Luis Gonzalez

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.

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.

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.

A menudo se discute cómo cifrar el alcance de la herencia de Kant en la metafísica de Schopenhauer. Del corazón y sustancia de su Tebas de las mil puertas, la ética, Aramayo cree oportuno tomarla como una radicalización del formalismo kantiano. A mi juicio, para delimitar qué hay de continuidad, y qué de ruptura, es necesario hacer un examen atento del puente que conduce de uno a otro. En este sentido, la crítica dedicada a Kant en Sobre el fundamento de la moral no ocupa un lugar accidental en su pensamiento único, pues contiene lo que le falta al apéndice crítico de su obra principal respecto al objeto que nos ocupa. Desde el análisis de conceptos hasta las lecturas genealógicas que se presentan en esta polémica, un mismo propósito subyace: la depuración del concepto de racionalidad práctica como solución a las aporías y los escollos del legado ético kantiano.

A imagem sugestiva "retorno do outro" ajuda a indicar o modo como a alteridade interpela no actual contexto de globalização. Esse "outro", o grande ausente da maior parte da história da filosofia ocidental, aparece com força renovada (ou, pelo menos, resiste aos embates da homo-geneização) frente à lógica económica, política e cultural, que pretende anulá-lo na imposição uniforme de um estilo de vida. O seu "retorno" abre possibilidades em várias perspectivas. Aqui apenas esboçamos o que significou este "retorno do outro" na irrupção do pensamento intersubjectivo, bem como as possibilidades que abre para a relação intercultural. The suggestive image, "turn to the other", gives an indication of how alterity challenges the current context of globalisation- This "other" is the great absent in the greater part of the history of Western philosophy. It appears with renovated strength (or at least resists the pressures of homogenisation) in the face of the economic, political, and cultural logic that seeks to annul it through the uniform imposition of a given lifestyle. Its return opens possibilities of varying kinds. Here we wish only to sketch the meaning of this "turn to the other" in the irruption of the inter-subjective thought and possibilities it opens for intercultural relations

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.

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.

Esta nota, que resume una conferencia pronunciada en octubre de 2011 en las Jornadas Nacionales de Liturgia de Barcelona, analiza y estudia la aportación de Sacramentum Caritatis al importante tema de la participación activa de los fieles en la liturgia. El autor concluye, entre otras cosas, que la sutil distinción entre condiciones personales para la participación y la participación misma enriquece el concepto de actuosa participatio acentuando sus dimensiones más hondas desde el punto de vista de la antropología sacramental.

La presente nota bibliográfica recopila la ingente obra de José Aldazábal, uno de los liturgistas españoles más fecundos en publicaciones de carácter sobre todo divulgativo, que, durante más de cuarenta años y formando parte del Centro de Pastoral Litúrgica de Barcelona, ha acompañado la pastoral litúrgica especialmente en España, pero también en los paísesiberoamericanos de lengua española. Interesará a los investigadores de la historia de la renovación litúrgica y a los estudiosos de la pastoral.