Syntactic reduction in Husserl’s early phenomenology of arithmetic

The paper traces the development and the role of syntactic reduction in Edmund Husserl’s (1856–1938) early writings on mathematics and logic, especially on arithmetic. The notion has its origin in Hermann Hankel’s (1839–1873) principle of permanence that Husserl set out to clarify. In Husserl’s early texts the emphasis of the reductions was meant to guarantee the consistency of the extended algorithm. Around the turn of the century Husserl uses the same idea in his conception of definiteness of what he calls “mathematical manifolds.” The paper argues that the notion anticipates the notion of reduction in term rewrite theory in computer science. The role of the reduction for Husserl is, however, primarily epistemological: its purpose is to impart clarity to (at least parts of) formal mathematics.