I've long been puzzled by the nature of quantities, but I've never really
followed the literature. Now I've read Jo Wolff's splendid monograph on the
topic. I'm still puzzled, but at least my puzzlement is a little better
informed.
The basic puzzle is simple and probably familiar. On the one hand, being 2m high
or having a mass of 2kg appear to be paradigm examples of simple, intrinsic
properties. On the other hand, these properties seem to stand in mysterious
relationships to other properties of the same kind. First, there's an exclusion
relationship: nothing can have a mass of both 2kg and 3kg. Second, there are
non-arbitrary orderings and numerical comparisons: one thing may be four times
as massive as another; the mass difference between x and y may be twice that
between z and w. If 2kg and 8kg are primitive properties, why couldn't an object
have both, and where does their quasi-numerical order and structure come from?
In chapter 3 of The Powers Metaphysic, Neil Williams presents a nice problem for dispositionalists: the "problem of fit".
Dispositionalists hold that there are fundamental dispositional properties. Now consider a particular rock and a particular glass. The rock might have a disposition to break the glass when thrown at it. And the glass might have a disposition to survive impact of the rock. These dispositions are incompatible: if the rock is disposed to break the glass, the glass can't be disposed to survive the impact. But if dispositions are fundamental, then what prevents the rock and the glass from having the incompatible dispositions? The dispositionalist seems to require a mysterious ban on recombination.
One of the many drawbacks of studying philosophy in Germany is that nobody kicks you when you spend years on your M.A. thesis. So hereby I publicly kick myself. As a consequence, this blog might become even more occupied with David Lewis than it already is.
To start this trend, here is a question about Lewis' functionalism. When a property P is multiply realizable, we cannot identify it with its realizers because then we would identify the realizers with each other, too. All we can do is locally identify P-in-k with its realizer in k, where k is a world or species or individual. Now what is P itself? In Lewis' papers on mind, he usually says that 'P' is systematically ambiguous or indeterminate, denoting the contextually salient realizer. (At least this is what I take him to say. He is not particularly explicit here.) The alternative would be to identify P with the diagonal property of being a P-realizer. The main reason why Lewis rejects this option (e.g. in 'Reduction of Mind') is that it is difficult to see how this diagonal property can occupy the causal role associated with 'P'. Difficult, but not impossible: In 'Finkish Dispositions' he proposes a solution, and consequently prefers identifying fragility not with the contextually salient realizer but rather with the diagonal property. Since then he apparently hasn't written anything more on the issue, so I would like to know if he has changed his mind on mental states (and heat, etc.) as well. (There may still be problems if the theoretical role is not entirely causal, so that even if the diagonal property can do the causal work, it might not be able to do the rest.) Or has he completely endorsed the third alternative – to simply leave the question unanswered: 'The folk well might have left this subtle ambiguity unresolved' ('Void and Object'). Can anyone help?