In my research I found an ebook called

*Continental Philosophy of Science*and started a thread elsewhere in this forum. Therein I quoted from a chapter on Deleuze which is relevant here so it is copied below:

"Deleuze reads differential calculus not as a pragmatic matter of using differential equations to discover the slope of a particular function at a particular point. Rather, he sees in the differential an entire ontology of difference that can actualize itself into various functions and, consequently, specific curvilinear patterns" (247).

"In the later collaboration between Deleuze and Guttari, the writings of Ilya Prigogine become increasingly important. Prigogine, whose book La nouvelle alliance appeared in 1979, argues for a self-ordering of chemical components into patterns and relationships that cannot be read off from the previous state of chemical disarray.... It is not the introduction of some sort of ordering mechanism that makes the chemical clock appear. It is an inherent capability of the chemicals themselves for self-organization that gives rise to this phenomenon. It is as though there were virtual potentialities for communication or coordination contained in the chemicals themselves, or at least in their groupings, that are actualized under conditions that move away from equilibrium. As Manuel De Landa notes, in an echo of Deleuze’s treatment of Spinoza, ‘Matter, it turns out, can express itself in complex and creative ways, and our awareness of this must be incorporated into any future materialist philosophy'" (247).

Dynamic systems remind me of Henri Bortoft from our previous discussion here. Here's an except from that relevant to many of the comments in this thread:

'Bortoft distinguishes between two types of wholeness: the counterfeit and the authentic whole. Both notions of wholeness are based on different faculties of cognition. The counterfeit whole is based on the intellectual mind abstracting from concrete sensual perception. That is, the mind is moving away from the concrete part to get an overview. The result leads to an abstract and non-dynamic notion of the whole. In contrast, the authentic whole is based on a different cognitive capacity, the intuitive mind that is based on opening some higher organs of perception. The intuitive mind is moving right into the concrete parts in order to encounter the whole. This encounter leads to perceiving the dynamic and living multiplicity of the whole.

'The distinctions between the two types of whole (the counterfeit and the authentic) correspond to two cognitive capacities (the intellectual mind and the intuitive mind) and to two notions of generalization (the abstracting general versus the concretizing universal) which are at the heart of Bortoft's work.

'Says Bortoft (1998, 285): “We cannot know the whole in the way in which we know things because we cannot recognize the whole as a thing. … The whole would be outside its parts in the same way that each part is outside all the other parts. But the whole comes into presence within its parts, and we cannot encounter the whole in the same way that we encounter the parts. We should not think of the whole as if it were a thing.”

'Bortoft claims that we can not know the whole in the way in which we know a thing, because the whole is not a thing. Thus, the challenge is to encounter the whole as it comes to presence in the parts. Says Bortoft (1998, 284):

“If the whole presences within its parts, then a part is a place for the presencing of the whole. … a part is special and not accidental, since it must be such as to let the whole come into presence. This specialty of the part is particularly important because it shows us the way to the whole. It clearly indicates that the way to the whole is into and through the parts. It is not to be encountered by stepping back to take an overview, for it is not over and above the parts, as if it were some superior all-encompassing entity. The whole is to be encountered by stepping right into the parts. This is how we enter into the nesting of the whole, and thus move into the whole as we pass through the parts.

* * *

As in dynamic systems the parts have an inherent capability (the "whole") for self organization that rearrange themselves into new organizational patterns during disequilibrium. But this new (and temporary) equilibrium, while still containing the parts, isn't of itself a new "whole" that included the former wholes a la cognitive models of hierarchical complexity (the counterfeit whole of Bortoft).

I'm reminded of Wilber's differentiation of enduring and transitional structures (that we've discussed here), where the former are transcended and included while the later are transcended and replaced. It seems he had the gist of the above but that it only applied things like worldviews, values and other self-related lines. He still maintained though that the actual cognitive structures were of the enduring kind.

Here's an excerpt from "Dynamical systems hypothesis in cognitive science":

"It should be acknowledged that the most widespread conceptualization of the mechanism of human cognition is that cognition resembles computational processes, like deductive reasoning or long division, by making use of symbolic representations of objects and events in the world that are manipulated by cognitive operations (typically serially ordered) which might reorder or replace symbols, and draw deductions from them. This approach has been called the computational approach and its best-known articulation is the physical symbol system hypothesis (Newell and Simon, 1972). The theoretical framework of modern linguistics (Chomsky, 1965) also falls within this tradition....the traditional approach hypothesizes that all processes of cognition are accomplished by computational operations that manipulate digital representations in discrete time. The mathematics of such systems is based on an abstract algebra dealing with the manipulation of strings and graphs of distinct symbol tokens. Indeed, Chomsky's work on the foundation of such abstract algebras (Chomsky, 1961) served as a theoretical foundation both for computer science and cognitive science, as well as modern linguistic theory."

Compare to this statement by Commons:

"Lastly, in the early 1960s, many others’ work (e.g., Krantz, Luce, Suppes, and Tversky, 1971; Suppes, Krantz, Luce, and Tversky, 1989; Luce, Krantz, Suppes, and Tversky, 1990) introduced the representational theory of measurement. It is the basis for the Model of Hierarchical Complexity" (315).

Here are some interesting excerpts comparing different schools of cognitive science: classical, connectionist, pragmatist, reductionist. From “Intertheory relations in cognitive science” by Jesus Ezquerro (in CRÍTICA, Revista Hispanoamericana de Filosofía. Vol. 36, No. 106, April 2004: 55–103):

"Functional properties have a mathematical nature, and the classical view takes algorithms as the best

way to capture them, because algorithms are specially apt to describe state transitions between formal, discrete, symbol-like representational structures. In this sense, an algorithm would be constituted by a set of formal rules that operate on representations. Yet, algorithm theory is only a part of mathematics. Other mathematical descriptions may be able to account for that intermediate level between mental and physical properties....level-2 explanations are not necessarily algorithmic but they admit of a different sort of mathematics, such as dynamic systems theory.

"The classical view, Horgan and Tienson contend, entails that cognitive functions have to be specifiable by means of general laws about cognitive states. These laws are realized in particular cognitive transitions, which can be specified by rules on the algorithmic level, so a computation can be determined. However, if there are no such general laws, then the cognitive function will not be tractably computable. In fact, they argue, this is the actual situation in cognitive functions (73).

"Connectionist systems could be thus characterized in this mathematical framework: their transitions do not generally conform to algorithmic relations but can be captured by dynamic mathematics (74-5).

"It might be that our mental life can better be modeled by means of dynamic systems mathematics, as Horgan and Tienson contend, instead of algorithmic operations" (77).