Mathematics, Measurement, Metaphor and Metaphysics I

Abstract

This paper relates philosophy’s metaphysical insistence on rigorous figure–meaning independence, and its own distrust of that insistence, to the potential for improved quantitative and qualitative methods in the sciences. Following Wittgenstein’s admonition that we pay attention to our nonsense, a kind of Socratic double vision is needed to simultaneously accept (1) that any meaningful discourse necessarily requires a significant degree of signifier–signified coordination, and (2) that an ideal degree of such coordination is never achieved in practice. A metaphysically informed theory of scientific method begins from the mathematical and hermeneutic implications of figure–meaning coordination. This paper explores the mathematical metaphysics of science, critically evaluates the often repeated maxim that fields of study are only as scientific as they are mathematical, and suggests that some forms of quantification are more mathematically astute, metaphysically informed, pragmatic and effective than others. In conclusion, the qualitative and quantitative aspects of three key features of measurement are briefly explored: (1) the deconstructive display and exploration of significant anomaly; (2) the metaphorically and numerically reductive identification, via sufficient reason and sufficient statistics, of new variables; and (3) the constructive application of technologically embodied sign–thing coordinations in research and practice.