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.