Anti-luck approaches to knowledge add conditions that exclude cases where someone believes something true mostly by luck. The safety condition requires that if the belief were held, the belief would very likely be true; sensitivity requires that if P were false, the belief would not be held. These modal conditions aim to capture the intuition that knowledge is incompatible with too much epistemic luck.
Test safety and sensitivity with lottery cases and fake barn cases. See why each condition handles some cases well but struggles with others. Consider whether combining conditions improves the account or creates new problems.
Your prerequisite work on Gettier cases showed that justified true belief is not sufficient for knowledge — someone can believe something, be justified in believing it, and be right, while still clearly not *knowing* it. The barn façade case is canonical: Henry drives through a region where nearly all visible structures are fake barn fronts, but happens to stop in front of the one real barn. He forms the belief "there is a barn in front of me," and he is justified (barn fronts look like barns) and true (it really is a barn). Yet philosophers widely agree Henry does not *know* there is a barn there. The reason is luck: he just happened to stop in front of the one real one. Anti-luck conditions are attempts to diagnose, precisely and rigorously, what kind of luck is incompatible with knowledge.
The sensitivity condition (Nozick) analyzes this in counterfactual terms: you know P only if, if P were false, you would not believe P. Consider the barn case: if there were no barn in front of Henry, he would still believe there was one (because he would be looking at a façade). Sensitivity fails — hence no knowledge. The condition has strong intuitive support. If my belief would remain unchanged even in a world where what I believe is false, something clearly has gone wrong. However, sensitivity runs into trouble with lottery cases. I believe I will not win the lottery; if I had won, I would believe I had won (I would see the ticket). My belief that I will lose is sensitive — but it seems odd to say I *know* I will lose before the draw.
The safety condition (Sosa, Williamson) reverses the conditional: you know P only if, in nearby possible worlds where you believe P by the same method, P is true. For Henry: in nearby worlds (driving through the same region), he believes "there is a barn" based on visual appearance, but in many of those worlds what he is looking at is a façade. Safety fails — hence no knowledge. Safety handles lottery cases more smoothly: in nearby worlds, I do not believe I won the lottery (I only believe it once I see the ticket), so my belief that I have not won can be safe.
The deeper point these conditions illuminate is that knowledge requires a certain kind of modal connection between your belief and the truth. It is not enough that you happened to believe truly; the truth must be reliably involved in why you believe. Your belief must not be the kind that would survive in error-worlds close to the actual one. Neither condition captures this perfectly — there are counterexamples to strong formulations of each — but they focus the investigation in a way that "justified true belief" never did. They explain *why* Gettier cases fail: in each case, the actual world happens to cooperate with the belief, but the nearby counterfactual structure reveals that the connection between belief and truth is fragile rather than robust. Anti-luck conditions try to make "not fragile" precise.
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