Luis Estrada-González

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.

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.

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.

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.

Early adolescence is a developmental stage that comprises some basic interactional processes with parents, which can be described as gaining autonomy while maintaining relatedness. Studying how maternal and paternal involvement influence the life satisfaction of sons and daughters during early adolescence is especially important while seeking to understand the challenges of this developmental stage. In this paper, we investigate the differential effects of maternal and paternal involvement, as assessed by sons and daughters, on their life satisfaction during early adolescence. We use a unique survey conducted in Chile, The National Survey on Student Trajectories and Transitions, focusing on a subsample of 497 early adolescents attending 5th to 8th grade. Our findings indicate that both paternal and maternal involvement are positively correlated with the life satisfaction of adolescents. We also find that the gender of adolescents moderates the effect of maternal involvement, so daughters who deemed the involvement of their mothers to be more positive reported greater life satisfaction. More positive paternal involvement correlates with greater life satisfaction for sons and daughters. We discuss some mechanisms that might bring about these differences.

School achievement and failure have become growing political and social concerns due to the negative consequences of school failure for individuals and society. The inclusive educational movement, which calls for equal access, permanence, participation, and promotion of all students worldwide, poses many challenges for schools and school systems. As a public policy strategy, some countries have provided additional funds for incorporating non-teaching professionals such as school psychologists and social workers in regular K-12 schools. However, there is lack of research on the effects of these psychosocial professionals on student outcomes. This national multilevel study explored the effect of psychologists (n= 8,469) and social workers (n= 3,524) on indicators of eighth-grade (n= 147,531) and 10th-grade (n= 106,347) students' academic achievement and dropout in Chile. A multilevel secondary analysis was performed using national records of non-teaching professionals working as school staff members, achievement scores on the national SIMCE test, and dropout rates based on official records. Results showed that after controlling for individual and school variables known to affect achievement and dropout, schools with psychologists and social workers working as staff members had lower short- and long-term dropout rates. The presence and higher number of school psychologists per school was positively associated with higher math achievement, with a reduced effect in low-SES schools. Lower-SES schools with more social workers had higher math scores. These results support policies that increase funding for school psychologists and social workers, since their incorporation partly explains better school achievement and less school failure when controlling for individual and school characteristics, but emphasize the need to further explore the mechanisms through which school achievement and failure are developed with the support of psychologists and social workers in schools. We discuss the need to regulate the type of prevention and intervention strategies from a whole-school, evidence-based approach, as well as to incorporate psychosocial training modules and comprehensive guidelines as part of professional training programs and as certified requisites for working in schools.

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.

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.

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.

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.

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.

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.

Schools are an essential part of students’ lives and can promote and facilitate their well-being. Although research on well-being among school-aged children and adolescents has distinguished subjective well-being from social well-being, very few studies examined student’s social well-being at school. SWS is understood as students’ valuation of the circumstances and functioning of their school. This framework posits that the context of the schools can shape students’ perception of feeling integrated and making significant contributions to their schools. However, not much is known regarding the joint contribution of individual, family, and school characteristics to students’ SWS. This study analyzed these joint contributions in a nationally representative sample of 6,389 children and adolescents enrolled in 5th–11th grades. Findings show that being female and younger were individual predictors of SWS. Students’ satisfaction with their family and fewer changes of schools were also significant contributors. When students’ perceptions of their schools were incorporated, the individual and family characteristics decreased or lost significance. In the full model, the highest contribution to SWS was explained by the school-level aggregated perception of school climate. These findings call for integrated policies and practices to foster students’ sense of belonging, feeling integrated, and contribution to their schools, with a focus on school-level interventions to improve SWS through positive and engaging school climates that foster students’ sense of agency.

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.

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.

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.

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.

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.

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.