Representational measurement theory: Is its number up?

Abstract

Representational measurement theory was proposed initially to solve problems caused by disciplinary aspirations of 19th-century mathematicians, who wanted to construe their subject as independent of its applications in empirical science. Half a century later, S. S. Stevens seized the opportunity provided by representational theory’s reconstruction of measurement as numerical coding to rubber-stamp psychology’s own aspirations to be counted as a quantitative science. Patrick Suppes’ version of representational theory rectified defects in Stevens’ theory, making it explicit that representational theory entails that mathematical structure is already embedded in empirical systems. However, Suppes’ theory neglected the fact that attributes, not objects, are the focus of measurement and when that oversight is corrected, it follows that empirical systems sustaining measurement already instantiate positive real numbers. Thus, in measurement, real numbers are estimated, not assigned from without. Representational theory not only misrepresents measurement; it refutes itself.