Symbolic logic isn’t as natural as informal reasoning in ordinary language, Aristotle’s syllogisms, or the diagrams in Euclid’s proofs. Cognitive scientists have been searching for a more natural logic, but each branch emphasizes different aspects. Linguists claim that the patterns of language reflect an underlying natural logic or a language of thought. Most logicians use algebraic notations for all versions of logic, natural or artificial. Formal linguists adapt logic to notations that have a more direct mapping to language. A widely used version is the discourse representation theory by Hans Kamp. Psychologists have emphasized the centrality of visual perception and mental imagery in human thought. Neuroscientists such as Antonio Damasio agree. A pioneer in logic, Charles Sanders Peirce, claimed that semiotics, the study of signs, is fundamental to all forms of thought. Language reflects the internal patterns of signs, and all notations for mathematics, logic, and computer programs are based on a disciplined ways of using linguistic patterns. More recently, the physicist Roger Penrose and the neuroscientist Stuart Hameroff claimed that quantum effects inside the neurons are critical to the power and flexibility of human reasoning.

This tutorial reviews these theories, the evidence for them, and the relationships among them. They all make important contributions, and Peirce’s semiotics provides a framework for relating them. He claimed that his graph logic represents “a moving picture of the action of the mind in thought.” Some philosophers, psychologists, and linguists believe he was right.