The Topology of Mathematics in the Mind and Its Interaction with Verbal and Written Language

Abstract

When we think of the human mind we most often think of its capacity for verbal language as we are the only living organism capable of speech. We are aware of the fact that the human mind is capable of mathematical thinking and think that mathematics was a later development of the human mind long after humankind had acquired language. In a book soon to be released in the Springer series Mathematics in the Mind edited by Marcel Danesi entitled A Topology of Mind—Spiral Thought Patterns, the Hyperlinking of Text, Ideas and More, we (Logan and Pruska-Oldenhof 2019) argue that human verbal language was as much a product of mathematical thinking as mathematics was a product of verbal thinking. We argue that the origin of verbal language, the origin of the mind, and the origin of mathematic thinking all happened at approximately the same time and that these three elements are basically interlinked. The human mind is a product of the brain and verbal language as was argued in The Extended Mind: The Emergence of Language, the Human Mind and Culture (Logan 2007), but verbal language as we have argued was dependent on the ability of humans to think in terms of sets employing a primitive form of set theory.