving mainly negation and implication hold good, whereas they are not valid in most well-known logics. Despite their intuitiveness, the connexive principles quickly lead to contradictions and even to triviality, i.e. (...) to the truth of every proposition. This chapter surveys the main arguments against the connexive principles and discusses some prospects for challenging those arguments and endorsing the connexive principles. (shrink)

I offer here a critical assessment of Beall and Ficara’s most recent take on Hegelian contradictions. By interpreting differently some key passages of Hegel’s work, I favor, unlike them, a no-gaps approach which leads to a different logic.

En The paradox of Addition and its dissolution (1969), Mario Bunge presenta algunos argumentos para mostrar que la Regla de Adición puede ocasionar paradojas o problemas semánticos. Posteriormente, Margáin (1972) y Robles (1976) mostraron que las afirmaciones de Bunge son insostenibles, al menos desde el punto de vista de la lógica clásica. Aunque estamos de acuerdo con las críticas de Margáin y Robles, no estamos de acuerdo en el diagnóstico del origen del problema y tampoco con la manera en la (...) que se proponen solucionarlo. En esta medida, en este texto mostraremos cómo la Regla de Adición sí trae problemas semánticos que pueden ser planteados desde diferentes perspectivas contemporáneas, como la extensionalidad del condicional, los principios proscriptivos y la validez conexiva. (shrink)

Béziau has recently argued that the logic LP commits dialetheists to trivialism and Martin has pointed out very clearly the main problems with that alleged result. My sole purpose here is to make the spirit of Martin’s reply more concise, exhibiting as clearly as possible the logical defects in Béziau’s reasoning. Additionally, I want to make some remarks on LP qua logic and not only as an interpreted language.

PurposeGraham Priest has recently argued that the distinctive trait of classical mathematics is that the conditional of its underlying logic—that is, classical logic—is extensional. In this article, I aim to present an alternate explanation of the specificity of classical mathematics.MethodI examine Priest's argument for his claim and show its shortcomings. Then I deploy a model-theoretic presentation of logics that allows comparing them, and the mathematics based on them, more fine-grainedly.ResultsSuch a model-theoretic presentation of logics suggests that the specific character of (...) classical logic consists in the structure that it confers to its truth values and in the structure of the evaluation indices of its formulas, and that this trait is useful to explain the specific character of the logics and the mathematics based on them.ConclusionThe extensionality of the conditional in classical logic is a by-product of other structural features of a logic, which are more likely to be what gives a kind of mathematics based on it its specific character. (shrink)

Beall has given more or less convincing arguments to the effect that neither classical logic, nor K3, nor LP, nor S3 can play the role he expects from logic: to be the basement theory for all true theories, including true theology. However, he has not considered all the pertinent competitors, and he has not given any reassurance that he has not gone too low in the hierarchy of logics to find his desired “universal closure of all true theories”. In this (...) paper, I put forward those additional arguments to show the superiority of FDE with respect to logics that include a detachable conditional but that are very much like FDE otherwise. I also discuss the problem that theological consequence might not contrapose even if theological consequence is supposed to extend FDE consequence and the latter does contrapose. (shrink)

En esta nota crítica (i) se hace una breve descripción de cada uno de los artículos que componen Orayen: de la forma lógica al significado, (ii) se señalan algunas cuestiones que no están claras en ellos o en las réplicas de Orayen y, (iii) en la medida de lo posible, se indica si los autores desarrollan ulteriormente los problemas abordados en sus artículos. The aim of this critical note is threefold: (i) it briefly describes and comments on each of the (...) articles of Orayen: de la forma lógica al significado; (ii) identifies some issues that may not be clear enough or not fully developed whether in the articles or even in Orayen's replies; (iii) as far as possible, it refers to further studies made by the authors themselves on the same, or quite related, subjects addressed by them in their papers. (shrink)

Philosophy of logic is a fundamental part of philosophical study, and one which is increasingly recognized as being immensely important in relation to many issues in metaphysics, metametaphysics, epistemology, philosophy of mathematics, and philosophy of language. This textbook provides a comprehensive and accessible introduction to topics including the objectivity of logical inference rules and its relevance in discussions of epistemological relativism, the revived interest in logical pluralism, the question of logic's metaphysical neutrality, and the demarcation between logic and mathematics. Chapters (...) in the book cover the state of the art in contemporary philosophy of logic, and allow students to understand the philosophical relevance of these debates without having to contend with complex technical arguments. This will be a major new resource for students working on logic, as well as for readers seeking a better understanding of philosophy of logic in its wider context. (shrink)

We present here some Boolean connexive logics (BCLs) that are intended to be connexive counterparts of selected Epstein’s content relationship logics (CRLs). The main motivation for analyzing such logics is to explain the notion of connexivity by means of the notion of content relationship. The article consists of two parts. In the first one, we focus on the syntactic analysis by means of axiomatic systems. The starting point for our syntactic considerations will be the smallest BCL and the smallest CRL. (...) In the first part, we also identify axioms of Epstein’s logics that, together with the connexive principles, lead to contradiction. Moreover, we present some principles that will be equivalent to the connexive theses, but not to the content connexive theses we will propose. In the second part, we focus on the semantic analysis provided by relating- and set-assignment models. We define sound and complete relating semantics for all tested systems. We also indicate alternative relating models for the smallest BCL, which are not alternative models of the connexive counterparts of the considered CRLs. We provide a set-assignment semantics for some BCLs, giving thus a natural formalization of the content relationship understood either as content sharing or as content inclusion. (shrink)

