On the Interpretation of Church's Thesis
Abstract
Church's Thesis states the equivalence of computable functions and recursive functions. This can be interpreted as a definition, as an explanation, as an axiom, and as a proposition of mechanistic philosophy.
A number of arguments and objections, including a pair of counterexamples based on Gödel's Incompleteness Theorem, allow to conclude that Church's Thesis can be reasonably taken both as a definition and as an axiom, somewhat less convincingly as an explanation, but hardly as a mechanistic proposition.