 The reasoning here is a double reductio. Assume (a) that P must either be true or false in Russell’s system, and (b) that P must either be provable or unprovable in Russell’s system. If (a), P must be true, for if we suppose that P is false, since P says of itself that it is unprovable, “it is true that it is provable”, and if it is provable, it must be true (which is a contradiction), and hence, given what P means or says, it is true that P is unprovable (which is a contradiction). Second, if (b), P must be unprovable, for if P “is proved, then it is proved that it is not provable”, which is a contradiction (i.e., P is provable and not provable in PM). It follows that P “can only be true, but unprovable”.