German mathematician Friedrich Ludwig Gottlob Frege (1848 – 1925) was a prominent figure in the field of logic and philosophy, who worked at the University of Jena. Frege significantly reconceived the discipline of logic by constructing a formal system that, in effect, constituted the first predicate calculus.
To ground his views about the relationship of logic and mathematics, Frege conceived a comprehensive philosophy of language that many philosophers still find insightful, though recent scholarship suggests that Frege borrowed a significant number of elements in his philosophy of language from the Stoics. Moreover, his lifelong project of proving that mathematics could be reduced to logic was not successful.
Frege attended the local gymnasium for fifteen years and then went on to study at the University of Jena. At Jena, Frege attended lectures by Ernst Karl Abbe, who thereafter became his mentor and who had a significant impact on Frege’s life.
Frege transferred to the University of Göttingen in 1871 and received his doctorate two years later, in 1873. In mathematics, wrote a thesis entitled Über eine geometrytrische Darstellung der imaginären Gebilde in der Ebene (“On imaginary geometric representations in the plane”) under the supervision of Ernst Schering. Geometric representations of imaginary forms in the plane allow us to perceive a correlation between real and imaginary elements in the plane.
In 1874, Frege completed his Habilitationsschrift titled Rechnungsmethoden, die sich auf eine Erweiterung des Grössenbegriffes gründen (“Methods of calculation based on an extension of the concept of quantity”). After submitting this thesis, Abbe immediately led Frege to become a Privatdozent at the University of Jena. Over the next five years, Frege checked out texts in mechanics, analysis, geometry, Abelian functions, and elliptical functions from the University of Jena.
In 1879, Frege published his first book, Begriffsschrift, which is a formula language of pure thought that is modeled after that of arithmetic. He was subsequently promoted to an extraordinarius professor at Jena. Frege’s next significant work was his second book, Die Grundlagen der Arithmetik: a logical mathematical investigation of the concept of number, published in 1884. Frege begins this work by criticizing previous attempts to define the concept of number, and then offers his own analysis.
In the years 1891–1892, Frege gave more thought to the philosophy of language that would help ground his philosophy of mathematics. He published three of his most well-known papers in this period. “Function and Concept” (1891), “On Sense and Reference” (1892a), and “On Concept and Object” (1892b) are all highly regarded works.
In 1893, he published the first volume of a technical work previously mentioned. In 1896, he was promoted to an ordentlicher Honorarprofessor (regular honorary professor). Six years later (on June 16, 1902), as he was preparing the proofs of the second volume of the Grundgesetze, he received a letter from Bertrand Russell, informing him that one could derive a contradiction in the system he had developed in the first volume. Although Frege never recovered from the fatal flaw discovered, his work still has a significant impact on the field. His attempts to salvage the work by restricting Basic Law V were not successful.
In the last phase of his life, from 1917 to 1925, Frege published only the papers and developed some unpublished fragments of his philosophical works. Unfortunately, his final years saw him develop more than just political conservatism – his diary from a brief period in 1924 shows sympathies for fascism and anti-Semitism. He died on July 26, 1925, in Bad Kleinen, Mecklenburg-Vorpommern.
