A Theory of Partial Truth for Scientific Statements (arXiv:2611.07179)
Capture from a fresh external surface (outside-vault topic, 2026-11-06). Single-author preprint by Gustavo E. Romero (Instituto Argentino de Radioastronomía, IAR; CCT-La Plata, CONICET; CICPBA; UNLP, Buenos Aires), submitted 4 Nov 2026, physics.hist-ph with astro-ph.IM cross-listing. The paper is already formally published: comment field reads "Published in Philosophies 2026, 11(5), 194" (MDPI, open access, CC BY 4.0), so this is not an unrefereed preprint sitting outside peer review — the arXiv copy and the journal version are the same text.
Both the abstract page (archived via archive_page, sha above, tls: verified) and the full 32-page PDF (extracted via extract_pdf, sha 5e81197ce29f732939e2b787e33458dd7ca6b6e1954f92f35e80d4871aa5f9b3, method pdftotext, tls: verified) were read directly. No recognition signals fired on either fetch — see Safety flags below.
The paper develops a formal, numerically-scaled alternative to simple true/false classification for scientific claims: a function V_E(p) ∈ [0,1] estimating how adequately a proposition p represents the facts, relative to a body of evidence E, built from the normalized discrepancy between an asserted value and an empirically measured one. It positions itself explicitly as a revision of Mario Bunge's own axiomatization of partial truth, undertaken to fix a specific logical defect a 2025 paper had identified in it.
Claim: Romero's valuation function treats "partial truth" as a measure of factual adequacy distinct from probability, confirmation, fuzzy-logic membership, and Popperian verisimilitude
Claim type: definitional / technical-mechanism (what the paper's central formal object is and is not). Source: same as frontmatter (Tier 1 — author's own paper, published venue of record). source_quote: "On the ontological interpretation adopted here, probabilities are attributed to events under specified physical conditions; propositions may state those probabilities but are not themselves bearers of probability." source_quote_2: "the proposed valuation VE estimates factual adequacy rather than probability: its interpretation and composition rules concern representational discrepancy and the aggregation of elementary content." source_url: https://arxiv.org/pdf/2611.07179 · source_sha: 5e81197ce29f732939e2b787e33458dd7ca6b6e1954f92f35e80d4871aa5f9b3
For a quantitative proposition asserting a scalar value μ against a measurement M = e ± δ, the paper defines a normalized discrepancy β_E(p) = min(1, |μ−e|/s_E(M)) against a characteristic scale s_E(M), and sets V_E(p) = 1 − β_E(p) (stated as "Axiom 4, Quantitative valuation" in the text). This is kept conceptually separate from measurement indeterminacy (δ, the width of the measurement interval): discrepancy is the mismatch between what is asserted and what is measured, not the precision of the measurement itself. The paper also distinguishes its target from verisimilitude (Popper, later Oddie and Niiniluoto) and from da Costa and French's "quasi-truth" (partial-structures theory): verisimilitude compares whole theories to a complete truth, while Romero's V_E scores specified, already-testable consequences against a specific evidence set.
Claim: The paper is an explicit, targeted repair of Mario Bunge's axiomatization of partial truth, prompted by a 2025 paper (Gracia Di Rienzo) that showed Bunge's recursive half-sum rule for conjunction gives different truth-values to logically equivalent statements depending on how they are parenthesized
Claim type: historical / technical-mechanism (a priority-and-correction claim about the theory's own lineage). Source: same as frontmatter (Tier 1). source_quote: "A recent analysis showed that a binary half-sum rule for conjunction can assign different values to logically equivalent expressions that differ only in their parenthesization [18]." source_quote_2: "Gracia Di Rienzo [18] establishes this incompatibility through the associativity of conjunction: (p ∧ q) ∧ r ≡ p ∧ (q ∧ r)." source_url: https://arxiv.org/pdf/2611.07179 · source_sha: 5e81197ce29f732939e2b787e33458dd7ca6b6e1954f92f35e80d4871aa5f9b3
The paper's reference list identifies the earlier axiomatic line of work being repaired as Mario Bunge, Matter and Mind (2010) and "The correspondence theory of truth" (Semiotica, 2012), plus Romero's own earlier papers "Truth and relevancy" (Metatheoria, 2017) and Scientific Philosophy (Springer, 2018), which had already distinguished truth from relevance in this framework. The identified flaw: under the old rule V_E(p∧q) = (V_E(p)+V_E(q))/2 applied recursively, grouping ((p∧q)∧r) versus (p∧(q∧r)) assigns the three components different implicit weights (1/4, 1/4, 1/2 versus 1/2, 1/4, 1/4), so — using the paper's own worked numbers V_E(p)=1, V_E(q)=0.5, V_E(r)=0 — the two groupings compute to 0.375 and 0.625 respectively for logically equivalent expressions. The source directly states: "The two equivalent expressions therefore receive different values." The reference is: Gracia Di Rienzo, A. "On Bunge's axiomatizations of 'partial truth'." Disputatio: Philosophical Research Bulletin 2025, 14, 175–184 (cited by Romero but not independently read for this capture — recorded as Romero's characterization of it, not independently verified against the Gracia Di Rienzo paper itself).
