Diagrammatic Reasoning

Charles Peirce's "diagrammatic reasoning" is central for my research as a method to generate knowledge (cf. CP 3.559 f.; 4.530 f.; 4.571). Understanding diagrammatic reasoning is key to understanding the possibilities of creativity, learning, and cognitive change.

"A diagram is a representamen which is predominantly an icon of relations and is aided to be so by conventions. Indices are also more or less used. It should be carried out upon a perfectly consistent system of representation, founded upon a simple and easily intelligible basic idea." (Peirce CP 4.418)

The fact that, according to Peirce, diagrams must be constructed by means of a certain representational system is essential for an adequate understanding of his concept of diagrammatic reasoning. He says that he developed this concept to describe the specific nature of 'The Reasoning of Mathematics.' In his so-called 'Carnegie Application,' he writes about the relevance of his discovery, and defines "diagrammatic reasoning," as follows:

"The first things I found out were that all mathematical reasoning is diagrammatic and that all necessary reasoning is mathematical reasoning, no matter how simple it may be. By diagrammatic reasoning, I mean reasoning which constructs a diagram according to a precept expressed in general terms, performs experiments upon this diagram, notes their results, assures itself that similar experiments performed upon any diagram constructed according to the same precept would have the same results, and expresses this in general terms. This was a discovery of no little importance, showing, as it does, that all knowledge without exception comes from observation." (Peirce NEM IV: 47-48; my italics)

A diagrammatic definition of diagrammatic reasoning (from: Michael H.G. Hoffmann, "Seeing Problems, Seeing Solutions. Abduction and Diagrammatic Reasoning in a Theory of Scientific Discovery," in Olga Pombo and Alexander Gerner, Abduction and the Process of Scientific Discovery (Lisboa: CFCUL/Publidisa, 2007), pp. 213 - 36, p. 225):

Michael H.G. Hoffmann