Empirical evidence for it comes in part from the fact that several independent attempts at formalization, such as Post's tag-systems and the lambda calculus, give rise to exactly the same class of functions.  
It is not susceptible to proof, as it is a claim that an ill-defined but intuitively understood concept is equivalent to a well-defined mathematical abstraction.  Empirical evidence for it comes in part from the fact that several independent attempts at formalization, such as Post's tag-systems and the lambda calculus, give rise to exactly the same class of functions.  FTP, name this statement, of fundamental importance to computability theory, which states that the concept of "algorithm" is exactly captured by the Turing machine.
It is not susceptible to proof, as it is a claim that an ill-defined but intuitively understood concept is equivalent to a well-defined mathematical abstraction.  
{Church's} thesis or {Church}-Turing thesis