Abstract:
Dedekind’s influence on the development of mathematics in 20th century is deep. For Dedekind the arithmetic is based on the laws of thought, i.e. the foundation of arithmetic is the laws of thought. The foundations of mathematics and arithmetic are 1. an object (Ding); 2. a set (system); 3. a function (Abbildung).
He considers the arithmetic as a part of logic. Can we say that Dedekind’s theory is a variant of traditional logicism? Can we say that Dedekind is logicist and his theory is close to Frege’s or Russel’s logicism? The aim of my talk is to consider these questions.
