The Psychodynamics of the Mathêmatika (original) (raw)

Mark Balaguer (Platonism and Anti-Platonism in Mathematics, 2001) argues that fictionalism and full-blooded Platonism are the two equally viable philosophies of mathematics, but there is no fact of the matter to decide between them. Full-blooded Platonism is the view -- roughly -- that any consistent mathematical system is true, and therefore that any self-consistent mathematical object exists (in a Platonic sense). I argue that there is a stronger sense of mathematical existence in that some mathematical objects are rooted in the neurodynamics of the brain, and therefore structure human psychodynamics. These are the mathematical structures that are potent and numinous in human experience. They include, as I will explain, the archetypal numbers, such as the Monad, Duad, Triad, and Tetrad. They include fundamental geometrical forms, such as circles, triangles, and mandala-like figures (whence the use of kharakteres as sunthemata in theurgy). And they also include fundamental intuitions of discreteness and definiteness, as opposed to continuity and indefiniteness. I will argue that as innate, unconscious psychodynamical Forms, certain mathematika, inherent in the human psyche, have qualitative psychological effects in addition to the quantitative properties studied in mathematics. Indeed, this is the valid core of Pythagorean numerology, as found in the Theologumena Arithmeticae. Therefore, a complete contemporary Platonic philosophy of mathematics must comprehend the inherent qualitative and quantitative aspects of mathematical objects.