 Notice now, first, that the proposition \(P\) enters only into the first and the third of these premises, and secondly, that the truth of both of these premises is easily secured.  Thus, for the first premise to be true, all that is needed is that \(\negt G\) entails \(P\), while for the third premise to be true, all that is needed, according to most systems of inductive logic, is that \(P\) is not entailed by \(G \amp k\), since according to most systems of inductive logic, \(\Pr(P \mid G \amp k) \lt 1\) is only false if \(P\) is entailed by \(G \amp k\).