Identifying mental actions for abstracting the logic of conditional statements

Abstract

In this paper, we provide a theoretical development of the mental actions that underlie reasoning about logic. Building explicitly on Piaget’s epistemology, we propose populating, inferring, expanding, and negating as four mental actions that, upon becoming reversible and composable, can give rise to the logic of universally quantified conditional statements. We adopt the view that logic is a metacognitive activity in which people abstract content-general relationships by reflecting across their content-specific reasoning activity. We explore how these four actions become reversible and composable in mathematics, suggesting that logic can be built psychologically upon the foundation of mathematical reasoning. Further, by exploring what it means for these actions to be reversible and composable, we propose how students may need to engage in these actions to refine and reflect on them so as to afford logical abstraction (in the manner we envision).