Relational Cuts and Intolerances: 1 A Methodology for Reading Science and Knowledge

The preceding series has traced recurring patterns: across quantum theory, evolutionary biology, neuroscience, AI, ethics, and complex systems, explanatory success is always accompanied by suppressed relational excess and the intolerances that follow. This post articulates a formal account of these phenomena, presenting a methodology for recognising, analysing, and interpreting relational cuts and their consequences in any domain of knowledge.

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1. The Explanatory Cut

Definition:

A relational cut is the stabilisation necessary for explanation to operate. It isolates certain variables, units, or levels of analysis, thereby rendering a field tractable and intelligible.

Key Features:

• Selective actualisation: Only particular aspects of the relational field are stabilised.

• Necessary exclusion: Relations, perspectives, and contingencies that cannot be formalised are suppressed.

• Generative power: Cuts make prediction, control, and optimisation possible.

Analytical Use:

Identifying the explanatory cut allows the reader to see what the explanation assumes and what it excludes structurally, rather than merely assessing its empirical adequacy.

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2. The Suppressed Remainder

Definition:

The remainder is the relational excess excluded by the cut: meaning, agency, contingency, or perspective. It is what persists outside the explanatory frame and inevitably presses back.

Key Features:

• Relational: The remainder exists in the network of relations that explanation cannot stabilise.

• Persistent: It reappears wherever the explanatory cut is applied.

• Non-resolvable: It cannot be incorporated into the explanation without destroying its function.

Analytical Use:

Mapping the remainder allows the reader to locate sites of resistance, unease, or ethical concern, and to understand them as structural rather than accidental.

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3. Intolerances as Diagnostic Signals

Definition:

Intolerances are the observable effects of relational excess pressing against explanatory cuts: resistance, debate, discomfort, ethical dilemma, or social friction.

Key Features:

• Not errors: They are not mistakes of science, modelling, or understanding.

• Structural markers: They indicate the boundaries of what can be explained within a given cut.

• Cross-domain recurrence: Similar intolerances arise wherever relational cuts are enacted, independent of discipline.

Analytical Use:

Recognising intolerance as signal allows one to read it relationally — not as a problem to solve, but as information about the explanatory structure itself.

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4. Relational Field Mapping

Definition:

The relational field is the totality of interactions, contingencies, and perspectives from which the explanatory cut draws.

Key Features:

• Dynamic: It cannot be fully stabilised, only partially constrained.

• Multi-scale: It spans levels of organisation and temporalities.

• Ethically and epistemically salient: Suppression of its elements generates real-world consequences.

Analytical Use:

Mapping the relational field clarifies the scope and limits of explanation, and guides attentive engagement with what remains suppressed.

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5. Methodological Steps

To apply this framework systematically:

1. Identify the cut: Determine what has been stabilised to make explanation tractable.

2. Map the remainder: Identify what relations, perspectives, or contingencies are structurally excluded.

3. Observe intolerance: Trace the manifestations of suppressed relations as debate, critique, resistance, or unease.

4. Analyse structural logic: Understand how the cut, remainder, and intolerance relate systematically.

5. Reflect relationally: Consider ethical, social, and epistemic consequences of the cut and the remainder.

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6. Advantages of the Method

• Provides cross-domain analytical clarity: applicable in physics, biology, neuroscience, AI, social sciences, and beyond.

• Avoids simplistic critiques of “incompleteness”: intolerance is a signal, not a failure.

• Integrates epistemic and ethical awareness: suppressed relations often carry normative or practical significance.

• Reveals patterns of human knowledge as structurally constrained rather than purely accidental.

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7. Concluding Principle

Every act of explanation necessarily produces both power and remainder. Relational cuts generate formal success; intolerances mark the boundaries of that success. Attentive engagement with the remainder allows us to read knowledge relationally, ethically, and responsibly.

This methodology does not resolve tension; it renders the structure legible, enabling scholars, practitioners, and citizens to navigate complex explanatory domains with clarity and care.