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)

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 theory of modality Buridan develops is linked to different propositions. This paper addresses one of those propositions. The aim is to show that, if the operator of necessity included in it is ignored, the proposition allows deriving, within first-order predicate logic, a reduction sentence with the characteristics required in Carnap’s framework. Besides, the paper tries to argue that the mentioned operator of necessity can be understood not only in a technical sense (as modal logic does), but also in the (...) way a naïve individual (without modal logical training) could interpret it. These latter arguments are given from the theory of mental models. (shrink)

Rudolf Carnap proposed three reduction rules to improve scientific language. Those rules indicate when it is correct to add a property in situations in which other properties are already had. Assuming the theory of mental models, it has been shown that the rules are not hard to use from the cognitive point of view. The key to argue that is to accept that the human mind works as dual-process theories claim. According to these theories, people can use two different systems. (...) One of them implies effort but the other one does not. Thus, the idea is that Carnap’s reduction rules can be applied resorting just to the system not implying cognitive effort. This paper goes one step further and poses that even from a Popperian perspective the reduction rules keep not being difficult. One might think that falsifiability requires cognitive effort because it needs to address situations in which the sentences are false. However, this paper tries to explain that, following the theory of mental models, that is not hard if the sentences are conditionals, and the sentences in the reduction rules have conditional structures. (shrink)

The suppression task challenges classical logic. Classical logic is monotonic. However, in the suppression task, an inference with the form of modus ponendo ponens is inhibited by adding a new premise. Several explanations have been given to account for this fact. The present paper indicates three of them as examples: that of the theory of mental models, that based on logic programming and closed world assumption, and that referring to Carnap's concept of state‐descriptions. Besides, the paper offers one more explanation (...) linked to Carnap's idea of reduction. It proposes sentences akin to a reduction sentence, a pair reduction, and a bilateral reduction sentence. Those sentences are related to the initial conditional in the suppression task. This proposal tries to stay within first‐order predicate logic. (shrink)

This paper describes a study about inter-understanding between Portuguese and Spanish. Based on Peano’s work, the study resorts to the logical relation of intersection between sets and applies it to words in Portuguese and Spanish meaning the same. The material is a text that is the abstract of a psychology paper. Each of the words in that text, which is written in Portuguese, is compared to its corresponding Spanish word by means of the relation of intersection. This is made by (...) considering the letters in the words to be elements in sets. The results show the potential that this methodology can have to provide percentages of inter-understanding between the two languages (and between any pair of languages). (shrink)

Women have played a prominent role in environmental preservation in all societies, including societies facing serious environmental problems. Women in places like Nigeria’s Niger Delta carry out tasks such as farming, fetching of firewood for domestic use, fetching of water, and the like. These activities involve the use of natural resources and thus make women more vulnerable when there are problems such as oil pollution, gas flaring, and other related activities that endanger the environment. In the Niger Delta women have (...) protested against oil related activities that damage their environment. They have also participated in other events to conserve their environment. The paper adopts an ecofeminist perspective in critiquing environmental mismanagement in the Niger Delta. It highlights the fact that women are prominent in campaigning for a sustainable Niger Delta. There is need for writers from academic and social circles writing on the Niger Delta not to ignore the women’s voices. (shrink)

The theory of mental models considers sentential connectives to refer to semantic possibilities. The theory also proposes that the possibilities can be amended by virtue of modulation processes, that is, processes in which semantics or pragmatics can have an influence. The definition of modulation the theory of mental models gives has been deemed as a scientific definition within Carnap’s framework. This is because it is easy to find reduction sentences corresponding to it. What seems to be harder is to think (...) about bilateral reduction sentences for that definition. This paper addresses this issue. It shows that at least a bilateral reduction sentence is possible for modulation. (shrink)

The semantic method of extension and intension presented by Rudolf Carnap may have some problems from the current perspective in cognitive science. For example, that method is strongly linked to logic, and it is hard to determine where its state-descriptions come from, how many they are, and what the relation of accessibility between them is. This paper tries to solve difficulties such as those by updating the method resorting to the theses and results of a contemporary reasoning theory: the theory (...) of mental models. Basically, the update consists of replacing the state-descriptions of the original method with the possibilities of the theory of mental models. That allows reformulating several relevant concepts in Carnap’s method in order to better adjust them to the real characteristics of human language. (shrink)

Drawing on the theory of ‘mental models’, I have previously shown that the valid syllogisms in the Aristotelian logical system, including all of its figures and moods, are very easy for the human mind. Indeed, they can even be used to predict inferences that people can make with quantified sentences. In this paper, I further argue that, if mental models theory is correct, then also the Aristotelian conversion rules are not hard for the human mind. My account here again focuses (...) on the distinction made by the mental models theory between canonical and noncanonical models. (shrink)

The mental models theory rejects that sentences are linked to logical forms. From its perspective, their most relevant aspect refers to the semantic possibilities that correspond to them. In this way, the theory has analyzed in detail the real semantic role that the traditional connectives in logic can play in reasoning. However, given that logical forms are not important in its framework, in this paper, it is argued that those connectives are not the only operators that the mental models theory (...) should review, and that there are other connectives present in most of the languages in general that can be interesting for it as well. That is the case of ‘but’ in English, which is addressed from the approach of the aforementioned theory here. (shrink)

This paper is intended to address the work “Against logical form”, authored by Johnson-Laird in 2010. In it, based on the theory of mental models, Johnson-Laird claims that the way people interpret sentences in natural language has nothing to do with logic. This is because that action is not related to logical forms. According to him, the mental activity is mainly linked to semantics and pragmatics. However, here, following arguments provided by López-Astorga, I try to show that the theory of (...) mental models can be linked to syntactic structures. My main point is made by dealing with an argument given in the mentioned Johnson-Laird’s paper. In principle, that argument seems to undermine proposals such as that of López-Astorga. However, the present work proposes otherwise. (shrink)

