Frege, Gottlob (1848–1925)

Life and Work

F. L. Gottlob Frege was born on November 8, 1848, in Wismar, northern Germany, in the state of Mecklenburg. He was the son of Alexander Frege, the principal of a private high school in Wismar. It is probable that the influence of his teacher at the local gymnasium, Leo Sachse, motivated Frege to study after school. Subsequently he enrolled as a student in mathematics, chemistry, physics, and philosophy; first from 18 69 to 1871 at the University of Jena under the encouragement of the famous physicists Ernst Abbe and Karl Snell; next he expanded his studies for 2 more years at Gttingen University, where he eventually obtained a doctoral degree in 1873 with the valued geometrical thesis translated as On a Geometrical Representation of Imaginary Figures in a Plane. Just one year later, Frege received his second doctorate (habilitation) for his work Methods of Calculation Based Upon an Amplification of the Concept of Magnitude, comprehending some initial steps of his theory of higher (complex) mathematical functions.

Also in the year 1874, upon recommendation of his academic teacher Abbe, Frege became a lecturer in mathematics at the University of Jena, where he would remain all his professional life. He taught extensively in all mathematical disciplines. His research, however, concentrated on the philosophy of logic. Persistent dialoguenoteworthy because Frege was extremely reserved in generalwith his Jena colleague and one of his few friends Rudolf Eucken, later a winner of the Nobel Prize in literature, supported Frege's philosophically mathematic thinking.

[Page 551]In 1879, Frege's seminal first work Concept Script, a Formal Language of Pure Thought Modelled Upon That of Arithmetic (Begriffsschrift) was published. He developed a principle for the construction of a logical language. In the aftermath of the Begriffsschrift, Frege was made associate professor at Jena University. Frege married Margarete Lieseberg, but unfortunately neither of their two children survived into adulthood, so they adopted a boy named Alfred.

Frege's book The Foundations of Arithmetic (Grundlagen) appeared in 1884. It comprised for the first time a complete system for the foundation of arithmetic based on a set of mathematically logical axioms. To gain higher recognition for his work, this book was written in completely nontechnical, natural language.

In conjunction with his profound research into the logical system of mathematics, Frege felt impelled to develop a philosophy of language. His major work on a linguistic system supporting the philosophy of logic is On Sense and Reference (1892). In this book, Frege's two famous linguistic puzzles were presented, distinguishing between sense and the denotation of terms in order to resolve the ambiguities of language.

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