Friedrich Ludwig Gottlob Frege

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Friedrich Ludwig Gottlob Frege


German Mmathematician and Philosopher

Gottlob Frege, a philosopher of mathematics and a mathematician in the realm of philosophy, was the founder of modern mathematical logic and one of the most important figures in the histories of logic, mathematics, and the philosophy of mathematics. Frege also helped to shape the discipline of the philosophy of language and influenced, among others, Ludwig Wittgenstein (1889-1951) and J. L. Austin.

Frege was born November 8, 1848, in Wismar, Mecklenburg-Schwerin, in what is now eastern Germany. His father, Alexander Frege, a high school principal in Wismar, died when Gottlob was 18. Three years later, in 1869, Frege became a student at the University of Jena, but after two years went on to the University of Göttingen, where he studied mathematics, philosophy, and the physical sciences. In 1871 he returned to Jena to become a lecturer and was promoted first to associate professor in 1879, then to full professor of mathematics in 1896.

Though a stunning intellect, Frege's political and personal beliefs reflected a life of bitterness. He resented the outcome of the Treaty of Versailles—the peace treaty signed between the Allies and Germany after the First World War—and thought the terms imposed by the Allies crippling to his native Germany. As a result he came to despise democracy, socialism, Catholics, Jews, and the French—blaming all of them for Germany's post-war decline. The aloof professor also felt, well before the war, as if his intellectual peers overlooked the importance of his work, which he not immodestly considered to be both vital and innovative. He retired from teaching in 1917 not long after the death of his wife and died July 26, 1925, in Bad Kleinen, Germany.

Frege's major contribution to mathematical logic was made in Concept-Script (1879). In this work, he first came to the idea of a formal system, that is, a system that uses a quantifier-variable notation to make the language of proof regulated and unambiguous. Such a system, he thought, would render the logic behind proofs clearer than it appears in ordinary language and provide philosophers with an easily understood means for representing their arguments.

Arguing against Kant and Mill, Frege next tried to define the basic principles of arithmetic in purely logical terms, a project which he undertook in his deceptively simple work, The Foundations of Arithmetic (1884). Here he reasoned that if he could explain arithmetic without recourse to non-logical concepts, he would disprove Kant's notion that arithmetic is "synthetic;" put slightly differently, Frege wanted to show that the laws of arithmetic are a priori, meaning not subject to experience but derivable from deduction alone.

In The Foundations of Arithmetic, Frege also developed the idea that words only gain meaning when embedded in a context. This led in 1892 to his famous distinction between "sense" and "reference," the latter term representing the actual object about which a speaker is talking, the former the various names given to that object. The important point of this distinction is that sense and reference can be at variance with one another and can thus lead to confusion in statements about identity. For instance, the planet Venus was for centuries known as the "Morning Star" in the eastern sky but as the "Evening Star" in the western sky without any knowledge on the part of speakers that both words denoted the same celestial body. Ever since its articulation, this distinction between sense and reference has been a source of ongoing debate among philosophers, yet, as with many of Frege's ideas, its subsequently revealed imperfections have not necessarily lessened its lasting importance.