  We show that the classical interpretations of Tarski's inductive definitions
actually allow us to define the satisfaction and truth of the quantified
formulas of the first-order Peano Arithmetic PA over the domain N of the
natural numbers in two essentially different ways: (a) in terms of algorithmic
verifiabilty; and (b) in terms of algorithmic computability. We show that the
classical Standard interpretation I_PA(N, Standard) of PA essentially defines
the satisfaction and truth of the formulas of the first-order Peano Arithmetic
PA in terms of algorithmic verifiability. It is accepted that this classical
interpretation---in terms of algorithmic verifiabilty---cannot lay claim to be
finitary; it does not lead to a finitary justification of the Axiom Schema of
Finite Induction of PA from which we may conclude---in an intuitionistically
unobjectionable manner---that PA is consistent. We now show that the
PA-axioms---including the Axiom Schema of Finite Induction---are, however,
algorithmically computable finitarily as satisfied / true under the Standard
interpretation I_PA(N, Standard) of PA; and that the PA rules of inference do
preserve algorithmically computable satisfiability / truth finitarily under the
Standard interpretation I_PA(N, Standard). We conclude that the algorithmically
computable PA-formulas can provide a finitary interpretation I_PA(N,
Algorithmic) of PA from which we may classically conclude that PA is consistent
in an intuitionistically unobjectionable manner. We define this interpretation,
and show that if the associated logic is interpreted finitarily then (i) PA is
categorical and (ii) Goedel's Theorem VI holds vacuously in PA since PA is
consistent but not omega-consistent.
