Termin liczba jako nazwa i jako funktor. Arytmetyka liczb naturalnych z liczbą-funktorem jako terminem pierwotnym

The distinction between number as a name and number as a functor alludes to the important Zahl-Anzahl distinction emphasised by Gottlob Frege. We start from Peano's expression of the axiomatics of natural numbers in the framework of Leśniewski's elementary ontology (OE). Next, we proceed to the enrichment of elementary ontology with Frege's predication scheme (OEsub) and propose such formulation of this axiomatics in which the primitive term natural number (N) is replaced by the term number-functor (A). The nominal constants natural number (N) and zero (0) as well as the functor of the successor (S) are defined here.