Abstract:Quantitative practice across statistics, engineering, and machine learning has been transformed by the automation of inference. Predictions are produced, validated, and deployed at scale and speed that human-mediated reasoning could not match. This shift intersects with a structural limit of reasoning that no methodological refinement dissolves: every inference rests on a finite specification of conditions, and what falls outside the specification does not appear as a widened uncertainty band -it does not appear at all. The choice of specification -the frame -is upstream of the inference and cannot be audited from inside the system that uses it. This paper offers a synthetic, application-oriented review. We argue that three categories of uncertainty operate in quantitative practice -aleatory, epistemic, and frame (or ontological) -and that the third, the residue of finite specification, is structurally invisible to formal analysis within the chosen frame and is the locus of most consequential failures. We trace why the limit applies equally to deductive and inductive reasoning, why no meta-level procedure dissolves the regress, and why current conditions of automated inference make epistemic humility -the practical disposition this argument supports -more, not less, important. We articulate the argument's specific resonances for five typical figures of contemporary quantitative work -the engineer, the statistician, the mathematician, the machine-learning practitioner, and the non-specialist recipient of expert claims -showing how the structural argument bears on each practice's natural defenses. The argument is not against rigor or against quantification; it is for distinguishing rigor earned within a frame from rigor with respect to the frame.
| Subjects: | Methodology (stat.ME) |
| Cite as: | arXiv:2605.23614 [stat.ME] |
| (or arXiv:2605.23614v1 [stat.ME] for this version) | |
| https://doi.org/10.48550/arXiv.2605.23614 arXiv-issued DOI via DataCite (pending registration) |
From: William FAURIAT [view email] [via CCSD proxy]
[v1]
Fri, 22 May 2026 13:21:05 UTC (29 KB)
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