Computer Science and Statistics
Logic; Square of Opposition; Critical Thinking; Education; Pedagogy; Logic Models
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Teaching classical logic can often be challenging, especially when working with students who lack any prior experience with the more technical aspects of critical thinking. The abstraction of statements into logical symbols and the implementation of various diagramming methods can be enough to frustrate novice logicians, leading to a lack of hope and sometimes failure of mastery. The unique difficulties in teaching classical logic can, in addition, exacerbate tricky pedagogical issues that arise on a day to day basis in the critical thinking classroom. For example, it can be challenging to convey complex information in a meaningful way when dealing with classes over fifty students. Oftentimes this leads to presenting lectures utilizing a very general approach to content delivery. Yet, not all students will respond to a generalized lecture approach to logic and critical thinking; in all likelihood, a majority of students do not learn well in such an environment. This project seeks to explore alternative methods for teaching logic and critical reasoning through the development of one innovative technique aimed at mastery of a specific, classical topic.
The focus of the project is the “square of opposition,” a model of reasoning as old as Aristotle’s philosophy that nevertheless forms a foundational part of beginning logic pedagogy even today. Despite the square’s longevity as a method of foundational reasoning, its intricacies often elude novice logicians, who struggle when attempting to make immediate inferences using the traditional representation of the square. As a result, a new visual model for both representing the reasoning of the square of opposition and using it to make inferences has been developed. “Dimo’s Square” evolved in response to students who did not demonstrate mastery of the traditional model of teaching the square of opposition and has many benefits that the classical square does not. The trajectory of Dimo’s Sqaure, an original alternative to traditional teaching of the square of opposition, is outlined in the project paper.
Firstly, the traditional model for presenting and teaching the square of opposition is presented. Second, “Dimo’s Square,” is introduced and explained. Third, a comparative analysis of Dimo’s Square and the traditional square of opposition is undertaken, highlighting significant differences between them (such as Dimo’s Sqaure requiring fewer rules to be memorized and more intuitive operational patterns). Finally, formal proofs showing the logical equivalence of Dimo’s Square and the traditional square of opposition are provided, demonstrating the logical equivalence of the models, which augers well for the pedagogical superiority of Dimo’s Square, in which nothing is lost conceptually despite enhanced technical mastery .