Racionality, consistency, reticulation and coherence: the case of renormalization in quantum field theory

Abstract

A study of the development of quantum field theory, in the period that goes from 1927 to 1971, highlights the fact that renormalization techniques played a fundamental role during the whole process. In particular, renormalization rehabilitated quantum electrodynamics in the late 40s and, later, also rehabilitated quantum field theory as a whole and helped consolidating gauge theories in the early 70s. The success of renormalization was such that, from its beginnings as a mere ad hoc theoretical device, it gradually earned the condition of a criterion for the construction and appraisal of theories in field physics. One of the aims of this article is to show that this change in the methodological status of renormalization can be understood in the context of Larry Laudan's reticulational model of rationality. In spite of the extraordinary theoretical and empirical progress achieved, however, there were always polemics regarding the place that renormalization should occupy within the conceptual structure of the discipline. These polemics revolve around the fact that renormalization apparently goes against a cognitive value that is regarded as fundamental, namely, consistency. The second aim of this paper is to show how the reticulational model helps to throw light upon this question as well. We attempt to show in which sense it was rational to accept renormalization in particle and field physics despite the problem of inconsistency. To this end we make use of the theses of the reticulational model, supplemented with theses from Putnam and Quine, and from the coherence theory of justification.