Safety and Sensitivity Conditions

What is wrong with Henry's belief in the fake barn district is not that it is false, because it is true, and not that his eyes are failing, because they are working. What is wrong is that he came within a few metres of believing the same thing falsely. The defect is not in the actual world at all. It is in how close he came.

That observation, once made precise, produces the most technically developed response to the Gettier problem. Its instrument is the counterfactual conditional, and its result is two conditions that look like rewordings of each other and are not.

The apparatus

The semantics is due to Robert Stalnaker and David Lewis, and epistemology borrows it without needing the metaphysics that comes with it. Nothing in what follows requires that possible worlds exist. All that is required is that some ways things might have gone are nearer to how things actually went than others, which is a judgement people make constantly and with reasonable agreement.

Two features of the apparatus matter. Closeness is a matter of overall similarity rather than of any single dimension, so a world in which one small thing differs may be far away if the difference propagates. And the ordering is vague at the edges, which means every modal condition on knowledge inherits a vagueness it cannot eliminate.

Sensitivity

Nozick's idea is that a knower is a detector. What makes a smoke alarm a smoke alarm is that it goes off when there is smoke and stays quiet when there is not. The second half is the important one, and it is what sensitivity captures: a device that sounds continuously is not detecting anything, however often it is right.

The condition handles Gettier cases directly. Had it been false that the man who gets the job has ten coins, Smith would still have believed it, since his belief rests on the president's remark and the count of Jones's coins, neither of which would change. Smith's belief is insensitive, and so are Gettier beliefs generally, because the feature that makes them true is not the feature they are responsive to.

Nozick's fourth condition, called adherence, is needed because sensitivity alone is too weak. It requires that the belief stay in place across small variations in which the proposition remains true, so that a knower is stable as well as responsive.

The relativisation to method is also not optional. A grandmother sees her grandson is well. Had he been ill, the family would have kept him away and told her he was fine, so she would still have believed him well, and the belief looks insensitive. Nozick's answer is that the condition is evaluated holding fixed the method actually used, which here is seeing him. Holding vision fixed, had he been ill and she had looked, she would have seen it.

What sensitivity costs

The condition's most notorious consequence is that it invalidates closure, and the next article is devoted to that. Its other well-known problem can be stated here.

Consider a belief that could not easily be false, but whose falsity would require a wildly different world. You believe you are not a brain in a vat. Had you been one, you would still have believed you were not. The belief is insensitive, so on Nozick's account you do not know it. Nozick accepted this, which is part of what makes the account interesting rather than merely defective, but many find the cost prohibitive.

Consider also beliefs formed by induction. You believe your chair will hold you. Had it been about to collapse, you would have believed it anyway, since nothing in your evidence would have differed. Sensitivity rules out a great deal of ordinary inductive knowledge, and the fixes have been strained.

Safety

Safety, defended by Ernest Sosa and by Timothy Williamson, reverses the direction of the conditional. Sensitivity starts from the falsity of the proposition and asks about belief. Safety starts from the belief and asks about truth.

The reversal is not a logical equivalence. If not-p then not-believe-p is not equivalent to if believe-p then p, because counterfactuals do not contrapose. This is the whole of the technical difference between the two conditions, and every divergence between them traces back to it.

What safety buys is the two cases that sensitivity loses. Your belief that you are not a brain in a vat is safe, since envatment worlds are remote, so safety lets you know it and preserves closure. Your belief that the chair will hold is safe, since chairs in close worlds do not collapse.

What safety keeps is the fake barn verdict. Henry's belief is unsafe, because worlds in which he looks a hundred metres further down the road and forms the same belief falsely are as close as worlds can get.

Where safety struggles

Necessary truths are the standard difficulty. A proposition that could not be false is true in every world, so every belief in it is trivially safe, including a belief in a theorem arrived at by a botched proof or by consulting a magic eight ball. Safety issues no verdict where it is most needed, and the repairs involve either restricting the condition to contingent propositions, which is ad hoc, or refining it to range over the method's outputs rather than the proposition's truth, which is closer to reliabilism.

Lottery cases press from the other side. You hold one ticket in a million and believe it has lost, before the draw, on the basis of the odds. The belief is unsafe, since a world in which your ticket wins is close in the relevant sense, and safety therefore says you do not know. Most find this the right answer. But your belief that you will not be able to afford a house this year rests on the same probabilistic footing and seems like something you know, and no clean line separates the two.

The scoreboard

Sensitivity explains the Gettier cases, the fake barns, and the intuition that a knower is a detector. It costs closure and most inductive knowledge.

Safety explains the Gettier cases and the fake barns, keeps closure, and keeps inductive knowledge. It costs the necessary truths and gives an uncomfortable treatment of lotteries.

Most of the field has gone with safety, and the reason is closure, which is where the argument goes next.

Next

The principle that Nozick's account has to abandon, why it looks undeniable, and what a theory gains by giving it up.