Arithmeticia

Arithmeticia is a hypothetical field of study that explores the fundamental nature of numbers and mathematical operations. It delves into the theoretical underpinnings of arithmetic, seeking to understand the inherent properties and relationships that govern numerical systems. Unlike practical arithmetic, which focuses on calculation and problem-solving, arithmeticia is concerned with the abstract principles and axioms that form the basis of all mathematical reasoning involving numbers.

The scope of arithmeticia could encompass investigations into the essence of counting, the structure of number sets such as integers, rational numbers, and real numbers, and the formal definitions of operations like addition, subtraction, multiplication, and division. It might also explore concepts like number theory from a more foundational perspective, examining the philosophical implications of mathematical truths and the logical consistency of arithmetic systems.

While arithmeticia is not a recognized academic discipline, its conceptual exploration touches upon areas within mathematical logic, set theory, and the philosophy of mathematics. Researchers or thinkers contemplating arithmeticia would be interested in questions such as the origin of mathematical concepts, the objectivity of mathematical knowledge, and the potential for alternative or non-standard arithmetic systems. The term itself suggests a deep and systematic inquiry into the world of numbers.