Is Hegel and Peirce Triadic a Multifractal?

Is Hegel and Peirce Triadic a Multifractal?

Blog entry by David M. Boje May 25, 2016, At Copenhagen Business School

Abstract: I am posting a response to Søren Brier’s (2014) The riddle of the Sphinx answered” On how C. S. Peirce’s transdisciplinary semiotic philosophy of knowing links science and spirituality. A chapter in Tandy, (ed.) Death and Anti-Death, Vol 12: One Hundred Years after Charles S. Peirce (1839-1914), An Arbor MI: Ria University Press. Here I develop ways that Peirce triadic builds on Hegel’s triadic, and both can be interpreted as multi-fractals. Both Hegel and Peirce go beyond Kant’s triadic. Søren calls Peirce the first true postmodern scholar, and one that worked to resolve the gaps between humanities and natural sciences, and between intuitionism and empiricism (p. 2). Søren contends that Peirce’s pragmaticist triadic has a way out of the quantum physics problematic of quantum consciousness (or quantum metaphysics) as tackled by Capra, Bohm, Penrose, Hameroff, and I would add Barad and Žižek to his list (p. 7). Triadic is a way to overcome Cartesian dualism of mind and body, subject and object, and so on. The relation of fractals and multifractals to Storytelling Dialectics is something I have written about as permeating all living organic systems, and not always in positive ways (Boje, 2014; Boje & Henderson, 2014; Henderson & Boje, 2015; Boje, 2015). For example, my colleagues Savall, Zardet, Peron — write about and study the (Taylor-Fayol-Weber virus) or TFW virus for short, which I have argued is a kind of fractal contagion infecting organizations. Can there be counter-fractal transformative processes we might learn from Hegel and Peirce? Triadic multifractal is a dynamic transformative and dialectical process of what Hegel (1807) calls self-movement, in negation of a negation in the interfusion of Being and Action.



As Peirce put it “Much as I would like to see Hegel’s list of categories reformed, I hold that a classification of the elements of thought and consciousness according to their formal classification of the elements of thought and consciousness according to their formal structure is more important” (as sited in Søren, 2014: p. 4). For Peirce, First, Second, and Third triadic is the mediating events of Reason between [evolutionary process ontology of] chance [indeterminateness, chaos] that brings forth First original events [quantum waves/particles], and the laws of [fractal selfsameness habit-taking potentialities of] Nature that produces sequences of the Second (EP 1: 243; Søren, p. 11-13). Hegel also writes about the triadic of mediating negation between contingencies (chance, or Tychism) and laws of Nature.

  • “To the observing consciousness, the truth of the law is found in experience, in the same way that sensuous being is [an object] for consciousness; is not in and for itself. But if the law does not have its truth in the Notion, it is a contingency, not a necessity, not, in fact, a law. But the fact that it is essentially in the form of Notion, not only does not conflict with its being accessible to observation, but rather for that very reason gives it a necessary existence, and makes it [an object] for observation” (Hegel, G W F. 1807, Phenomenology of Spirit: # 249).


“And here is a similarity to modern quantum mechanics, where particles-waves only have a certain probability or tendency to exist when measured” (Søren, 2014: p. 13). In Peirce’s synechism “the worlds ontological foundation is a plenum, or a field where everything is connected to everything else in a hyper-complexity” like we find in multifractality (Søren, p. 14). Peirce uses terms like fallibilism (we can not know everything) and infinitesimalalism (we can keep dividing into smaller units).

Both Hegel and Peirce have Triadic models that can be considered as multifractals. There are several kinds of fractals that can be used to described Hegel and Peirce triads, such as Sierpinski Triangle, Branching Fractal, Mandelbrot Fractal, and so on.

Benoit Mandelbrot (1975) coined the term fractals. Mandelbrot’s definition of fractals: “irregular and/or fragmented at all scales” (Nottalle, 2011: 44).

