Visual Fallacy: Affirming the Consequent

The sketch of a mathematical model exploring the possible role of graphical intuition in the cognitive processes underlying the formal logical fallacy known as “affirming the consequent”. The piece describes this cognitive distortion in terms of a faulty abstraction resulting from the unconscious mental corruption of the indices of the abstraction and concretion functions of a pair of Galois connections (the adjoint operators labeled alpha and gamma 1, 2). The fallacy itself is visually portrayed as the erroneous commutation of a diagram of logico-graphical morphisms between statements, themselves represented by C.S. Pierce’s existential graphs. Partially inspired by the self-defacing and radically interdisciplinary art and architecture of Neil Spiller’s Dorian Gray Column, this work intends to blur the lines at the intersection of art, mathematical psychology, and cognitive science.