The literature has shown that the theory of mental models is able to describe human inductive processes. That theory has been related to the structure of inductive inferences, such as Gautama’s Syllogism indicates. On the other hand, the theory of mental models has also been linked to modal system K. This paper argues that there can be a connection between Gautama’s Syllogism and system K, not in rigorous logical deductions but in describing how the human mind can work. They can (...) refer to two different moments of inductive reasoning; the rule of necessitation of K can be a key element in the second of those moments. (shrink)

An important contribution of the so-called ‘Indian logic’ is the set of predications developed by Jain philosophers. However, if assessed based on western classical logic, Jaina logic in general and its predications in particular are clear examples of incorrect or inconsistent frameworks. Against this last idea, in this paper, it is argued that Jaina logic has a great potential to explain the way human beings really make inferences, and that comparing it to modern standard logic can be a mistake. To (...) do that, a current semantic approach about reasoning, the one of the mental models theory, is used. (shrink)

La teoría de los modelos mentales ofrece una explicación de cómo los seres humanos infieren conclusiones. Tal explicación no es coherente con la lógica clásica. Admite inferencias que son incorrectas en dicha lógica. Dos de esas inferencias son consideradas aquí. Una de ellas permite derivar que las cláusulas de un condicional son posibles si ese condicional es verdadero. La otra autoriza a deducir que las cláusulas de una disyunción son posibles si esa disyunción es verdadera. Recurriendo al modo que en (...) Crisipo de Solos entiende las relaciones condicionales, este trabajo propone dos axiomas que describen las estructuras de esas dos inferencias. La idea es que tales axiomas podrían ser incluidos en un hipotético sistema axiomático que intentara reproducir cómo son los procesos inferenciales humanos. (shrink)

La teoría de la disciplina formal sostiene que el estudio de las matemáticas desarrolla las habilidades lógicas de los individuos. Attridge e Inglis realizaron un experimento con el fin de comprobar si esta teoría es correcta o no. Su conclusión fue que sus resultados mostraban que, si bien las matemáticas pueden, efectivamente, mejorar las capacidades lógicas, es necesario asumir la interpretación defectuosa del condicional. Sin embargo, López-Astorga contraargumentó que eran posibles otras interpretaciones de sus resultados, que tales resultados no prueban (...) que la interpretación material del condicional no es válida y que la teoría de los modelos mentales también los puede explicar. En este trabajo, comento los problemas vinculados a las otras interpretaciones posibles propuestas por López-Astorga y trato de mostrar que la mejor opción para la interpretación de los resultados de Attridge e Inglis es asumir la teoría de la lógica mental. (shrink)

ABSTRACT: The mental models theory predicts that, while conjunctions are easier than disjunctions for individuals, when denied, conjunctions are harder than disjunctions. Khemlani, Orenes, and Johnson-Laird proved that this prediction is correct in their work of 2014. In this paper, I analyze their results in order to check whether or not they really affect the mental logic theory. My conclusion is that, although Khemlani et al.'s study provides important findings, such findings do not necessarily lead to questioning or to rejecting (...) the mental logic theory. RESUMO: A teoria dos modelos mentais prevê que, enquanto as conjunções são mais fáceis do que as disjunções, para os indivíduos, quando negadas, as conjunções são mais difíceis do que as disjunções. Khemlani, Orenes e Johnson-Laird provaram que essa previsão está correta, em seu trabalho de 2014. Neste trabalho, analiso os seus resultados, a fim de verificar se eles realmente afetam a teoria da lógica mental ou não. Minha conclusão é que, embora o estudo da Khemlani, Orenes and Johnson-Laird forneça resultados importantes, tais resultados não conduzem necessariamente a minar ou rejeitar a teoria da lógica mental. (shrink)

Espino and Santamaria experimentally demonstrate that, if the syllogisms in the first figure are not presented as is the usual practice, that is, separating their two premises into two different lines, but linking the two premises into one line by means of a full stop, individuals tend to draw from such premises conclusions in which the subject and the predicate are not in the customary order, but rotated. In their view, this finding is consistent with the assumptions of the mental (...) models theory. Nevertheless, in this paper, I will show that what this fact really depends on the approach that is adopted, since a framework based on formal logic also has resources to explain it, and hence can lead us to assume theses different from those proposed by Espino and Santamaria. Espino y Santamaría demuestran experimentalmente que, si los silogismos de la primera figura no son planteados como se hace tradicionalmente, esto es, separando sus dos premisas en dos líneas diferentes, sino en una sola línea uniendo las dos premisas mediante un punto seguido, los individuos tienden a deducir a partir de tales premisas conclusiones en las que el sujeto y el predicado no se encuentran en el orden habitual, sino invertidos. Desde su punto de vista, este hallazgo es consistente con los supuestos de la teoría de los modelos mentales. No obstante, en este trabajo, vamos a mostrar que lo que tal hecho significa verdaderamente depende del enfoque que se adopte, ya que un marco basado en la lógica formal también cuenta con los recursos para explicarlo y, por tanto, puede conducirnos a asumir tesis diferentes a las propuestas por Espino y Santamaría. (shrink)

The double negation has always been considered by the logical systems from ancient times to the present. In fact, that is an issue that the current syntactic theories studying human reasoning, for example, the mental logic theory, address today. However, in this paper, I claim that, in the case of some languages such as Spanish, the double negation causes problems for the cognitive theories mainly based on formal schemata and supporting the idea of a universal syntax of thought in the (...) human mind. Thus, I propose that, given those problems, semantic frameworks such as that of the mental models theory seem to be more appropriate for explaining the human inferential activity. (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)