The constantly recurring argument: Inferring quantity from order

The inference from order to quantity is fundamental to psychometrics because the sorts of attributes that psychometricians aspire to measure are experienced directly only as ordered and, yet, it is concluded that such attributes are measurable on interval scales (i.e., that they are quantitative). This inference has been a feature of psychometrics since early last century, before which it permeated scientific thought and played a role in the development of psychophysics. Despite this, its cogency has been analysed only rarely. Elsewhere, I have argued that it is not deductively valid, a point that might be considered obvious except that attempts have been made to show otherwise. Its invalidity displayed, it is easily shown that it is not inductively reasonable either. However, it might still be urged that the inference from order to quantity is an inference to the best explanation: that is, that quantitative structure is reasonably abduced from order. I argue that the opposite is true: the most plausible hypothesis is that the sorts of attributes psychometricians aspire to measure are merely ordinal attributes with impure differences of degree, a feature logically incompatible with quantitative structure. If so, psychometrics is built upon a myth.