> Then again Hegel was not the first to adumbrate a theory of
> internal relations. As ontological atomism is a metaphysical
> hypothesis that can't be tested or refuted via experiments,
> who cares if it's true or not? A formalized model/doctrine
> of internal relations helps alot in biology [embryology,
> cell permeability etc.] geometry and, possibly, plasma
> physics; but it pays to be careful in avoiding a reification
> of holism and the notion of inseparability as constitutive
> of the contingencies of identities in social dynamics.
> Popper and his ilk were pointing out the ways Hegel's
> doctrine unwittingly supported Nazi beliefs of "the group".
> A model/doctrine of internal relations that doens't make
> sufficient room for autonomy and separability is suffocating
> of *difference* and *otherness*. As I've said before, Carol
> Gould does a great job of navigating the very complex issues
> involved.
Your idea that ontological claims can't be grounded in experience (which you misidentify with grounding them in "experiments") is itself grounded in an implicit ontology - atomism. It isn't just ontological claims that can't be grounded if this interpretation of "experience" is accepted, however. As Whitehead shows, the only claim that can be grounded is "solipsism of the present moment." Those who misidentify "logic" with "formal logic" are, as I said earlier, psychologically immune to reductio ad absurdum arguments of this kind.
You repeatedly claim that "formalized models" e.g. non-linear algebra and "multi-valued logic," can be used to represent internal relations. In the case of non-linear algebra this is certainly mistaken since, as Whitehead shows, algebra requires that the identity of "variables" in the logical sense be sustained through changes in their relations. I suspect this is also true of multi-valued logic and that what you are doing is confusing the identity of a logical "variable" with its truth value.
Keynes attempted to develop a multi-valued logic in A Treatise on Probability on the basis of the idea of directly intuitable objective probability relations. This was an attempt to work out a theory of probability within an atomist ontology. On the basis, he claims, of criticism by Frank Ramsey who pointed out that no such relations could be perceived, he abandoned this approach and embraced the idea (it happens to be Whitehead's) that probability could be grounded in "human logic" - this is an aspect of the emptying of "formal logic" of content to which he makes reference in the same context. He associates the concept with Ramsey but rejects Ramsey's attempt to elaborate it in terms of Peirce's pragmatism. Whitehead elaborates it as a method of grounding both degrees of belief and ontological beliefs. It involves demonstrating that "empiricist" claims about experience embody unacknowledged interpretive ontological premises e.g. atomism and then attempting to show that these claims misdescribe our direct experience. This is also Husserl's answer to the reductio ad absurdum - "solipsism of the present moment" - that issues from "empiricist" premises.
Can you show by way of an example how a multi-valued logic enables the *identity* of "variables" to vary with changes in their relations i.e. how it can be used to represent internal relations?
Your statement about "a reification of holism and the notion of inseparability as constitutive of the contingencies of identifies in social dynamics" that doesn't allow for "autonomy and separability" seems (it's in Ian-speak) to indicate you don't understand the concept, certainly as it's made use of in Whitehead and Marx. They make it consistent, as I've repeatedly tried to show, with full self-determination, i.e. full autonomy, in the sense I've specified i.e. relations are conceivable in which human "individuals" achieve full rational self-consciousness. Moreover, though in an ideal community each individual would have this "identity," each is unique precisely because of internal relations since what Whitehead calls the "standpoint" of each, the location of each within the system of internal relations, necessarily differs to some degree from the "standpoint" of every other. These two features combined are the basis of Husserl's idea of "transcendental intersubjectivity" as the ultimate ground of knowledge.
"Holism" in the sense of "Nazi beliefs of 'the group'" has nothing to do with the idea if by this you mean some notion of a "group" as an entity existing apart from and independent of the individuals that compose it. In Popper, this kind of argument is another cheap shot associated with his honouring of his own principle that "critical rationalism" requires you to make someone else's argument as strong as possible before criticizing by egregiously violating it at every possible opportunity. Pretty much every time he invokes it, e.g. just before criticizing the concept of "internal relations" in critical theory, he immediately proceeds to attack demagogically a straw man.
Ted