 Suppose that a stable reflexive reasoner of type 4 believes that they are stable.We will show that they will (sooner or later) believe every proposition formula_16 (and hence be inconsistent).Take any proposition formula_11 The reasoner believes formula_69 hence by Löb's theorem they will believe formula_23 (because they believe formula_71 where formula_72 is the proposition formula_73 and so they will believe formula_74 which is the proposition formula_23).