The Basic Laws of Arithmetic: Exposition of the System
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AlbakiReads Editorial Frege’s logical foundation for arithmetic
Frege’s logical foundation for arithmetic
Frege’s exposition sets out to derive arithmetic from pure logic, defining logical propositions and rules of inference before using them to establish arithmetic’s fundamental claims. It stands as a central historical document in logicism: the project of treating arithmetical truths as logical truths rather than empirical or synthetic principles. The system also brings questions of meaning and language into its logical framework, linking the work to later concerns in analytic philosophy. The edition translates key sections of the original work. Its underlying set-theoretical system was later shown to be inconsistent, a limitation that makes the volume especially useful for examining both the ambition and the difficulties of foundational programs in mathematics.
Good fit for readers who enjoy
- Students of the history and philosophy of mathematics
- Readers studying formal logic, inference, and logicism
- Researchers interested in the connections among logic, arithmetic, and language
Themes
LogicismFoundations of arithmeticFormal logicSet theoryMeaning and language
Based on publisher information and book metadata.
Book Overview Basic Laws of Arithmetic: Exposition of the System by Gottlob Frege is a seminal work that aims to establish arithmetic and mathematical ...
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 system's 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 to modern philosophical inquiries into meaning and language.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
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 system's 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 to modern philosophical inquiries into meaning and language.
This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1964.
Book Details Format: Paperback | Pages: 208 | Language: English | Publisher: UNIV OF CALIFORNIA PR | ISBN: 0520307992
FormatPaperback
Pages208
LanguageEnglish
ISBN0520307992
EAN9780520307995
PublisherUNIV OF CALIFORNIA PR
Edition1
AccessoriesNo Accessory
ConditionNew
Product TypeQUALITY PAPERBACK BOOKS
Weight0.6 Pounds
Length8.5 Inches
Width5.5 Inches
Height0.48 Inches
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