In his famous paper, Turing briefly describes his machine and then states (p. 232) (emphasis mine):
It is my contention that these operations include all those which are used in the computation of a number. The defence of this contention will be easier when the theory of the machines is familiar to the reader.
Does this mean that all numbers that could ever be computed by a machine or a human being can be computed by a Turing Machine?
If yes, what proof has Turing, beside "It is my contention"?
Does Turing defend this contention later on, in the same paper or elsewhere?