[hist-analytic] A Mathematical Analogy to Mind/Body Supervenience
Baynesr at comcast.net
Baynesr at comcast.net
Sun Sep 25 12:01:11 EDT 2011
Here's another selection from my notebook. Again, I'm not firm on this; just taking notes.
Kim says that the presence of the supervenient property is "absolutely determined by the subvenient property." Consider a mathematical analogy. Take the standard case of area under a curve between two limits of integration. If you change the shape of the curve you do not necessarily change the area lying underneath it between two limits.
If you change the area of the curve you need not change the shape of the curve, even though the shape of the curve and the area are functionally related by the fundamental theorem of calculus. Note that the area of a curve can be "realized" (recall Putnam) in various ways, varying with the shape of the curve. The area of beneath the curve, however, "supervenes" on the limits (of integration): If the limits are changed so, too, is the area (ceteris paribus) under the curve. But what the limits ARE is not determined by the area. Similarly, although mental properties may supervene on physical properties they are not determined by the physical properties upon which they supervene. Or, at least, further argument is required.
Regards
Steve Bayne
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