A proof method under "complex refutability"
Last modified: April 25, 2006
"Complex refutability" is the type of refutability characterizing a sixth system of negation that may be constructed in formalist mathematics but is not included in Curry's Foundations of Mathematical Logic. It has been shown to be constructed by adjoining Peirce's Law to either classical negation (LK) or intutionalist negation (LJ). Its epistemological foundation has been, in analogy to terminology introduced by Lakatos, denoted "complex justificationism". This paper illustrates the method of proof (and refutation) structured by complex justificationism. In particular, it gives an example how the data theory inhering in that proof method drives the evolution from one "scientific research program" to another in a well-defined subfield of a particular social science. It does this, first by presenting the pertinent scientific research program(s) as well as the theories characterizing them, and then by presenting empirical data that test two theories against one another. This test is shown to drive not just the superseding of one theory by another but of one scientific research program by another, and in progressive fashion. The notion of "problemshift", introduced by Lakatos early on but discarded later by him because it reveals the flaw in the "methodology of research programs", encapsulates such progress. The particular social science here concerned is the study of international relations. The particular subfield of that social science is the theory of Soviet foreign policy making, specificially during the late Cold War period. This paper is a sequel to the author's "Complexity Science and Knowledge-Creation in International Relations Theory", in Institutional and Infrastructural Resources, in Encyclopedia of Life Support Systems (Oxford: Eolss Publishers for UNESCO, 2002), available at http://www.robertcutler.org/download/pdf/en02eolx.pdf