ABSTRACT
The semantic operations attached to a formal system are functions of the mind which understands and correctly operates the system. Formalisation can be extended to hitherto unformalised semantic operations, but only if the resulting formal system can in its turn relies on yet unformalised semantic operations. The elimination of 'psychological elements' by formalisation thus remains necessarily incomplete. The purpose of formalisation lies in the reduction of informal functions to what philosophers believe to be more limited and obvious operations; but it must not aim at their elimination. A formalised deductive system is an instrument which requires for its logical completion a mind using the instrument in a manner not fully determined by the instrument; while the mind of the person using the instrument requires no such logical completion. Inter-personal dealings like listening to or addressing a person exclude the observing of one person's mental operations by the other in the sense in which mind one experimentally observes mind two.
