The five ways of ordering
At the bottom vertex of each triangle stands a small symbol. It does not say what the concept is, but rather how its three parts are ordered — according to which question they emerge from one another.
An object can be ordered in several ways, and each poses a different question. Five recur again and again. Where two hold at once, two symbols stand side by side; where none stands, the division is either an endpoint or not yet assigned.
Development of the Concept
The question: How does the concept determine itself out of itself?
Universal, particular, individual — not three things standing side by side, but three moments of the same thing. The universal is determined by the particular, the particular comes alive through the individual, the individual becomes intelligible through its reference back to the universal.
The sign is the construction of this page itself: a triangle with an inverted one inside it, whose points touch the midpoints of the sides.
Kinds
The question: What kinds are there?
The members exclude one another, together cover the object, and draw their boundaries where the thing itself makes distinctions. They stand side by side and do not emerge from one another — a dog is a kind of mammal, not a stage of it.
Three separate figures, without a frame. The spacing carries the meaning.
Parts
The question: What is it made of?
A whole is broken down. A heart is a part of a dog, but not a kind of dog. The number of parts is determined by the thing itself and can be arbitrary.
A single closed shape, differentiated within.
Connection
The question: What is it connected to?
Here nothing is classified or broken down, but linked. A concept spins threads to other domains, and the network is the order. This way of proceeding connects what lies in different fields — and it is here that the most widespread criticism of systematic thinking sets in.
Several figures, connected by lines.
Process
The question: What moves, and toward what?
Not every sequence is a process. “First this, then that, then this” is not yet an ordering by process — what matters is that the change itself has a form. A process can grow, mature, recur, tip over, or decay.
Hence a curved path rather than a straight arrow: a straight arrow says “progress,” but what is meant is “here, the course is what counts.”
When Two Signs Stand Side by Side
World history is divided into the Orient, antiquity, and the Christian world. It bears two signs, process and kinds. The course is the advance of a single thought — one is free, some are free, all are free — and the three realms are what it embodies itself in.
Art is divided into the ideal, the art forms, and the individual arts. Here too two signs stand together. The ideal is the concept of art, the art forms are its history, the individual arts are kinds: three questions put to the same object, arranged one after another, because a table of contents knows only a sequence.
In the first case, one thing reaches into the other; in the second, one thing lies beside the other.
Cross-References Between the Triangles
Alongside the order within a triangle, there are references between triangles that lie apart from one another and yet belong together. They stand in the sidebar on the right, and a symbol indicates how they are connected.
≡ Positional Equivalence
Both stand at the same point in their threefold movement. 1111 and 2111 are each the first moment of the first moment — the kinship is structural, not substantive. Whoever has grasped the one recognizes in the other the same movement in different material.
◆ The Same Object
The same thing appears in several places within the system, because the system passes through it more than once. Hinduism appears in the philosophy of religion and in world history; China in both of these and in the history of philosophy. This is the most common kind of reference and the least contested.
↗ Anticipation or Resumption
One place anticipates what another unfolds — or reaches back to what was begun there. The Phenomenology and the Philosophy of Spirit stand in this relation to each other; so too do a concept and its first historical shape.
⚡ Conflict
Two places determine the same thing differently. Marx’s inversion refers back to Hegel’s dialectic, but not as correspondence — as contestation. References of this kind are rare, and the most revealing.
The five ways are developed in full in Systematisches Denken by Kai Froeb — free to read: