Denying Descartes and wary of Wittgenstein: Response to Franz

Psychometrics is not inherently Cartesian

Modern psychometrics’ defining characteristic is the practice of psychological testing. Based on test performances, “measurements” of psychological attributes are estimated. While these sometimes include presently occurring mental states (such as anxiety, to take Franz’s, 2022, example), more often than not they are merely dispositional concepts, including intellectual abilities, personality traits, and social attitudes. Generically, these are called “psychological attributes” only because they are invoked to explain performance on psychological tests. Doubtless, some psychologists endorse a Cartesian view because, since the 1960s, the dominant position has been that mental processes are coded neural representations. However, psychologists have attempted measurement with psychological tests since the early 1900s ¹ and for much of its history mainstream psychometrics resisted Cartesian temptations.

Take Charles Spearman, a pivotal case because of his influence. His most significant contribution was factor analysis, which is a method for redescribing matrices of correlation coefficients between test scores as loadings of each test on a set of mathematically concocted variables called “factors.” Spearman found that when each test involves cognitive tasks of the same general sort within tests but different between tests, each will have a positive loading on a general factor, designated g, and he claimed that each test had a nonzero loading on a factor specific only to it, designated s. He believed that, via factor analysis, g and the various s’s were measured. Nonetheless, he declined to define g and the s’s in mental terms, in particular, to even label g “intelligence.” He simply defined them as products of factor analysis. When tempted, he speculated that g measured the level of the brain’s energy and each s, the efficiency of the relevant specific neurological structures. If he saw himself as measuring anything beyond factor analytic constructs, it was hypothetical physiological quantities. ²

Spearman’s preference to define g and s via the analytic operations producing them dovetailed with operationism. He was not an operationist, but operationism flourished in the 1930s because it suited the ambient intellectual climate, one Spearman shared. ³ In particular, psychologists endorsed operationism to counter mentalism, which was seen then as a stumbling block to psychology’s acceptance as a science. ⁴ According to operationism, the meaning of a concept is synonymous with the operations used to measure it. ⁵ Reflexively, the concept of measurement itself was operationally defined as “the assignment of numerals to objects or events according to rule” (Stevens, 1946, p. 667), ⁶ ensuring that the attributes tests “measured” were not anything mental, but operational fabrications.

During the 1950s, operationism was supplemented by construct validity. Cronbach and Meehl (1955) ⁷ intended their concept to replace operational definitions, but because of the success of such definitions in muting criticisms, they were retained. Construct validity was a spin-off from logical positivism and extended the positivists’ program of redefining psychological concepts in physicalist language. The “nomological network” (Cronbach & Meehl, 1955, p. 290) connecting each construct with others and ultimately with observable variables was said to define the “theoretical constructs” psychologists thought they were measuring. Folk psychological labels were still applied to constructs, but without any serious mental intent and because a construct’s network of relationships was constantly under revision, it meant that definitions were perpetually unfolding. What was constant in this flux was the definition of constructs via correlation coefficients and constructs were valued principally for their usefulness “to make predictions about observables” (Cronbach & Meehl, 1955, p. 290).

Both operational definitions and the concept of construct validity are logically flawed, but the pertinent point is that each remains a means of ducking Descartes. As long as these endure, “measured” psychological attributes are ontologically uncommitted dispositions. However, it is still pertinent to remind psychologists that their claims to measure presuppose answers to empirical questions. Anyone entering psychology now might think that Cartesian mentalism is its default philosophical position, but psychometrics owes no allegiance to Descartes. It is an ideological chameleon, superficially adopting whatever philosophical stripes are fashionable while rusted onto its one idée fixe: “Our mental tests measure something” (Kelley, 1929, p. 86).

The issue of psychological measurement is both conceptual and empirical

Where Franz’s argument promises results is when applied to attempts to measure currently occurring mental states, such as anxiety, because then aspirations to measure something mental are explicit. Franz claims that in seeking interval or ratio scale measurement, psychologists presuppose Hölder’s (1901) axioms, ⁸ which he thinks entail that addition applies to mental states. This he adjudges meaningless and concludes that claims to measure mental states are likewise. But this reasoning misrepresents Hölder: his axioms apply not to objects but to attributes; they concern not operations of addition but relations of additive composition; ⁹ and interval scales measure differences between magnitudes, not magnitudes per se. Taking Franz’s example of anxiety, consider the following reconstruction.

