The Universal & Atomic Elements of Organization
A falsifiable scientific theory proposing that the same irreducible structures organize both thought and reality — from the quantum to the social scale.
O-Theory proposes that four irreducible structures — Distinctions, Systems, Relationships and Perspectives (DSRP) — form the universal grammar of organization. Rather than being merely useful ways of thinking, these structures are hypothesized to be the atomic elements from which every organized phenomenon emerges, whether in cognition, biology, physics, mathematics, society, or the cosmos.
| D | S | R | P |
| Distinctions | Systems | Relationships | Perspectives |
| Identity ↔ Other | Part ↔ Whole | Action ↔ Reaction | Point ↔ View |
| D := (i ↔ o) | S := (p ↔ w) | R := (a ↔ r) | P := (ṗ ↔ v) |
This is a living scientific evidence compendium: an open, continually evolving collection of independent empirical research, formal theory, mathematical proofs, cross-disciplinary analyses, applications, critiques, and proposed falsifications. Every entry is included because it supports, refines, challenges, or attempts to falsify the theory.
Scientific theories are strengthened not only by evidence that confirms their predictions, but also by surviving attempts to falsify them. This compendium brings both together: independent evidence from researchers who were not testing DSRP and proposed counterexamples evaluated against the formal theory.
One counterexample is enough to falsify O-Theory. Until then, the question remains: do the same four structures organize everything from quantum systems to human thought?
Independent convergence is one of the strongest forms of scientific evidence because researchers arrive at the same conclusion while investigating different questions for different reasons.
The number is not the point. Researchers in different fields, studying different questions with different methods, repeatedly arrived at the same structural predictions—almost always without testing DSRP or using its language.
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This compendium began as the peer-reviewed literature review “A Literature Review of the Universal and Atomic Elements of Complex Cognition,” published in the Journal of Systems Thinking with 109 studies. That paper is the peer-reviewed foundation. What you see here is its living, continuously updated version . New studies are checked before they are added, and the collection now holds and keeps growing. Open any card to see what the researchers found, why it bears on DSRP, and where the original review discusses it, the fuller account.
The collection is updated continuously, so the citation carries the date you consulted it rather than a study count — the count changes weekly, and putting it in the reference would make the same collection look like a different work to everyone who cites it. To cite a single claim or study, use its own address: every one has a permanent link.
This is the adversarial half of the compendium. Where the evidence track asks what converges on DSRP, this one asks what would end it: a single organized phenomenon whose structure needs a fifth pattern, a ninth element, or a fifth structural dynamic. It holds written up from candidates across territories, and resolutions — the general answers those cases settle against. Every case is published whether it held or failed, including the ones still open.
Cite this rather than the evidence collection when the point is what survived attack. The two are separate works with separate addresses: one asks what converges on the theory, the other asks what would end it, and a reference to the first does not support a claim about the second. Case and resolution numbers change when the record is revised, so cite a case by its own permanent link rather than by number.
This collection is meant to keep growing. Send us a study, paper, book or critique that bears on DSRP, whether it supports the theory or cuts against it, and we will read it and decide whether it belongs.
Authors Lima, João Alberto de Oliveira and Griffo, Cristine and Almeida, João Paulo A. and Guizzardi, Giancarlo and Aranha, Marcio Iorio
Year 2021
Publisher Legal Theory
Kind of work article
Discipline Law & Jurisprudence
Secondary disciplines Logic, Philosophy
Applied false
Read it at the publisher 10.1017/S1352325221000070
To analyze Hohfeld's eight fundamental legal concepts through the theory of opposition and to extend earlier hexagon-based accounts to incomplete legal systems that tolerate conflicting positions.
Not applicable (conceptual and formal analysis).
Formal analysis using the theory of opposition, comparing deontic hexagon accounts of Hohfeld's concepts with projections of a three-dimensional logical cube.
The authors show that the hexagons used for Hohfeld's concepts are selected projections of a logical cube, which accommodates incomplete legal systems and distinguishes strong liberty from weak permission. They report that liberty is a non-derived position under a weak-hexagon reading, that a complete conflict-tolerant system leaves only contradictory oppositions, and that an incomplete conflict-tolerant system supports a trichotomy and a strong hexagon. They criticize Hurd and Moore's deontic hexagon as structurally redundant and propose a parallel hexagon for constitutive norms and power positions.
The paper recasts Hohfeld's eight legal concepts as a structure of oppositions and correlations, showing how the standard hexagon models are projections of a richer logical cube that can handle incomplete and conflicting legal systems.
Hohfeld's scheme is built from jural opposites and correlatives, which maps onto distinctions (what a position is against what it is not) and relationships (the correlative pairing of one party's position with another's). The authors' formal treatment makes both explicit. The fit is partial: the paper is about logical oppositions among concepts, and the perspective of right-holder versus counterparty is not treated as a pattern in its own right. This record rests on the publisher page, which was read in part.
Patterns it shows D, R
Formal proof or model
Added 2026-10-14
How to cite this Lima, João Alberto de Oliveira and Griffo, Cristine and Almeida, João Paulo A. and Guizzardi, Giancarlo and Aranha, Marcio Iorio (2021). Casting the Light of the Theory of Opposition onto Hohfeld's Fundamental Legal Concepts. Legal Theory.