In this paper, we evaluate Button’s claim that knot is a nasty connective. Knot’s nastiness is due to the fact that, when one extends the set \ with knot, the connective provides counterexamples to a number of classically valid operational rules in a sequent calculus proof system. We show that just as going non-transitive diminishes tonk’s nastiness, knot’s nastiness can also be reduced by dropping Reflexivity, a different structural rule. Since doing so restores all other rules in the system as (...) validity-preserving, we are inclined to conclude that there, knot is not that nasty. However, since motivating non-reflexivity is harder than motivating non-transitivity, we also acknowledge that disagreement with our conclusion is possible. (shrink)

En este artículo discutimos la tesis de Jc Beall según la cual no hay negación lógica. Evaluamos la solidez del argumento con el que defiende su tesis y presentamos dos razones para rechazar una de sus premisas: que la negación tiene que ser excluyente o exhaustiva. La primera razón involucra una presentación alternativa de las reglas de la negación en sistemas de secuentes diferentes al que Beall presupone. La segunda razón establece que la negación no tiene que ser excluyente o (...) exhaustiva. (shrink)

Based on his Inclosure Schema and the Principle of Uniform Solution (PUS), Priest has argued that Curry’s paradox belongs to a different family of paradoxes than the Liar. Pleitz (2015, The Logica Yearbook 2014, pp. 233–248) argued that Curry’s paradox shares the same structure as the other paradoxes and proposed a scheme of which the Inclosure Schema is a particular case and he criticizes Priest’s position by pointing out that applying the PUS implies the use of a paraconsistent logic that (...) does not validate Contraction, but that this can hardly seen as uniform. In this paper, we will develop some further reasons to defend Pleitz’ thesis that Curry’s paradox belongs to the same family as the rest of the self-referential paradoxes & using the idea that conditionals are generalized negations. However, we will not follow Pleitz in considering doubtful that there is a uniform solution for the paradoxes in a paraconsistent spirit. We will argue that the paraconsistent strategies can be seen as special cases of the strategy of restricting Detachment and that the latter uniformly blocks all the connective-involving self-referential paradoxes, including Curry’s. (shrink)

ABSTRACT In this brief note we explore a couple of features of the semantics for indicative conditionals provided by Field. Those features strikingly resemble some controversial principles in connexive logic. We will show that although Field’s semantics has the technical means to stand to the mentioned features, more work is needed to make some of its outcomes less unintuitive.

Five major stances on the problems of the possibility and fruitfulness of a debate on the principle of non-contradiction (PNC) are described: Detractors, fierce supporters, demonstrators, methodologists and calm supporters. We show what calm supporters have to say on the other parties wondering about the possibility and fruitfulness of a debate on PNC. The main claim is that one can find all the elements of calm supporters already in Aristotle’s works. In addition, we argue that the Aristotelian refutative strategy, originally (...) used for dealing with detractors of PNC in Metaphysics, has wider implications for the possibility and fruitfulness of an up-to-date debate on PNC, at least in exhibiting some serious difficulties for the other parties. (shrink)

After the intense attention the relevance logic community and its friends gave to McCall’s ideas on connexive implication during the late 1960s and nearly.

Estrada-Gonzalez-Olmedo-Garcia_On-the-plenitude-of-truth.-A-defense-of-trivialism-by-Paul-Kabay2.

Like theories, reconstructions of episodes in the history of science can possess, or lack, certain virtues such that, when we face two or more different reconstructions of the same episode, we assume that we should choose the most “virtuous one”. However, we will argue that, with dissimilar reconstructions of the same episode, it is not always necessary to separate the “good ones” from the “wrong ones”, and that, as a matter of fact, each reconstruction could provide different but perhaps equally (...) relevant data about the episode, about science in general, and about particular philosophical theses. In order to help us to identify these benefits, we will present a criterion that guides the search for historiographical reinforcement of philosophical theses and we will use it to evaluate three different reconstructions of the same scientific episode. (shrink)

