Romero's 2026 valuation function V_E scores factual adequacy, distinct from probability, confirmation, and Popperian verisimilitude

philosophy-of-sciencepartial-truthverisimilitudeformal-logicmeasurement-uncertainty

Gustavo E. Romero's "A Theory of Partial Truth for Scientific Statements" (arXiv:2611.07179; Philosophies 2026, 11(5), 194) defines a valuation function V_E(p) ∈ [0,1] estimating how adequately a proposition p represents the facts relative to a body of evidence E. The paper is explicit that this is not a restatement of an existing formal notion under a new name: "probabilities are attributed to events under specified physical conditions; propositions may state those probabilities but are not themselves bearers of probability," and V_E "estimates factual adequacy rather than probability."

For a quantitative proposition asserting a scalar value μ against a measurement M = e ± δ, V_E is built from a normalized discrepancy β_E(p) = min(1, |μ−e|/s_E(M)) against a characteristic scale s_E(M), giving V_E(p) = 1 − β_E(p) ("Axiom 4, Quantitative valuation"). This discrepancy is kept conceptually separate from the measurement's own indeterminacy δ (the width of the measurement interval): V_E scores the mismatch between what is asserted and what is measured, not the precision of the measurement itself.

The paper also distances V_E from two existing research programs it could be mistaken for: Popperian verisimilitude (Popper, later Oddie and Niiniluoto), which compares a whole theory to a complete truth; and da Costa and French's "quasi-truth" (partial-structures theory). V_E instead scores specified, already-testable consequences against a specific, named evidence set — see claim-romero-2026-fixes-bunge-parenthesization-flaw-with-elementary-set-aggregation for how multi-component propositions combine under this scheme.