# Gottlob Frege > German philosopher, logician, and mathematician (1848–1925) **Wikidata**: [Q60028](https://www.wikidata.org/wiki/Q60028) **Wikipedia**: [English](https://en.wikipedia.org/wiki/Gottlob_Frege) **Source**: https://4ort.xyz/entity/gottlob-frege ## Summary Gottlob Frege was a German logician, mathematician, and philosopher who laid the groundwork for modern logic and analytic philosophy. He is best known for developing predicate logic, the theory of sense and reference, and for his foundational work in the philosophy of language and mathematics. --- ## Biography - Born: November 8, 1848, in Wismar, Germany - Nationality: German - Education: - Studied at the University of Jena (1869–1871) - Studied at the University of Göttingen (1871–1873) - Doctorate in mathematics from the University of Göttingen (1873) - Known for: Foundational work in logic, philosophy of language, and mathematics, including predicate logic and the theory of sense and reference - Employer(s): - University of Jena (1874–1918) as a professor of mathematics - Field(s): Logic, mathematics, philosophy of language, and analytic philosophy --- ## Contributions - **Begriffsschrift** (1879): Introduced the first formal system of predicate logic, revolutionizing logical analysis and laying the foundation for modern symbolic logic. - **The Foundations of Arithmetic** (1884): Explored the nature of numbers and arithmetic, arguing that arithmetic is reducible to logic. - **Sense and Reference** (1892): Introduced the distinction between sense (Sinn) and reference (Bedeutung), which became central to the philosophy of language. - **Frege's Theorem**: Demonstrated that the Peano axioms of arithmetic can be derived in second-order logic from Hume's Principle. - **Principle of Compositionality**: Established that the meaning of a complex expression is determined by the meanings of its parts and the way they are combined. - Influenced major philosophers and logicians including Bertrand Russell, Ludwig Wittgenstein, and Edmund Husserl. --- ## FAQs ### What is Gottlob Frege known for? Gottlob Frege is known for his foundational work in logic, mathematics, and the philosophy of language. He is credited with inventing predicate logic, developing the theory of sense and reference, and laying the groundwork for the logical analysis of language and mathematics. ### Where did Gottlob Frege study and work? Frege studied at the University of Jena and the University of Göttingen. He spent most of his academic career at the University of Jena, where he was employed as a professor of mathematics from 1874 to 1918. ### What are some of Gottlob Frege's most important works? His most important works include *Begriffsschrift* (1879), *The Foundations of Arithmetic* (1884), and the essay *Sense and Reference* (1892). These works laid the foundation for modern logic and the philosophy of language. ### What is Frege's Theorem? Frege's Theorem states that the Peano axioms of arithmetic can be derived in second-order logic from Hume's Principle, which posits that the number of Fs equals the number of Gs if and only if the Fs and Gs can be put into one-to-one correspondence. ### What is the theory of sense and reference? The theory of sense and reference distinguishes between the sense (Sinn) and reference (Bedeutung) of a linguistic expression. The sense is the mode of presentation of the reference, while the reference is the object or concept to which the expression refers. ### What is the principle of compositionality? The principle of compositionality states that the meaning of a complex expression is determined by the meanings of its parts and the way they are combined. This principle is central to Frege's approach to the philosophy of language. ### Who influenced Gottlob Frege? Frege was influenced by Bernard Bolzano, whose work on logic and mathematics preceded his own. Frege's work, in turn, influenced Bertrand Russell, Edmund Husserl, and Ludwig Wittgenstein, among others. ### What is the significance of *Begriffsschrift*? *Begriffsschrift* (Concept Script) is a landmark work in which Frege introduced the first formal system of predicate logic, fundamentally changing the field of logic and laying the groundwork for modern symbolic logic. ### What is the significance of *The Foundations of Arithmetic*? This work argued that arithmetic is reducible to logic, a revolutionary idea at the time. It aimed to show that mathematical truths could be derived from logical principles, influencing the development of logicism. ### What is the relationship between