Tractatus Logico-Philosophicus - Ludwig Wittgenstein
Ludwig Wittgenstein.
Ludwig Wittgenstein (1889-1951)


My grandfather had an extensive library filled with theological and philosophical literature, mostly collected by his father, a great humanist and teacher of Latin and Greek, and his maternal grandfather, a vicar and theologian who led a tragic life (he lost five of his six children to tuberculosis, and his wife to mental illness). As a teenager I spent many hours exploring this library. Unfortunately, there was not much to satisfy my interest in mathematics and the natural sciences beyond The Origin of Species and some elementary schoolbooks, so I started reading some of the dusty philosophical tomes.

Initially I was impressed with the depth of the concepts and reasoning that I encountered. I became acquainted with the great names: Plato, Aristotle, Descartes, Pascal, Spinoza, Locke, Kant, Hegel, Schopenhauer - alas not by reading them in the original but rather by having their ideas presented in histories of philosophy and treatises from the latter part of the 19th century. To me it became more and more difficult to see philosophy as a body of knowledge. In essence it seemed to be an ongoing discussion and battle of opinions. In striking contrast to the natural sciences, there did not seem to be a general progression, with a steadily increasing body of agreed results. Even in such an abstract field as mathematics, enormous strides had been made in the 19th century. Thanks to Cauchy, Weierstrass, and Dedekind, stringent understandable and agreed definitions had been established of concepts such as "continuity" and "limiting value", without having to resort to fuzzy expressions such as "infinitely small increment" or "when N becomes infinitely large". A similar foundation seemed to be lacking in the field of philosophy.

From Tidsexistensens apologi: "Space itself cannot possibly be limited, for then it must be limited by a surface with space on only one side." "Time is similar to a line. But a line can be extended indefinitely, so there is no first or last point in time."

I was especially annoyed with the respected 19th century Swedish philosopher Pontus Wikner, whose treatise Tidsexistensens apologi ("Apology for Temporal Existence", or probably more understandably "In defense of the concept of temporal existence") discussed such concepts as time and space and causality in a rather contrived way, and of course in the total absence of any knowledge of the impending revolution in physics. - While this and many similar works no doubt were inspired by admirable aspirations "to touch the face of God", they seemed to me to lack any demonstrable relationship to the real world. Instead, they made me develop a strong aversion to metaphysics. I suppose this placed me in the camp of "the anti-metaphysics logical positivists". - Of course, the hubris of a teenager, who dared to express such opinions about centuries' worth of philosophical investigations, was roundly ridiculed and condemned by older and wiser members of the family :-)

Instead, the rather unusual route of science fiction novels had brought me to "general semantics" and the phenomenon of language, and from there to the writings of Bertrand Russell and Ludwig Wittgenstein. Russell wanted to fuse logic and mathematics. (It took him a whole book just to define the natural numbers!) He tried to bring a more "scientific" approach to philosophical analysis. A statement could only be true in the scientific sense if it could be verified. (Later, Karl Popper proposed that there are no scientific truths; there are only hypotheses or models, but these must be falsifiable in order to qualify as science. To my mind, this is just a refinement of Russell's position.)

When I read Wittgenstein's Logisch-Philosophische Abhandlung, I found it immensely appealing. Part of its attraction was undoubtedly that it was said to have been written in the trenches of Word War I by a then young, unknown soldier, and that it claimed to offer definitive answers to what is knowable in philosophy. Actually, Wittgenstein was already 25 when WWI broke out, and he had studied under Bertrand Russell 1911-1913.

Ludwig Wittgenstein.As a person, Wittgenstein was something of an enigma. He was the son of a successful Austrian industrialist and was educated as an aeronautical engineer. In WWI he served as a volunteer in the Austrian army. After the war, and a brief period as a prisoner-of-war in Italy, he became an elementary school teacher in Austria. He inherited a large fortune but donated it to his sisters, and for a time he served as a humble gardener in a monastery. Only in 1929 did he return to England to teach, and to continue his philosophical investigations. He became a professor of philosophy at Cambridge at the age of 50 in 1939, and stayed in England until his death in 1951.

