What this lesson covers
The first three steps of the relationality derivation: from the impossibility of nothing, through existential coherence and relational coherence, to self-sustaining closure. By the end, you will understand why there must be something, why that something must relate, and why relating must close into a self-sustaining unit.
Why it matters
Most philosophical systems start with an assumption: there are atoms, or there is God, or there is consciousness. The relationality derivation starts with a question: can there be nothing? The answer — no, and here is why — produces the first structures of the derivation. Every subsequent structure is forced by the nature of what came before. This lesson covers the first three forcing arguments: the foundation on which everything else is built.
Prerequisites
None. This is the starting point.
Core concepts
The impossibility of nothing
Think about what it would take for there to be nothing at all. Not empty space — nothing. No vacuum, no darkness, no absence. For “nothing” to hold, “nothing” would need to be identical to itself (nothing = nothing) and different from something (nothing ≠ something). But those requirements — a thing (itself), equivalence (nothing = nothing), and negation (nothing ≠ something) — are already something. Nothing defeats itself.
This is not a trick. It is a structural observation: the concept of nothing requires the very things it denies. What remains after nothing fails are three residues: Thing, Negation, and Equivalence. These are not chosen or assumed — they are what nothing needed in order to fail.
The Hegelian philosophical tradition calls this kind of move “determinate negation” — the attempt to think pure nothingness produces determinate content. (For more on this, see Hegelian Becoming.) The relationality derivation draws on this insight but develops it through its own forcing method rather than through Hegel’s dialectic.
Step 1: Existential coherence
Now something exists — Thing, Negation, Equivalence. What must be the case for something to exist? This is not a choice; it is a question about what existence requires.
A thing is determined by its inequivalence to what it is not. There is no way around this: to be this rather than that, a thing must do two things. It must include itself in what it is (Including) and exclude what it is not (Excluding).
These are acts — ongoing dynamics, not static properties. A thing does not “have” identity the way a box has contents. A thing maintains itself through the continuous interplay of including and excluding.
The acts produce conditions. Inclusion is the condition of what something is. Exclusion is the condition of what something is not. Including does; inclusion holds.
But including and excluding can pull apart. Without something holding them together, the interplay could dissolve. Given how equivalence relates thing and not-thing, there must be a minimal structure stabilizing the interplay: Coherence.
What now exists: Thing, Negation, Equivalence, Including, Excluding, Inclusion, Exclusion, Coherence.
What is undetermined: how coherence is sustained. Coherence is a structure, but nothing yet maintains it.
Step 2: Relational coherence
Coherence exists but nothing sustains it. Given that sustained coherence is determined by the relation between inclusion and exclusion, it cannot not derive Relating — the continuous act that maintains their interplay.
Think of it this way: coherence is like a bridge between two riverbanks (inclusion and exclusion). The bridge exists, but who maintains it? The act of relating is the ongoing work of keeping the bridge standing.
Relating can relate to itself. This produces Reflexive Sequence — indefinitely deep self-relation. Each time relating relates to itself, it produces a deeper structure. There is no natural stopping point.
Given how relating engages inclusion and exclusion, it cannot not derive Relation — the stabilized condition in which they are coherently maintained. Relation induces Positional Invariance: inclusion and exclusion stay distinct and ordered no matter how deep you go.
Given that relation relies on relating for its persistence, it cannot not derive Relational Form — the minimal structure formalizing their interplay. Relational form establishes Composition: forms can be placed side by side into ordered wholes.
What now exists: all of the above, plus Relating, Reflexive Sequence, Relation, Positional Invariance, Relational Form, Composition.
What is undetermined: what holds relational form together. There is form, but nothing mediates between relating (the act) and relation (the condition).
Step 3: Self-sustaining closure
Relational form exists, but nothing holds it together — nothing mediates between relating (the act) and relation (the condition). Given this gap, it cannot not derive Sustaining — the act that mediates between them, ensuring their joint persistence.
Sustaining produces Self-Coherence — relating and relation unified as a single dynamic. Self-coherence produces Closure — the structure of self-maintenance. The unit is now self-sustaining: it maintains itself through its own activity.
Think of a flame. A flame sustains itself through its own process — the burning produces the heat that sustains the burning. A self-sustaining relational unit is analogous: relating sustains relation, which sustains relating, and closure is the name for this self-maintaining loop.
What now exists: a self-sustaining relational unit with closure.
What is undetermined: the unit has no boundary. It has not distinguished itself from its outside.
The pattern: act, condition, structure
Notice the repeating pattern in each step. Something is undetermined. The nature of what exists forces:
- An act — a dynamic of determination (something does something)
- A condition — a relation that holds (something is the case)
- A structure — a form that stabilizes the interplay of act and condition
This act/condition/structure pattern recurs throughout the derivation. It is not imposed from outside — it is what forcing looks like when determination, relation, and structure are the three residues of nothing’s failure.
Worked example
Trace the forcing argument for step 2 (relational coherence):
- What exists? Coherence — a structure stabilizing the interplay of including and excluding.
- What is undetermined? How coherence is sustained. The structure exists, but nothing actively maintains it.
- What is forced? The act of relating — because sustained coherence is determined by the relation between inclusion and exclusion, and that relation requires an ongoing act to maintain it.
- What does the act produce? Relating produces the condition of relation (inclusion and exclusion coherently maintained) and the structure of relational form (the minimal configuration formalizing the interplay).
- What is now undetermined? What holds relational form together — there is no mediator between relating (act) and relation (condition).
This “undetermined” is the seed of step 3.
Check your understanding
1. Why can there not be nothing?
For nothing to be nothing, it needs a thing (itself), equivalence (nothing = nothing), and negation (nothing ≠ something). These are already something. The concept of nothing requires the things it denies.
2. What is the difference between Including (the act) and Inclusion (the condition)?
Including is something a thing does — the ongoing act of including itself in what it is. Inclusion is what holds as a result — the condition of what something is. The act is dynamic; the condition is what the act maintains.
3. Why does coherence require relating?
Coherence is a structure — it describes the minimal unit stabilizing the interplay of including and excluding. But a structure alone does not sustain itself. Sustained coherence requires an ongoing act (relating) that actively maintains the interplay between inclusion and exclusion.
4. What does closure accomplish that relational form does not?
Relational form formalizes the interplay of relating and relation but does not mediate between them. Closure is what happens when sustaining mediates between act and condition, producing self-coherence — the unit now maintains itself through its own activity. Relational form is the blueprint; closure is the self-sustaining engine.
Common mistakes
- Treating “nothing” as a place or a state. Nothing is not empty space. The argument is about the coherence of the concept of nothing itself — whether the concept can hold without producing content.
- Thinking of acts as one-time events. Including, excluding, relating, sustaining — these are ongoing dynamics, not events that happen and finish. The unit maintains itself continuously.
- Confusing the act/condition/structure pattern with a temporal sequence. The three are co-determined. Including does not happen “before” inclusion — they are aspects of the same determination.
- Assuming closure means the derivation stops. Closure means self-maintenance, not completeness. The unit is self-sustaining, but it has not yet distinguished itself from its outside. The derivation continues.
What comes next
The self-sustaining unit has closure but no boundary. It has not distinguished itself from its outside. The next lesson — Boundary and Reflexion — derives how closure forces boundary, and how boundary forces the unit to engage itself.