Claim: Romero's fix replaces recursive pairwise averaging with a single aggregation over a fixed, complete set of "elementary" components, which the paper shows removes the parenthesization dependence for that same worked example
Claim type: technical-mechanism (the paper's own stated formal contribution). Source: same as frontmatter (Tier 1). source_quote: "The present reformulation addresses that instance by abandoning recursive binary averaging and retaining component counts and weights correctly when combining disjoint groups." source_url: https://arxiv.org/pdf/2611.07179 · source_sha: 5e81197ce29f732939e2b787e33458dd7ca6b6e1954f92f35e80d4871aa5f9b3
Under the revised rule, both groupings of the same three-component example are evaluated from the identical elementary set {p, q, r} and the paper reports both reduce to (1 + 0.5 + 0)/3 = 0.5 regardless of how the conjunction is parenthesized. The paper is explicit that this does not amount to a general numerical calculus for arbitrary negation/disjunction — it states the domain "is not assumed to be closed under negation or disjunction, and no general numerical rules for these connectives are postulated" — and that the arithmetic-mean aggregation rests on substantive, flagged assumptions (comparability of component valuations, appropriateness of compensation between an inaccurate and an accurate component) rather than being forced by the mathematics alone.
Claim: The paper's single real-world (non-hypothetical) worked example applies the framework to a massive star's stellar-wind mass-loss rate, using a published Chandra X-ray observation of ζ Puppis as the evidence base
Claim type: technical-mechanism / quantitative (a specific numeric worked application, and the published figure it is anchored to). Source: same as frontmatter (Tier 1, for what Romero's paper itself states and computes). source_quote: "Consider the massive star ζ Puppis. Cohen et al. [34] analyzed 16 X-ray emission lines or line complexes observed with Chandra space telescope on 28–29 March 2000." source_quote_2: "They estimate this systematic contribution to the indeterminacy of the inferred mass-loss rate to be a factor of two, substantially larger than the quoted statistical contribution." source_quote_3: "The asserted value is introduced here to illustrate the assessment and is not attributed to Cohen et al." source_url: https://arxiv.org/pdf/2611.07179 · source_sha: 5e81197ce29f732939e2b787e33458dd7ca6b6e1954f92f35e80d4871aa5f9b3
Romero's paper reports the central estimate from Cohen et al. as ṅ = 3.5 × 10⁻⁶ M☉ yr⁻¹, with a statistical measurement-indeterminacy contribution of ±0.3 × 10⁻⁶ M☉ yr⁻¹, and a separately estimated systematic contribution (from elemental-abundance assumptions in the wind-opacity modeling) "a factor of two" larger than that statistical figure. Romero then evaluates a hypothetical illustrative proposition p: Ṅ = 4.0 × 10⁻⁶ M☉ yr⁻¹ (explicitly not attributed to Cohen et al., introduced only to demonstrate the method) against this evidence, using the central estimate as the characteristic scale, and computes V_E(p) = 1 − |4.0−3.5|/3.5 = 6/7 ≈ 0.857. [unverified-quant — needs primary] for the Cohen et al. figures themselves: this capture sources the 3.5×10⁻⁶ M☉ yr⁻¹ central estimate and its stated uncertainties only to Romero's citation of them, not to a direct read of Cohen, D.H. et al., "A mass-loss rate determination for ζ Puppis from the quantitative analysis of X-ray emission-line profiles," Monthly Notices of the Royal Astronomical Society 2010, 405, 2391–2405 (DOI 10.1111/j.1365-2966.2010.16606.x) — the astronomical number itself has not been independently checked against that MNRAS paper.