Hegel - Christianity


Hegel Triadic as Sierpinski Triangle Fractal 

“The triadic-dialectics of Hegel (abstract, negative, concrete) and Fichte (thesis, antithesis, synthesis) posit that propositions/claims have flaws within themselves which cannot be resolved unless mediated by thing outside the context; a pure being (awareness in itself) is indistinguishable from nothing and thus require something determined or concrete as a mediation (a more recent example may be the hand-held spear negated into a thrown spear and then synthesized into bow with a quiver of arrows). From the resulting concrete/synthesis, the two lesser moments are sublated into higher categories and the process repeats until a future equilibrium (progress)”



“Hegel’s principle posits a cognitive tension or paralysis between abstractions (ideas) and their indetermincies which can only be realized through something more concrete (ideas and our awareness undergo differentiation which are eventually realized in sensible things). Every resolution of previous flaws/contradictions expands both possibility/realized spaces while new antagonisms emerge from their mediations.”

“Peirce names his categories simply “Firstness,” “Secondness,” and “Thirdness.” Something may appear to us either as a “First,” a “Second,” or a “Third,” there is no other possibility” Source

Firstness, Secondness, Thirdness Triadic

  • Experience of immediate presentness without any conscious realization of a separation between ourselves and an object (as, for instance, in case of an intense feeling of red).
  • As not even a contrast between subject and object can be experienced in this way, phenomena belonging to firstness are only imaginable as “positive qualitative possibility.”


  • Experience of actual facts.
  • Dyadic relation between facts (e.g. ego‹alter), without mediation.
  • Experience of brute resistance, without recognizing anything as something.
  • Experience of a law or a habit as determining actual cases of secondness.
  • For instance, if something is regularly perceived as something determinate.
  • Awareness of the reality of thirdness is condition of the possibility of forecasts.
  • The reality of thirdness is evident from, or, as Peirce says, “consists in” nothing but the determination of “future facts of secondness.”




I teach systems theory (or systemicity, as I prefer to approach it), and link quantum, dialectic, to Hegel to get around the hierarchic levels approaches to systems thinking:

Next, instead of a hierarchy of systems, such as Boulding, and von Bertalanffy assert, let’s try a different approach. Hegel uses a triadic of Essence, Form and Notion. this forms a double inversion, or if you prefer two doublings. Essence/Form/Notion triadic has form as its middle term. Essence is in-itself of the Notion. Essence falls apart in moments of subsistence, of placing content into Form of the Parts-Whole systems thinking, its presuppositions are Notions. The ‘True’ Real (Essence) is dialectic to Form, which is just another category schemata. And Form is dialectic to Notion, and Notion to Essence, and both are category Ideations. Here is how it works in practice in systems thinking. The Essence is said to be Parts and Wholes. The Whole is always said to be greater than the sum of the Parts. Just classify the Parts, and the relations, is the usual advice. This Notion/Essence comes to define the empirical content set into Form of the ground (Žižek, 1993: 136). The Content is sorted into Form-al ground, into the Framework (level 1 in Boulding’s Hierarchy of systems). It is still a tautological gesture. This can be seen in the next move, as systems theory translates the Parts are Greater than the Whole montra, into the parts-relations: Inputs-Throughputs-Outputs-Feedback loops (levels 2, 3, and in all the 9 levels, since its a cumulative model where higher levels incorporate the part-identities/functions of lower levels). Look at what has happened. The Essence (Wholes & Parts) sorts Content, into another abstract form, the next Notion (Inputs-Outputs-Throughputs-Feedback). In the Essence/Form/Notion Inputs becomes anything: people, animals, money, information, and any other resources. Throughput is any sort of process within the [unknown] boundaries of production, distribution, and consumption. Outputs are going elsewhere, just as Inputs come from somewhere, but the space or place of this is left to the imagination” (Source,

Several others have referred to how Hegel can be seen as a fractality:


According to Hegel, if negation is the inner life-force of the dialectic, then triadic structure is its organic, fractal form” (Source).


As a 1996 beginner’s guide to Hegel phrases it, this “triadic structure” is the “organic, fractal form” of the effusive thinker’s logic” (Source).

“Hegel calls this dynamic aspect of his thinking the power of “negation”. If negation is the inner life-force of the dialectic, then triadic structure is its organic, fractal form.  Oh boy he even introduced FRACTAL geometry into this amalgam” (Source).


