Luis Gonzalez

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.

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.

La España ayer nacionalcatólica vive hoy el «después de» los atentados terroristas del 11-M. Esta forma atroz que tuvieron los integristas islámicos de hacer irrumpir el sacro en la esfera pública y el mismo giro laicista del nuevo Ejecutivo, ponen de manifiesto de modo bien distinto las enormes dimensiones del debate de fondo religioso suscitado en nuestra sociedad. En España, el sacro ha saltado nuevamente a la esfera pública poniendo en tela de juicio las consolidadas relaciones entre política y religión desarrolladas en la Constitución de 1978 y a partir de la firma del Concordato de 1979 entre la Santa Sede y el nuevo Estado democrático. Además, estas circunstancias se suman a dos hechos sólo aparentemente paradójicos: la creciente pluralidad religiosa y los procesos de secularización de la sociedad española. Por este motivo, estamos en condiciones de afirmar que, por debajo de las diversas medidas concretas de los programas políticos, en nuestro país se está desarrollando con una particular virulencia un gran debate de fondo religioso. Por eso consideramos que la “nueva” teología política de J.B. Metz sigue siendo un instrumento válido desde el que salir cristianamente a la palestra del pensamiento y del quehacer público. De este modo, el objetivo del presente estudio no es otro que considerar nuestro país en el interior del discurso teológico como un verdadero locus theologicus.

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.

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.

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.