Spencer-Brown, Peirce, Girard, and the Origin of Logic

Abstract

Abstract This article will show how René Girard’s hypothesis of the scapegoat victim is the indirect basis of the discipline that unfolds the necessary consequences of the distinction between two possible states; that is, formal logic. To support this unusual view on the foundation of logic, two systems of formal logic will be analyzed: the calculus of indications created by George Spencer-Brown in the 1960s and the system of existential graphs created by Charles S. Peirce in the late nineteenth century. The first system shows that logic is based on elemental difference, and the second displays that logic is based on an original act of expulsion, the expulsion of the opposite of logic, which will be called the illogical. It will then be argued that Girard’s theory allows the full understanding of the expulsion of the illogical; that is, the emergence of the elemental difference upon which logic is based. It is not argued that logic, as a symbolic system of inferences, is directly based on Girard’s theory. It is rather argued that, as shown by the work of Spencer-Brown, formal logic is based on elemental distinction and negation from where they had their roots in the scapegoat mechanism. Finally, concerning a real and specific pattern of inference, a link is suggested between apagoge and the founding murder.