A quantitative assessment of how receiving evidence E changes the credibility of a hypothesis H, usually expressed as a directed measure of evidential support (for example, the difference in posterior and prior probability, a likelihood ratio, or another formal update metric) under an explicit evidential framework.

Principle

Degree of confirmation quantifies evidential impact: confirmation is the change in rational support for H produced by E given the background framework (priors, likelihoods, and updating rule).

Demonstration

Illustrative scenario — Situation: Prior P(H)=0.2; evidence E observed with likelihood P(E|H)=0.8 and P(E|¬H)=0.2. Recognition: Compute posterior P(H|E) by Bayes' rule = (0.8×0.2)/(0.8×0.2+0.2×0.8)=0.5. Action: The degree of confirmation can be measured as ΔP = 0.5−0.2 = 0.3 or as likelihood ratio 4:1. Consequence: The agent raises credence in H proportionally to the computed confirmation.

Misapplication

Equating high posterior probability with strong confirmation without referencing prior or alternative hypotheses. The error ignores that a high posterior may reflect a high prior rather than strong evidential impact; confirmation concerns change due to E, not absolute posterior alone.

Consequence

Degree of confirmation guides belief updating, model comparison, and evidential reasoning; it determines how much evidence should alter confidence in hypotheses and informs decisions contingent on updated credences.

Reversal

In non-Bayesian frameworks (e.g., frequentist testing or likelihoodist interpretations) confirmation is characterized differently; likewise, evidence that increases probability by a small absolute amount may still be practically decisive depending on context and utilities.

Boundary

Clearly within: Bayesian measures ΔP(H)=P(H|E)−P(H) or likelihood ratios. Boundary case: qualitative judgments of support when numerical priors are unavailable. Clearly outside: mere correlation between variables that is not evaluated as a change in support for a specific hypothesis.

Semantic Tension

Degree of Confirmation ↔ Explanatory Power/Fit: evidence can increase credibility without improving explanatory coherence, requiring trade-offs in theory assessment.

Synthesis

Confirmation is a relational quantity about how evidence alters support for a hypothesis within a stated framework; it is not synonymous with truth or with the absolute probability of the hypothesis.