Finite Quantities in Arizona

My favourite session at the recent Arizona Ontology Conference was on Daniel's paper Finite Quantities.

Daniel argues that there is suggestive evidence from science to the effect that certain fundamental quantities are quantized rather than continuous. That, for Daniel, is to say that not all properties of the form having n units of X are instantiated, for certain fundamental X such as mass, charge or perhaps distance. Rather, for these X, there is some minimal n such that the property having n units of X is instantiated, and for all other instantiated properties of this form, 'n' is replaced with some multiple of this minimum.

It is commendable to get clear about what the quantized hypothesis looks like, and Daniel gets quite a lot clearer about it than most other discussions I know of.

However, having clarified that it is not a claim about the necessity (nomic, metaphysical or otherwise) of this restriction on the instantiation of certain properties, or about the non-existence, unreality or other substandardness of such properties (assuming that properties can exist uninstantiated), the view does not seem so very surprising or controversial.

It strikes me as a much more modest and palatable claim than the claims that quantizers - including Daniel - often sound like they are making. It sounds considerably less shocking, for instance, than the claim that 'there is no such thing as' (say) 1/2 n units of mass, or that although I may express things like "1/2 n units of mass" in language there is 'no quantity corresponding to these representations' and that 'these quantities are not physically real' (p. 2).

Moreover, clarity as to the exact nature of the quantizer's thesis seems to make some of Daniel's argumentative moves puzzling.

One of Daniel's main opponents in the paper is someone who says that every time (say) a mass of six units is instantiated, the thing which instantiates the property having six units of mass also instantiates having three units of mass (twice over) and having two units of mass (three times over).

But let's be clear about two readings of 'having three units of mass'. On the first, it means 'having at least three units of mass'. On the second, it means 'having exactly three units of mass (and no more)'.

Now no-one would deny that everything which instantiates having six units of mass also instantiates having at least three units of mass. That would be silly. The quantizer, in this (made up) case, must instead be looking at denying that the property of having exactly three units of mass (and no more) is instantiated by anything.

But once we are clear that this is what is meant, the opponent's position looks silly. Obviously something which instantiates having six units of mass does not instantiate having exactly three units of mass (and no more).

On neither reading, then, does it seem as if a Daniel-style quantizer and the opponent he describes in his paper have a sensible dispute such that they might need to look at the science to resolve it.