It has been almost a year since I wrote “Knowledge as the Art of Drawing Distinctions” and during all this time I have been pondering about the utility of that essay.
The idea of dissolving knowledge into its formal ingredients is exciting in and of itself. Yet, to fulfill my vision and crystallize such insight into a working technology — a new tool for knowledge exploration — I had to spend more time with these ingredients to understand their nature and their relationships.
In what follows, I will expose the result of such work. Both answers and open questions.
Knowledge about any topic starts with inquiry; a question — driven phase where one forges more and more accurate descriptions by attempting to fit hypotheses and conjectures with observed facts until a stable understanding emerges.
To say that my object of interest is “that thing” implies that one has to be is capable, at least perceptually, to distinguish it from everything else. And that is a per-requisite for any investigation or study.
Thus, the act of understanding finds its roots in perceptual distinction†. The formulation of such distinction passes through both conceptual and linguistic refinements. The result of which is a description integrating both ontology and the perceived logic of the object under consideration.
No-fold Distinction (Monad)
Now before speaking about any particular knowledge or specific subject of study, I want to contemplate a certain language centered around the word “thing” and its derivatives, everything, anything, something and nothing.
Think about when and why do you use such words.
You will first notice that they are omnipresent in your speech. Second, that there is a generality that comes with them which makes them preferable words when we don’t want to be specific.
The extent of their importance is proportional to how difficult it would be to go without them. You would have to be specific all the time unable to make generic statements. 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 generic claims.
Claims for which a generic vocabulary is necessary. The very same language I am arguing about here. Thus, all of what we speak of or reference to is simply an instance of the concept of thing.
Thing is THE primary category.
When I say “that thing”, it means that I recognize it as something different from the rest. It is a part of everything; a special part since I am capable of selecting it.
In fact I don’t even have to say this or that, just saying “thing” is enough. The mere invocation of the concept implies a selection and thus an act of distinction.
The two-fold dichotomy, this and the rest — that is not this — is fundamental, even necessary to knowledge.
“What is there? Everything.” — Quine
The take away of this section is a statement about the primacy of the “thing”-notion. We don’t have to select a specific case to showcase our techniques. Any specific knowledge is automatically about an instance of the prime concept.
To avoid repeating the word “thing”, I will prepend the words category, concept or notion with either “prime” or “THE”, i.e. the prime category or THE concept would equivocally refer to, thing.
By applying our procedures and techniques of reasoning on this prime concept, we operate at a generic layer whose results are guaranteed to hold and apply to particular topics through specification.
Beyond the primary distinction which is the immediate translation of a perceptual contrast, further distinctions can be added. They correspond to various considerations one can have about the thing of interest.
An approach I see here is that we start from the primary category and see the possible distinctions we can apply on it.
To this day, I could only find 2 types of principled distinctions.
Two — fold Distinction (Diad)
They split the plane of manifestation in the “absolute” sense in two. The dichotomy is most 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.
“Ignorance is the inability to pick something from everything and not only say this is different but also explain in which manner.” — Self.
Instances of a two-fold distinction are numerous. Thus, I will choose two examples which I shall refer to in subsequent writings.
Quine’s distinction considers things as to their nature. Whether they obey the natural rules or not. This criterion has the perk of being observer independent, that is, regardless of the person we would all agree on his dichotomy, namely, that things are either concrete or abstract.
A concreta — a concrete thing — is material and is manifest in the real world. We can experience it through our senses because it has the ability to interact with other material things. Its interactions are regulated by the laws of nature and manifestations.
An abstracta — an abstract thing — is immaterial and unphysical. It escape our sense yet it is part of our experience. Abstract things are perceived through intellect because only they are capable of interaction and cause according to the laws of reason and imagination.
Another interesting distinction is due to Whitehead and his process philosophy. For him everything is in a state of flux and invariance through change is distinctive criterion. His approach is observer dependent implying that people and more generally things experience change differently. According to a chosen scale, things split into either continuants or occurrents.
A continuant is an invariant. It has stable characteristics which enables us to recognize it as the same individual regardless of the assumed appearances through time. For the chosen scale in which something is a continuant, it has a stable identity.
An occurent 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 of its characteristics. The only identification one can provide for it is through reference to its location within the flux.
A note regarding Whitehead’s primitives to contrast with Quine’s. If something is let’s say a continuant on a certain spatio-temporal scale that doesn’t mean that it will remain so if we change the scale. A stone is invariant on a daily to monthly scale but that changes if we speak about millions of years.
Three — fold Distinction (Triad)
A three — fold distinction is the product of a relative reading on the same thing. That splits the space into three possible considerations, (1) the thing relative to itself, (2) relative to something else and (3) as mediating a relation between other things.
The principle behind this distinction is “relative considerations”. It is the second moment of understanding.
“Understanding is merely a fitting of relations.” — Self.
Instance of the three-fold kind are somewhat rare but quite powerful when found. In what follows I detail two of the most influential cases.
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.
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 a cause-effect relationship it maintain 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 relationship — as, Mother, Wife, etc. Now such individual can exhibit mediation (thirdness) whereby they play a role in instantiating a relation such as, Motherhood relating a Mother with her Child or Marriage relating a Wife with a Husband.
The second instance, which to be fair preceded Peirce, goes back to Kant. His primitives — thesis, antithesis and synthesis — rely on the combination of the two first to produce a third.
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 partner. 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.
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.
Throughout this exposition I strove to forward the symmetry and natural progression of the ideas and principles within this topic. Starting with the monadic principle about the primacy of “thing”, followed by diadic and triadic principles necessary behind the conception of knowledge itself. To top it off, 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. Yet 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.
To close this discussion on a daring note, I will advance a conjecture with a test for it.
No-Higher-Fold Distinction Conjecture — one cannot find principled irreducible distinctions higher than three — fold.
The test is a direct consequence of the truth of conjecture. Let’s say one finds a principled four-fold distinction. It ought to be reducible to either the aggregation product or cross product of 2 two — fold distinctions.
An indirect but still remarkable implication is that, while the first and second moment of understanding are such that at first we just try to absorb the contrast but then we contemplate the relation produced by the contrast, higher fold distinctions would imply other moments of understanding.
Can you think of any? Making the difference between two things and accounting for the relations between things is as far as I have seen human reasoning go.
As long as the conjecture holds true, it should be interesting to note that the highest fold for the generators of human knowledge is 3.
