The Ancestral

Abstract

Frege’s Begriffsschrift heralded the thesis that logic is informative. To demonstrate its informativity, Frege showed how to formulate the notion of the ancestral relation within ^cpLogic alone,without aid of any non-logical intuitions of sequence. The ancestral is the key to the notion of mathematical induction — something Kant thought could only be explained by abductively hypothesizing that the mind imposes on the data of sense a consecutive temporal ordering. This structuring, he held, is the foundation of our grasp of the consecutive series of natu­ral numbers. Frege objected to Kant’s theory. In showing that induction is part of pure logic, Frege’s work was the first step in his demonstration that no distinctly non-logical intuitions are needed in arithmetic.