Die Grundlagen der Arithmetik

In this seminal work, the author embarks on a meticulous examination of what it means to count. Written at a time when mathematics was turning toward ever tighter proofs, the text sets out to clarify the very notion of number itself. It treats the subject not merely as a collection of rules but as a philosophical problem demanding rigorous analysis.

The book surveys a wide range of questions: are the laws of arithmetic analytic truths or synthetic ones? Are they known a priori, or do they depend on experience? By engaging with thinkers such as Kant, Leibniz, Mill, and later logicians, the author critiques existing definitions of addition, the concept of unity, and the relationship between numbers and physical objects. Each chapter dissects a specific issue, from the validity of the equation 2 + 2 = 4 to the status of induction in arithmetic.

Readers will find a clear, step‑by‑step argumentation that exposes hidden assumptions and invites reflection on the foundations of everyday calculation. The careful historical references and logical precision make it a valuable guide for anyone curious about how numbers acquire their meaning beyond mere counting.