  There are three main possibilities here: (i) Plato simply missed the fact that the second argument is invalid; (ii) Plato intended his readers to recognize the argument as invalid; and (ii) Plato unintentionally misstated P5* as P5. (In any event, it is interesting to note that, whereas P3 but not P2 functions as a premise in the first argument, P2 but not P3 functions as a premise in the second argument.)