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What can be said at all can be said clearly; and whereof one cannot speak thereof one must be silent.
Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things. If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.
A tone must have a pitch, the object of the sense of touch a hardness, etc.
The logical picture of the facts is the thought.
The totality of true thoughts is a picture of the world.
We cannot think anything unlogical, for otherwise we should have to think unlogically.
The truth is, we could not say of an “unlogical” world how it would look.
To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.
We could present spatially an atomic fact which contradicted the laws of physics, but not one which contradicted the laws of geometry.
An a priori true thought would be one whose possibility guaranteed its truth.
We could only know a priori that a thought is true if its truth was to be recognized from the thought itself (without an object of comparison).
In the proposition the thought is expressed perceptibly through the senses. 3.11 We use the sensibly perceptible sign (sound or written sign, etc.) of the proposition as a projection of the possible state of affairs. The method of projection is the thinking of the sense of the proposition.
I conceive the proposition—like Frege and Russell—as a function of the expressions contained in it.
In the language of everyday life it very often happens that the same word signifies in two different ways—and therefore belongs to two different symbols—or that two words, which signify in different ways, are apparently applied in the same way in the proposition. Thus the word “is” appears as the copula, as the sign of equality, and as the expression of existence; “to exist” as an intransitive verb like “to go”; “identical” as an adjective; we speak of something but also of the fact of something happening.
In order to avoid these errors, we must employ a symbolism which excludes them, by not applying the same sign in different symbols and by not applying signs in the same way which signify in different ways. A symbolism, that is to say, which obeys the rules of logical grammar—of logical syntax. (The logical symbolism of Frege and Russell is such a language, which, however, does still not exclude all errors.)
In order to recognize the symbol in the sign we must consider the significant use.
The sign determines a logical form only together with its logical syntactic application.
If a sign is not necessary then it is meaningless. That is the meaning of Occam’s razor. (If everything in the symbolism works as though a sign had meaning, then it has meaning.)
No proposition can say anything about itself, because the prop-ositional sign cannot be contained in itself (that is the “whole theory of types”).
A function cannot be its own argument, because the functional sign already contains the prototype of its own argument and it cannot contain itself. If, for example, we suppose that the function F(fx) could be its own argument, then there would be a proposition “F(F(fx))”, and in this the outer function F and the inner function F must have different meanings; for the inner has the form φ(fx), the outer the form ψ(φ(fx)). Common to both functions is only the letter “F”, which by itself signifies nothing. This is at once clear, if instead of “F(F(u))” we write “(3φ) : F(φu) . φu = Fu”.
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Definitions are rules for the translation of one language into another. Every correct symbolism must be translatable into every other according to such rules. It is this which all have in common.
What signifies in the symbol is what is common to all those symbols by which it can be replaced according to the rules of logical syntax.
The geometrical and the logical place agree in that each is the possibility of an existence.
Although a proposition may only determine one place in logical space, the whole logical space must already be given by it. (Otherwise denial, the logical sum, the logical product, etc., would always introduce new elements—in co-ordination.)
(The logical scaffolding round the picture determines the logical space. The proposition reaches through the whole logical space.)
The thought is the significant proposition.
The totality of propositions is the language.
Man possesses the capacity of constructing languages, in which every sense can be expressed, without having an idea how and what each word means—just as one speaks without knowing how the single sounds are produced. Colloquial language is a part of the human organism and is not less complicated than it. From it it is humanly impossible to gather immediately the logic of language. Language disguises the thought; so that from the external form of the clothes one cannot infer the form of the thought they clothe, because the external form of the clothes is constructed with quite another
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Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language. (They are of the same kind as the question whether the Good is more or less identical than the Beautiful.) And so it is not to be wondered at that the deepest problems are really no problems.
All philosophy is “Critique of language”
The proposition is a picture of reality.
The proposition is a model of the reality as we think it is.
At the first glance the proposition—say as it stands printed on paper—does not seem to be a picture of the reality of which it treats. But nor does the musical score appear at first sight to be a picture of a musical piece; nor does our phonetic spelling (letters) seem to be a picture of our spoken language. And yet these symbolisms prove to be pictures—even in the ordinary sense of the word—of what they represent.
It is obvious that we perceive a proposition of the form aRb as a picture. Here the sign is obviously a likeness of the signified.
And if we penetrate to the essence of this pictorial nature we see that this is not disturbed by apparent irregularities (like the use of # and b in the score). For these irregularities also picture what they are to express; only in another way.
The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world. To all of them the logical structure is common. (Like the two youths, their two horses and their lilies in the story. They are all in a certain sense one.)
In the fact that there is a general rule by which the musician is able to read the symphony out of the score, and that there is a rule by which one could reconstruct the symphony from the line on a gramophone record and from this again—by means of the first rule—construct the score, herein lies the internal similarity between these things which at first sight seem to be entirely different. And the rule is the law of projection which projects the symphony into the language of the musical score. It is the rule of translation of this language into the language of the gramophone record.
The possibility of all similes, of all the imagery of our language, rests on the logic of representation.
My fundamental thought is that the “logical constants” do not represent. That the logic of the facts cannot be represented.
The proposition is a picture of its state of affairs, only in so far as it is logically articulated.
4.05 Reality is compared with the proposition. 4.06 Propositions can be true or false only by being pictures of the reality.
Can we not make ourselves understood by means of false propositions as hitherto with true ones, so long as we know that they are meant to be false? No! For a proposition is true, if what we assert by means of it is the case; and if by “p” we mean ∼p, and what we mean is the case, then “p” in the new conception is true and not false.
4.0621 That, however, the signs “p” and “∼p” can say the same thing is important, for it shows that the sign “∼” corresponds to nothing in reality. That negation occurs in a proposition, is no characteristic of its sense (∼∼p = p). The propositions “p” and “∼p” have opposite senses, but to them corresponds one and the same reality.
The object of philosophy is the logical clarification of thoughts.
Philosophy is not a theory but an activity. A philosophical work consists essentially of elucidations. The result of philosophy is not a number of “philosophical propositions”, but to make propositions clear. Philosophy should make clear and delimit sharply the thoughts which otherwise are, as it were, opaque and blurred.
4.1121 Psychology is no nearer related to philosophy, than is any other natural science.
The theory of knowledge is the philosophy of psychology.
Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.
To be able to represent the logical form, we should have to be able to put ourselves with the propositions outside logic, that is outside the world.
4.121 Propositions cannot represent the logical form: this mirrors itself in the propositions. That which mirrors itself in language, language cannot represent.
