In Search of the Roots of Formal Computation

摘要

In a culmination of a long development, it was seen clearly in the early 1930s that steps of formal computation are also steps of formal deduction as defined by recursion equations and other similar principles of arithmetic. Followers of Kant's doctrine of the synthetic a priori in arithmetic missed by a hair's breadth the proper recursive definition of addition that appeared instead first in a book of Hermann Grassmann of 1861. A line can be followed from it to Hankel, Schroder, Dedekind, Peano, and Skolem, the last mentioned marking the birth of recursive arithmetic, a discipline firmly anchored in the foundations of mathematics by the presentation Paul Bernays made of it in his monument, the Grundlagen der Mathematik of 1934.