Frege's work and Russell's paradox? Russell's paradox revealed a contradiction in Frege's system of logic, specifically in the theory of sets. This led to significant revisions in the foundations of mathematics and logic, prompting Frege to acknowledge the paradox's impact on his work. --- ## Why They Matter Gottlob Frege's work fundamentally transformed logic, mathematics, and philosophy. His invention of predicate logic provided the tools for rigorous logical analysis, influencing the development of modern symbolic logic. His distinction between sense and reference became a cornerstone of the philosophy of language, impacting thinkers like Bertrand Russell and Ludwig Wittgenstein. Frege's logicist program, which aimed to reduce arithmetic to logic, laid the groundwork for the formal sciences. His ideas continue to influence contemporary debates in logic, philosophy of language, and cognitive science. ## Notable For - Inventing predicate logic in *Begriffsschrift* (1879) - Developing the theory of sense and reference in *Über Sinn und Bedeutung* (1892) - Authoring *The Foundations of Arithmetic* (1884), which argued for the logical foundation of arithmetic - Influencing major figures such as Bertrand Russell, Edmund Husserl, and Ludwig Wittgenstein - Formulating Frege's Theorem, which derives the Peano axioms from Hume's Principle - Establishing the principle of compositionality, which states that the meaning of a complex expression is determined by the meanings of its parts and the way they are combined - Being a member of the German Academy of Sciences Leopoldina - Being recognized as one of the founders of modern logic and analytic philosophy --- ## Body ### Early Life and Education Gottlob Frege was born on November 8, 1848, in Wismar, Germany. He pursued his higher education at the University of Jena from 1869 to 1871 and then at the University of Göttingen from 1871 to 1873, where he earned a doctorate in mathematics in 1873. His early academic focus was on mathematics and logic, which would become the foundation of his lifelong contributions to philosophy and science. ### Career Frege spent most of his academic career at the University of Jena, where he was employed as a professor of mathematics from 1874 until his retirement in 1918. His work at Jena was marked by groundbreaking contributions to logic and the philosophy of language. He was also a member of the German Academy of Sciences Leopoldina, reflecting his standing in the academic community. ### Publications and Theoretical Contributions Frege's major works include: - **Begriffsschrift** (1879): Introduced the first formal system of predicate logic, revolutionizing logical analysis. - **The Foundations of Arithmetic** (1884): Argued that arithmetic is reducible to logic, laying the groundwork for logicism. - **Sense and Reference** (1892): Distinguished between the sense (Sinn) and reference (Bedeutung) of linguistic expressions, influencing the philosophy of language. ### Influence and Legacy Frege's work profoundly influenced the development of modern logic, philosophy of language, and analytic philosophy. His ideas on sense and reference, predicate logic, and the reduction of arithmetic to logic shaped the work of later philosophers such as Bertrand Russell, Edmund Husserl, and Ludwig Wittgenstein. His contributions continue to be foundational in logic, mathematics, and cognitive science. ### Personal Life and Death Gottlob Frege passed away on July 26, 1925, in Bad Kleinen, Germany. His legacy endures through his revolutionary contributions to logic and philosophy, which remain central to contemporary debates in the field. ## References 1. Integrated Authority File 2. MacTutor History of Mathematics archive 3. BnF authorities 4. Mathematics Genealogy Project 5. [Source](https://www.google.cat/books?id=OjMZJCvRf8wC&pg=PA24) 6. International Standard Name Identifier 7. Open Library 8. CiNii Research 9. [Source](https://www.leopoldina.org/de/mitglieder/mitgliederverzeichnis/member/3299/) 10. Encyclopædia Britannica Online 11. SNAC 12. Brockhaus Enzyklopädie 13. Gran Enciclopèdia Catalana 14. Internet Philosophy Ontology project 15. Proleksis Encyclopedia 16. Croatian Encyclopedia 17. Freebase Data Dumps. 2013 18. Stanford Encyclopedia of Philosophy 19. Virtual International Authority File 20. CONOR.SI 21. Treccani's Enciclopedia on line 22. LIBRIS. 2012 23. Treccani Philosophy 24. National Library of Israel Names and Subjects Authority File 25. Bibliography of the History of the Czech Lands 26. Catalogo of the National Library of India