 Symbolically, \(A \rightarrow B\) should not be asserted in circumstances where the speaker knows that \(A\) is false because the statement not-\(A\) is true and simpler; similarly, if the speakers knows \(B\) is true, \(B\) is a shorter simpler statement; and if the speaker knows both of those facts, then not-\(A\) and \(B\), is more informative. Thus the only circumstances in which the conditional is appropriate is where the speaker is ignorant of the truth values of \(A\) and \(B\), but has some good reason to think that if \(A\) does prove to be true, \(B\) will as well. On this account, the truth conditions of the conditional are those of the material implication, but the appropriate assertibility of a conditional tracks the conditional probability of \(B\) given \(A\).