  Standard expositions of Goedel's 1931 paper on undecidable arithmetical
propositions are based on two presumptions in Goedel's 1931 interpretation of
his own, formal, reasoning - one each in Theorem VI and in Theorem XI - which
do not meet Goedel's, explicitly stated, requirement of classically
constructive, and intuitionistically unobjectionable, reasoning. We see how
these objections can be addressed, and note some consequences.
