Ludwig Wittgenstein (1889–1951) was born into one of the richest families of turn-of-the-century Vienna. His father had made a fortune from engineering enterprises, and the family entertained such artists as Brahms, Mahler, and Gustav Klimt. Wittgenstein was not an exceptional student, but did well enough in school to pursue studies in aeronautical engineering at the University of Manchester. His study of engineering quickly led him to an interest in the mathematics that underlie engineering, and then to an interest in the philosophy that underlies mathematics.
On the recommendation of Gottlob Frege, in 1911 Wittgenstein went to study with Bertrand Russell, one of the leading philosophers of the day. The roles of teacher and pupil were soon reversed, and Wittgenstein's first contribution to philosophy, the 1913 "Notes on Logic," was dictated to Russell.
Wittgenstein's intensive studies were interrupted by the onset of the ##First World War##. Wittgenstein signed up with the Austrian army, and constantly requested placement in the most dangerous places, for he had a morbid desire to confront death. During this time, Wittgenstein worked intensively on fundamental problems in the philosophy of logic. He ultimately applied his conclusions to the nature of language, reality, and ethics, among other topics. By the end of the war, he had completed a draft of his Logisch-Philosophische Abhandlung, which was first published in 1921 and translated into English in 1922 as Tractatus Logico-Philosophicus. Before the war ended, however, Wittgenstein was taken prisoner by the Italians. He had to mail his manuscript to Russell from a prisoner-of-war camp.
After the publication of the Tractatus, Wittgenstein felt he had nothing more to contribute to philosophy. He spent the 1920s in a variety of positions, working as a schoolteacher in a small Austrian village, as a gardener, and as an amateur architect. During this time, he still had some connection with the philosophical world, notably in his conversations with Frank Ramsey on the Tractatus that gradually led Wittgenstein to recognize that this work was flawed in a number of respects. In the late twenties, Wittgenstein also came into contact with the Vienna Circle of logical positivists, who were greatly inspired by his work on the Tractatus.
Somewhat reluctantly, Wittgenstein accepted a teaching position at Cambridge (the Tractatus was submitted as his doctoral dissertation), and spent the best part of the rest of his life there. He remained skeptical about philosophy, and persuaded many of his students to pursue more practical careers in medicine or elsewhere. Throughout the thirties and early forties, he worked out his more mature philosophy, but did not publish. The only work he felt was suitable for publication was the first part of the Philosophical Investigations, but he insisted that it not be published until after his death. He succumbed to cancer in 1951, and the Investigations were published in 1953. Following their publication, a number of posthumous writings culled from Wittgenstein's notebooks or from lecture notes taken by his students at Cambridge were also made public.
Though the Tractatus was written in the trenches of World War I, it is difficult to determine what influence the war had on Wittgenstein's work. Perhaps if it had been written under less stressful circumstances, it would have discussed logic exclusively, and would have omitted the reflections on ethics and death that are found near the end of the book. Even so, the Tractatus bears the marks of the war far less than most literature written during that time.
Two other aspects of Wittgenstein's historical milieu are worth noting. One aspect is the intellectual atmosphere of turn-of-the-century Vienna. At the time Vienna was the capital of the grand, but declining, Austro-Hungarian Empire that was to be torn apart at the end of the First World War. It was a center of intense intellectual activity, with musicians such as Brahms and Mahler, artists such as Klimt and Schiele, and great thinkers such as Sigmund Freud and Robert Musil. Wittgenstein's family patronized many Viennese artists, and Wittgenstein had a very musical upbringing. He was also brought into early contact with the philosophy of Schopenhauer, whose philosophy of the will would provide an interesting balance to the logicist influence of Frege and Russell.
Another aspect is the modernist movement in early 20th century literature. This movement pervaded the intellectual climate, from Pound, Eliot, or Joyce in literature, to Picasso or Kandinsky in painting, to Webern or Schonberg in music, even to Einstein in physics and Richard Reti in chess. Modernism was motivated by a dissatisfaction with older, linear forms of thinking, and an eagerness to find new, subversive ways of representing. This was accompanied by a stronger interest in form over content: how things were put together became as important, if not more so, than what they were put together in order to say. At any rate, Wittgenstein can be seen as imbued with the spirit of his times to an extent. His attempts to rethink the very nature of logic are driven by a similar desire to dispense with an older, linear mode of thinking, and the system he develops (and the form he writes it in) is austerely architectural.
