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The margin for error principle states that if you know something, you must rule out all possibilities that differ marginally from the actual case. When combined with the observation that borderline cases of knowledge are inevitable due to vagueness, this principle generates powerful constraints on knowledge conditions. It explains how knowledge requires not merely true justified belief but safety from near-miss cases.
From indexical contextualism, you know that knowledge attributions are context-sensitive — what it takes to count as knowing varies with the standards of the attributing context. The margin for error principle approaches a related but distinct question: what structural feature of knowledge explains why borderline epistemic situations exist at all? Why is it that you can be in a situation where you're not quite knowing, even though you have a true belief formed through ordinary reliable processes?
The basic principle, developed by Timothy Williamson, is this: if you know that p, then in all nearby possible worlds — worlds that could easily have been actual, where things are only marginally different — p is still true. Put differently, knowing requires a safety margin: the actual world must be far enough from any error-world that your belief couldn't easily have been false. If the actual world sits right at the boundary — so close to a world where p is false that your cognitive processes couldn't reliably distinguish the two — then you don't know p, even if p is true and you believe it. The case isn't just unlucky; it's structurally too close to call.
A concrete illustration: you're estimating the number of people in a large lecture hall. If there are 200 people, you can probably tell it's not 50 people or 500 — you're safely within your discriminatory capacity and you know roughly how many are there. But do you know there are at least 198? Here the margin shrinks. A hall with 198 people and one with 199 would look identical from where you stand. If you believe "there are at least 198," you might be right, but your cognitive process couldn't have reliably distinguished an error — a 197-person scenario would generate the same belief. This is the margin for error constraint: your belief that "at least 198" isn't knowledge because near-miss error worlds aren't ruled out.
The principle generates a connection to safety conditions on knowledge, which say roughly that knowledge requires not easily being wrong. Guesses fail this condition — if you guessed correctly, then in a nearby world where the guess landed differently, you'd have a false belief. Williamson's insight is that the same structural constraint explains both why guesses aren't knowledge and why borderline perceptual judgments aren't knowledge: in both cases, the actual world sits too close to error. This also helps explain the puzzle of vagueness and knowledge: for genuinely borderline cases (is this chip red or orange? is this person tall?), the margin for error principle implies you cannot know which side of the boundary you're on, because any such judgment would be indistinguishable from an erroneous one in a marginally different scenario. Knowledge, on this view, is inherently a matter of being far enough from error — not merely of being right.
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