An example that gives credibility to this theory is Ackermann's function, which is mu-recursive but not primitive recursive.  
This concept was recently attacked by Mendelson, who used analogous concepts like Tarski's theorem and Weierstrass' theorem.  An example that gives credibility to this theory is Ackermann's function, which is mu-recursive but not primitive recursive.  In addition to recursiveness, another property required by this theory is lambda-definability.  Generally considered intrinsically unprovable, this thesis relies on the computability of a Turing machine.  FTP, identify this thesis that states any function regarded naturally as computable can be computed by a suitable Turing machine
This concept was recently attacked by Mendelson, who used analogous concepts like Tarski's theorem and Weierstrass' theorem.  
Church-Turing thesis