Specifying safety and quasi-factive evidence for the knowledge-first package: closeness, method-relativization, and the epistemic status of measurement reports

Timothy Williamson's knowledge-first epistemology combines the thesis that one's evidence is what one knows ($E=K$) with an anti-luck safety condition on knowledge and the factivity of knowledge. Shaffer (2022) argued that this package, applied to ordinary measurement reports (which are only approximately true), yields a form of skepticism: such reports fail safety because worlds with unknown systemic instrument error are close, so they are not knowledge and hence not evidence. The open repair problem left by that argument is to specify the closeness relation, to decide whether method-relativized safety can block the modal counterexamples from unknown systemic errors, to reconcile (or principledly revise) factivity with a safety constraint that tolerates the small residual risk of error carried by approximately true reports, so that measurement reports count as evidence without Moorean contradiction, and to give a precise account of quasi-factive evidential status. Defenders of the knowledge-first package have not answered the measurement-driven objection, method-relativized subjunctive conditions face an unresolved dilemma, and the factivity debate remains contested with no reconciliation — the problem is open.

Background

Knowledge-first epistemology, developed by Timothy Williamson in Knowledge and its Limits (2000), holds that knowledge is analytically basic and cannot be decomposed into more primitive conditions. Two of its central commitments matter here. First, the $E=K$ thesis: a subject's evidence consists exactly of what that subject knows. Second, factivity: knowledge implies truth, so one can know only what is true. Williamson supplements these with an anti-luck condition: knowledge must not be true merely by luck. The most influential anti-luck condition is the safety condition — a belief that $p$ is safe only if, in all close possible worlds (worlds relevantly similar to the actual world in respect of how the belief was formed), the subject would not believe that $p$ via the same belief-forming method $M$ unless $p$ were true. Safety thus depends on a closeness (similarity) ordering over possible worlds, and on how belief-forming methods are individuated — that is, how finely or coarsely the mechanism by which a belief was formed is to be described when the condition is applied; both are notoriously contested. A Moorean contradiction is the strain produced by asserting a sentence of the form '$p$, but I do not know that $p$,' which any theory implying that ordinary assertions fall short of knowledge risks generating.

Michael J. Shaffer, in a series of papers, pressed a measurement-driven objection to this package. Measurement reports — propositions such as 'the thermometer reads 104 °C' produced by properly used instruments — are only approximately true, since every instrument has systematic and random error. His 'approximation argument' (Shaffer 2015, 2019) runs: measurement reports are paradigmatic evidence and paradigmatic assertable claims; but given instrument error, close worlds in which the instrument suffers an unknown systemic error (e.g. a miscalibrated thermometer that reads systematically high) contain a subject forming the same belief via the same method while the report is false; so such reports are unsafe, hence not knowledge, hence (by $E=K$) not evidence — a reductio of the package, or alternatively a measurement-driven skepticism. Shaffer proposed instead that evidence is only quasi-factive: false-but-approximately-true measurement reports can constitute evidence (Shaffer 2015), and defended a non-factive reading of knowledge against the factive orthodoxy (Shaffer 2021, 2022 companion). The 2022 paper 'Safety, Evidence, and Epistemic Luck' critically explores Williamson's view of evidence in light of the problem of epistemic luck; its critique leaves a cluster of unsolved design problems for defenders of the knowledge-first package and for safety theorists generally.

Problem Statement

Construct (or definitively refute the possibility of) a coherent repair of the safety-based, knowledge-first anti-luck package that secures the evidential and knowledge status of ordinary measurement reports. The repair problem comprises four interrelated questions: (1) under what specification of the closeness relation underlying the 'no close risk' safety condition do worlds involving unknown systemic instrument error leave ordinary measurement beliefs safe, so that the measurement-driven skepticism is avoided? A successful specification must steer between two failure modes: worlds so distant that safety trivializes (losing its anti-luck force — as happens if worlds in which the instrument carries an undetected systematic error are simply stipulated to be non-close, rendering every actual measurement belief safe by construction) and worlds so close that ordinary perception and measurement beliefs are all unsafe. (2) Can method-relativized safety (safety restricted to a specific belief-forming mechanism $M$), developed together with a principled individuation of methods — a rule fixing how finely the mechanism $M$ is to be described — block the modal counterexamples arising from unknown systemic errors? (3) Can factivity be reconciled — or must it be principledly revised — with a safety constraint that tolerates the small residual risk of error carried by approximately true measurement reports, so that ordinary measurement reports count as evidence while Moorean contradictions are avoided? The standard case types of this literature — Gettier cases (justified true beliefs that are nevertheless true only by luck, e.g. a stopped clock showing the right time), lottery cases (highly probable beliefs about losing lottery tickets that are not knowledge), and fake-barn cases (perceptual beliefs formed in an area dotted with indistinguishable barn façades) — form relevant background here, though intuitions about such cases are themselves contested. (4) What precise account of evidential status — its possession conditions and norms — accommodates approximate or quasi-factive measurement reports (the approximation argument) while preserving the desirable epistemic norms of evidence (support, update, and use in practical reasoning)? The four questions form one problem because they are jointly constrained: the closeness specification and method individuation fix what the safety condition excludes, which fixes which measurement reports are knowledge, which — under the package's $E=K$ thesis — fixes what counts as evidence. Because the critique targets the package as a whole, a repair must also determine which of its commitments ($E=K$, factivity, the safety condition) can be held fixed and which must be principledly revised; an internally inconsistent package is not a coherent repair. A constructive repair must therefore answer all four questions in a jointly consistent way, while the disjunctive 'or refute' route is completed by a principled argument that one of the four cannot be answered in the required way under any specification.

References

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