How is it that false statements, such as “horses have eight legs”, can be just as meaningful as true statements, such as “horses have four legs”?
Where does logical structure come from? We can describe what the world would be like if the laws of physics were different – could we do the same for the laws of logic?
Are there facts about ethics?
If we ever managed to answer the philosophical questions that humans have pondered for thousands of years, what would life look like on the other side?
All of these questions and more are addressed in Ludwig Wittgenstein’s early work, the Tractatus Logico-Philosophicus – often referred to simply as “the Tractatus” – which was first published 100 years ago.
The Tractatus was the only philosophy book Wittgenstein published during his lifetime. The fact that he wrote much of it as a prisoner of war in Italy during the first world war gave it a particular existential and mystical twist.
An idiosyncratic, sometimes baffling, yet manifestly brilliant set of intricately numbered aphorisms largely concerning formal logic, the Tractatus has had an enormous influence on philosophy, although almost nobody has agreed with its key claims.
One of its fiercest critics was Wittgenstein himself. He started questioning his own conclusions just a few years after its publication.
In this slim volume, Wittgenstein set out to solve all the problems of philosophy by showing how such problems arise because we misunderstand the true logic of our language. If we clear away this misunderstanding, he claimed, we will recognise that:
What can be said at all can be said clearly and what we cannot talk about we must pass over in silence.
That “must” is at least partly a moral imperative.
The Tractatus seeks to map out a particular kind of logical structure, which Wittgenstein claimed underlies both reality and language. He assumed that the two must mirror each other or language could not function, which it clearly does.
He posited that within this logical structure lies a multitude of specific facts, each of which can be stated clearly. The structure itself cannot be talked about, but it can be “shown”.
All other statements, including Western philosophy’s extensive discussions of ethics, theology and metaphysics, Wittgenstein briskly labels “nonsense”.
Logical atomism
Scientific knowledge greatly advanced when chemists developed the periodic table, which systematically presents the different kinds of atoms of matter. This enabled chemists to write formulas describing how those atoms combine to make everyday substances such as water, sugar and soil.
Analogously, when Wittgenstein was writing the Tractatus, early analytic philosophers, such as Bertrand Russell, dreamed that they might identify atoms of meaning. They sought to formulate all possible combinations of those atoms using predicate logic. This project is known as logical atomism.
When the young Wittgenstein arrived in Cambridge in 1911, Russell became his teacher. Wittgenstein diligently set about completing Russell’s logical atomist program. His vehement repudiation of its methods would give force and momentum to his later work.
The Tractatus’ commitment to logical atomism may be seen in the way it presents facts as entirely specific and discrete. “Each item can be the case or not the case,” writes Wittgenstein, “while everything else remains the same.”
In the world, facts consist in the existence of states of affairs, which are composed of simple objects.
In language, facts are represented by atomic propositions, composed of simple names. What are these simple objects? Wittgenstein says they “make up the substance of the world”, but he provides no examples.
The Picture Theory of Meaning
Wittgenstein’s answer to the question of how language can meaningfully describe what is false is his Picture Theory of Meaning.
How can statements be pictures? Here Wittgenstein has in mind the way in which a statement which is true or false does not merely list terms, but arranges them into a structure.
For example, consider the terms “Megan”, “Harry” and “loves”. By arranging them into different “pictures”, we can describe quite different situations, each of which can be true or false while the others remain the same:
Harry loves Megan.
Megan loves Harry.
Harry loves Harry.
In this way, Wittgenstein suggests, our language invokes a kind of enormous space, where every possible statement has its own place:
A picture presents a situation in logical space, the existence and non-existence of states of affairs.
Because this “space” contains all that is false and merely possible, as well as all that is true, it is much broader than the physical space in which we move and live.
The exact relationship of this space to physical space is an interesting question.
The limits of language
Once we lay out logical space systematically, we see that some important matters have no place there. A key example is the nature of the structure itself which enables language to mirror reality. Thus, Wittgenstein says,
Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to represent it – logical form.
To understand Wittgenstein’s point here, consider this mirror, which reflects a streetscape in a somewhat distorted fashion. The mirror explicitly represents the streetscape, but it cannot represent the relationship between the streetscape, itself, and the light which enables it to represent the streetscape.
This metaphor of language “mirroring” reality has shaped many philosophers’ thinking about truth, through a so-called Correspondence Theory of Truth. Many have found this theory attractive, insofar as it seems to entail that “reality is out there”.
The metaphor does have strong critics, most notably Richard Rorty in his book Philosophy and the Mirror of Nature (1979). But Wittgenstein appears to place a strong anti-realist message within the realist metaphor when he famously says:
The limits of my language mean the limits of my world.
He explains this as follows:
Logic pervades the world: the limits of the world are also its limits. So we cannot say in logic, “The world has this in it, and this, but not that” […] since it would require that logic should go beyond the limits of the world…
To illustrate this point, imagine that I state, "The world contains no true contradictions". Superficially, this might appear to resemble the statement, "The world contains no eight-legged horses", which is clearly meaningful. But it is actually quite different.
