The “official” history of connexive logic was written in 2012 by Storrs McCall who argued that connexive logic was founded by ancient logicians like Aristotle, Chrysippus, and Boethius; that it was further developed by medieval logicians like Abelard, Kilwardby, and Paul of Venice; and that it was rediscovered in the 19th and twentieth century by Lewis Carroll, Hugh MacColl, Frank P. Ramsey, and Everett J. Nelson. From 1960 onwards, connexive logic was finally transformed into non-classical calculi which partly concur with (...) systems of relevance logic and paraconsistent logic. In this paper it will be argued that McCall’s historical analysis is fundamentally mistaken since it doesn’t take into account two versions of connexivism. While “humble” connexivism maintains that connexive properties only apply to “normal” antecedents, “hardcore” connexivism insists that they also hold for “abnormal” propositions. It is shown that the overwhelming majority of the forerunners of connexive logic were only “humble” connexivists. Their ideas concerning connexive implication don’t give rise, however, to anything like a non-classical logic. (shrink)

Stoic logic assumes five inference schemata attributed to Chrysippus of Soli. Those schemata are the well-known indemonstrables. A problem related to them can be that, according to standard propositional calculus, only one of them, modus ponens, is clearly indemonstrable. Nevertheless, I try to show in this paper that the mental logic theory enables to understand why the Stoics considered such schemata to be basic kinds of arguments. Following that theory, four of them can be linked to ‘Core Schemata’ of mental (...) logic and the only one that is more controversial is modus tollens. However, as I also comment, some assumptions of Stoic philosophy, which can be interpreted from the mental logic theory, can explain why this last argument was included into the set of the indemonstrablesas well. (shrink)

Además de los indemostrables, la lógica estoica incluye varias reglas de reducción. En este trabajo, analizo la primera de ellas con el fin de comprobar si fue derivada formalmente a partir de los indemostrables o los estoicos pudieron plantearla a partir del uso de sus capacidades naturales de razonamiento. De esta manera, trato de mostrar que tenemos razones para apoyar ambas posibilidades y, basándome en un enfoque semántico como el de la teoría de los modelos mentales, de ofrecer argumentos al (...) respecto. (shrink)

Resumen Atendiendo a la lógica estándar, solo uno de los cinco indemostrables propuestos por Crisipo de Solos es realmente indemostrable. Sus otros cuatro esquemas son demostrables en tal lógica. La pregunta, por tanto, es: si cuatro de ellos no son verdaderamente indemostrables, por qué Crisipo consideró que sí lo eran. López-Astorga mostró que si ignoramos el cálculo proposicional estándar y asumimos que una teoría cognitiva contemporánea, la teoría de la lógica mental, describe correctamente el razonamiento humano, se puede entender por (...) qué Crisipo pensó que todos sus indemostrables eran tan básicos. No obstante, en este trabajo trato de argumentar que la teoría de la lógica mental no es el único marco que puede explicar esto. En concreto, sostengo que otra importante teoría sobre el razonamiento en el presente, la teoría de los modelos mentales, también puede ofrecer una explicación al respecto.According to standard logic, only one of the five indemonstrables proposed by Chrysippus of Soli is actually indemonstrable. The other four schemata are demonstra-ble in that logic. The question hence is, if four of them are not really indemonstrable, why Chrysippus considered them to be so. López-Astorga showed that, if we ignore standard propositional calculus and assume that a current cognitive theory, the mental logic theory, truly describes human reasoning, it can be explained why Chrysippus thought that all of his indemonstrables were so basic. However, in this paper, I try to argue that the mental logic theory is not the only framework that can account for that. In particular, I hold that another important reasoning theory at present, the mental models theory, can offer an explanation in that regard as well. (shrink)

The theory of mental models is a current cognitive approach trying to describe the way people make inferences. According to this theory, people reason from possibilities or models linked to sentences. Sometimes, such possibilities or models are transformed by the action of a semantic modulation. The point this paper is intended to make is that Stoic logic also has the machinery to explain semantic processes such as that of modulation. This is shown by means of the criterion Chrysippus of Soli (...) provided for conditional sentences and the theory of sign related to that criterion. (shrink)

The mental model theory is an approach with clear psychological, linguistic, and cognitive consequences. This paper delves into some of the epistemological conclusions that can be drawn from it. In particular, it addresses the process why knowledge acquisition can modify the inferences people tend to make. That process is described by means of an example based on a well-known logical schema related to the conditional: Modus Tollendo Tollens.

En este artículo se analiza el debate sobre la forma adecuada de entender el condicional producido en el siglo IV a. C. El análisis se lleva a cabo mediante el método proporcionado por Rudolf Carnap para estudiar el significado de las expresiones, es decir, mediante el método de extensión e intensión. Los resultados de ese análisis parecen mostrar que, aunque, según Sexto Empirico, el debate fue sobre cuatro criterios diferentes para comprender el condicional, en realidad tres de esos criterios parecen (...) ser iguales y tienen una forma lógica común muy clara en el marco de Carnap. (shrink)

The main issue of the present Article is a discussion about the conditional proposition in Stoic- Megarian Logic. There were, in Stoic-Megarian school, many theories of meaning to interpret these propositions. Since conditional propositions made the structure’s core of their Logic, so for the understanding of the key concept of their thought, we need searching, prior to anything, in the semantics of these propositions. We will, in the first place and much survey, compare between Stoic-Megarian Logic and Aristotelian Logic and (...) present where is the state of conditional propositions in the Stoic-Megarian Logic; then, in the second place, we explore all kinds of conditional proposition and their conditions of truth values in Stoic-Megarian Logic and compare them with the concept of implication in modern logic and reinterpret them with new instruments in modern logic. Most logicians, in this field, evaluate and compare Stoic-Megarian conditional propositions with definitions of Material implication, strict implication, and Natural laws and we, in this Article, evaluate and analyze these propositions with this perspective and ideas. (shrink)

The current formal theories trying to account for reasoning and language often need to resort to the thesis of the pragmatic or implicit premises to explain the real role pragmatics plays in the human inferential activity. The main aim of this paper is to show that, although they did not propose theories in this way, the Stoics, by means of their concept of ‘sign’, already offered the essential arguments and foundations necessary to describe the real action of both pragmatics and (...) the premises coming from general knowledge when we make inferences. (shrink)

Šiuo straipsniu mėginama parodyti, jog Indijos ir stoikų logika yra panašesnės viena į kitą nei į standartinę logiką. Šiuo tikslu analizuojama ištrauka iš Kathāvatthu, kurioje pateikiamas sąlyginio teiginio apibrėžimas dažnai interpretuojamas kaip atitinkantis modernioje teiginių logikoje vartojamą materialiosios implikacijos sampratą. Teigiama, jog tokia interpretacija nėra visiškai pagrįsta. Todėl daroma išvada, jog tai, kas iš tiesų sakoma aptariamoje ištraukoje, nuosekliai susiję su Chrisipo Soliečio pasiūlytu sąlyginio teiginio teisingumo kriterijumi.