The Tractatus can only be properly understood when set against the philosophy of Frege and Russell. Gottlob Frege (1848–1925) is generally credited as the founder of analytic philosophy. Spurred by the rigorization of mathematics in the 19th century, Frege set out to show that the truths of mathematics could all be derived from logic, and would not have to rely on "pure intuition," as Kant had argued. To show this, Frege had to invent modern logic. Whereas the logic of Aristotle, which had changed little in the previous 2400 years, was based on the subject-predicate form of grammar, Frege's logic analyzed sentences between concepts and objects, allowing for a great deal more flexibility. In particular, it allowed Frege to introduce the concept of generality into logic. While traditional logic would analyze a sentence such as "all horses are mammals" by dividing it into the subject, "all horses," and the predicate, "are mammals," Frege analyzed it into the object "horse" and the concept "mammal." Frege's analysis would read: "For all x, if x is a horse, then x is a mammal."
According to Frege, concepts are functions in the mathematical sense, but applied more broadly. That is, the concept "mammal" can be expressed as the function "x is a mammal" where any object can be inserted for x. Any function can then mean one of two things: either "the true" (e.g. if x is "my mother") or "the false" (e.g. if x is "the Eiffel Tower"). This would lead Frege into difficulty, as phrases like "the concept of a horse" could be substituted for x, and could thus be considered objects.
One of Frege's significant contributions was to flush psychology out of logic and the analysis of sentences. Kant, for instance, distinguished analytic and synthetic judgments according to how these judgments were framed in the mind. Frege insisted the analytic/synthetic distinction had nothing to do with psychology, but rather with justification: a judgment that can be justified by means of logic alone is analytic, whereas a judgment that must be justified by referring to the world is synthetic. Effectively, Frege argued that the meaning of sentences has nothing to do with what goes on in the head, and everything to do with their logical structure.
Wittgenstein's other major influence was Bertrand Russell (1872–1970), with whom he studied at Cambridge. Russell himself was an admirer of Frege's, and built on Frege's work to a large extent. His major work, the Principia Mathematica, co-authored by Alfred North Whitehead, was a Frege-inspired effort to derive all of mathematics from logical axioms.
Russell's first encounter with Frege was in 1902 when he discovered a fundamental paradox (called "Russell's Paradox") in Frege's logic, which led to his development of the "Theory of Types." Unlike either Frege or Wittgenstein, Russell turned increasingly toward an empirical philosophy. He argued that the language we normally use consists solely of descriptions: if I talk about "the queen of England," I am offering a description of a woman I have never met. A full analysis of language will rid propositions of descriptions, by replacing them with objects we are acquainted with. The only things we are directly acquainted with, according to Russell, are sense data. Thus, all language can ultimately be analyzed down to remarks on present or past sense data with which we are directly acquainted.
Frege and Russell shared a "universalist" conception of logic. They saw logic as the most fundamental set of laws, which are universally applicable. While the laws of physics deal only with physical phenomena, and the laws of grammar deal only with language, the laws of logic deal with everything. They saw logic as providing a framework for rationality. This logic could be formalized into a small number of simple, self-evident axioms, and equally self-evident laws of inference. The propositions of logic could then be deduced from these axioms by means of the laws of inference, and these propositions would stand as the laws to which all rational thought must adhere.
Another significant influence on Wittgenstein's thought, from an entirely different quarter, was the German philosopher Arthur Schopenhauer (1788–1860). Schopenhauer's major work, The World as Will and as Idea distinguished between two stances we can take toward experience. On one hand, there is the "world as idea," which is the world as it appears to our senses, and as we experience it. On the other hand, there is the "world as will," which constitutes an awareness of our own agency, as beings who can define our world according to our will. According to Schopenhauer, it is only through this awareness of our own agency that we can tap into the true nature of reality. While Schopenhauer's influence is most present near the end of the Tractatus, the book as a whole bears a mystical outlook that distinguishes Wittgenstein from either Frege or Russell.
The Tractatus was a controversial work upon publication, and its influence was widespread. It resolved the many tensions that lingered in Frege's and Russell's work, marking an end to the early period of analytic philosophy. The most distinguished followers of the Tractatus were the logical positivists of the Vienna Circle, who flourished in the late 1920s and early 1930s. However, their reading of the Tractatus was mistaken on a number of points, and borrowed heavily from Russell's empiricism.
Wittgenstein's influence has not been confined to philosophy. He is one of the few philosophers of the 20th century to capture the imagination of the general public. He has been read and puzzled over widely, and his work has inspired artists and thinkers in a variety of fields.