Professor R. L. Goodstein's neat proposal for formalising and proving the Policeman — the logical truth mentioned in my paper — illustrates the main thesis of that paper, viz., that in formalising the logic of indirect discourse one needs to avoid assigning what was said, and the report that it was said, to different levels of a semantical hierarchy. But there are two main difficulties in his proposal:

1. It is not quite clear whether the axioms and rules of Prof. Goodstein's system are to be such that substitutivity of the biconditional is maintained for all wff. If so, the system takes no account of the referentially opaque quality of indirect discourse. For example, the analogue for “If Sir Walter Scott always says the same as the author of Waverley, then George III says that anything Sir Walter Scott says is true if and only if George III says that anything the author of Waverley says is true” would be provable, though this statement is not logically true. If “A(x){Bx→x)” is well-formed (as it must be for Professor Goodstein's proof), the corresponding theorem is

2. In interpreting the letters “A”, “B”, etc. as operators, so that sentences are the substitution-instances both for variables like “x” and for schematic functions of those variables like “Ax”, Professor Goodstein's system does not provide for formalising logical truths in which ordinary predication also plays a part: e.g., “If the policeman says that all women are dangerous drivers and anything the policeman says is true, then no non-dangerous drivers are women”.