Using the Semantic Propositional Calculus (SPC) to Determine the Validity of Categorical Syllogisms: A Contribution to the Structural Teaching Approach (STA)

A description is provided of how to use the Semantic Propositional Calculus (SPC) for a clear, compact notation that can be applied to approachdiverse topics in logic and mathematics. With two equivalent formulations (one corresponding to set theory and the other to the SPC), it is possible to determine the validity – or invalidity – of the categorical syllogisms. The parallel use of the SPC (preserving the syntax of the propositional calculus) and of resources from set theory facilitates learning in an area of logic and an area of mathematics. The joint learning of diverse branches of the same discipline, or of distinct disciplines which are closely related in different ways, is an essential aspect of the STA.