Vagueness Without Principled Ignorance: Instrumental Deficits, Community Norms, and a Challenge to Williamson’s Margin for Error Principle

Technical Summary: Vagueness Without Principled Ignorance

Problem Statement
The paper addresses the central tension in the philosophy of language regarding the nature of vagueness, specifically challenging Timothy Williamson's epistemic conception. Williamson argues that vague predicates (e.g., "bald," "heap") are semantically precise but generate "ineliminable epistemic blindspots." According to his Margin for Error Principle (MFE), because human discriminative capacities are inherently imprecise, one cannot safely know the exact boundary where a predicate applies without risking error in counterfactually adjacent scenarios. Consequently, there exists a principled, structural barrier to knowing where a vague predicate ceases to apply. The paper contests the assumption that this epistemic inaccessibility is a fundamental, ineliminable feature of cognition or reality, arguing instead that it is a contingent limitation of current measurement capabilities.

Methodology
The paper employs a theoretical reconstruction and critique of Williamson's epistemic framework, supplemented by a linguistic-functionalist analysis and an examination of the concrete/abstract distinction. The methodology involves:

1. Reconstructing Williamson's MFE: Analyzing the safety requirement on knowledge and how it generates iterative constraints that preclude knowledge at the margins of sorites series.
2. Applying the Measurement Deficit Hypothesis (MDH): Drawing analogies from the history of empirical science (specifically the transition from pre-thermometric uncertainty to precise measurement) to argue that current ignorance regarding vague predicates is instrumental rather than principled.
3. Integrating Linguistic Functionalism: Utilizing frameworks from Wittgenstein, Lewis, and Dummett to posit that semantic content is constituted by functional roles within speech practices, rather than by mind-independent facts.
4. Leveraging Computational Sociolinguistics: Citing empirical work (e.g., Labov) and modern computational methods (corpus analysis, machine learning) to demonstrate that community-level predicate usage exhibits stable statistical structures that can be mapped with high resolution.
5. Distinguishing Domains: Applying a distinction between abstract/metaphysical entities (where principled unknowability may exist) and concrete, observable phenomena (where referents are physically measurable).

Key Contributions
The paper advances two primary arguments and proposes a new theoretical account:

1. The Measurement Deficit Hypothesis (MDH): The author argues that the epistemic blindspots identified by Williamson are not the result of a structural cognitive limitation but of "instrumental ignorance." The inability to pinpoint the boundary of a vague predicate is a deficiency in the tools available for tracking linguistic practice. With sufficiently advanced computational sociolinguistic tools, the community-relative extensions of vague predicates can be mapped with statistical precision.
2. The Concrete/Abstract Distinction: The paper argues that Williamson's MFE is misapplied to predicates denoting concrete, observable phenomena (like hair count or physical height). While principled epistemic inaccessibility may apply to metaphysical entities (e.g., the Ding an sich), it does not apply to linguistic categories whose referents are physical facts. Since language is a human artifact constituted by convention, its boundaries are, in principle, accessible to the very agents who create and sustain them.
3. The Pragmatic Calibration Account (PCA): Synthesizing the above, the paper proposes the PCA. This account posits that vague predicates do not possess a single, hidden, sharp threshold. Instead, they admit of Community-Relative Semantic Schemes (CRSS). These are multiple, determinate, context-indexed specifications of a predicate's extension, constituted by the functional norms of specific sub-communities or communicative purposes (e.g., a perceptual scheme for social recognition vs. a statistical scheme for medical diagnosis).
4. Refutation of Objections: The paper addresses three substantive objections:
   • Aggregation Circularity: It argues that aggregating individually uncertain judgments yields a precise statistical distribution (a determinate fact about usage), not a vague result.
   • Normativity: It contends that on a functionalist view, norms of correctness are constituted by stable community practices, not by external transcendent rules; thus, usage facts are semantic facts.
   • Measurement-Level Replay: It argues that while measurement has finite precision, this does not recreate Williamson's principled blindspot. Improved tools can progressively narrow the margin of uncertainty, converting ignorance into convergent instrumental approximation.

Results and Claims
The paper concludes that the "epistemic blindspot" Williamson identifies is not a permanent feature of the human condition but a contingent gap in our epistemic toolkit.

• On Vagueness: Apparent semantic indeterminacy for concrete-referent predicates reflects a failure to specify and measure the operative community-relative scheme, not an inherent indeterminacy in the world or language.
• On the Sorites Paradox: The paradox is not a logical or metaphysical failure but a problem of underspecification. It arises from asking for a single boundary without fixing a specific CRSS. Once a scheme is fixed, the question has a determinate answer.
• On Knowledge: We can, in principle, have knowledge of the extension of vague predicates by calibrating them against the functional norms of the linguistic community using systematic analysis.

Significance
The paper claims that its significance lies in shifting the debate from a metaphysical or logical puzzle to a practical problem of measurement and specification. By reframing vagueness as a "measurement deficit," the PCA:

• Preserves classical logic and bivalence without requiring ineliminable ignorance.
• Provides a philosophical foundation for existing legal practices (e.g., using community standards to define "obscenity" or "reasonable force") and computational linguistics (where large language models learn semantic distributions from corpora).
• Suggests that the "confession" of not knowing where baldness ends is merely an admission that we have not yet looked carefully enough at how we speak, rather than a deep philosophical truth about the limits of knowledge.