In a recent paper, Lehrer and Paxson suggest the following analysis of non-basic knowledge: S has non-basic knowledge that h if and only if (i) h is true, (ii) S believes that h, and (iii) there is some statement p that completely justifies S in believing that h and no other statement defeats this justification. The complete justification that p provides S to believe h is defeated by q if and only if (i) q is true, (ii) the conjunction ofp and q does not completely justify S in believing h, (iii) S is completely justified in believing q to be false, and (iv) if c is a logical consequence of q such that the conjunction of c andp does not completely justify S in believing h, then S is completely justified in believing c to be false. 1
Ernest Sosa has presented three objections to this analysis. 2 I believe that two of these objections do point up shortcomings in the defeater analysis, but a simple alteration in the analysis will be seen to avoid these difficulties. Furthermore, this alteration allows us to drop clause (iv), hence simplifying the defeater conditions. In regard to Sosa's other objection, I argue that it is misguided and does not require any alteration in the analysis.
I begin with Sosa's objection that turns on a modification in the pyromaniac example. The pyromaniac has always found that Sure-Fire matches light when struck and this evidence completely justifies him in believing that the match he now holds will light when struck. Sosa asks us to further imagine that the pyromaniac is also completely justified on the basis of past experience in believing that upon the ignition of the match he will smell powder when appropriately situated, etc. But this time he will not smell powder, etc., because he will be struck with temporary paralysis. Sosa then claims:
... if we take the proposition (q) that he will not smell powder.., and conjoin it with the pyromaniac's evidence (p), the resulting conjunction (q and p) will not completely justify him in believing (h) that the match will ignite. But should this preclude his