Can the logic of indirect discourse be formalised?

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Abstract
Recent attempts to analyse or explicate assertion-statements and other kinds of indirect discourse in formal terms seem to have overlooked an even greater difficulty than the familiar problems arising about equivalence, synonymy, translatability, etc. This difficulty is created by the fact that in judicial, journalistic, or historical fact-finding, as well as in everyday conversation, we frequently cite statements about a witness's truthfulness alongside the report of his testimony as the premisses from which we argue about the facts. It is then an essential part of our argument that it should appear to jump from one level of statement to another, and perhaps back again. So that the difficulty emerges: how can the formalisation of such an argument adopt any of the usual hierarchy-principles as a guarantee against semantical antinomies? Consider, for example, If the policeman testifies that anything, which the prisoner deposes, is false, and the prisoner deposes that something, which the policeman testifies, is true, then something, which the policeman testifies, is false and something, which the prisoner deposes, is true.

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