GODEL, HOLONS, HEGEL and MEANING

Gödel, Holons, Hegel and Meaning 
By Giorgio Piacenza Cabrera

Gödel’s Incompleteness Theorem demonstrates a logical dynamic that uses the same principles as Holons: If the system is consistent, it also is incomplete. Also, the consistency of axioms cannot be proven from within the system.

Holons are understood as both structural ontological and structural logical whole-parts. Holons are consistent units (they are whole) but holons also are incomplete (they need to extend and connect with other holons to be consistent). Some self-evident aspects of holons corresponding to axioms (such as their unitary or whole quality) cannot be logically proven in a complete way from within their system of component parts. We need to reach outside the whole and this, of course, forms a new relation, which in turn constitutes a new unit or whole and so on, supposedly ad infinitum.

Hegel’s Dialectic functions similarly to these holon dynamics. In a sense, a thesis is a posit or element which requires the quality of wholeness or completion. The antithesis is partialness or incompletion and their synthesis is a relation which also instantly generates (or just is) a new thesis. Holons in relation become part of a system of holons at the same level of depth and this relation instantly forms a new unit or holon. If we state that a thesis is like an independent pole, the antithesis is like a dependent pole, the synthesis is like an independent and dependent entity (a holon). It is whole or independent and partial or dependent.

If everything that is both recognizable and conceivable (both meaningfully and in the exteriority of nature) forms holons, Gödel’s Theorem of Incompleteness applies universally and not only to the domain of arithmetic. Gödel revealed the limitations of binary logic pertaining to the aim of creating a self consistent arithmetic and to establish mathematics in these grounds. Since systems of ideas can also be considered as holons, the limits in the search for self-consistent logical systems of ideas using an exclusive binary logic (with a strong “excluded middle”) are also revealed by Gödels discovery. All systems of ideas which have a unitary quality are expected to reach out to other systems to remain consistent.

Maybe these discoveries establish that a dialectical logic is a more general case than binary logic, but I wonder whether if with dialectical logic instead of doing away with the excluded middle (required to make differentiations that work with duality). Aren’t we simply extending our understanding of how the relations between what is recognized offer a more encompassing, multivalued and logically necessary possibilities? Thus in the so called “Second Tier” awareness haven’t we simply increased our awareness of logical possibilities implicitly taking in a “both-and” kind of logic even while retaining an “either-or” kind of logic? 

Having we just expanded our understanding of what the Identity Principle -the most essential principle of thought- is capable of? Haven’t we just expanded our attitude away from the concretely differentiated in an epistemological shift towards the possible or potential and less differentiated in relation of that which is? Aren’t we perceiving a greater magnitude of being embedded in the relation among particulars?

The holon is dialectic because of the following: BOTH the thesis and the antithesis are true AND the synthesis is also true. In contrast, using a binary logic with a strong excluded middle we would say: EITHER the thesis is true OR the antithesis is true.

Interestingly, we need to associate the same principles with other open-ended philosophies that could be considered as multi systemic, Second Tier and an improvement in rigor and logical thinking. For instance, Hegel’s dialectic, Gödel’s Incompleteness Theorem and also Archie J. Bahm’s Organicism utilize or depend upon the partially complete and partially incomplete relations of Complementary Pairs. It is our capacity to intuit relations that which transcends and includes a simple reductionist dualistic mode of thinking. This capacity probably depends upon a meaningful, unqualifiable ATTITUDE before the Identity Principle which could also be conceived as the Principle of Recognition of What Is.

If we hold on to the complete and partial truth of the mutual exclusion of opposites, we utilize logic to recognize what is concrete and mutually exclusive. If we discover -besides the truth of exclusivity- that opposites also unavoidably require of each other, we establish a dialectical opening towards a new mode of integrating what is recognizable as real. We open our being and awareness to Integral Thinking.


Gödel’s great discovery doesn’t just demolish pretenses to self-consistent truth sought from within formal systems; pretenses sought out by important logical mathematicians like David Hilbert and Bertrand Russell. Actually, the great mathematician Gödel was a Platonist, a believer in intuitively derived rational foundations for discursive thinking, foundations that could take mathematicians outside from the never ending need to reach out for ways to demonstrate relative systems from without those systems. As I see it, he wanted to establish that non formal, intuited knowledge is the basis of the axioms of the exactness of mathematical knowledge and that this exactness of mathematical knowledge cannot be absolutely demonstrated from within.

As said before, I think that we begin by recognizing that which IS and the modes of relation of that which IS in a more ample or inclusive way. I think that intuitive intellectual perception transcends the incompleteness or insufficiency of either-or logic demonstrated by Gödel. That which IS discloses directly to the intellect in various ways every time we recognize something. I think that perceiving what is incomplete in duality and the non dual perception of Being combine allowing any kind of recognition to manifest. 

That which by definition must be (according to René Descartes’ sharp- and probably irrefutable- understanding of St. Anselm Ontological Argument), in fact, the only posit and definition that requires existence for the definition or posit to be recursively self-consistent with itself must be the essence of identity in contingency and non contingency. This reveals as the Perfect Being that transcends and includes duality, reveals more and more inclusive ways of how that which IS can both manifest itself and be understood. Here epistemology converges with ontology, understanding with the requirement of being, a being as infinite, undefined space containing everything and allowing all forms, all holons to meaningfully, sentiently express under the strictures of limitation or time.

The Four Dimensions of Reality Under an Emerging Post Orthodox Integral Theory Idea

The Four Dimensions of Reality Under an Emerging Post Orthodox Integral Theory 
By
Giorgio Piacenza

To appreciate this evolving exploration on the nature of reality one needs to be acquainted with Ken Wilber's Integral Theory.

