  In this paper, we argue that formal systems of first order Arithmetic that
admit Goedelian undecidable propositions validly are abnormally
non-constructive.
  We argue that, in such systems, the strong representation of primitive
recursive predicates admits abnormally non-constructive, Platonistic, elements
into the formal system that are not reflected in the predicates which they are
intended to formalise.
  We argue that the source of such abnormal Platonistic elements in these
systems is the non-constructive Generalisation rule of inference of first order
logic.
  We argue that, in most simply consistent systems that faithfully formalise
intuitive Arithmetic, we cannot infer from Goedel's reasoning the Platonistic
existence of abnormally non-constructive propositions that are formally
undecidable, but true under every interpretation.
  We define a constructive formal system of Peano's Arithmetic, omega2-PA,
whose axioms are identical to the axioms of standard Peano's Arithmetic PA, but
lead to significantly different logical consequences.
  We thus argue that the formal undecidability of true Arithmetical
propositions is a characteristic not of relations that are Platonistically
inherent in any Arithmetic of the natural numbers, but of the particular
formalisation chosen to represent them.
