The RR and RA Layers: The Mixture Problem and the Nature of Discovery

In the history of philosophy—especially the philosophy of mathematics and science—a persistent debate has revolved around whether laws, logic, and mathematical truths are human inventions or independent realities. Instancology offers a powerful lens to clarify and resolve this debate by distinguishing between the RR (Relative Relative) and RA (Relatively Absolute) layers.

1. The RR Layer: The Zone of Mixture

Within the RR layer, all products of human or artificial agents—language, symbols, logic as formal systems, meaning, and the pursuit of truth—are mixed and entangled. Here:

Logic is constructed as a system of rules and tools for reasoning.

Symbols are invented and manipulated: languages, mathematical notation, programming code.

Meaning is assigned and is fluid, context-dependent, and often culturally variable.

Truth is negotiated, provisional, and often based on agreement or proof within a system.

In RR, the very act of philosophizing, theorizing, or formalizing inevitably blurs the boundaries between what is discovered and what is created. This mixture is why, for centuries, thinkers have debated whether logic and mathematics are inventions or discoveries.

2. The RA Layer: The Realm of Necessary Law

Contrastingly, the RA layer is where logic, mathematical truths, and physical laws exist independently of human minds or symbols. In RA:

The law of non-contradiction, for instance, is not up for debate or invention—it is a structural necessity of reality.

Mathematical truths (such as the Pythagorean theorem) are invariant; they are not dependent on human culture, language, or consensus.

Physical laws operate whether or not they are named or described by anyone.

Instancology insists that these necessary laws are not constructed by the RR; they exist to be discovered.

3. The Mixture Problem: The Source of Long-Standing Debate

Because traditional philosophy has not sharply distinguished RR from RA, debates persist. In the RR layer, everything appears as a product of human activity; in the RA layer, some realities are recognized as independent and necessary. The confusion arises precisely because, in RR, truth, meaning, logic, and symbols are all bound together in a dynamic, evolving mixture.

4. Scientific and Mathematical Discovery: Paradigm Shifts as Whole Instances

Genuine breakthroughs in science or mathematics rarely occur through gradual deduction or induction from prior RR-layer knowledge. Instead, they arrive as sudden paradigm shifts—as the revelation of a new whole instance (in Instancology’s sense).

Einstein’s relativity, non-Euclidean geometry, and quantum mechanics are not simple extensions of previous knowledge but the appearance of entirely new paradigms—Whole instances that reconfigure all that came before.

After such breakthroughs, those who understand the new paradigm often “kick away the ladder,” abandoning the incremental steps that led up to the leap.

This process cannot be fully captured by RR’s methods of symbol manipulation or logical deduction alone. The moment of paradigm shift—what Instancology calls WuXing (悟性, flash of insight)—is the point where the RA layer shines through, and a new necessary structure is revealed rather than constructed.

5. Philosophical Significance

For philosophy, this recognition is crucial. Most philosophical traditions have focused on knowledge as something justified step by step within RR. Instancology demonstrates that true access to RA requires an epistemic leap—a flash of insight—that cannot be reduced to prior steps.

Science and mathematics are advanced not only by cumulative work in RR but by paradigm-shifting insights that open new domains of RA.

Philosophy must account for the role of sudden Whole-instance revelation, not just logical or methodological progress.

6. Resolution

Instancology resolves the debate:

Logic and laws exist in RA; humans (in RR) only access them by discovering or revealing new Whole instances.

The confusion and debate result from the inherent mixture of truth, meaning, logic, and symbols within RR.

True progress is marked by paradigm shifts—by leaping from RR’s entanglement into the independent realm of RA through insight.