The notion of ?-definability is due jointly to the present author and S . C . Kleene, successive steps towards it having been taken by the present author in the " Annals of Mathematics ", vol . 34 ( 1933 ), p . 863, and Kleene in the " American Journal of Mathematics ", vol . 57 ( 1935 ), p . 219 . The notion of recursiveness in the sense of ? below is due jointly to Jacques Herbrand and Kurt G�del, as is there explained.
12.
:" Rather, G�del obtained his definition [ of the class of general recursive functions ] through modification of Herbrand's ideas . . .; and Wilfried Sieg has argued that his real purpose in the final section of the 1934 paper [ the lecture notes ] was " " to disassociate recursive functions from [ Herbrand's ] epistemologically restricted notion of proof " " by specifying " " mechanical " rules for deriving equations . " What was more " general " about G�del's notion of " general " recursiveness was, Sieg suggests, that Herbrand had intended only to characterize those functions that could be " proved " to be recursive by " finitary " means [ 250 ] ."