There is no doubt that he was an intensely serious person, although by no means lacking in humor. (His friend Malcolm recounts how Wittgenstein joked during a walk on a starry night, that the constellation Cassiopeia spelled "W" for "Wittgenstein" rather than "M" for "Malcolm".) The fact that three of his four brothers had committed suicide must have cast a long shadow over his life. In general he preferred solitude and liked to retreat to the countryside. His passion was his lifelong exploration of the nature of language and its relationship to reality.

His book - the only one published in his lifetime - mirrored his personality: it was austere and minimalistic. It was divided into seven chapters, each containing a short proposition which was then further examined in subsections, systematically numbered down to as much as three or four sublevels. Here are the "headings" of the seven chapters (the full text of the original is available on-line; so is the full text translated into English):

  1. The world is everything that is the case.
  2. What is the case, the fact, is the existence of atomic facts.
  3. The logical picture of the facts is the thought.
  4. The thought is the significant proposition.
  5. Propositions are truth-functions of elementary propositions. (An elementary proposition is a truth-function of itself.)
  6. The general form of truth-function is: . This is the general form of proposition.
  7. Whereof one cannot speak, thereof one must be silent.

Scattered among the propositions, one can find some that have become familiar epigrams, such as "The limits of my language mean the limits of my world" or "What can be said at all can be said clearly" (from the preface) or "Whereof one cannot speak, thereof one must be silent" (which happens to be the totality of ch. 7).

Despite its clarity and economy of expression, opinions vary about how the book should be understood. It is clear that Wittgenstein wanted to explore the limits of what can be expressed, and therefore of what can be thought and said. He also wanted to put logic on a firm footing.

For me the key finding is Proposition 6.5: For an answer which cannot be expressed, the question too cannot be expressed. The riddle does not exist. If a question can be put at all, then it can also be answered.

This means (my interpretation) that a question such as Why does the universe exist? does not just fall outside the realm of science; it is actually devoid of semantic content. The word "Why" is being misused. It refers to a cause-and-effect relationship, and as such can only be legitimately used within the universe. - Yet, Wittgenstein was also something of a religious mystic. He wrote in Proposition 6.522: "There is indeed the inexpressible. This shows itself; it is the mystical."

Something that has attracted a lot of attention is the penultimate Proposition 6.54: "My propositions are elucidatory in this way: he who understands me finally recognizes them as senseless, when he has climbed out through them, on them, over them. (He must so to speak throw away the ladder, after he has climbed up on it.) - He must surmount these propositions; then he sees the world rightly." This seems to invalidate his own teachings except as a tool, or a scaffold, on the way to a higher level of understanding, much as I imagine that a teacher of Zen might express himself.

Philosophical Investigations cover.Regardless of how this should be understood, I found myself very much in agreement with Wittgenstein's view that philosophy should aim at the logical clarification of thoughts. Philosophy should not be a body of doctrine but a process, seeking to explore the limits to what we can know. In my opinion, the philosopher's task should not be to speculate about the unknowable, but rather to point out when we transgress the boundaries of what is knowable (usually through the misuse or misunderstanding of language). For instance, I think that Goedel's incompleteness theorem makes him one of the outstanding philosophers of the 20th century.

Much - perhaps too much - has been made of Wittgenstein's tendency to distance himself from his "Tractatus" in his later years. He became less sure that he had "solved" the "central" problems in philosophy, and there was a change of style in his investigations. He became more verbose, and, some would claim, less lucid. His focus shifted to how language is actually used (and misused). But his misgivings about the strict self-consistency of "Tractatus" were already there in his Proposition 6.54.

Some additional web links

  1. Internet Encyclopedia of Philosophy article
  2. Wikipedia article
  3. Stanford article
  4. The Wittgenstein Archives at the University of Bergen, Norway
  5. An amusing fantasy (in the form of a dream) by a university student in Austin, Texas, based on the recollections of some of Wittgenstein's disciples.

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    Last edited or checked June 6, 2013. (Fixed a broken link May 30, 2017.)

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