Sensitivity and Closure

Kelly Becker, in his book Epistemology Modalized, gives a nice modal account of knowledge:

S knows that p iff:

1. p is true
2. S believes that p
3. S’s belief that p is formed by a belief-forming process or methodw that produces a high ratio of true beliefs in the actual world and throughout close possible worlds (reliability condition).
4. If p were false, S would not believe that p via the methodn S actually uses in forming the belief that p (sensitivity condition). (Epistemology Modalized, p.88)

Methodsw are individuated very narrowly, but not so narrowly as to include specific belief contents.  Specific belief contents are however included in methodsn.  Becker individuates a methodw as the narrowest specific-content-neutral method or process that is causally operative in belief formation.  An example of a methodw might be forming beliefs about which people are in the vicinity based on quick looks in at least dim lighting.  A methodn on the other hand might be something like If what I am looking at now has short legs and floppy ears (and such and so other features) then it’s a dachshund.

Becker also makes a serious and interesting case against closure under known entailment, and he takes it, as epistemologists generally do, that sensitivity is incompatible with closure:

The sensitivity component of our theory somehow predicts this result – I do not know not-[sceptical hypothesis] because, if it were false, I would believe it anyway. (Epistemology Modalized, p.120)

But in fact, it isn’t clear that his account of sensitivity is incompatible with closure.  Take a standard BIV case.  I believe I am not a BIV, yet 4 holds: if I was a BIV I would not believe that I was not a BIV via the methodn I actually use in forming the belief that I am not a BIV.  My method, after all, involves coming to know ordinary propositions about the world around me by interacting with it, and inferring from these ordinary propositions that I am not a BIV.  Since brains in vats cannot employ the same kinds of methods that embodied humans do, my belief that I am not a BIV is sensitive according to Becker’s analysis.