  Turing's oracle can be seen simply as a mathematical tool, useful for exploring the mathematics of the uncomputable. The idea of an oracle allows the formulation of questions of relative rather than absolute computability. Thus Turing opened new fields of investigation in mathematical logic. However, there is also a possible interpretation in terms of human cognitive capacity. On this interpretation, the oracle is related to the ‘intuition’ involved in seeing the truth of a Gödel statement. M. H. A. Newman, who introduced Turing to mathematical logic and continued to collaborate with him, wrote in (Newman 1955) that the oracle resembles a mathematician ‘having an idea’, as opposed to using a mechanical method. However, Turing's oracle cannot actually be identified with a human mental faculty. It is too powerful: it immediately supplies the answer as to whether any given Turing machine is ‘satisfactory,’ something no human being could do. On the other hand, anyone hoping to see mental ‘intuition’ captured completely by an oracle, must face the difficulty that Turing showed how his argument for the incompleteness of Turing machines could be applied with equal force to oracle-machines (Turing 1939, p. 173). This point has been emphasised by Penrose (1994, p. 380). Newman's comment might better be taken to refer to the different oracle suggested later on (Turing 1939, p. 200), which has the property of recognising ‘ordinal formulae.’ One can only safely say that Turing's interest at this time in uncomputable operations appears in the general setting of studying the mental ‘intuition’ of truths which are not established by following mechanical processes (Turing 1939, p. 214ff.).