5.8.3 Left–right asymmetry and admission

5.8.3 Left–right asymmetry and admission

In some applications a right Kan extension may encode observational or constraint-based completion, while a left Kan extension propagates semantics after a declared mechanism or theory intervention. This is a useful analogy, not an automatic causal interpretation. A left Kan extension becomes interventional only when the map \(J\) carries an independently specified mechanism-change semantics. Likewise, a right Kan extension becomes observational only relative to a declared evidence interface.

The two universal transports can help expose underdetermination. Agreement between suitable left and right extensions is evidence of a tightly constrained expansion; divergence can reveal choices not settled by the old theory. Neither outcome decides scientific acceptance. Admission must still test doctrine preservation, transport of trusted consequences, resistance to countermodels, novel predictions, and performance on evidence not used to construct \(J\).