Born the youngest of eight children into a wealthy Viennese industrial family, Wittgenstein originally studied engineering, first in the Realschule in Linz, then in Berlin. In 1908 he went to Manchester to study aeronautics. Becoming fascinated by the philosophy of mathematics, in 1911 he visited Frege, who advised him to study under Russell in Cambridge. Until the First World War he worked as Russell’s protégé and collaborator, on problems in the foundations of logic and mathematics. During the war he served in the Austrian army, and completed the manuscript that was published in 1921 as the Tractatus Logico-Philosophicus (trs. into English in 1922). Convinced that he had definitively solved all soluble problems of philosophy he abandoned the subject for rural school-teaching in Austria, until 1929 when contact with the Vienna circle (see logical positivism), mathematical intuitionism, and above all Ramsey persuaded him that there remained work for him to do, and he returned to Cambridge, where he became professor in 1939. During the Second World War Wittgenstein worked as a hospital porter at Guy’s hospital in London, and then as a laboratory assistant in Newcastle. He resigned his chair in 1947, and died of cancer in Cambridge. He was undoubtedly the most charismatic figure of 20th-century philosophy, living and writing with a power and intensity that frequently overwhelmed his contemporaries and readers.

It is usual to divide Wittgenstein’s work into the early period, culminating in the Tractatus, and the late period from 1929 until his death, whose most famous expression is the Philosophical Investigations, published in 1953 (other doctrines of the late period were not published in Wittgenstein’s lifetime, but collected from notebooks and lecture notes). Both periods are dominated by a concern with the nature of language, the way in which it represents the world, and the implications this has for logic and mathematics. In the early work language is treated in relative abstraction from the activities of human beings, but in the late period concern with the philosophy of mind, the nature of certainty, and even ethics, is reintroduced. The early period is centred on the picture theory of meaning, according to which a sentence represents a state of affairs by being a kind of picture or model of it, containing elements corresponding to those of the state of affairs and a structure or form that mirrors the structure of the state of affairs that it represents. All logical complexity is reduced to that of the propositional calculus, and all propositions are truth functions of atomic or basic propositions. Since atomic propositions must therefore be logically independent of one another the nature of the ‘atoms’ from which they are constructed remains elusive. For Russell at the time atoms were primitive elements of experience, but although the Tractatus was a major influence on logical positivism (which also emphasizes primitive elements of experience) there is no reason to suppose that Wittgenstein makes the same equation. The Tractatus moves to a denial of factual or cognitive meaning to sentences whose function does not fit into its conception of representation, such as those concerned with ethics, or meaning, or the self, and ends with the famous repudiation of its own meaningfulness. Doctrines about logical form are amongst the things that can be shown but not said: ‘whereof we cannot speak, thereof we must be silent.’

In the later period the emphasis shifts dramatically to the actions of people and the role their linguistic activities play in their lives. Thus whereas in the Tractatus language is placed in a static, formal relationship with the world, in the later work Wittgenstein emphasizes its use in the contexts of everyday social activities of ordering, advising, requesting, measuring, counting, exercising concern for each other, and so on. These different activities are thought of as so many ‘language games’ that together make up a form of life. Philosophy typically ignores this diversity, and in generalizing and abstracting distorts the real nature of its subject-matter: a work like the Tractatus is the product of thinking that language has to be one thing or another, whereas the correct method is to look and see what it actually is. When attention to detail is abandoned, the real function of statements is missed, and ‘language goes on holiday’. The approach is a variety of pragmatism, although Wittgenstein shied away from being associated with any kind of theory, supposing that what is needed is instead a cure for the philosophical impulse, a therapy rather than a theory. Wittgenstein’s later writing typically deploys analogies, aphorisms, new perspectives, and invitations to look at old phenomena in new ways, rather than conventional linear arguments, in order to cure us of the urge to generalize. In all this he was following the Austrian phenomenological tradition of Brentano and especially Husserl, who anticipated the need not to think, but to look, i.e. to pay more attention to the contours of the actual phenomena, and less to preconceptions about what they must be like. Philosophy, for this tradition, also makes no discoveries, strictly speaking, but only reminds us of what we find when we turn our attention in unfamiliar directions.

The most sustained and influential application of these ideas was in the philosophy of mind. Here Wittgenstein explored the role that reports of introspection, or sensations, or intentions, or beliefs actually play in our social lives, in order to undermine the Cartesian picture that they function to describe the goings-on in an inner theatre of which the subject is the lone spectator. Passages that have subsequently become known as the rule-following considerations and the private language argument are among the fundamental topics of modern philosophy of language and mind, although their precise interpretation is endlessly controversial.

In addition to the Tractatus and the Investigations, collections of Wittgenstein’s work published posthumously include Remarks on the Foundations of Mathematics (1956), The Blue and Brown Books (1958), Notebooks 1914–1916 (1961), Philosophische Bemerkungen (1964), Zettel (1967), and On Certainty (1969). There are admirable biographies by Ray Monk and Brian McGuinness.

http://www.wittgen-cam.ac.uk/ An online archive of material on Wittgenstein, including an illustrated biography

http://www.philosophytalk.org/shows/wittgenstein-0 An audio discussion of Wittgenstein by three American philosophers