Arithmetic and Logic

Arithmetic and logic are fundamental branches of mathematics and philosophy that deal with numbers and reasoning. Arithmetic focuses on the basic operations of numbers, like addition and multiplication. Logic, on the other hand, examines the rules of valid reasoning and argument structure. In proof theory, which studies mathematical proofs' structure and validity, arithmetic provides specific examples of mathematical statements, while logic establishes the principles that determine whether these statements are true. Together, they form the foundation for constructing mathematical arguments and understanding relationships between different concepts in a rigorous way.