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No Such Thing as an Ontological Free Lunch

(I had to write this post, just so I could use that title.)
In D.M. Armstrong's book Universals: an Opinionated Introduction, he discusses the pros and cons of a number of theories of the metaphysics of properties. Chapter three deals with "resemblance nominalism." According to resemblance nominalism, properties can be accounted for in terms of degrees of resemblance between the various objects having the property. So, for instance, on object is red if and only if it resembles some paradigmatic red objects. This theory is plagued by the "Resemblance Regress." Armstrong quotes Bertrand Russells' version as the "classical exposition" of the difficulty (p. 53):

If we wish to avoid the universals whiteness and triangularity, we shall choose some particular patch of white or some particular triangle, and say that anything is white or a triangle if it has the right sort of resemblance to our chosen particular. But then the resemblance required will have to be a universal. Since there are many white things, the resemblance must hold between many pairs of particular white things; and this is the characteristic of a universal. It will be useless to say that there is a different resemblance between each pair, for then we will have to say that these resemblances resemble each other, and thus at last we shall be forced to admit resemblance as a universal. The relation of resemblance therefore, must be a true universal and having been forced to admit this universal, we find that it is no longer worthwhile to invent difficult and implausible theories to avoid the admission of such universals as whiteness and triangularity.

I, however, think Plato has a better right to be called the "classical exposition:"

�... forms are like patterns set in nature, and other things resemble them and are likenesses; and this partaking of the forms is, for the other things, simply being modeled on them.�
�If something resembles the form,� he said, �can that form not be like what has been modeled on it, to the extent that the thing has been made like it? Or is there any way for something to be like what is not like it?�
�There is not.�
�And is there a compelling necessity for that which is like to partake of the same one form as what is like it?�
�There is.�
�But if like things are like by partaking of something, won't that be the form itself?�
�Undoubtedly.�
�Therefore, nothing can be like the form, nor can the form be like anything else. Otherwise, alongside the form another form will always make its appearance and if that form is like anything, yet another; and if the form proves to be like what partakes of it, a fresh form will never cease emerging.� (Parmenides 132d-133a, tr. Mary Louise Gill and Paul Ryan)

It should be noted that Plato is, strangely, a sort of "resemblance realist," and is not talking about resemblance nominalism of the type Armstrong describes.At any rate, while Armstrong does not actually accept resemblance nominalism, he does think that it can escape from this, by introducing "particularized natures." As he says:

One major trouble that Russell ... overlooked is that all solutions to the Problem of Universals, including realism about universals, require a fundamental relation. But if so, the regress Russell finds in the case of resemblance reappears with the other theories ... Given the natures a and b, they must resemble to the exact degree they do resemble ... the resemblance is not an additional fact about the world over and above the possession by a and b of the particularized natures that they have. The relation supervenes on the natures, and if it supervenes, I suggest, it is not distinct from what it supervenes upon ... I think that this means that we do not have to take it too seriously metaphysically. It is an ontological free lunch.(pp. 54-56)

There is, however, no such thing as an ontological free lunch. Resemblance as a fundamental and unexplainable properties of fundamental unexplainable particularized natures adds greatly to the overall complexity of a theory and is therefore not by any means "free," regardless of Armstrong's claim about supervenience.

Posted by Kenny at February 3, 2007 4:14 PM