The Basic Laws of Arithmetic : Exposition of the System
Saved in:
| Title: | The Basic Laws of Arithmetic : Exposition of the System |
|---|---|
| Description: | 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.Many titles in the Voices Revived program are also newly available as ebooks, offered at a discounted price to support wider access to scholarly work. |
| Authors: | Gottlob Frege, Montgomery Furth |
| Resource Type: | eBook. |
| Subjects: | Logic, Symbolic and mathematical |
| Categories: | MATHEMATICS / Arithmetic |
| Database: | eBook Collection (EBSCOhost) |
| FullText | Links: – Type: ebook-pdf – Type: ebook-epub Text: Availability: 0 |
|---|---|
| Header | DbId: nlebk DbLabel: eBook Collection (EBSCOhost) An: 3724816 RelevancyScore: 1110 AccessLevel: 6 PubType: eBook PubTypeId: ebook PreciseRelevancyScore: 1109.74133300781 |
| IllustrationInfo | |
| ImageInfo | – Size: thumb Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$3724816$PDF&s=r – Size: medium Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$3724816$PDF&s=d |
| Items | – Name: Title Label: Title Group: Ti Data: The Basic Laws of Arithmetic : Exposition of the System – Name: Abstract Label: Description Group: Ab Data: 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.Many titles in the Voices Revived program are also newly available as ebooks, offered at a discounted price to support wider access to scholarly work.</DIV – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Gottlob+Frege%22">Gottlob Frege</searchLink><br /><searchLink fieldCode="AR" term="%22Montgomery+Furth%22">Montgomery Furth</searchLink> – Name: TypePub Label: Resource Type Group: TypPub Data: eBook. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Logic%2C+Symbolic+and+mathematical%22">Logic, Symbolic and mathematical</searchLink> – Name: SubjectBISAC Label: Categories Group: Su Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Arithmetic%22">MATHEMATICS / Arithmetic</searchLink> |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=3724816 |
| RecordInfo | BibRecord: BibEntity: Classifications: – Code: 511.3 Scheme: ddc Type: prePub Languages: – Code: eng Text: English Subjects: – SubjectFull: Logic, Symbolic and mathematical Type: general Titles: – TitleFull: The Basic Laws of Arithmetic : Exposition of the System Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Gottlob Frege – PersonEntity: Name: NameFull: Montgomery Furth – PersonEntity: Name: NameFull: Gottlob Frege – PersonEntity: Name: NameFull: Montgomery Furth IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2022 – D: 05 M: 03 Type: profile Y: 2026 Identifiers: – Type: isbn-print Value: 9780520307995 – Type: isbn-print Value: 9780520359079 – Type: isbn-electronic Value: 9780520312364 Titles: – TitleFull: The Basic Laws of Arithmetic : Exposition of the System Type: main |
| ResultId | 1 |
