Second Gettier Case. Imagine again Smith and Jones. Smith has good reasons to think that Jones owns a Ford. Smith then thinks he has good reason to believe statements like, “Either Jones owns a Ford or Brown is in Barcelona.”. Smith is indeed justified to believe this, since the justified belief “Jones owns a Ford” entails the justification of the belief, “Either Jones owns a Ford or Brown is in Barcelona”(because disjunctive “or” statements are true if only one half of the statement is true). Let’s say that Jones actually was leasing the Ford and actually now owns an Audi. Also, let’s just say that Brown happens to be in Barcelona. Smith’s belief is true, but only by luck. Gettier thinks this is a case of a justified true belief that is not knowledge.
First Case vs. Second Case. The first kind of case deals with conjunctive statements made by using “and”. The second kind of case deals with disjunctive statements that use “or”. This is the main difference between the two kinds of cases. What they share in common is that they are both counterexamples to the traditional definition of knowledge!