We can make “logical pictures” of a world that contains eight-legged horses and another which does not, and we can compare them. But we arguably cannot do that with the logical structure of our own language.
For instance, try to “picture” a world where it is true that "it is raining and it is not raining". Would you take your umbrella there?
Stating vs showing
Towards the end of the Tractatus, Wittgenstein suddenly abandons logic and bursts into a series of aphoristic musings on ethics, death, God, scepticism, the meaning of life, and the purpose of philosophy.
This might appear to be a bewildering range of topics, but for Wittgenstein they are united by being not stateable. They are, rather, “shown” or “made manifest”.
He flatly denies there are facts about ethics:
The sense of the world must lie outside the world. In the world everything is as it is, and everything happens as it does happen: in it no value exists […] It is clear that ethics cannot be put into words.
But don’t people frequently talk about ethics?
Such people are confused, Wittgenstein suggests. The goodness or badness of an action does not reside in some sort of further fact – as if God might reward us for a “good” action by giving us money, or punish us for a “bad” action by bopping us on the head. Rather, goodness or badness must “reside in the action itself”.
A related issue is the will, understood as our overall attitude of optimism or pessimism. This also lies outside the world. Wittgenstein says:
If the good or bad exercise of the will does alter the world, it can only change the limits of the world, not the facts […] The world of the happy man is a different one from that of the unhappy man.
From here we move on to death. Wittgenstein offers a “New Epicurean” argument that death is not to be feared, drawing an original parallel between the ungraspable limits of logic and of life:
Death is not an event in life […] Our life has no end in just the way in which our visual field has no limits.
This then leads to God and the mystical:
It is not how things are in the world that is mystical, but that it exists.
Now Wittgenstein is ready to resolve all the questions of philosophy. Philosophy’s goal, he states, is simply to state what can be stated (“the propositions of natural science”) and demonstrate the error in trying to state anything else:
and then, whenever someone else wanted to say something metaphysical, to demonstrate to him that he had failed to give a meaning to certain signs in his propositions.
But does the Tractatus itself fit this program? Its numbered aphorisms hardly appear to be “propositions of natural science”. Wittgenstein attempts to head off this objection through his famous metaphor of a ladder that is climbed up and then kicked away:
My propositions serve as elucidations in the following way: he who understands me finally recognizes them as senseless, when he has used them – as steps – to climb up beyond them. (He must so to speak throw away the ladder, after he has climbed up on it.)
And this brings us to the work’s notorious final statement:
What we cannot speak about we must pass over in silence.
Reception and enduring influence
Despite its brilliance, the Tractatus is arguably a young man’s book, possessed of a naive certitude that stuffs many major philosophical problems under the rug.
Soon after it was published, Wittgenstein suffered a crisis of faith in its ideas. He spent much of the rest of his philosophical career critiquing it. His masterwork, Philosophical Investigations, published just after his death in 1951, contains many remarks parodying logical atomism and transcendental philosophising about language.
Meanwhile, the logical positivist circle in Vienna read the Tractatus and were enormously inspired. They invited Wittgenstein for a research visit in 1927. Wittgenstein came, but refused to answer any questions about his book, stating that he could no longer understand the thinking of someone who would write such stupid things. Instead, he sat with his back to his audience reciting poems by Indian mystic Rabindranath Tagore.
The logical positivists were not amused. They nevertheless adopted a host of Tractatarian ideas. Most notably, they stressed the importance of formal logic in philosophical analysis. They also insisted on maintaining a strict separation between scientific facts and all other statements, such as value statements.
After many Vienna Circle members fled Europe for the US during the second world war, logical positivism developed into the analytic philosophy that still dominates the English-speaking world. But the idea that philosophical problems could be resolved once and for all has been almost entirely abandoned. Professional philosophy today is a much more complex, piecemeal enterprise than the young Wittgenstein envisaged.
The purity of the Tractatus’ original vision continues to exercise a fascination in popular culture, which seems unlikely for a work largely concerning formal logic.
It has been set to music more than once. It has inspired graffiti in Chicago. Independent filmmaker Derek Jarman has made a full-length Wittgenstein biopic, whose final scene contains one of the most insightful and beautiful summations of the Tractatus’ vision, and its fatal flaws.
In the scene, John Maynard Keynes approaches Wittgenstein on his deathbed, describing him tenderly as a “very clever young man”, who had dreamed of reducing the world to pure logic in order to purge it of “imperfections and indeterminacy”.
But this resulted in a world of perfectly smooth ice, which was uninhabitable. So the older, wiser Wittgenstein learned to make do with a world filled with “tarnished and battered” ordinary meanings. Yet part of him was still “homesick” for the ice world, which was “radiant and absolute and relentless”.
This had caused a tension he never managed to resolve. 100 years after the publication of the Tractatus, this dilemma continues to move people who love philosophy.