Frege's theorem

Frege's Theorem posits that every meaningful statement in arithmetic can be derived from basic logical principles and a few fundamental axioms. Essentially, it argues that the truths of mathematics are intrinsically linked to logical reasoning. By demonstrating that arithmetic can be reduced to logic, Frege challenges the notion of mathematics as a separate discipline, suggesting instead that it is grounded in purely logical structures. This idea has profound implications, influencing the philosophy of mathematics and our understanding of how logical thought underpins numerical concepts.