The Galilean equivalence

It is tempting to think that there is nothing more to physical quantities than their nomic role: that to have a certain mass just is to behave in such-and-such a way under such-and-such conditions.

But it is also tempting to think that the "Galilean equivalence" of inertial mass and gravitational mass is a true identity; i.e., that

Inertial mass = gravitational mass.

However, the role associated with "inertial mass" is completely different from the role associated with "gravitational mass". So if having such-and-such inertial mass is having the relevant dispositions associated with "inertial mass", and likewise for gravitational mass, then the Galilean equivalence could not be an identity. It would rather state an empirical law, according to which two distinct quantities always have the same value.

To be sure, the relevant role properties--having the dispositions associated with "inertial mass" and "gravitational mass" etc.--exist, and they are not identical. But what's implausible is that fundamental physical reality contains two (or seven, according to Wikipedia) distinct kinds of mass, each a physically fundamental quantity. The much more plausible hypothesis that there is a single quantity here that plays a variety of roles.

So we need to distinguish between the nomic role associated with physical terms like "inertial mass" and the property or quantity picked out by the terms: the property of having such-and-such inertial mass should not be identified with the property of resisting acceleration in such-and-such a manner, even though that is how "inertial mass" is defined.

That is one lesson from the Galilean equivalence. One could still hold that physical properties are purely dispositional, as long as the dispositions are not the ones conventionally associated with the relevant terms. For example, one might hold that both "inertial mass" and "gravitational mass" pick out the same complex disposition that combines the roles associated with either term.

However, it is not clear why we should say that this complex dispositional property is a single fundamental property, rather than a conjunction of several distinct and simpler properties. The individual roles of inertial mass and gravitational mass certainly look simpler than the combined role. It would be nice we had a physical story explaining the identity of inertial and gravitational mass in terms of another, simpler dispositional property from which the different mass dispositions could be derived. But we don't seem to have such a story, and it is conceivable that none can be found.