Black - against quidditism.pdf - Ted Sider

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Downloaded By: [New York University] At: 21:44 25 May 2010 102 Against Quidditism abstract or concrete: the laws supervene on the arrangement of qualifies iff any possible world with the same pattern of qualities has the same pattern of laws. Nevertheless, I think this formulation has a severe difficulty, a difficulty which is already there in Lewis's statements of the doctrine, but which leaps to our attention once we regard possible worlds as mathematical structures, namely, it relies on an oversimple notion of 'quality'. Philosophers, even philosophers of science, tend to talk about qualities (or properties, or universals) and relations, and make claims such as 'laws have the form of generalized conditionals, in the simplest case represented by the schema "For any x, ifx is A then x is B"' [15]. But examination of any textbook of fundamental physics reveals nothing to which this picture easily applies. The equations expressing fundamental laws are indeed implicitly universally quantified, but they connect not simple monadic qualities, but mathematically represented quantities. A particular quantity is a determination of a determinable, and its mathematical representation (say as a real number, or a vector, or a tensor, or a projection operator on a Hilbert space) determines a structure of internal relations between determinations of the same determinable without which the equation expressing the law makes no sense. 21 Lewis construes such determinables as 'families' of properties [10, p. 53], so that a variable quantity like mass would be a family of plain properties, the various particular masses. He also, as we have seen, hypotbesises that spatiotemporal relations--distance relations between points--may be the only fundamental relations [14, p. 474]. It is unclear to me how we are to take this. Take two particles, one with twice the mass of the other. Does a full description of the supervenience base already include this relational fact, or does it only include the fact that one path in spacetime instantiates one property and another a distinct property, so that, at the fundamental level, before we start talking about supervening laws, different masses have no more to do with one another than a mass with, say, a charge? The latter option seems to me unworkable: the supervenience base has become so narrow that in order to get the system of laws offthe ground we would have to start with some infinitely complex laws relating all the various masses to each other, or alternatively something like Newton's second law of motion would splinter into continuum-many distinct laws, one for each combination of mass and force. It seems therefore that the location of a particular quantity as a determination of a determinable, and thereby its mathematical relations to other such determinations, must already be given as part of the supervenience base. But often the mathematical structure of a variable quantity can itself only be understood in relation to other quantities. A key example here, originally raised as an objection to Lewis's view by Denis Robinson [19], is a classical vector field--can this be an arrangement of local qualities? On this example, Lewis now says: I said qualities were intrinsic; that means they can never differ between duplicates; and I would have said offhand that two things can be duplicates even if they point in different directions. Maybe this last opinion should be reconsidered, so that vector- valued magnitudes may count as intrinsic properties. What else could they be? Any 21 I am not of course the first person to point this out--see for example [24].
Downloaded By: [New York University] At: 21:44 25 May 2010 Robert <strong>Black</strong> 103 attempt to reconstrue them as relational properties seems seriously artificial. [14, p. 474] On the contrary; I think any attempt to construe vector-valued magnitudes as other than relational is hopeless. Lewis is thinking of the simple case of flat space (or spacetime), where we can straightforwardly talk about the same vector-valued magnitude being present at distinct points. But in the general case of a vector field defined on a manifold, the field consists of an assignment to each point of the manifold of a vector in the tangent space at that point. Each point has its own tangent space, and though all the tangent spaces are isomorphic, there is no privileged isomorphism, and thus no sense in which one can compare directions at different points. We have thus at each point a determination of a different determinable, these determinables themselves being linked together in the tangent bundle by the differentiable structure on the underlying manifold. Another example of the complex relational nature of physical quantities is provided by Lewis's suggestion of a possible world where a quark flavour has traded places with a quark colour. But a quark colour doesn't look remotely like an intrinsic quality. According to my (limited) understanding of these things, the colour state of a quark is represented by a state vector in a three-dimensional Hilbert space; any three orthogonal normalised vectors in this space can be taken as the basic three colours, and (most importantly) because of colour symmetry, it makes no sense to talk of the colour of a single quark, but only of the combination of colours when three quarks (or a quark and an antiquark) are joined together. Given the kinds of conceptual linkage between fundamental quantities of which the above are examples, I think the moral is that Lewis has not provided us with a statement of Humeanism which is compatible with the conceptual structure of physical theory (and this point does not depend just on fancy pieces of quantum mechanics which few if any of us understand). The jury seems to me still to be out on whether or not the Humean can provide a description of the supervenience base which does not presuppose the structure of fundamental laws which gets erected upon it. 22 University of Nottingham Received: August 1998 Revised: October 1999 REFERENCES 1. D. Armstrong, 'The Causal Theory of Properties: Properties according to Shoemaker, Ellis and others', forthcoming in Philosophical Topics. 2. R. <strong>Black</strong>, 'Chance, Credence, and the Principal Principle', British Journal for the Philosophy of Science 49 (1998), pp. 371-385. 3. G. Boolos, 'To Be is To Be a Value of a Variable (or To Be Some Values of Some Variables)', Journal of Philosophy 81 (1984), pp. 430M9. 4. G. Boolos, 'Nominalist Platonism', Philosophical Review 94 (1985), pp. 327~44. 22 Thanks to David Lewis and an anonymous referee for helpful comments on an earlier draft of this paper.
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