The Tractatus Logico-Philosophicus (1921) by Ludwig Wittgenstein breathes a very intriguing air, which draws you in and encapsulates you as you work your way through the collection of short statements towards the final conclusion. Along this path one is utterly aware of the fact that one is treading continuously on very unfamiliar ground – ground that offers much resistance to the understanding.
Wittgenstein’s project is twofold: first, he wants to develop his logical theory and, second, he wants to explain how this conception of logic relates to the world of facts. That is, the work deals with two theories, one logical the other epistemological. And the conclusions Wittgenstein draws from them are extraordinary.
As he states in his opening sentence, the world is the totality of facts – each fact is divided from each other fact. Whether this division is finite and infinite isn’t clear to me (I guess it doesn’t really matter for Wittgenstein’s theory anyway). We perceive these facts in the sense that we picture them in our thoughts, where the logical-pictorial form of each picture corresponds to the fact it represents. That is, the logical structure of our thoughts corresponds with the logical structure of the facts in the world. In short: at its foundation the world consists of indivisible, independent facts and each corresponds to a single indivisible, independent logical element.
When we think, our thoughts are translated (so to speak) in propositions. Or rather: our propositions are expressions of our thoughts, which are themselves, ultimately, pictures of facts. These propositions are either elemental (i.e. they are the most simple, undividable units of thoughts) or they are composites of elemental propositions (i.e. they are complexes). Wittgenstein applies the (then) new method of symbolic logic to unearth the fundamental logical structure underneath (and common to) all these linguistic expressions of our thoughts. He digs up the general form of a proposition – or rather truth function – which collects different elemental propositions containing variables into one complex and generates a truth value for the whole depending on the specific value of the variables.
But here there arises a fundamental issue. Logical propositions are either true or false, depending on the particular input (the values of the variables). The particular input of a variable isn’t really all that interesting to the logician – what he or she discovers is a general, lawlike structure which is tautological in the sense that, through the propositional relations, the input rigidly determines the output. These logical propositions are thus necessary, while the particular input in the formulae, since it consists of variables, is accidental. That is, all particular facts (the facts of the world) are accidental. This leads Wittgenstein to conclude that logic is the exploration of all that’s lawlike, while everything outside logic – the world of facts – is accidental.
After developing his logical theory, he applies his apparatus to physic and psychology (i.e. scientific propositions):
“[Physics] is an attempt to construct according to a single plan all the true propositions that we need for a description of the world.” (pp. 82-83)
“The laws of physics, with all their logical apparatus, still speak, however indirectly, about the objects of the world.” (p. 83)
This is a radical stance: causality manifests itself in the world but isn’t part of physics. All laws are logical necessities and are about the relations between facts, not about the particular facts (their descriptions) themselves. The key point is that we can experience and talk about the particular facts in the world but can never transcend them. The world has no sense, or rather: it cannot be discovered within the world. According to Wittgenstein all propositions (and thus our thoughts about the world) are of equal value. That is, of no value. There is no value in the world – all questions about religion, ethics, aesthetics, etc. are transcendental. Since words apply only to the phenomenal world of experience, we cannot talk about the subjects of religion, ethics, aesthetics, etc. That is, we cannot ask any questions about them in the first place.
Wittgenstein concludes in one of his final paragraphs:
“We feel that even when all possible scientific questions have been answered, the questions of life remain completely untouched. Of course, there are then no questions left, and this itself is the answer.” (p. 88)
“The solution of the problems of life is seen in the vanishing of the problem.” (pp. 88-89)
“There are indeed things that cannot be put into words. They make themselves manifest. They are what is called mystical.” (p. 89)
And he ends his work with the infamous words:
“What we cannot speak about, we must pass over in silence.” (p. 89)
It is very easy to read these final pages and accept his claims at face value. But there is more depth to these words than a superficial reader notices. In fact, Wittgenstein has ended up in a very eccentric position: along the way he has built a self-contained and tautological logical apparatus which is entirely separated from the world, the totality of facts, which we experience in life. This apparatus is subsequently used to destroy all claims of logical necessity in physics and psychology and reduce these sciences to the status of collections of statements about particular facts in the world. Finally the apparatus is used to show how only facts in the world can be put into words and everything else transcends this world and thus the possibility of speaking about them. That is, all things outside the world (including the world itself) lack sense, are nonsense. And since the logical apparatus itself is cut off from the world of facts, the final act of Wittgenstein is to throw away his tool and end up with the only thing real: the mystical. He says:
“My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical, 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 it.) He must transcend these propositions and then he will see the world aright.” (p. 89)
As he himself points out in the preface, after solving all the philosophical questions – by pointing out they are (literally) nonsense – there is not much achieved. He has cleared up all the human, all too human, pretence of thinking ourselves able to talk about the world in scientific and logical terms – all that rests is our living in the world. It is not surprising that after writing his Tractatus, Wittgenstein decided he had solved (or dissolved?) philosophy once and for all: all that remained was living a life that was in accord with the mystical. He was a man who was throughout his life obsessed with religion and ethics, and so he decided to work as a gardener in a monastery (he was rejected), as a school teacher (he was dismissed due to his loose hands), as a proletarian in Soviet Russia (he was rejected and offered a position as professor of philosopher in Kiev – which he rejected). Basically all his attempts at living like a saint failed miserable, and in 1929 he decided to return to Britain to return as a professor of philosophy in Cambridge. There he radically altered his views on his former philosophy and developed a whole new philosophy which was as radical and influential as the first one.
Wittgenstein was a very remarkable man, but also a very problematic character. This shows in the Tractatus: it is as unconventional, extreme and original as no philosopher since Plato. Perhaps it helped that he wasn’t trained as a philosopher but as an engineer in aeronautics – coming from a mathematical background and stepping into philosophy at a very late point in his education he was free from all the common prejudices and restrictions which education tends to foster. For example, some academic colleagues remarked that he never read Aristotle, which perhaps is rather a compliment than a dismissal. Being intellectually free he was able to invent two highly original philosophies which are more spectacular and ground-breaking than the works of most other twentieth century philosophers.
(Please feel free to add any additional info or correct any mistakes I've made in this review!)