4.0
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.
The silent adjustments to understand colloquial language are enormously complicated.
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 t he 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" (but not at all in Mathner's sense). Russell's merit is to have shown that the apparent logical form of the proposition need not be its real form.
The proposition is a picture of reality.
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 his is not disturbed by apparent irregularities (like the use of �musical sharp�and �musical-flat�in the score).
For these irregularities also picture what they are to express; only in another way.
4.014
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 images of our language, rests on the logic of representation.
In order to understand the essence of the proposition, consider hieroglyphic writing, which pictures the facts it describes.
And from it came the alphabet without the essence of the representation being lost.
This we see from the fact that we understand the sense of the propositional sign, without having had it explained to us.
The proposition shows its sense.
The proposition shows how things stand, if it is true. And it says, that they do so stand.
4.023
The proposition determines reality to this extent that one only needs to say "Yes" or "No" to it to make it agree with reality.
To understand a proposition means to know what is the case, if it is true.
(One can therefore understand it without knowing whether it is true or not.)
One understands it if one understands it constituent parts.
The translation of one language into another is not a process of translating each proposition of the one into a proposition of the other, but only the constituent parts of propositions are translated.
(And the dictionary does not only translate substantives but also adverbs and conjunctions, etc., and it treats them all alike.)
4.026
The meanings of the simple signs (the words) must be explained to us, if we are to understand them.
By means of propositions we explain ourselves.
4.027
It is essential to propositions, that they can communicate a new sense to us.
4.03
A proposition must communicate a new sense with old words.
The proposition communicates to us a state of affairs; therefore it must be essentially connected with the state of affairs.
And the connection is, in fact, that it is its logical picture.
4.031
In the proposition a state of affairs is, as it were, put together for the sake of experiment.
One can say, instead of, this proposition has such and such a sense, this proposition represents such and such a state of affairs.
4.032
The proposition is a picture of its state of affairs, only in so far as it is logically articulated.
(Even the proposition "ambulo" is composite, for its stem gives a different sense with another termination, or its termination with another stem.)
4.04
In the proposition there must be exactly as many things distinguishable as there are in the state of affairs, which it represents.
They must both possess the same logical (mathematical) multiplicity (cf. Hertz's Mechanics, on Dynamic Models).
This mathematical multiplicity naturally cannot in its turn be represented. One cannot get outside it in the representation.
Reality is compared with the proposition.
Propositions can be true or false only by being pictures of the reality.
4.061
If one does not observer that propositions have a sense independent of the facts, one can easily believe that true and false are two relations between signs and things signified with equal rights.
One could, then, for example, say that "p" signifies in the true way what "~p" signifies in the false way, etc.
4.062
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.
4.063
An illustration to explain the concept of truth. A black spot on white paper; the form of the spot can be described by saying of each point of the plane whether it is white or black. To the fact that a point is black corresponds a positive fact; to the fact that a point is white (not black), a negative fact. If I indicate a point of the plane (a truth-value in Frege's terminology), this corresponds to the assumption proposed for judgment, etc. etc.
But to be able to say that a point is black or white, I must first know under what conditions a point is called white or black; in order to be able to say "p" is true (or false) I must have determined under what conditions I call "p" true, and thereby I determine the sense of the proposition.
The point at which the simile breaks down is this: we can indicate a point on the paper, without know what white and black are; but to a proposition without a sense corresponds nothing at all, for it signifies no thing (truth-value) whose properties are called "false" or "true"; the verb of the proposition is not "is true" or "is false" -- as Frege thought -- but that which "is true" must already contain the verb.
4.064
Every proposition must already have a sense; assertion cannot give it a sense, for what it asserts is the sense itself. And the same holds of denial, etc.
One could say, the denial is already related to the logical place determined by the proposition that is denied.
The denying proposition determines a logical place other than does the proposition denied.
The denying proposition determines a logical place, with the help of the logical place of the proposition denied, by saying that it lies outside the latter place.
