 As is clear, strictly speaking, Turing’s thesis is not provable, since, in its original form, it is a claim about the relationship between a formal and a vague or intuitive concept. By consequence, many consider it as a thesis or a definition. The thesis would be refuted if one would be able to provide an intuitively acceptable effective procedure for a task that is not Turing-computable. This far, no such counterexample has been found. Other independently defined notions of computability based on alternative foundations, such as  recursive functions  and abacus machines have also been shown to be equivalent to Turing computability. These equivalences between quite different formulations indicate that there is a natural and robust notion of computability underlying our understanding. Given this apparent robustness of our notion of computability, some have proposed to avoid the notion of a thesis altogether and instead propose a set of axioms used to sharpen the informal notion. There are several approaches, most notably, an approach of structural axiomatization where computability itself is axiomatized (Sieg 2008) and one whereby an axiomatization is given from which the Church-Turing thesis can be derived (Dershowitz &amp; Gurevich 2008).