#distinction #monad #diad #triad Related to, [[Knowledge is The Art of Drawing Distinctions]] ![[The Fundamental Distinctions.excalidraw.png]] The idea of dissolving knowledge into its formal ingredients[^1] has motivated me for years. Dissatisfied by the focus of the available literature, I was set explore this topic myself. Satisfying my interest wasn’t that simple. I had to spend more time digesting the claims I made in “[[Knowledge is The Art of Drawing Distinctions]]” to understand the essence of these ingredients. I realized that distinctions break down into types. Each with its underlying principle and corresponding level of understanding. To cultivate such realization, I started from base considerations. Inquiry is our most powerful tool for knowledge building. It is a tentative process where one formulates gradually better descriptions. A stable understanding emerges in an attempt to fit hypotheses and conjectures with observed facts. The perceptual distinction of the object of interest from everything else is a pre-requisite for any investigation or study. The formulation of such distinction passes through both conceptual and linguistic refinement until we obtain a coherent description. # No-fold Distinction (Monad) The act of understanding finds its roots in perceptual distinction[^2]. We start by referring to our interest as “that thing” until we have a word for it. Regardless of the topic, the word “thing” and its derivatives—everything, anything, something and nothing, serve as placeholders for when we lack the right words or wish to be generic. The importance of the thing-vocabulary is proportional to how difficult it would be to go without it. You would have to be specific all the time unable to make generic statement. Incapable of abstraction. Yet, knowledge relies on abstraction and the ability to formulate all-encompassing laws. It is what constitutes its descriptive power. All of the specific being subsumed under general claims. Claims for which a generic vocabulary is necessary. The very same language I am emphasizing here. All of what we speak of or reference to is simply an instance of the concept of thing. Thing is the base category. When I say “that thing”, it means that I recognize it as something different from the rest. It is a part of everything; yet a part of interest since I am capable of selecting it. And that is an act of distinction. All of the above is a statement to the primacy of the concept, thing. Any specific knowledge is automatically about an instance of this prime concept. By applying our procedures and techniques of reasoning on this prime concept, we operate at a generic layer. The results and conclusions are guaranteed to hold and apply to any topic or sub-topic through specification. Beyond the no-fold distinction which is the immediate translation of a perceptual contrast, further distinctions can be effected. They correspond to various considerations one can have about the object of interest. I tried to enumerate the many ways one can effect meaningful discernment. I could only find 2 types of principled distinctions. # Two—fold Distinction (Diad) Two-fold distinctions polarize the plane of manifestation. The induced dichotomy is often based on a criteria or property, (1) present in a part of the manifestation and (2) absent in the rest. The principle of such distinction is “discernibility”. It is the first moment of understanding. As, “Ignorance is the inability to pick something from everything and not only say ‘this is different’ but also explain in which manner.” Instances of two-fold distinction are numerous. Thus, I will only choose two since they will be part of subsequent writings. A first example goes back to Quine who distinguishes things as to their nature. Whether they obey the natural laws or not. This criterion has the perk of being observer independent. Regardless of 'who?', we would all agree on his dichotomy, namely, that things are either concrete or abstract. Something concrete is material and manifest in the real world. We can experience it through our senses because it has the ability to interact with our material bodies. Its interactions are regulated by the laws of nature. An abstract object is immaterial and unphysical. It escape our senses yet it is part of our experience. Abstract things are perceived through intellect because only they are capable of cause according to the laws of reason and imagination. A second two-fold distinction is due to Whitehead’s process philosophy. For him everything is in a state of flux and invariance through change is distinctive point. According to a chosen scale, what is observed splits into continuants and occurrents. A continuant is an invariant. It has stable characteristics which enables us to recognize it as the same entity regardless of the assumed appearances through time. For the chosen scale in which something is a continuant, it has a stable identity. An occurrent is in a state of flux that prevents it from being recognized by any set of characteristics. Such an object is constantly morphing in all aspects. The only identification one can provide for it is through reference of its location within the flux. This approach is observer dependent as different entities experience change differently. Changing the scale doesn’t guarantee that that the first attribution remain unchanged. The two examples above are just a small subset of a large body of two-fold distinctions that are omnipresent in human knowledge. Moving to the second type, # Three—fold Distinction (Triad) A three—fold distinction is the product of a relative reading on the same thing. It splits the space of being into three possible considerations, (1) the thing relative to itself, (2) relative to something else and (3) as mediating, a relation between two other things. The principle behind this type of distinction is “relative considerations”. It is the second moment of understanding where we connect the newly realized knowledge with our pre-existing comprehension. Where, “*Deeper understanding is merely a fitting of relations.