 Statements like (\ref{funassert}) would later be referred to by Hilbert &amp; Bernays (1934) (who provided the first textbook treatment of recursion) as verifiable in the sense that their individual instances can be verified computationally by replacing variables with concrete numerals. This is accomplished by what Skolem referred to as the “recursive mode of thought”. The sense of this phrase is clarified by the following properties of the system he describes: 