Teaching of logic

The Marlo diagram can represent and solve, at least in theory, logic problems with an unlimited number of terms. In López Aznar (2014), (2018b), it was confirmed that the diagram far exceeded the requirements which, according to Moktefi & Shin (2013), are expected from any diagrammatic system. Diagrams are created when trying to add the ability of expressing implicit possibilities to the Venn diagram. This idea was developed in 2013 when studying Johnson Laird's theory of mental models, in González Labra (1998). Diagrams prioritise the concept of "being associated to" instead of the concept of belonging and inclusion. This has allowed the recombining of their DNA with the connective network models, described in Crespo (2006). In López Aznar (2017), (2018a), the Marlo diagram is translated into tree diagrams that show the logical connec-tives as the simple elimination of different possibilities. This idea is already present in the classic truth tables, but logical trees make it possible to simulate how truth and falsity propagate through the networks of a cognitive system. The diagram has been in development since 2013, in high school classes, with the help of students and other teachers who are experts in mathematics.

RESUMO O papel da lógica na filosofia é fundamentalmente metodológico já que é fa-zendo uso das diferentes estruturas de demonstração que teses filosóficas são estabelecidas. Dada a variedade dos modos de apresentação dos textos filosó-ficos, entendo que para que a tese do papel da lógica na filosofia-em sentido amplo-possa ser defendida, a lógica deve ser tomada sua concepção mais larga, abarcando tanto a lógica formal quanto a informal. Argumento que, mesmo considerando as várias formas de demonstração filosóficas e as diver-sas relações possíveis entre lógica e filosofia, há uma continuidade entre os métodos formais e informais de demonstração. Para mostrar esta continuida-de, partirei da noção fundamental de inferência lógica para estabelecer os critérios de diferenciação entre o formal e o informal, e reconstruirei breve-mente a história filosófica da lógica para mostrar suas transformações e seu distanciamento progressivo do lugar metodológico na filosofia. Finalmente, considerando a literatura recente sobre lógica formal e informal, aponto os problemas relativos às suas diferenças e, partindo do reconhecimento de que lógica cumpre um papel metodológico na filosofia, argumento que a lógica formal e informal são práticas que estão em continuidade e se beneficiam mutuamente. No que diz respeito ao modo como a lógica informal se benefi-cia da lógica formal, o artigo investigará as vantagens e limitações em se to-mar os sistemas de dedução natural como instrumento de análise de demons-trações em linguagem natural. No que diz respeito aos modos como a lógica formal pode se beneficiar da lógica informal, procuraremos mostrar que avanços na lógica formal decorrem, além dos esforços de formalização de provas informais, de uma análise informal das estratégias de cálculo e dos princípios segundos os quais uma certa linguagem lógica opera.
ABSTRACT The role of logic in philosophy is fundamentally methodological since it is through the usage of different demonstrative structures that philosophical theses are established. Given the variety of modes of presentation of philosophical texts, I understand that for the thesis of the methodological role of logic in philosophy - in an encompassing sense - to be defended, logic has to be taken in its most general conception, involving both formal and informal logic. I argue that, even considering the various forms of philosophical de- monstration and the various possible relationships between logic and philo- sophy, there is a continuity between formal and informal methods of de- monstration. In order to show this continuity, I will start from the fundamen- tal notion of logical inference to establish criteria for distinguishing between the formal and the informal, and I will briefly reconstruct the philosophical history of logic to show its transformations and its progressive distancing of its methodological role in philosophy. Finally, considering the recent literatu- re on formal and informal logic, I will point out problems with respect to their differences and, from the recognition that logic plays a methodological role in philosophy, I will argue that formal and informal logic are practices that are in continuity and are mutually beneficial. With respect to the way in which informal logic benefits from formal logic, the article will investigate the advantages and the limitations in taking systems of natural deduction as instruments of analysis of demonstrations in natural language. With respect to how formal logic benefits from informal logic, I will show that advances in formal logic depend upon not only efforts for formalising informal proofs, but also from an informal analysis of calculi strategies and from the princi- ples according to which a logical language operates.

Logical abilities are a ubiquitous ingredient in all those contexts that take into account soft skills, argumentative skills or critical thinking. However, the relationship between logical models and the enhancement of these abilities is rarely explicitly considered. Two aspects of the issue are particularly critical in our opinion, namely: (i) the lack of statistically relevant data concerning these competences; (ii) the absence of reliable indices that might be used to detect and measure the possession of abilities underlying the aforementioned skills. This paper addresses both aspects of this topic by presenting the results of a research that we conducted between October and December 2020 on students enrolled in various degree courses at the University of Florence. The dataset has been collected by a three-stage initiative. We started from an entrance examination to assess the students' initial abilities. This test included ten questions, each regarding a specific aspect of logical reasoning. Then, students underwent a short training course to strengthen their knowledge of logic. At the end of the short course, students underwent a final examination to evaluate the effectiveness of the training. To verify the effectiveness of the training program we used students’ characteristics into a Structural Equation Model comparing the distribution of abilities before and after the training.