*” Instance of the three-fold kind are somewhat rare but quite powerful when put to used. Peirce was historically the first to give a principled account for three-fold distinctions. His famous primitives of firstness, secondness and thirdness are an immediate application of the triadic principle given above. Peirce believed that these categories of firstness, secondness, and thirdness were fundamental to understanding how meaning and knowledge are created and interpreted. They provide a framework for understanding the dynamic processes of representation, interpretation, and semiotic communication. *Firstness* is the aspect of inherence in something. It is a characterization that is based on intrinsic qualities that are independent of anything else. *Secondness* is the aspect of reaction to something. It is a characterization of something based of a cause-effect relationship it maintains with something else. *Thirdness* is the aspect of mediation between two things. It is a characterization of something as the relation that bring a first and a second together. To illustrate, an individual can be recognized independently (firstness) of any external relationship as a human being or let’s say as a subtype such as Woman. The same individual can be classified relative (secondness) to many other things—*implied external relationships*—as, Mother, Wife, etc. Now such individual can exhibit mediation (thirdness) whereby it plays a role in instantiating a relation such as, Motherhood, relating a Mother with her Child or Marriage, relating a Wife with a Husband. An instance triadic distinction goes back to Hegel and his progression—*thesis, antithesis and synthesis*. Based of the principle of combining two opposites to produce a third. This pattern is a fundamental process through which ideas and concepts progress and evolve. A thesis refers to a general claim or opinion about a thing. It is a statement and a starting point for considerations. Within the sphere of its application, it is considered to be true in and of itself (independent) without the need for external justification. The antithesis is the expression of an opposing idea. It is always defined with contrast to a thesis and thus its truth depends on the falsity of its associate. All further statements are either partnered with the thesis or the antithesis and are thus by affiliation opposed. A synthesis is born out of the combination of a thesis with its antithesis. It is a proposition that reconciles two conflicting ideas. As it promotes a mode of understanding whereby both the thesis and antithesis are maintained and hold true. A statement can be considered a thesis in relation to itself. The comparison and interaction with other statements or positions determine whether it functions as an antithesis or part of a synthesis. The synthesis arises through the mediation and reconciliation of conflicting thesis and antithesis. To illustrate, Kant’s categories of understanding offer the best examples. The progression of Unity-Plurality-Totality under the heading of Quantity takes Unity to be the thesis which makes Plurality by definition the antithesis. Totality is then Plurality considered as Unity, that is, the synthesis of both. # Retrospective Throughout this exposition I worked to forward the symmetry and natural progression of the ideas and principles involved in the making of knowledge itself. Starting with the monadic principle about the primacy of “thing”, followed by diadic and triadic principles necessary behind the conception of knowledge itself. Both the two- and three-fold principles are advanced as the first and second moment of understanding making the no-fold principle the zeroth moment by extension. While working on this theme, I looked for principled higher than three—fold distinctions without success. I read somewhere that Peirce did attempt to find such constructs, that is, Quiads, Peniads, etc. However, he soon realized that they are reducible in term of more basic distinctions. I advance a **No-Higher-Fold Distinction Conjecture** by saying that, *one cannot find a principled irreducible distinctions higher than three—fold*. If the No-Higher-Fold Distinction Conjecture holds true, it suggests that the human capacity for understanding and reasoning may be inherently limited. This implies that our cognitive processes, at their core, involve perceiving and comprehending the differences between two things and accounting for the relations between them. By recognizing and contrasting dualities or dichotomies, we engage in the process of understanding. We observe, compare, and seek to absorb the contrast between different entities or concepts. This initial moment of understanding allows us to discern and articulate the distinctions between them. However, the conjecture suggests that there is more to our cognitive abilities than merely perceiving differences. Once we have absorbed the contrast, we move beyond it and contemplate the relations produced by the contrast. We seek to understand how these entities or concepts interact, connect, or influence one another. This contemplation of relational dynamics represents the second moment of understanding. Beyond these two moments, the conjecture posits that there are no higher-fold distinctions that we can make in a principled and irreducible manner. This implies that any further complexity or multiplicity of distinctions can be reduced or derived from combinations of two- and three- fold distinctions. For example, a four-fold distinction would be reducible to the product of two two-fold distinctions. If this conjecture is valid, it suggests that the human capacity for knowledge generation, at its highest level, relies on three-fold distinctions. These distinctions form the foundational building blocks of our intellectual endeavors, allowing us to explore and explain the relationships and interplay between various elements of knowledge. In conclusion, the No-Higher-Fold Distinction Conjecture presents an intriguing perspective on the nature and boundaries of human understanding and leaves open the question of whether there exist higher-fold distinctions beyond our current cognitive reach. [^1]: [[Knowledge is The Art of Drawing Distinctions]] [^2]: [[The Knowledge-Language-Perception Complex]]