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Ludwig Wittgenstein was born in Vienna in 1889 and died in Cambridge in 1951. He studied engineering, first in Berlin and then in Manchester, and he soon began to ask himself philosophical questions about the foundations of mathematics. What are numbers? What sort of truth does a mathematical equation possess? What is the force of proof in pure mathematics? In order to find the answers to such questions, he went to Cambridge in 1911 to work with Russell, who had just produced in collaboration with Whitehead (1861-1947) Principia Mathematica (1910-1913), a monumental treatise which bases mathematics on logic. But on what is logic based? Wittgenstein's attempt to answer this question convinced Russell that he was a genius. During the 1914-8 war he served in the Austrian army and in spare moments continued the work on the foundations of logic which he had begun in 1912. His war-time journal, Notebook s 1914-16 (1961), reveals the development of his ideas more clearly that the final version, Tractatus Logico- Philosophicus, which he published in the early 1920s
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