The Church-Turing thesis is the view that all our various equivalent models of computability correctly capture the intuitive idea of what it means for a function to be computable. Thus, the thesis asserts that we have got the right model of computability. This is not a mathematical thesis, but a philosophical one. An important piece of evidence in favor of this view is that all the attempts at reifying the concept of computability have turned out to be equivalent to each other.
