and whose value for any given formula. Advances in Mathematics, 39, 215-239. The notion of algorithm, computation, a step-by-step procedure or a defined method to perform calculations has been used informally and intuitively in mathematics for centuries. Copeland,.J., Proudfoot,. If attention is restricted to functions of positive integers then Church's thesis and Turing's thesis are equivalent, in view of the previously mentioned results by Church, Kleene and Turing. Lecture notes taken by Kleene and Rosser at the Institute for Advanced Study.
The narrow version of thesis M is an empirical proposition whose truth-value is unknown. American Behavioral Scientist, 40, 690-716. The above-mentioned evidence for the Turing-Church thesis is not also evidence for Thesis. Perhaps the fullest survey is to be found in chapters 12 facisng histroy togther unused essays and 13 of Kleene (1952). Scientific American, 280 (April 76-81. Church used the (informal) expression 'effectively calculable' to indicate that there is an effective method for calculating the values of the function. Statements that there is an effective method for achieving such-and-such a result are commonly expressed by saying that there is an effective method for obtaining the values of such-and-such a mathematical function.