Williamson and Hawthorne, among others, endorse a closure principle about knowledge that employs the concept of a competent deduction. The straightforward version is that if you know p and competently deduce q from p, then you know q. As most realize, there are qualifications needed, but I’ll ignore them here.
Here’s a question about the principle. Suppose a competent deduction of q from p by S occurs, and suppose that the deduction is constituted by a certain sequence of brain states in S. Now, suppose we have another person, S’, just as competent at deduction as S who also knows p. Further, suppose that a mad neuroscientist produces in S’ the same sequence of brain states that constituted the deduction of q from p by S. Did S’ just competently deduce q from p?
Another question. Assume S’ comes to believe q as a result of what the neuroscientist does. Does S know q?