----- Original Message ----- From: "Ted Winslow" <egwinslow at home.com>
>
> There's no argument here. I reproduced Whitehead's *argument* for
you. It's
> very clear. It's about any form of reasoning that makes use of the
> "variable". As he indicates, It doesn't just apply to algebra. One
thing
> plus another thing only makes two things if the identities of the
things
> added together are maintained in a way that makes the outcome of the
process
> of adding them together (changing their relations) "two things".
Where is
> the mistake in this reasoning?
========== I wasn't responding because there is a mistake in the reasoning. I accept there are limits to a calculus of variability and compositional plasticity with regards to mathematical modeling of agent saturated social and biological systems. This, however makes any temporally rigorous theory of descriptions under the subject-predicate form even more vulnerable to underdetermination, incommensurability and skepticism. We're all too familiar with the politics of describing/explaining social dynamics. Yes, Whitehead tried to obviate these problems with the subject-superject model and the doctrine of feelings, but he sneaks in a version of the 'pre-established harmony' with his (i) and (vii) of the categorial obligations and 'the primordial nature of God'. These attempt to justify/rescue epistemological optimism. I think we can be moderately optimistic about using non-linear math, which we're just beginning to explore, without having to resort to the manner in which W. resorted to a metaphysics of nature to justify his epistemological optimism even as it conceded some strategic ground to the skeptics on relating math to aspects of social dynamics. Whether we can have a mathematics of the experience of the activity of doing mathematics, well that's an issue for another millenium......
>
> How explicitly does Carol Gould improve on Hegel and Whitehead's
concept of
> internal relations?
>
> Ted
============ She explicates how to; avert the slippery slope of Bradley's infinite regress problem on relational properties; she's excellent on the distinction between a class and it's members and the accompanying problems of reification and the fallacy of misplaced concreteness; and she makes considerable room for independence, she struggles mightily to rescue us from a potentially suffocating holism which can lead to authoritarianism under conditions of potentially or actually intractable social conflict. All without presuming any metaphysics of nature. I doubt there's too much in her chapter "Ontological Foundations of Democracy" that H and W. would quibble with.....
Ian