Saturday, September 09, 2006

Holism and dependence

In their paper "There is no question about physicalism," Crane and Mellor try to undermine one of the arguments that Davidson uses to defend the position that there are no strict laws linking the mental and the physical. Davidson says that the mental is holistic and normatively constrained by rationality. Crane and Mellor attack both these lines, but I will focus on what they say about holism. They say that physical laws are holistic too. The example they give is f=ma. They say that given some value for f, one cannot know the values for m or a. The variables are interrelated in the same way as the various beliefs that one has. They conclude, pace Davidson, that holism doesn't prevent strict laws linking the mental and the physical.

The point that Crane nad Mellor try to make seems to rest on conflating dependence with holism. This is an intuitive distinction, but I think it holds. Dependence would be when a change in one thing necessitates a change in the dependent things. In the case of f=ma, changing one variable changes the quotient or product of the others depending on the variable. Holism seems like a more global claim where in order to know one thing about the system, you have to know a very large amount about it. Holism implies dependence, but not conversely. The difference doesn't come across enough when the "system" is the three variables in the equation f=ma, since it doesn't take much to know a lot about it. I think it can come out clearly in the following way. The variables in the force equation are functionally dependent, so you can have a binary function from two to the third. This function can be curried to produce a unary function to a unary function to the value of the third variable. I don't think that holistic systems are in general functionally dependent. They are relationally dependent, so that knowing the values of 2/3 of the system's variables constrains but does not determine the remaining third. In other words, no functions, so no currying. I will need to get a more detailed specification of holsim to expand this idea, but I think the point is there. Crane and Mellor conflate (inter-)dependence with holism, so I don't think their objection goes through.

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