 Another attempt to salvage a part of Hilbert’s program was made by Isaacson (Isaacson 1987). He defends the view that in some sense, Peano Arithmetic may be complete after all (Isaacson 1987). He argues that true sentences undecidable in Peano Arithmetic can only be proved by means of higher-order concepts. For instance, the consistency of Peano Arithmetic can be proved by induction up to a transfinite ordinal number (Gentzen 1938). But the notion of an ordinal number is a set-theoretic, and hence non-arithmetical, concept. If the only ways of proving the consistency of arithmetic make essential use of notions which arguably belong to higher-order mathematics, then the consistency of arithmetic, even though it can be expressed in the language of Peano Arithmetic, is a non-arithmetical problem. And generalizing from this, one can wonder whether Hilbert’s conjecture that every problem of arithmetic can be decided from the axioms of Peano Arithmetic might not still be true.