Difficulties about inferential knowledge

We must now try to extend our account to cover knowledge that is based upon reasons.

In Chapter Eleven, Section One, this problem was raised in a preliminary way. Suppose that A truly believes that p on the sole basis of evidence ‘q’. What further stipulation must we make about ‘q’ in order to ensure that A knows that p is true?

We saw that A must know that q is true. This demand leads to an infinite regress if all knowledge is belief based upon further evidence. But we have now given an account of non-inferential knowledge, so that we can argue that the regress of reasons is finite. For simplicity, let us assume that the regress terminates at ‘q’, so that A knows that q non-inferentially.

But it is insufficient that ‘p’ be true, that A believes that p and that A know that q (non-inferentially). It is further necessary that ‘q’ be, as an objective matter of fact, a conclusive reason for believing that ‘p’. ‘q’ need not be a logically conclusive reason for believing that p, but it must be a conclusive reason. (It will be remembered from the discussion in Chapter Six, Section Eight, that good reasons, of which conclusive reasons are the best sort, need not be reasons which actually operate in anybody's mind.)

For suppose it not to be the case that ‘q’ is a conclusive reason for ‘p’. Then, although A knows that q, and so ‘q’ is true, it will be possible (and not merely logically possible) that ‘p’ is not true.