On Wittgenstein's Theory of Language

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The topic for discussion in this paper has its roots in Wittgenstein's Tractatus, specifically the picture theory of meaning found in sections 2.12 through 2.201. I believe this very short and simple section admirably sums up the thrust of his theory of language, and his idea that philosophy is nothing more than the clarification of facts. The use of symbolism employed by a picture, a thought, or a sentence to convey truth rather than falsehood about the world shows that the picture is a model of reality—that "in the picture and the pictured there is something identical in order that the one can be a picture of the other at all." In this way, the logical structure between the picture and the fact must also exist between the sentence and the fact.

Contrary to his theory that what exists between the picture and the fact can only be shown and not said, it appears that it can be said as well, since the sentence must have the same structure as the fact—like a painting, a photograph, or even music—unless, of course, it doesn’t have a corresponding fact, as in the case of insanity. Otherwise, how could language develop at all? ("The world is everything that is the case.") Further, these pictures are logical facts about the world. They must be logical in order to exist, and anything that is not logical does not exist. My discussion will consider the possibility that mysticism is illogical, hence nonsensical. I will show that Wittgenstein’s theory of language is exactly analogous to the law of definite proportions in physical science and to his picture theory of meaning, which essentially states that we can only logically give names to those things which already have a reference, and that this theory was predetermined by the law of definite proportions.

The law of definite proportions states that a compound always contains elements in certain definite proportions, never in any other combinations. In this way, it is possible to make compounds out of elements, and the same number of elements will always be required to make certain compounds. This was discovered (and continues to be discovered) by accident, by experiment, by combining different elements until a useful (or sometimes destructive) compound is formed. The Periodic Table of Elements best demonstrates this theory. Moreover, the law has a wider meaning. In electrolysis, for example, water always yields 2 parts hydrogen and 1 part oxygen, regardless of the water's source or composition. Furthermore, water always has the same properties: it is wet, it dissolves salt and sugar, and always freezes at the same temperature. The properties of water do not depend on our will, nor do any other physical elements or compounds in the world.

Examples from Wittgenstein that support this theory include:

• An atomic fact is a combination of objects;
• It is essential to a thing that it can be a constituent part of an atomic fact;
• In logic, nothing is accidental: if a thing can occur in an atomic fact, the possibility of that atomic fact must already be prejudged in the thing (this is the law of definite proportions);
• If all objects are given, then all possible atomic facts are also given;
• Objects contain the possibility of all states of affairs;
• The configuration of objects forms the atomic fact;
• In atomic facts, objects hang one in another like links of a chain;
• The totality of existent atomic facts is the world;
• Although a proposition may determine only one place in logical space, the whole logical space must already be given by it.

This final statement leads into the discussion about language and reference and supports the idea that language must have a corresponding object as its reference; otherwise, it is meaningless and, as Wittgenstein points out, better left unsaid. The necessity that language have a logical reference may prove that mysticism is nonsense.

Wittgenstein writes, "From the existence or non-existence of an atomic fact, we cannot infer the existence or non-existence of another." In other words, saying God exists because the world is orderly does not justify inferring God from orderliness, a popular but flawed argument. Why should orderliness equal godliness? This is not a tautology. The logic of the world can only be shown in tautologies. The total reality is the world, and the world is all that is the case. The propositions of the logic of language must always be true if they are to say anything true about the world. Or as he states, "If from the fact that a proposition is obvious (A therefore B) it does not follow that it is true, then obviousness is no justification for our belief that it is true." This alone suffices to explain the non-existence of God logically. If the world is all that is the case and the total reality is the world, then it makes no logical sense to speak of an idea (mysticism) that has no reference. At most, this is solipsism: the picture and the sentence do not correspond to anything in reality. He writes, "In the picture and the pictured there must be something identical in order for one to be a picture of the other at all." When we think about mysticism, the only pictures we can form are pictures of facts—and these facts belong to the world, not outside it. As he points out, not every picture must be spatial: "The logical picture can depict the world" since it shares the same logical structure as its fact. In this way, we can imagine the existence of California from New York, since the picture has the same structure as California and our experience supports the inference. However, when mystics use visions to support similar inferences, they tell us nothing about the world, only about their state of mind. This is solipsism, and sometimes solipsism turns to insanity when the pictures of the mind become so jumbled as to lose correspondence with reality.

