Consequences of a diagrammatic representation of Paul Cohen's forcing technique based on C.S. Peirce's existential graphs

Abstract

This article examines the forcing technique developed by Paul Cohen in his proof of the independence of the Generalized Continuum Hypothesis from the ZFC axioms of set theory in light of the theory of abductive inference and the diagrammatic system of Existential Graphs elaborated by Peirce. The history of the development of Cohen's method is summarized, and the key steps of his technique for defining the extended model M[G] from within the ground model M are outlined. The relations between statements in M and their correspondent reference values in M[G] are modeled in Peirce's Existential Graphs as the construction of a modal covering over the sheet of assertion. This formalization clarifies the relationship between Peirce's EG-βand EG-γ and lays the foundation for theorizing the abductive emergence of the latter out of the former. © 2010 Springer-Verlag Berlin Heidelberg.