Grundgesetze Der Arithmetik. Anglais

The creator of modern logic was born in the Pomeranian town of Wismar. His father was headmaster at a school for young ladies, which Frege's mother took over after her husband's early death. Frege studied mathematics at the University of Jena. His studies were encouraged by Ernst Abbe, who encouraged him to obtain a doctorate at Gottingen and then helped him secure a position as lecturer at Jena in 1874. Although trained as a mathematician, Frege also studied with Lotze at Gottingen, and his work shows the influence of both Leibniz and Kant. After the publication in 1879 of Frege's first important work, the Begriffschrift (Conceptual Notation), he was promoted to professor, and he remained at the University of Jena the rest of his life. The Begriffschrift was the basis of his new system of logic, which he then sought to apply to the task of deriving number theory entirely from logic, via the theory of classes. This he did in The Foundations of Arithmetic (1884). The next decade saw several of Frege's other important papers on the philosophy of logic and language, including "Function and Concept" (1891), "Concept and Object" (1892), and "Sense and Reference" (1892). Frege was an extreme critic of "psychologism" in logic, mathematics, and philosophy of language---that is, of any view that attempts to treat logic or other sciences pursuing necessary truth as sciences whose subject matter is the actual functioning of the human mind as it can be empirically observed. His critique of psychologism had a far-reaching impact on philosophy in the twentieth century, strongly influencing the development not only of logical positivism and analytical philosophy in English-speaking countries, but also of neo-Kantianism and the phenomenological movement on the continent. After the publication of the Foundations, Frege became aware of certain deficiencies in the logical basis of his theory, which he attempted to remedy in his two-volume Fundamental Laws of Arithmetic (1893--1903). Shortly thereafter, Frege received a letter from Bertrand Russell, which pointed out a contradiction in his theory, since it allowed classes to include themselves as members. Take the class of all classes that are not members of themselves, Russell said; if you assume it is a member of itself, then it follows that it is not, and if you assume it is not, then it follows that it is. Frege attempted to evade the Russell Paradox in a hastily composed appendix, but it was ad hoc and has generally been viewed as unsuccessful. Even apart from this, he later became convinced that the whole project of founding mathematics on logic was doomed to failure.