"In order to discover whether the picture is true or false we must compare it with reality. It cannot be discovered from the picture alone whether it is true or false. There is no picture which is a priori true." Mystics must logically be having false visions, since their pictures cannot be a priori true. He writes that what is thinkable is also possible, but we cannot think anything illogical. The basic premise of mysticism—that life is eternal and that eternal life may be glimpsed on earth—is, as Wittgenstein says, "not only in no way guaranteed, but this assumption in the first place will not do for us what we always tried to make it do." In death, the world does not change; it ceases—death is not an event of life since it is not lived through! Logically, if an answer cannot be given, then the question cannot be asked. Most questions, he says, arise from our misunderstanding of the logic of language. This leads to his most eloquent description of philosophy: it is about language clarification only. "The object of philosophy is the logical clarification of thoughts." It is about demonstrating that when people speak, they must provide meaning for the signs (names) of their propositions; otherwise, they should say nothing. All other sciences have nothing to do with philosophy. This is why it is so important that our law schools and judicial system, especially the Supreme Court, be comprised of philosophers—every decision they make is a philosophical problem of language.

Overhauling the problems of language involves elucidating how we give names to propositions (the signs). This problem is about determining whether the structure of language has something logically in common with the structure of the fact. The signs employed in propositions he calls names. The object and the name are one: A=A and vice versa. Names differ from propositions in that propositions say how a thing is, while names say what a thing is. The sign is written or spoken and is the part of the symbol perceptible by the senses. He points out that one word may have two different symbols—such as Green is green—but they are often applied in the same way in propositions. This is where confusion arises in language and meaning. It may also occur when two different words are supposed to be equal—like life and conception, abortion and murder—when they are not equal because they have different symbols. To remedy this, Wittgenstein says we must employ a symbolism that obeys the rules of logical grammar. This might be simpler than it looks, if only because of his fundamental rule: say nothing except what can be said. Or, as he says, "If a sign is not necessary, then it is meaningless." "The totality of propositions is the language."

The only thing all things logically have in common, he says, is that every correct symbolism must be translatable into every other. This means objects can only be mentioned in connection with some definite property, creating the problem of generalization (more or less solved in The Blue and Brown Books). It is impossible to give a name to one object that also refers to every other object, since many variables are involved with atomic facts. Hence, it is impossible to say anything about the world as a whole—one can only make statements about bounded portions of the world. This is correct philosophically, as it eliminates meaningless generalizations. After all, the particular case is really all anyone can talk about. "Since we cannot give the number of names with different meanings, we cannot give the composition of the proposition." In other words, the sense of the proposition should be immediately understood. When it is not, and we have to verify it, it shows the proposition is fundamentally false in the first place.

According to Wittgenstein, the logical picture of facts (the thought of the object) must have the same logical structure as the fact. This can only be shown; it cannot be said, and hence cannot be shown with a sign (spoken or written word). The reason for this is solipsism. Language disguises thought, he says, like clothing disguises the body. I wonder if it is logically necessary that language (the signs) disguise thought (hence the fact), or if this happens both intentionally and unintentionally. If signs were rightly expressed, wouldn’t they have the same logical structure as the facts they are meant to infer? This relates to intuitively knowing language—whether in modern art, physics, poetry, or as infants acquiring language. He says we possess the capability to construct languages without knowing how or what each word means, just as we speak without knowing how we produce the sounds. From this, it is possible to grasp the logic of language intuitively. Yet, until we understand the logical structure of signs, we continually fall into the trap of giving no meaning to certain signs in propositions. But when we speak and all signs have meaning, then these signs should also have the same logical structure as their facts.

It is important that language itself be the structure for its fact (and if it is a tautology, it logically is), because (6.113) if propositions are logical, their characteristic mark is that we can see from the symbol alone that they are true. This, as Wittgenstein says, contains the whole philosophy of logic. Further, the most important fact about non-logical propositions is that we cannot immediately see whether they are true or false from the propositions alone; we must verify them with corresponding facts in the world. When language gives a tautology, it shows it is connected a priori with its corresponding structure in reality. This is how language and certain abstractions can be grasped before we understand them. This is why mysticism does not work. Sections 2.21-2.201 and 6.113-6.1201 of the Tractatus nicely summarize Wittgenstein’s entire theory of language, meaning, and naming.