Further leads
- Gracia Di Rienzo, A. "On Bunge's axiomatizations of 'partial truth'." Disputatio: Philosophical Research Bulletin 2025, 14, 175–184 — the 2025 critique this paper is a direct response to; not independently read, worth fetching to verify Romero's characterization of the associativity flaw.
- Cohen, D.H.; Leutenegger, M.A.; Wollman, E.E.; Zsargó, J.; Hillier, D.J.; Townsend, R.H.D.; Owocki, S.P. "A mass-loss rate determination for ζ Puppis..." MNRAS 2010, 405, 2391–2405 — the primary astrophysical source behind the paper's one real-world worked example; would resolve the
[unverified-quant]flag above. - Mikenberg, Da Costa & Chuaqui (1986) and da Costa & French, Science and Partial Truth (Oxford, 2003) — the "partial structures"/quasi-truth tradition Romero distinguishes his account from; a candidate adjacent theory of scientific truth for a future quasi-truth concept note.
- Cevolani, G.; Schurz, G. "Probability, approximate truth, and truthlikeness..." Australasian Journal of Philosophy 2017, 95, 209–225 — cited as giving an "approximate truth" measure (fraction of true components) that Romero's unweighted valuation coincides with in the classical bivalent limit.
- Elgin, C.Z. True Enough (MIT Press, 2017) — contrasted account of "felicitous falsehoods" in idealized models; Romero explicitly distinguishes graded factual adequacy from Elgin's notion of epistemic value via understanding.
Entity candidates
- Mario Bunge — person — the foundational figure whose own axiomatization of partial truth (Matter and Mind, 2010; "The correspondence theory of truth," Semiotica, 2012; also the author of the semantics/truth-bearer framework in refs 3, 21, 25) this entire paper is built on top of and explicitly revises; flagged first, ahead of the paper's own author, per the instruction to catch the older figure a priority/correction claim actually rests on. Not yet in the vault (
vault_entitylookup: unknown). - Gustavo E. Romero — person — sole author; astrophysicist and philosopher of science at the Instituto Argentino de Radioastronomía (IAR, CONICET), author of the paper's own immediate predecessors ("Truth and relevancy," 2017; Scientific Philosophy, 2018). Not yet in the vault (
vault_entitylookup: unknown). - Agustín Gracia Di Rienzo — person — author of the 2025 critique ("On Bunge's axiomatizations of 'partial truth'," Disputatio) that identified the parenthesization/associativity flaw this paper is written to fix; the proximate trigger for the whole revision.
- Karl Popper / Ilkka Niiniluoto / Graham Oddie — persons — originators and developers of verisimilitude/truthlikeness theory, the main rival research program the paper distinguishes itself from.
- Newton da Costa / Steven French — persons — originators of partial-structures theory and "quasi-truth," the complementary (not rival) formal tradition the paper situates itself alongside.
- Catherine Z. Elgin — person — author of True Enough (2017), source of the "felicitous falsehoods" account of idealization the paper distinguishes its own narrower question from.
- Gerhard Schurz — person — relevance-logic theorist (cited twice, 1991 and 2024) whose deductive-relevance criteria are explicitly contrasted with the paper's own numerical relevance weights.
- ζ Puppis — concept/term — the massive star used as the paper's sole real-world worked example of the valuation method, via its Chandra-derived stellar-wind mass-loss rate.
- Philosophies (journal) — concept/term — the MDPI open-access philosophy-of-science journal (2026, 11(5), 194) this preprint is the arXiv copy of.
Safety flags
None. Both the arXiv abstract page (archived) and the PDF full text (extracted, TLS verified) read as ordinary scholarly philosophy-of-science content throughout — no addressed-to-AI language, override language, claimed authority, tier self-assignment, file-system instructions, credential requests, or urgency framing encountered on either source.