Philosophical Foundations of Law’s Relationship with Mathematics: Is Law Having Mathematical Certainty?

Mathematics is often given as an example of the precision and perfection of reasoning. The success achieved through the methods of mathematics has encouraged the use of mathematical techniques in various fields and among thinkers. In particular, the logical axioms, which are the indisputable truths about mathematical concepts, have been applied in the field of law with the success seen in the natural sciences. Logic has often served as a tool for law, helping it achieve its purpose. Lawyers use logical techniques to address deficiencies in legal practice. In this regard, logical techniques are considered to provide mathematical certainty in law. Positivists and natural law theorists approach mathematical certainty differently. While the positivist approach focuses on the purely axiomatic dimension of mathematics, the natural law perspective emphasizes the a priori domain. In this context, we discuss whether the synthetic a priori plane of mathematical propositions is valid for legal rules. By examining the historical development of logic and mathematics, this study explores their influence on the mathematical certainty of law and its relationship with legal concepts and the world of existence. This study also aims to evaluate the ontological domains of mathematics and law from a philosophical perspective. The main objectives of this study are to evaluate the ontological relationship between mathematics and law and to examine the extent to which mathematical precision can be applied in the field of law.