 Such expressions can be operated on concretely by adjoining or removing strokes in a manner which mirrors the arithmetical operations of successor and predecessor which figure in Skolem’s “recursive mode of thought“. This observation in turn informed Hilbert’s explanation of the meaning of functional assertions like (\ref{funassert}) in terms of their logical derivability from recursive definitions which also serve as procedures for computing the values of functions they define  (Hilbert 1920, 54–57).