Nowadays there is a growing tendency in the philosophy of science to think that some phenomena cannot be exhaustively explained, or even described, by a single theory or a particular approach. Thus, we are occasionally required to use various approaches in order to give account of the phenomenon we are analyzing. And sometimes, we can appreciate this as an invitation to be pluralist in certain respects about our understanding of a particular aspect in science. -/- During the last decade applications (...) of pluralism have increased and led to several other relevant debates in the philosophy of science. By the strengthening of pluralism, new questions have emerged, and more importantly, new alternatives have been offered in dealing with problems about how to interpret the ontology and the ontological commitments of particular theories, or how to apply strategies to analyze and understand specific episodes from the history of science, or how to work within different, and sometimes incompatible, explanations about a particular phenomenon, among others. In general, pluralism seems to be a very rich and yet not enough explored path for the philosophy of science in general. -/- Today, it is recognized that, at least for methodological purposes, the application of pluralism to the study of science can offer a great number of benefits. One of them would be the opportunity of analyzing the role that some epistemic virtues -such as scope, fruitfulness, consistency, and simplicity, to name just a few- play in the scientific activity. From the different pluralist positions, a lot has been said about empirical adequacy, refutability and explanatory power yet consistency power, yet, consistency has not been equally dealt with. -/- As a matter of fact, the lack of consistency and its philosophical implications have been studied from an angle that does not necessarily involve a pluralism of any kind. At the moment, it is commonly accepted that inconsistencies are more frequent in scientific development that the traditional philosophy of science could have expected and the idea that inconsistency is not always a synonym of logical anarchy, as it was suggested in the classical literature of logic and the philosophy of science, has been gaining support. All this has been possible, mostly, thanks to the emergence of paraconsistent logics and the availability of case studies that show how inconsistency is not an uncommon phenomenon in science. -/- But pluralism does not necessarily entail inconsistency toleration nor vice versa. Accordingly the main motivation for this volume is to explore the links between pluralism and inconsistency toleration in science, in order to connect the reflections on inconsistency toleration with broader and major issues in philosophy of science. In order to do so, we will suggest two different lines of investigation: first, to focus on the implication of some pluralistic accounts in the philosophy of science, regarding inconsistency; and second to analyze the implications of some paraconsistent approaches regarding pluralism in science. (shrink)

En este artículo tratamos de hacer plausible la hipótesis de que las conectivas de diferentes lógicas no necesariamente difieren en significado. Utilizando el tratamiento categorista de las conectivas, argumentaremos contra la tesis quineana de que la diferencia de lógicas implica diferencia de significado entre sus conectivas, y ubicamos el cambio de tema en la diferencia de objetos más bien que en una tal diferencia de significado. Finalmente, intentamos mostrar que ese tratamiento categorista es una forma de minimalismo semántico, de acuerdo (...) con el cual no todos los elementos semánticos usuales son relevantes para determinar el significado de las conectivas. (shrink)

Realist dialetheism is the view that there are contradictions in reality. One argument against this idea says that it is impossible because it has to make room for the possibility of a trivial reality, which is metaphysically impossible. Another argument against it says that the metaphysical structure of reality is such that it is impossible to have contradictions in it. I argue here that both arguments fail to establish the impossibility of realist dialetheism because they are based on a misconception (...) about the notions of negation and contradiction, which leads them, in the first case, to wrongly hold that dialetheism has to be compatible with trivialism, and, in the second case, to assume that the validity of the Aristotelian principle of non-contradiction prevents the existence of dialetheias. (shrink)

El ejercicio utópico de la voluntad política que caracteriza el XIX latinoamericano se desgrana en las categorías de unidad continental, unidad cultural, unidad en el concepto de Patria, etc.; clausurando un apretado siglo de extrema densidad social y política, un siglo de utopía en el discurso. Una Ilustración insuficiente, el coste del hibridismo, las comunidades imaginadas, las dependencias encadenadas, las resistencias, los logros y los fracasos, traducen el sacrificio, la traición y la inconclusión de la tarea emancipatoria. Si podemos contemplar (...) hoy día el descubrimiento de América como el comienzo de una empresa civilizatoria, y admirar sus obras más allá del trabajo infatigable de una destrucción que no ha cesado, es sólo en virtud de esta tradición de crítica y resistencia , a lo largo de un proceso social, artístico y literario ininterrumpido hasta el día de hoy. (shrink)

La tendencia natural de identificar complejidad con algo complicado y confuso, es una forma también natural de simplificar las redes complejas del fenómeno del conocimiento y de los saberes. En este artículo se presentan las orientaciones y puntos de partida del pensamiento complejo en la perspectiv..

Reflexiones en torno a la formación profesional española.

En las páginas que siguen, vamos a realizar una lectura política del pensamiento de Derrida, dirigiendo nuestra atención, primero, a la deconstrucción de la escritura para centrarnos en el significado político de la différance , segundo, a la institución filosófica como vehículo de elaboración y transmisión del saber y, tercero, a lo que el pensador francés ha reunido bajo el rótulo figuras de lo imposible , con especial atención a la hospitalidad, la responsabilidad y la justicia.

The presence of the past is of prime importance in today's Mexican society. According to José Fuentes Mares, among the “peoples of the world the Mexican is the one who lives history the most”. With regard to the unsatisfactory relations between Mexico and North America, the journalist Alan Riding asks himself: “How can a people who relish the past to the point of intoxication understand another that looks constantly to the future?” In the Republic of Mexico, according to him, “the (...) entire past of the country throws a dense shadow over the present”. Conforming to a universal custom, every country divides its present past into four groups (survival, residues, memories and history), but in few nations are the four groups as copious as in this one. Although Mexico is rapidly shedding many old customs and is selling residual objects to foreign collectors on the sly, its historical treasure is still enormous, perhaps the largest in the world. (shrink)