Frege's Deductive System in Basic Laws of Arithmetic

This study offers a critical analytical study of Gottlob Frege's deductive system as presented in Basic Laws of Arithmetic. Frege's project aimed to derive the entirety of arithmetic from purely logical axioms through a rigorously constructed symbolic language, first introduced in Begriffsschrift and later refined in the Basic Laws of Arithmetic. The research highlights the essential features of Frege's system—consistency, completeness, and rigor—while examining its symbolic apparatus, primitive notions, definitions, axioms, and rules of inference. Special emphasis is placed on Axiom V, which, while central to Frege's logicist program, ultimately led to the system's collapse due to Russell's paradox. Nevertheless, Frege's effort remains a landmark intellectual and methodological achievement, transforming logic from a tool of Aristotelian syllogism into a symbolic science comparable in precision to mathematics.In conclusion, the paper argues that Frege's deductive system should be regarded not only as the first formal deductive system in modern logic but also as a philosophical and epistemological project seeking to establish logic as the ultimate foundation of mathematical truth. Accordingly, Frege's work continues to serve as both a historical turning point and an enduring source of inspiration for contemporary logical and mathematical thought.