Fallibilism permits knowledge despite the possibility of error—one can know a proposition even though one could, under different circumstances, have been mistaken about it. This preserves the intuition that ordinary empirical knowledge is genuine while acknowledging human fallibility. Fallibilism requires specifying what degree of reliability or justification suffices for knowledge when infallibility is impossible, making it the dominant view in contemporary epistemology.
Examine ordinary cases of knowledge despite acknowledged fallibility: knowing who won yesterday's game despite potential error in memory, knowing scientific facts despite potential revision. Specify what degree of justification suffices.
You have already wrestled with the question of what knowledge requires — justified true belief at minimum, and something more to close Gettier cases. One implicit assumption in many classical formulations is that genuine knowledge requires infallibility: if you truly know P, then you could not possibly be wrong about P. This sounds intuitive at first. But consider what it would mean in practice. Do you know what you had for breakfast this morning? You could be misremembering. Do you know that the sun will rise tomorrow? You could be wrong about the laws of physics. Do you know that your friend is named what she says she is named? You could be being deceived. If infallibility is required for knowledge, almost nothing qualifies — a conclusion so extreme that it drives many epistemologists toward fallibilism.
Fallibilism makes the more moderate claim: knowledge is compatible with the mere logical possibility of error. You can know P even though, in some nearby or not-so-nearby possible world, you would have been wrong about P. What matters is not that error is impossible but that your belief-forming process is reliable enough in actual conditions — that it produces true beliefs with sufficient regularity in the kinds of circumstances you actually inhabit. Your memory is generally reliable about recent events, your perceptual faculties about nearby objects under normal lighting. That reliability suffices for knowledge even though neither is infallible.
This connects directly to your prerequisite study of reliabilism. Reliabilist accounts of justification hold that a belief is justified when it is produced by a reliable cognitive process. Fallibilism complements this view: if reliability (not infallibility) is the standard for justification, then knowledge through reliable-but-fallible processes is genuine knowledge. The key move is distinguishing two different senses of "could be wrong": (a) there exists some logically possible world where I am wrong, and (b) in the actual conditions of my current situation, my belief-forming process is likely to have gone wrong. Fallibilism permits (a) while still requiring that (b) be false. You can know something while acknowledging logical possibility of error; you cannot know something when your process is actually unreliable.
The practical upshot is that ordinary empirical knowledge — the kind we rely on in science, daily life, and decision-making — is vindicated. Fallibilism is the dominant position in contemporary epistemology precisely because it preserves the intuition that we genuinely know many things while honestly acknowledging that human cognition is not perfect. The philosophical challenge it faces is specifying the threshold: exactly how reliable must a process be? This boundary problem is real, but it is a problem about drawing a precise line, not a reason to think there is no difference between knowledge and lucky guessing.
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