Luis Estrada-González

We show that Wiredu’s result in [26] is not the doom for connexive set theories, not even for those based in logics similar to CC1, one of the original target logics. For this purpose, we present the necessary assumptions for Wiredu’s proof, making some precisions on the connexive requirements. Then we present a non-reflexive variant of CC1 in which Wiredu’s proof can be blocked. Finally, we discuss the prospects of a connexive set theory based on both the non-reflexive and non-transitive variants of CC1, which, even assuming non-triviality, are not very rosy.

Following the strategy in [15] to develop inconsistent models for relevant arithmetics, we formulate a connexive variant of arithmetic by replacing the conditional of RM3 with the Belikov–Loginov conditional. We obtain thus the connexive logic cRM3 which serves as a base logic for arithmetics cRM3$^{i}$, cRM3$^{i\sharp }$, cRM$^{\sharp }$, cRMn$^{i}$, and cRM$^\omega $. We compare these with their counterparts RM3$^{i\sharp }$, RM$^{\sharp }$ and $\mathbf{RM}^\omega$ that extend relevant arithmetic $\mathbf{R}^\sharp$.

Mortensen introduced a connexive logic commonly known as 'M3V'. M3V is obtained by adding a special conditional to LP. Among its most notable features, besides its being connexive, M3V is negation-inconsistent and it validates the negation of every conditional. But Mortensen has also studied and applied extensively other non-connexive logics, for example, closed set logic, CSL, and a variant of Sette's logic, identified and called 'P2' by Marcos. In this paper, we analyze and compare systematically the connexive variants of CSL and P2, obtained by adding the M3V conditional to them. Our main observations are two. First, that the inconsistency of M3V is exacerbated in the connexive variant of closed set logic, while it is attenuated in the connexive variant of the Sette-like P2. Second, that the M3V conditional is, unlike other conditionals, "connexively stable", meaning that it remains connexive when combined with the main paraconsistent negations.

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

Really full blooded platonism (RFBP) is aimed to achieve a complete picture of the mathematical landscape by accepting inconsistent mathematics. I distinguish various senses of completeness relevant to the debate and argue that the move to inconsistency-tolerance might not be enough to achieve a complete picture of the mathematical landscape in any of those senses, for there is positive reason to endorse a richer Platonism with place for trivial parts in the mathematical landscape. © 2017 Elsevier B.V., All rights reserved.

According to common wisdom, the connective tonk defined by Prior trivializes any theory that contains it. However, it should not be forgotten that whether an argument holds or not depends to a large extent on the underlying notion of logical consequence. Logical consequence is usually assumed to be Tarskian, that is, reflexive, transitive and monotonic. However, Belnap had already conjectured that tonk might not be so problematic in a non-transitive logic, which Cook finally proved in 2005. In this paper we improve on Cook’s result in two ways: our hypothesis is simpler (namely, we use fewer interpretations than he did and we do not rely on a disjunctive consequence relation) and it is not ad hoc (namely, our working consequence relation is not designed merely to avoid triviality under tonk).

We show that Wiredu’s result in [26] is not the doom for connexive set theories, not even for those based in logics similar to CC1, one of the original target logics. For this purpose, we present the necessary assumptions for Wiredu’s proof, making some precisions on the connexive requirements. Then we present a non-reflexive variant of CC1 in which Wiredu’s proof can be blocked. Finally, we discuss the prospects of a connexive set theory based on both the non-reflexive and non-transitive variants of CC1, which, even assuming non-triviality, are not very rosy.

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.

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.

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.

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.