Basic Laws of Arithmetic
{"WorkMasterId":5908,"WpPageId":275816,"ParentWpPageId":193828,"Slug":"basic-laws-of-arithmetic","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/gottlob-frege/basic-laws-of-arithmetic/","RelativeUrl":"theos/humanities/philosophy/philosophers/gottlob-frege/basic-laws-of-arithmetic/","HasFullText":false,"RawHtmlLength":68441,"CleanHtmlLength":15187,"Kicker":"Philosophy Work","Title":"Basic Laws of Arithmetic","Deck":"Frege attempts a rigorous logicist derivation of arithmetic in his mature formal system, centered on logical laws, value-ranges, and Basic Law V.","BackLink":{"Text":"Back to Gottlob Frege","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/gottlob-frege/"},"AuthorCard":{"Label":"Author","Title":"Gottlob Frege","Url":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/gottlob-frege/","MediaHref":"","ImageSrc":"https://chrisdeasy.com/wp-content/uploads/gottlob-frege-01-frege-c-1879.jpg","ImageAlt":"Gottlob Frege, c. 1879","FilterTerra":"Western Europe","ClickText":"Gottlob Frege","ClickHref":"https://chrisdeasy.com/theos/humanities/philosophy/philosophers/gottlob-frege/","Copies":["1848 CE – 1925 CE","Wismar","German logician, mathematician, and philosopher whose concept-script, modern quantificational logic, logicism, sense-reference distinction, concept-object analysis, and anti-psychologism helped launch analytic philosophy and reshape logic, language, mathematics, and truth."]},"ContextCards":[{"Label":"Period","Key":"Period:4","Title":"Modern History","DateText":"1800 CE – 1944 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-modern-history/"},{"Label":"Era","Key":"Era:11","Title":"Long 19th Century","DateText":"1870 CE – 1913 CE","Url":"https://chrisdeasy.com/theos/humanities/philosophy/eras-of-thought/philosophers-of-modern-history/philosophers-of-the-long-19th-century/"},{"Label":"Composition","Title":"1893 CE","Url":"","DateText":""}],"DateNote":"Displayed year written/published is 1893 for volume I; the Date Note records volume II in 1903.","GeoCards":[{"Label":"Region","Key":"Region:1"},{"Label":"Terra Avita","Key":"TerraAvita:1"},{"Label":"Terra Avita Region","Key":"TerraAvitaRegion:3"},{"Label":"Modern Country","Key":"Country:DEU:1"}],"OriginalTitle":"Grundgesetze der Arithmetik","Language":"German","DisciplineCards":[{"Label":"Primary Discipline","Key":"Discipline:logic"},{"Label":"Secondary Discipline","Key":"Discipline:philosophy-of-science"}],"Tradition":"Modern logic / analytic philosophy / philosophy of mathematics","FullText":null,"CoreThesis":["Frege attempts a rigorous logicist derivation of arithmetic in his mature formal system, centered on logical laws, value-ranges, and Basic Law V."],"Classification":{"AlternateTitles":"Basic Laws of Arithmetic; Grundgesetze der Arithmetik I-II; Basic Laws of Arithmetic, derived using concept-script","KeyConcepts":"logicism; Basic Law V; value-ranges; extensions; arithmetic; proof; concept-script; Frege\u0027s theorem; Russell\u0027s paradox; formal system; numbers; functions","Methodology":"Axiomatic formal system, derivation, symbolic proof, explicit definitions, and foundational reconstruction of arithmetic.","Structure":"A two-volume work published in 1893 and 1903; SQL stores the opening publication year while Date Note records the two-volume publication history."},"Arguments":["Frege attempts a rigorous logicist derivation of arithmetic in his mature formal system, centered on logical laws, value-ranges, and Basic Law V."],"Influence":{"InfluencedBy":"Leibniz, Kant, Bernard Bolzano, Hermann Lotze, Ernst Abbe, German mathematical training, nineteenth-century logic, arithmetic foundations, and anti-psychologism.","InfluenceOn":""},"Significance":["Accepted as Frege\u0027s mature logicist system and the setting of Russell\u0027s paradox.","Central for philosophy of mathematics, abstraction principles, formal systems, set-theoretic paradoxes, type theory, and the history of logic."],"EvidenceNote":["Approved direct work. 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