The Basic Laws of Arithmetic: Exposition of the System

Gottlob Frege's Basic Laws of Arithmetic is a foundational work in the history of mathematical and philosophical thought, which aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Despite its failure due to inconsistency in its underlying set theory, the work remains influential in formal logic, language philosophy, and reasoning standards. UC Press's Voices Revived program makes this important work accessible again with a new translation.

Format: Hardback
Length: 208 pages
Publication date: 13 May 2022
Publisher: University of California Press

Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical analysis as logical systems derived from pure logic. Published in 1893, it represents a cornerstone in the history of mathematical and philosophical thought. Frege's primary objective was to substantiate logicism, the view that truths of arithmetic are not irreducibly mathematical, synthetic a priori, or empirical, but are instead expressions of logical truths. The book lays out three core tasks: defining logical propositions and rules of inference, and deriving arithmetic's fundamental truths from these logical principles. While Frege's meticulous approach to these tasks helped establish mathematical logic as a discipline, his work ultimately failed to achieve its purpose, as the set theory underpinning his system proved inconsistent, a flaw brought to his attention by Bertrand Russell. Despite its failure as Frege envisioned it, the work remains profoundly influential. Frege's exploration of logical truth and inference pioneered formal logic, including propositional calculus, quantification theory, and set theory. His philosophy of language, embedded within the systems semantics, offers a deep and nuanced understanding of meaning that continues to resonate within analytical philosophy. Moreover, Frege's precise and rigorous standards of reasoning surpass many subsequent works, including the more widely adopted Principia Mathematica. Although his logicism is untenable in its original form, Frege's ideas remain a vital resource for understanding the intersection of logic, mathematics, and language, making his Grundgesetze a crucial study for philosophers, logicians, and historians. This translation of key sections emphasizes its ongoing relevance.

Weight: 408g
Dimension: 216 x 140 x 15 (mm)
ISBN-13: 9780520359079