Ludwig Wittgenstein was born in 1889 into one of the richest families in Austria. His father was a self-made man and a steel magnate. Ludwig was the youngest of eight children and grew up in a very musical family. His brother Paul had a successful career as a concert pianist even after losing his right arm in the First World War. As a child, Ludwig was not an exceptional student, and he was sent to a technical school in the hope that he would learn engineering and follow his father in the family business. For one year, he was a pupil at the same school as a younger boy named Adolf Hitler.

Wittgenstein developed an interest in the nascent field of aeronautics and went to the University of Manchester to study aeronautical engineering. While he was there, he became increasingly preoccupied by mathematical and philosophical questions. Understanding that the highest authority on these questions at the time was Bertrand Russell, Wittgenstein impulsively traveled to Cambridge in 1911 and requested that Russell take him on as a student. Russell was hesitant at first but was soon impressed by Wittgenstein’s intelligence. Within a year, the roles were reversed, and Russell was looking up to the young Wittgenstein as the greatest hope for the field of logic.

Wittgenstein’s work on logic was interrupted by the First World War. Wittgenstein enlisted in the Austro-Hungarian army and served on the eastern front. Driven by a desire to face his own mortality, he constantly requested the most dangerous assignments and was twice decorated for bravery. While in the trenches of the eastern front, Wittgenstein completed his Tractatus Logico-Philosophicus, which he believed solved all the problems of logic and philosophy. After the war, Wittgenstein gave his large fortune away to his siblings and, satisfied that he had nothing more to offer philosophy, took a position as a schoolteacher in the mountains of rural Austria. Gradually, he became convinced that the Tractatus was flawed and that he had more to contribute to philosophy, and by 1929 he found himself back at Cambridge.

For nearly twenty years, Wittgenstein taught on and off at Cambridge, never entirely happy with his role as philosopher but unable to abandon his calling. He was known for his severity and his unusual teaching style, and he persuaded many of his brightest students to abandon philosophy for more practical pursuits. During these years, he kept extensive notebooks outlining his thoughts. The only notes he deemed fit for publication are the 120-odd pages that make up the first part of the Philosophical Investigations, but many of his other notebooks have survived and have been published. Wittgenstein requested that none of his work be published during his lifetime. He died of cancer in 1951, and the Investigations were published in 1953.

The Vienna of Wittgenstein’s youth was a place of tremendous decline and reinvention. On one hand, Vienna was the seat of the declining Habsburg Empire, whose internal conflicts were among the leading causes of the First World War. On the other hand, the decline of the old order led to tremendous intellectual and artistic innovation, as the Viennese struggled to build a new order. Turn-of-the-century Vienna was the birthplace of psychoanalysis with Freud, of modern music with Schönberg, and of modern architecture with Adolf Loos, and it was home to such innovative artists as Gustav Klimt and Egon Schiele. One would not be remiss in identifying Wittgenstein’s revolutionary work in the Tractatus as a further manifestation of the innovative spirit of early twentieth-century Vienna.

Wittgenstein’s adult life spanned the first half of the twentieth century, a time of great upheaval for Europe. Just as the modern age seemed to be promising a future of prosperity and material comfort for all, two world wars ripped Europe apart and permanently ended its preeminent position on the world stage. Austria was hit harder than most of Europe. At the beginning of the century, Austria was a vast empire covering much of central and eastern Europe. After the First World War, it was reduced to its present diminished size, and in the Second World War it became a willing pawn of the Nazi Reich. Wittgenstein’s family was half Jewish, and they had to forfeit much of their great wealth to buy their safety from the Nazis.

Wittgenstein was brought into philosophy by Bertrand Russell, who was one of the founders of the analytic movement in philosophy. Russell and Gottlob Frege were the two foremost figures in a movement that brought advances in the field of mathematical logic to bear on philosophical questions. They found that logical analysis could reveal the deep structure of language, which could in turn expose the source of much philosophical confusion. Russell and Frege shared what is known as a universalist conception of logic. They believed logic to be the most fundamental set of laws: while the laws of physics govern physical phenomena and the laws of grammar govern grammatical phenomena, the laws of logic are supremely universal and govern all phenomena. Exploring and codifying the laws of logic, then, is a supremely important activity.

Wittgenstein’s Tractatus is largely a response to the work of Frege and Russell, and it is impossible to appreciate it fully without a strong grasp of the work of those two philosophers. By contrast, the Philosophical Investigations are interesting precisely in the way that they do not seem to fit into any particular context. In the Investigations, Wittgenstein is concerned primarily with the very impulse to think philosophically more than he is with any particular philosophical views. Nevertheless, we find in the Investigations a preoccupation with language, and we can see the enduring influence of Frege and Russell in Wittgenstein’s conviction that a proper understanding of language will expose the hidden flaws in philosophical reasoning.