Criteria for Falsification Under Partial Substitutions

Determine principled criteria within the Kleiner–Hoel formal framework for when a "partial substitution"—a replacement of the system under test by a functionally similar system that keeps the inference function inf fixed while changing only a subset (rather than all) of the theory’s predictions pred—should count as falsification, including thresholds or conditions on the extent of prediction–inference mismatches that warrant falsification versus permissible tolerance.

Background

The paper formalizes testing theories of consciousness by comparing a prediction function (pred), which maps observations of a system’s workings to experiences, with an inference function (inf), which maps input/output data (e.g., reports, behaviors) to experiences. A theory is considered falsified when there are systematic mismatches between pred and inf, especially under "universal substitutions" that hold inference data fixed while changing all predictions.

To avoid over-sensitivity, the authors restrict attention to universal substitutions, but note that real-world cases may involve "partial substitutions" where only some predictions change. The treatment of such partial cases is left indeterminate, raising an explicit uncertainty about how much divergence suffices for falsification and when mismatches should be tolerated for well-confirmed theories in edge cases.

Clarifying the falsification threshold for partial substitutions is crucial for making the formal framework operational across realistic experimental contexts, where substitutions may not uniformly alter all predictions while inferences remain constant.