Instead of “adding” the anxiety felt this morning to that felt this afternoon, as Franz (2022) describes, Hölder’s axioms concern levels of anxiety and entail relations like the following: my current level of anxiety is entirely composed of two discrete parts: one equal to the level of anxiety felt this morning and the other to that felt this afternoon. Of course, our concept of anxiety cannot comfortably accommodate such relations, which leaves the fine grain of claims to measure anxiety on ratio scales opaque. However, most psychometricians would be content to descend to interval scales.

Interval scales are ratio scales measuring differences. For example, a temperature of 20°C means one differing from water’s freezing point by 20 one-hundredths (i.e., one fifth) of the difference between water’s boiling and freezing points. With interval scales, Hölder’s axioms apply to differences between levels of the relevant attribute ¹⁰ and to that end have been simplified, ¹¹ thereby enabling an interval scale for anxiety to be based upon relations of this sort: the difference between the level of anxiety I feel in the dentist’s chair and the level I feel giving a lecture is greater than the difference between the level I feel getting a vaccine jab and the level I feel negotiating heavy traffic. These two differences between levels of anxiety may well be different from each other, but logically that does not imply that either one is greater than the other. In particular, if levels of anxiety differ not only in degree but also in kind, ¹² then pairs of differences are not comparable in degree. That is, if the level of anxiety felt in the dentist’s chair is not only greater than that felt giving a lecture, but differs qualitatively from it and, likewise, if the level of anxiety felt getting a vaccine jab is not only greater than but also differs qualitatively from that felt driving in heavy traffic, the differences between these pairs are chalk and cheese. There is not space here to analyse the concept of anxiety, but suffice it to note that such analysis might show that our current concept is logically incompatible with the concept of quantitative structure.

However, because things are often more complex than we think, it is possible that our current conceptualisation misfits the phenomena of anxiety in all its richness, in which case empirical investigations might alter our concept, including its logical relation to quantitative structure. The history of science is a history of conceptual change. For example, were Aristotle asked whether temperature differences are comparable (e.g., is the difference between the temperature of the wine in this cup and that of the soup in this pot greater than the difference between the temperature of the water in this pitcher and that of the milk in this bowl?), his reply might have been that the question is idle because there is no way to test answers. In ancient Greece, the concept of temperature derived from the idea that each element of any substance is either hot or cold and intermediate temperatures exist, in a liquid, say, because of the ratio of hot to cold elements. ¹³ At the time there was no way to identify these hypothetical elements. However, once it was shown by empirical research that temperature is a continuous quantity measurable by thermometers, the concept of temperature was enriched sufficiently for ordinal comparisons of differences to be sensible.

Might not similar enrichment be possible with mental concepts? Franz (2022) says not: “it is misleading to think that there are fundamental shortcomings of our everyday psychological language that can be compensated for by empirical methods” (p. 137), but rather than explain himself, his preferred authority is quoted:

The meanings of words are determined by their rule-governed use, and they are given by what are accepted as correct explanations of community of speakers. For explanations of meaning function as rules or standards for the correct use of the expression concerned. (Bennett & Hacker, 2003, p. 382; as quoted in Franz, 2022, p. 137)

This does not explain Franz’s own dualism between mental concepts (considered immutable) and physical ones (considered mutable). Experience shows that language rules evolve, including conventions for psychological discourse. ¹⁴ Furthermore, if grammar ¹⁵ depends upon facts ¹⁶ and these facts reflect the vagaries of human interests, language must be plastic. Thus, rules of language provide no basis for conceptual analysis and a “non-anthropomorphic, objective basis for the criteria employed in conceptual analysis” (Hibberd, 2016, p. 816) ¹⁷ is required. Only logic can provide this because it is rooted in the reality talked about, not in the conventions governing ways of talking about it. ¹⁸

Based upon logic, conceptual arguments regarding the measurability of mental states will have merit and I have used them ¹⁹ to show that current conceptualisations of mental states, while permitting relations of greater than and less than between levels, ²⁰ do not sustain quantitative speculations, much less support the presupposition that mental states are measurable.

Franz’s (2022) fundamental flaw is that Descartes and Wittgenstein are presented as exclusive alternatives and other non-Cartesian positions, such as direct realism, ²¹ are ignored. According to direct realism, mental phenomena are not inner states, but external relations between organisms and environmental situations, and are open to direct observation by others. On this view, there is no reason to think of mental concepts as immutable. Thus, I conclude that in order to resolve the issue of whether mental states are measurable, both conceptual analysis and empirical methods are needed. ²²