Some random thoughts on Sosa

Sosa's response to radical skeptics is like this:

according to radical skeptics, our belief that we are not brains in a vat is not sensitive, hence is not knowledge; but to conclude this way, radical skeptics have to assume that the requirement of knowledge is sensitivity; contraposition does not work on counterfactual conditionals, which implies that sensitivity and safety are not equivalent; further, the plausibility of the sensitivity requirement is derived from the plausibility of the safety requirement; radical skeptics hold to the sensitivity requirement because they get confused with the two; if we clear the confusion away and hold to the safety requirement instead of the sensitivity requirement, then radical skeptics can no longer claim that our belief that we are not brains in a vat is not knowledge. So radical skepticism (i.e. skepticism based on radical scenarios) is no longer a threat.

Here I do have a problem. Indeed, contraposition does not work on counterfactuals, which means the following formula, as a general claim, is false: A>B <=> B>A. But this does not mean that contraposition does not hold in particular cases. The claim that contraposition as a general claim fails does not entail that contraposition always fails on every occasion. So we should not hurry to claim that the safety requirement and the sensitivity requirement are not equivalent.

So Sosa thinks that radical skepticism is not a problem as long as we hold to the safety requirement instead of the sensitivity requirement. But there is a problem with the safety requirement also. According to the safety requirement, a belief p is safe if and only if not easily could p have failed. A revised version of the safety requirement, basis-related safety, states that a belief p is basis-relative safe if and only if p has a basis such that on that basis p could not easily have failed. From the definition, you can see why our belief that we are not brains in a vat is safe and basis-relative safe. But dreams loom around as a threat. Dreams are part of our ordinary life. In Sosa's words, that we are dreaming rather than awake is a nearby possibility rather than a remote possibility. Hence our belief that we are not dreaming is not safe, and not basis-related safe either. Therefore, Sosa proposes that the safety requirement be abandoned and aptness be put in its stead.

But how do we tell whether a possibility is nearby or remote? Since I have read very little Sosa, I won't claim that Sosa never gives an answer to this question. But when I was discussing this with a group of people some of whom knows Sosa really well, I noticed that they tended to interpret the remoteness of possibilities in terms of the closeness relation among worlds. As we all know, the closeness relation among worlds is widely used to construct semantics for counterfactuals. But is Sosa really intending to borrow from or rely upon the possible worlds semantics for counterfactuals? I have no idea, perhaps further reading would give me a definite answer.

But even if we agree on understanding the remoteness of possible scenarios in terms of closeness among worlds, we still have a problem. A natural conjecture is that a possible scenario is remote if it can only be housed in a world not close to the actual world; a possible scenario is nearby if it can be housed in a world close by. But think of the lottery case. Imagine a billion lottery tickets are sold to a billion people, each person having one ticket. You have one ticket. Tell me whether the scenario of your winning the lottery (suppose there is only one winning ticket) is nearby or remote. If we understand this in terms of closeness among worlds and presume it is totally random which ticket is the winning ticket, then at least one world in which you have the winning ticket is as close as any world in which you don't. So the scenario in which you win is nearby. But in the sphere closest to the actual world, the worlds in which you have the winning ticket take up a very tiny portion, probably 1/billion. So one feels (at least I do) inclined to agree that the possible scenario in which I win is remote, since it is highly unlikely. So this lottery case should remind us that the best way to understand remoteness may not be in terms of closeness among worlds.