 In the approaches discussed above, all beliefs in the belief set are treated equally in the sense that they are all taken seriously as beliefs in their own right. However, due to logical closure the belief set contains many elements that are not really worth to be taken seriously. Hence, suppose that the belief set contains the sentence \(p\), “Shakespeare wrote Hamlet”. Due to logical closure it then also contains the sentence \(p \vee q\), “Either Shakespeare wrote Hamlet or Charles Dickens wrote Hamlet”. The latter sentence is a “mere logical consequence” that should have no standing of its own.