“Interesting for Fractal Geometry, Chaos Theory, Quantum Theory and more modern developments of mathematics and science, Hegel writes that seeing the unity of necessity and freedom is the final hurdle.  To see that no part of reality is absolutely necessary, but no part is absolutely free, and the two hang together as opposites like light and darkness, this is the final stage that lets us see things as they are.  This would be the final and total grasp of the wheel as solid and empty, or the rock as thing and perception/assumption.  Now, Hegel believes, reason goes forth as true science and simply Nature itself, with a ground to continue to investigate and understand things with all the branching of the Idea by which we could ever understand them to be.  All becomes a single Idea, that is one with the world” (Source).


“The universe NOW is a product of its preceding ‘self-iterations’, of its preceding ‘meta-fractal’ ‘self-layerings’, of all of its prior ‘self-hybrid’ ‘self-nestings’, and also of its “mere” nestings, of its “mere” hybridizations, among the different degrees of those ‘self-hybrid self-nestings’. Moreover, as we noted also earlier, each such ‘self-nesting’ is also an ‘ontological self-revolution’ in the history of the cosmos — the emergence of new, previously unprecedented ‘cosmo-ontology’; the irruption of a new ‘meta-«physis»’, and, if you will, in some senses, of a new ‘contra-«physis»’, a new “antithesis” kind of being, as well!” (Source).


“Living systems autopoietically interact with the world they perceive semiotically and physically with the part of the world they do not perceive yet”; “As dicisigns depends on neither human consciousness nor on human language, they are natural propositions…” (Søren, 2014: p. 18). For multifractality, then the dynamic transformative processes are a dynamic development of reasoning that is only partly based in linguistic turn, and the other part is on the ‘unutterable’ as Hegel (1807: # 110) calls it:


“They speak of the existence of external objects, which can be more precisely defined as actual, absolutely singular, wholly personal, individual things, each of them absolutely unlike anything else; this existence, they say, has absolute certainty and truth. They mean ‘this’ bit of paper on which I am writing—or rather have written—‘this’; but what they mean is not what they say. If they actually wanted to say ‘this’ bit of paper which they mean, if they wanted to say it, then this is impossible, because the sensuous This that is meant cannot be reached by language, which belongs to consciousness, i.e. to that which is inherently universal. In the actual attempt to say it, it would therefore crumble away; those who started to describe it would not be able to complete the description, but would be compelled to leave it to others, who would themselves finally have to admit to speaking about something which is not. ”


There have been a few graphic attempts to express Hegel’s negation of negation fractally in triadics:















These next images express dialectic triadic form in branching fractals


Hegel Triadic as a Branching Fractal of Triads (Source)


These are examples of branching Fractal images of Hegelian Dialectics?





Hegel Triadic as a Branching Fractal of Triads (Source)


“The lord and bondsman (master/slave) analogy is a primary example where two consciousnesses seek self-determination through mutual recognition but fail to do; the lord identifies with his power over the bondsman through penalty of death while the slave identifies with mastery over/objectification of the environment in compensation of the threat by his master. Neither parties become fully self-determined or free as the recognition is asymmetric. The lord cannot kill his slave for otherwise he loses his identity; the bondsman remains powerless in other affairs. This struggle towards the self-determination of individuals cannot be resolved outside of ethical life (e.g. personal morality) whose concrete form would ultimately be actualized in the State. Such a process is grounded in Hegel’s logic which has a triadic structure” (Source).







Under each key part – there are 3 more subheadings. For instance:

  • Sign and Representation 
  • Sign
  • Laws
  • Quality
  • Object – beyond the sign to which it refers
  • Icon – Representative of a symbol
  • Symbol – Means of convention
  • Index – Expressions
  • Interpretant – The part of the model that looks at Senses
  • Rheme – The mental concept
  • Direct Fact – Self explanatory
  • Argument – The reason


Seeking source for above figure

Rhema (ῥῆμα in Greek) literally means an “utterance” or “thing said” in Greek. It is a word that signifies the action of utterance.



CASE ONE: Fractal-Branching of Departments in a College of Business

CASE TWO: GOLD Graphic Arts Consulting Firm

CASE THREE: Daniel Q. Boje’s entreprenurship, Fractal-Spiral Story of the Trash Compactor (see full article pdf)

CASE FOUR: Fractal Analytics Consulting Company

CASE FIVE: BIGstory and bigDATA, Mike Bonifer’s new consulting company used Quantum and Fractal Storytelling

CASE SIX: Tonya Henderson’s Study of Fractal-Spirals


New Mexico State University

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#antenarrative, #storytelling