Mapping the Edge of Logic: A Comprehensive Paradox Resolution Sweep

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Mapping the Edge of Logic: A Comprehensive Paradox Resolution Sweep

By John Gavel

What happens when paradoxes meet adaptive logic? I ran 6,400 simulations across 10 foundational paradoxes and 8 logical frame types, testing how each context handles recursive tension, self-reference, and semantic collapse. The results? A map of coherence, contradiction, and emergent insight.

 Key Findings from the Comprehensive Sweep

1. Paradox Resolution Rates Are Low—By Design

ParadoxResolution Success Rate
Liar, Gödel12.5%
Russell, Cantor7.0%
Sorites4.7%

These are stress tests. Paradoxes expose the limits of contextual closure and force frames to confront their own boundaries.

2. Naive Logic Performs Best—But Not Most Robustly

Naive frames resolved 21.2% of paradoxes, outperforming typed (13.8%) and fuzzy (9.4%) logic. But this success often reflects early collapse, not deep coherence.

3. Russell’s Paradox Finds Its Match in Category Theory

The best-performing configuration:

  • Paradox: Russell

  • Frame: Category

  • Resolution Probability: 0.75

  • Parameters: Closure Threshold = 5.0, Coherence Strength = 0.7, Coupling Strength = 0.9

This suggests morphism-based logic can absorb self-reference more gracefully than stratified or fuzzy systems.

4. Coupling Strength Is the Dominant Driver

With a correlation of 0.413, coupling strength most strongly predicts resolution. Paradox resolution is relational, not just rule-based.

 Scaling Sweep: When Frames Adapt Under Pressure

I ran an additional 5,760 simulations testing scaling mechanisms—adaptive expansions triggered by paradox complexity.

1. Complex Paradoxes Benefit Dramatically

ComplexityResolution SuccessScaling Success
Simple8.2%0.0%
Complex54.0%28.5%

Scaling isn’t optional—it’s essential when paradoxes exceed the coherence bounds of their native frames.

2. Naive Frames Dominate Scaling

Despite their fragility, naive frames showed the highest scaling success. Their lack of constraint makes them mutationally flexible, even if unstable.

3. Adaptation Drives Resolution

Correlation between adaptation count and resolution probability: 0.749 This validates my core thesis: recursive adaptation is the engine of coherence.

Theory Validation

  • Resolution Probability (Base): 0.101

  • Resolution Probability (Scaled): 0.152

  • Improvement: +0.051

  • High-Resolution Tests (>0.7): 130 out of 12,160 total runs

No frame achieved universal resolution—but that’s the point. Paradox is a signal, not a flaw. Resolution requires context expansion, not rule enforcement.

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