However this brief article also seeks to go beyond the current state of that theory. Moreover, it seeks to overcome the simplistic dichotomy of "physical" vs "metaphysical" whereupon "metaphysical" is simply understood as "non physical" or as "speculative" and "non real." In my view understanding the metaphysical in a more comprehensive way can help us to practice better physical and even inter realm science.

In traditional rational metaphysics discovering the principles that organize observable reality was considered very important and fundamental. With the success of manipulative forms of techne and science under the use of a strong either-or excluded middle logic, the search for essential principles was left behind. Nonetheless, as progress in the sciences and in theoretical frameworks continues beyond mutually exclusive views, an integration within a Meta Pattern begins to form. Objects of awareness may appear as mathematical proportions capable of defining the physical characteristics of a universe. Probabilities become actualities as we observe the quantum realm and dialectical paterns arising from thinking of opposites as complementary give equal importance to semingly incompatible ideas. Mind, matter, the one and the many became not just mutually exclusive but amenable to a higher form of integration.

Does "reality" consist of ideas, or of particles and matter. Perhaps of relations? If reality is one, how can it also be many? Is emergentism incompatible with emanationsism? By assigning these and other posits along axes defined by polar extremes and considering these extremes as mutually involved with each other, rather than as mutually exclusive, we may come to understand and Integral and Organicistic view suitable for a more inclusive Metaphysics.

I posit that the relation between realms of experience can be better understood not just in an experiential but in a rational and scientific way. I posit that "metaphysics" doesn't just refer to first principles of reality but to how these first principles relate with the Interior (mental, meaningful or qualitative) dimensions of reality and with the Exterior (physical, objective, quantitative) dimensions of reality.

Although I'm basically in favour of a pansychic view, in order to explore this view with greater definition, I'm trying to see previously incompatible metaphysical theories under a Meta Pattern. I'm also trying to consider a dialectical logic that brings more integrative distinctions between opposites such as "mind" and "matter." I'm somewhat influenced by the emanationism of Plotinus, by Poortman's idea of "vehicles of consciousness" and by the pre hispanic, Andean concept of the "three worlds" (Kay Pacha, Hanan Pacha and Uku Pacha) related under the principle of complementarity (Tinkuy, Yanantin and Masintin) and reciprocity (Ayni).

I'm trying to develop a balanced understanding between dialiectical logics or reasoning and the idea of using strong excluded middle "either-or" logic. The former may apply more to an organic, living and participatory understanding of reality and the former to the more concrete exterior patterns of reality

I also think that the possible meanings or interpretations behind the findings of quantum physics need to be incorporated as indicative of a relation between what Integral Theory calls the "three realms" and I think that this relation will help us to construct a model that doesn't just present what has been called "tetra meshing" or the simultaneous arising of the four dimensions of reality in each realm, but what could perhaps be considered as "causal" relations between these realms.

The four dimensions of reality seem to stem from the intrinsic dual or polar nature of "holons" which according to Arthur Koestler and to Ken Wilber's Integral Theory are wholes and parts simultaneously. I think that both polar relations and holons display apparent completeness and actual incompleteness and, for this reason, holons follow what have been called the "Twenty Tenets." They seek to include more of reality and are open to a cautious association with other holons. They also seek to preserve their integrity or to maintain their distinctiveness.

These four dimensions of reality (or actually of contingent, duality-based, phenomenological reality) seem to derive from a self evident reason: One can reasonably asset that the tensional and yet complementary nature of polar opposites are associated with asserting that one of the poles is real, that its opposite pole is real, that what subsumes polarity is real and that both poles are independently real. These distinctions generate four extreme positions and (at least) four intermediate positions with the central position acting as mediator and unifying connection with a non conceptual non duality core within it. We still need to use incomplete definitions knowing that they are incomplete: The non conceptual "principle" or non dual "way" of the Tao may be "behind" the "polar nature" of the Tao.

The four dimensions that poles generate may be associated with preferred kinds of logic and with the interplay between dialectical logics and strong excluded middle logics. In Integral Theory, they correlate with the "Interior" the "Exterior" the "Individual" and the "Collective" dimensions that form quadrants or, rather, qyadratic AREAS of expression where other elements of reality may express (stages of development, lines of development, states and types).

Supposedly, Integral quadrants arise when a level of multi systemic awareness has been reached but they seem to have arisen at least partially within the Andean model of the "Chakana." Other than the Andean model which is linked to the concepts of "Tinkuy" "Ayni" "Yanantin" and "Masintin," I also think that integral quadrants arose before Ken Wilber's momentous "eureka" moment (by mid 1990's) when he inductively observed a Meta Pattern in his home where he had physically grouped many theories and answers about the nature of reality. Archie J. Bahm. E.F. Schumacher Carl Jung and Wolfang Pauli seemed to have achieved similar insights: Complementary quadrants or, rather, quadratic models that are organized under similar principles underlying the rational dialectical view of polar opposites and holons; nonetheless, models which emphasize different concerns. This is why I'm linking to a previous (also evolving)article that sheds more light on these mutually reinforcing models which demonstrate a common organizing pattern. The article's title is "Other Integral Quadrants in History."

I think that whether in a new "Integral Age" of cognitive and participatory, co-creative understanding we can make progress on the "mind-body problem," on the physics of subtle realms, on the compatibility of opposing metaphysical positions, on re integrating first metaphysical principles with science, and on whether science and philosophy may integrate again under a grander and yet useful overarching conception relates with how the problem of duality is expanded to cover more of reality's complexity in a non exclusionary way.