Friedrich Ludwig Gottlob Frege German logician, mathematician and philosopher Date of Birth: 08.11.1848 Country: Germany

Biography of Friedrich Ludwig Gottlob Frege

Friedrich Ludwig Gottlob Frege was a German logician, mathematician, and philosopher, known as a representative of the school of analytical philosophy. He was born in Germany, and his father was a school teacher who taught mathematics. Frege began his higher education at the University of Jena in 1869. Two years later, he moved to Göttingen, where he defended his dissertation in mathematics titled "Über eine geometrische Darstellung der imaginären Gebilde in der Ebene" (On a Geometric Representation of Imaginary Figures in the Plane) in 1873.

After defending his dissertation, Frege returned to Jena, where he wrote his habilitation thesis under the guidance of Abbe. The thesis was titled "Rechnungsmethoden, die sich auf eine Erweiterung des Größenbegriffes gründen" (Calculation Methods Based on an Extension of the Concept of Magnitude) and was completed in 1874. He then received a position as a privatdozent in 1875. In 1879, he became an extraordinary professor, and in 1896, he became an ordinary professor.

One of Frege's most well-known students was Rudolf Carnap, who later became a member of the Vienna Circle and authored important works in the philosophy of science. Despite all of Frege's children dying before reaching adulthood, he took in an adopted son in 1905. The popularization of his ideas by Carnap, Bertrand Russell, and Ludwig Wittgenstein made Frege well-known in certain circles in the 1930s.

In the English-speaking world, his works became widely known only after World War II, largely due to many logicians and philosophers, who considered Frege's legacy an important contribution to the development of philosophical thought (such as Rudolf Carnap, Kurt Gödel, and Alfred Tarski), being forced to emigrate to the United States. They contributed to the appearance of English translations of Frege's major works, which brought him widespread recognition.

Frege's contribution to logic is often compared to that of Aristotle, Kurt Gödel, and Alfred Tarski. His revolutionary work, "Begriffsschrift" (Concept Script) published in 1879, marked the beginning of a new era in the history of logic. In "Begriffsschrift," Frege reexamined several mathematical problems and provided a clear interpretation of the concepts of functions and variables. Essentially, he invented and axiomatized predicate logic, thanks to his discovery of quantifiers, the use of which gradually spread to all of mathematics and helped solve the medieval problem of multiple generality.

These achievements paved the way for Bertrand Russell's theory of descriptions and "Principia Mathematica" (written by Russell together with Alfred Whitehead), as well as the famous Gödel's incompleteness theorem. Frege introduced a distinction between the sense (German: Sinn) and reference (German: Bedeutung) of a concept denoted by a particular name, which is known as Frege's triangle or the semantic triangle: sign - sense - reference. In his system, the reference referred to the object domain associated with a certain name, while the sense referred to a specific aspect of considering this object domain.

For example, someone may know the names Mark Twain and Samuel Clemens without realizing that they refer to the same person because they "present him in different ways," which means that their senses are different.