How plausible is the hypothesis that psychological attributes are quantitative?

[Matt Williams]

Since Benjamin seemed keen to renew some discussion on this group, there is an issue I've been wanting to ask you all about...

So Michell has pointed out that a fundemental assumption of psychometrics is that psychological attributes are quantitative; that (almost) none of us have actually tested this assumption; and that it is possible to test this assumption using the conjoint measurement model.

One reasonable response to Michell's critique, then, is to go out and collect data and apply the conjoint measurement model to test the quantitativity hypothesis. And I believe some of you do such things?

But my question is: Is it actually remotely plausible that psychological attributes are quantitative? I.e., what prior probability should we place on this hypothesis?

I've been pondering one possible reason to be skeptical of the quantitativity hypothesis. It's this: In the natural sciences, only a few independent quantitative variables have ever been identified - length, mass, temperature, and so forth (think of the base SI units). Then there are a number of other quantitative variables that are combinations or derivatives of other variables (e.g., the derived SI units).

Furthermore, the quantitative variables that have been identified are basic physical quantities that are measured in many different fields. They are not brand new variables that emerge as a unique property of a specific type of object or organism. Biologists, for example, may measure the mass or temperature of an organism, but they haven't come across uniquely biological quantitative variables (or not as far as I know anyway).

I suppose it's plausible that there might be human behaviours that turn out to be dependent on quantitative physical variables - the mass of some neurological structure or whatnot. But why would we think that there exist variables that are genuinely psychological - i.e., not just well-known physical variables or derivations thereof - and that are also quantitative? Is there any precedent to suggest that such a discovery is likely?