and Ullman 1979, pp. 146-147). In contrast, Theorems 3 and 4 contain no assumptions on the machine C but its capability to process an effective procedure P **according to Theorem 1. In particular, the effective procedure** P
and the machine C **are regarded as different entities. Thus, Theorems 3 and**
4 can be applied to any machine capable of processing the effective procedure P.

If one requires that a creative machine can execute any Turing machine it can compute any computable function and evaluate uncomputable functions as described in this paper.

One might ask whether the machine C **in Theorem 3 can be modeled**
by a Turing machine generating computable functions, say T**, into which an**
effective procedure P **according to Theorem 1 is incorporated. But according**
to Theorem 3 the machine C could apply P to T **to generate a computable** function that is not generated by T. Therefore, the Turing machine T **cannot** model the machine C**, that is, it cannot generate a computable function**
beyond the limits of any given Turing machine.

Turing [1936, p. 232] writes: "the motion of the machine ... is **completely**
determined by the configuration" which comprises a condition from a **"finite** number of conditions" and a "scanned symbol". The behavior of a creative machine cannot be completely determined in advance because it contains informal concepts such as computable functions which cannot be reduced to a finite description given in advance (see Theorems 3 and 4). But at any moment and at the most basic level the next "instruction" is completely determined by the present state of a creative machine, which can be regarded as a finite string of symbols or binary digits, and the input processed **by the**
creative machine.

Turing [1936, pp. 249-250] attempts to show that his machines can compute "all numbers which would naturally be regarded as computable" and supposes that the "number of states of mind" is finite. G¨odel **[1990b, p. 306]**
points out that "mental procedures" may "go beyond mechanical **procedures** ... mind, in its use, is not static, but constantly developing, i.e., that we understand abstract terms more and more precisely as we go on using them ... although at each stage the number and precision of the abstract **terms**
at our disposal may be finite, both (and, therefore, also Turing's number of distinguishable states of mind) may converge toward infinity in the course of the application of the [mental] procedure". The "abstract terms" refer to abstract concepts such as "a certain concept of computable function" (G¨odel 1990a, p. 271) and "the use of abstract terms on the basis of their meaning"