 Following the doctrine of types, we must replace ‘all propositions’ by ‘all propositions of order \(n\)’ for a given \(n\). Hence the Liar sentence becomes “it is not true of all propositions \(p\) of order \(n\), that if I affirm \(p, p\) is true”, which is a proposition of order \(n + 1\). Then the Liar is simply false rather than contradictory; and this solves the paradox. Similar arguments solve the other paradoxes.