Certification Bound

Canonical definition

The Certification Bound is the limit on what an Individual can claim for a Hypothesis, and it follows from Bayesian updating operating only over the Hypotheses the Hypothesis Space represents. Updating returns the available Hypothesis the Evidence fits most closely, which is the best supported in the space rather than the best supported; where the true Hypothesis is absent the operation neither fails nor reports its own incompleteness, and the Individual arrives at the nearest available Hypothesis with whatever confidence the Evidence warrants, that Hypothesis being the least wrong the space permits. The shortfall is undetectable from inside for two reasons: identifying it would require setting the Hypothesis Space against what it omits, and stating the omission is the operation the space cannot perform (Type I Exclusion); and certainty carries no information about correspondence (Certainty-Truth Independence), a restricted space producing high confidence more readily than a complete one because fewer candidates compete for the probability mass. No Individual is therefore ever in a position to assert a Truth. The strongest warrant available is that a Hypothesis is the least wrong of those the Individual’s Hypothesis Space contains, given the Evidence that has reached them. Distinction from Truth. The Certification Bound governs warrant rather than truth-value. A Belief in the Truth-Tracked Regime tracks a decohered Referent and is true, and reality goes on confirming it; what the Individual can state about it is still that nothing has contradicted it and that their space holds no better candidate. Truth is a property of the relation between a Belief and the state of affairs it concerns, and warrant is a property of an operation run over a space whose edges the operator cannot see. The Certification Bound therefore constrains assertion and leaves the Truth-Value of Beliefs untouched. The regime outside the Certification Bound. Where the check is constitutive rather than contingent, as in the mathematically provable case, the Belief and its verification are the same act and no space of competing candidates exists over which a posterior is taken. A proof is not a posterior, and the Certification Bound reaches only what is arrived at by updating.