ABSTRACT
The statement that every computable function is recursive is known as Church's Thesis. It was proposed by Church about 1934 and has since come to be accepted by almost all logicians. Since the notion of a computable function has not been defined precisely, it may seem that it is impossible to give a proof of Church's Thesis. This chapter tries to give arguments for Church's Thesis which seem to be convincing. The first argument is that all the computable functions which have been produced have been shown to be recursive, using, for the most part. Another argument comes from various attempts to define computable precisely. The Church's Thesis is used in two ways. First, there are many natural and interesting questions about computable functions. One of the best ways to convince oneself of Church's Thesis is to examine many such examples and see that in every case the function turns out to be recursive.
