On substandard substantive theory and axing axioms of measurement: A response to Humphry:

My response to Humphry begins with some reflections upon why it is that after more than a century, psychometrics still lacks plausible substantive theories underwriting its claims to measure mental attributes and I explore the possibility that it is more myth-based technology than science. Historically, psychometrics has lacked any interest in coming to grips scientifically with the logical commitments of the presumption, implicit in the theories it does have (e.g., its Item Response Theories), that the attributes it aspires to measure are continuous quantities. This lack of interest might also explain Humphry's misunderstanding of what is involved in the measurement theory axiom of continuity and his curious claim to have located a paradox therein. However, his attempt to rule the entire corpus of measurement theory as irrelevant to the enterprise of constructing and investigating substantive, psychometric theories betrays a failure to recognise that the form of substantive, quantitative theories also raises issues requiring empirical investigation.