The <i>Zahl-Anzahl</i> Distinction in Gottlob Frege: Arithmetic of Natural Numbers with <i>Anzahl</i> as a Primitive Term

Abstract

The starting point is Peano’s expression of the axiomatics of natural numbers in the framework of Leśniewski’s elementary ontology. The author enriches elementary ontology with the so-called Frege’s predication scheme and goes on to propose the formulations of this axiomatic, in which the original natural number (N) term is replaced by the term Anzahl (A). The functor of the successor (S) is defined in it.

Keywords

• peano’s axiomatics of natural numbers
• leśniewski’s elementary ontology
• frege’s predication scheme
• frege’s <i>zahl-anzahl</i> distinction