The first movement asks what makes being possible. Every ontology typically begins by assuming something is. Relationality takes one step earlier and asks: what makes being possible in the first place? Before any object or predicate can exist, there must be a most primitive operation that carves out one region of possibility from another. This primordial act — differentiation — creates a boundary and with it the first relational tension: interior versus exterior, inclusion versus exclusion. In Lakota cosmology, creation begins with a great dividing act, mirroring this notion that existence emerges through an initial separation. The remainder of logic unfolds from the stability of this single act of distinction.
The argument
Deriving existential coherence
To claim that something exists is not trivial. At minimum, it is to claim that something is not what it is not — that is, something not-equal not-something. This claim has dynamics that must be derived: what are something, negation, and equivalence? How is it they result in something existing?
Given a thing is determined by its inequivalence to anything that is not itself, it cannot not derive there is a dynamic of determination. In the context of something existing, this dynamic is the acts of including and excluding: something includes itself in what it is; something excludes everything it is not. These are not choices or postulates. They are what it means for a thing to be determined at all. A thing that includes everything is nothing in particular; a thing that excludes nothing is indistinguishable from everything else.
Given that negation is determined by how it relates to something and equivalence, it cannot not derive there are dynamics of relation. In the context of something existing, these dynamics are the conditions of inclusion and exclusion: inclusion is the condition of what is something; exclusion is the condition of what is not something.
Given that equivalence is determined by how it relates something and not-something, and is related to negation, it cannot not derive there are dynamics of structure. In the context of something existing, this dynamic is the structure of coherence: a minimal unit that stabilizes the interplay between including and excluding, ensuring that equivalence holds coherently. This coherence ensures type-homogeneity: while including and excluding are oppositional acts, they are the same type of act on the same structure. This principle — that oppositional dynamics are nevertheless acts of the same kind — recurs at every level of the derivation.
The algebra of recognition
Once distinctions exist, they can relate to one another. Two recognitions may overlap, one may contain another, or they may be entirely disjoint. This comparative activity further stabilizes the field opened by differentiation: inclusion measures coherence (one recognition being part of another), and exclusion measures disjointness (separation). Together these relations provide the first relational grammar from which logical operations emerge.
To recognize something is simultaneously to decide what it is with (included) and what it is not with (excluded). In Lakota thought, the phrase Mitákuye Oyás’iŋ (“all my relations”) reflects a deep awareness that existence is defined by inclusion in a community of beings, while sacred boundaries also define what something is distinct from. This step formalizes that relational ethic.
The consistency requirements of including and excluding produce the logical operations that form the core of relationality:
- Together — combining what two distinctions share. If both A and B are included, their overlap is included.
- Either — combining their scope. If either A or B suffices, their combined range suffices.
- Implies — conditional relating. The field learns its own laws by finding within itself the conditions under which one presence guarantees another. This is internal sufficiency: having A inherently gives having B. From a relational perspective, certain patterns carry others with them — if the clouds gather, rain follows — the logic of sufficiency emerges from within the relations themselves.
- Negate — denying. The boundary of what a distinction excludes.
Reflexive stability
Recognition and its logic are not yet full reasoning. The operations allow recognitions to relate conditionally, but they do not guarantee coherence over time or repetition. For a relation to achieve persistence — to be an enduring law or principle — it must withstand being applied to itself repeatedly: when applied again and again, eventually no further change occurs.
The act of iteration expresses this requirement of self-consistency. Iteration is not mere redundancy — it is self-confirmation. One tests an operation against itself, feeding its output back into its input, until stability appears. Where this self-application stabilizes, a law or invariant emerges. In oral traditions, a story told and retold, if it stays consistent, carries truth. Reflexive stability is the point at which relation becomes cosmologically lawful: the patterns of relation that survive iteration are those that structure reality.
Deriving relational coherence
Determining thing, negation, and equivalence provides minimal dynamic determination for cohering something existing, but leaves unresolved dynamics that must be derived: the minimal coherence determines how including and excluding stabilize together, but leaves undetermined the dynamics by which this coherence is sustained.
Given that the sustained coherence of existing is determined by the relation between inclusion and exclusion, it cannot not derive there is a dynamic of determination. In the context of something existing, this dynamic is the act of relating: the continuous act that maintains the interplay between including and excluding. This act introduces reflexive sequence: each relational unit can relate to itself, producing an indefinitely extensible sequence of deepened relational units. Reflexive lineage is the traceable sequence of relational structures generated by successive self-relation, preserving the ancestry of a unit across reflexive deepening.
Given that the act of relating is determined by how it engages and sustains inclusion and exclusion within a unified coherence, it cannot not derive there is a dynamic of relation. In the context of something existing, this dynamic is the condition of relation: the stabilized condition in which inclusion and exclusion are coherently maintained. This condition induces positional invariance: inclusion and exclusion must always be distinct and ordered within any relational structure, preserving their roles through reflexive deepening.
Given that the condition of relation is determined by its reliance on the ongoing act of relating for its persistence, it cannot not derive there is a dynamic of structure. In the context of something existing, this dynamic is the structure of relational form: the minimal structural configuration that formalizes the interplay of relation and relating, ensuring the dynamic’s coherence. This structure establishes reflexive compositionality: relational forms at any depth can be composed side by side into ordered composites, preserving coherence across both depth and breadth. A composite is an ordered configuration of two or more relational units, held together at a shared reflexive sequence to form a structured whole.
Determining relating, relation, and relational form provides the minimal dynamic determination for cohering the relational dynamic unit, but leaves unresolved dynamics that must be derived: what coheres relational form itself?
What arises
Terms: Distinguish, Entails, Excludes, Together, Either, Implies, Negate, Top, Bottom, Iterate
Phenomena: Recognition — what is established by acts of distinction. Coherence — the requirement that acts of including and excluding stabilize consistently.
Processes: Differentiation — the primitive act of drawing distinction. Iteration — self-application producing stabilization.
Mathematical correspondence
The structure earned here corresponds to what mathematicians call a complete Heyting algebra — a logical structure in which not every question has a determinate answer. The truth that appears here is not a primitive binary value but the persistence of a distinction — a boundary that continues to recognize itself. This reflects the relational stance: some matters are genuinely indeterminate until relational activity resolves them. The law of excluded middle fails because existence is relational, not substantial.
What incites Movement II
Relational form has been earned, but what coheres relational form itself remains undetermined. The interplay between relating and relation must be self-sustaining — and the dynamics of that self-sustenance have not yet been derived.