The point at which the simile breaks down is this: we can indicate a point on the paper, without knowing 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.
4.0641
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.
That one can deny again the denied proposition, shows that what is denied is already a proposition and not merely the preliminary to a proposition.
4.1
A proposition presents the existence and nonexistence of atomic facts.
4.11
The totality of true propositions is the total natural science (or the totality of the natural sciences).
4.111
Philosophy is not one of the natural sciences.
(The word “philosophy” must mean something which stands above or below, but not beside the natural sciences.)
4.112
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.
Does not my study of sign-language correspond to the study of thought processes which philosophers held to be so essential to the philosophy of logic? Only they got entangled for the most part in unessential psychological investigations, and there is an analogous danger for my method.
4.1122
The Darwinian theory has no more to do with philosophy than has any other hypothesis of natural science.
4.113
Philosophy limits the disputable sphere of natural science.
4.114
It should limit the thinkable and thereby the unthinkable.
It should limit the unthinkable from within through the thinkable.
4.115
It will mean the unspeakable by clearly displaying the speakable.
4.116
Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.
4.12
Propositions can represent the whole reality, but they cannot represent what they must have in common with reality in order to be able to represent it—the logical form.
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.
That which expresses itself in language, we cannot express by language.
The propositions show the logical form of reality.
They exhibit it.
4.1211
Thus a proposition “fa” shows that in its sense the object a occurs, two propositions “fa” and “ga” that they are both about the same object.
If two propositions contradict one another, this is shown by their structure; similarly if one follows from another, etc.
4.1212
What can be shown cannot be said.
4.1213
Now we understand our feeling that we are in possession of the right logical conception, if only all is right in our symbolism.
4.122
We can speak in a certain sense of formal properties of objects and atomic facts, or of properties of the structure of facts, and in the same sense of formal relations and relations of structures.
(Instead of property of the structure I also say “internal property”; instead of relation of structures “internal relation.”
I introduce these expressions in order to show the reason for the confusion, very widespread among philosophers, between internal relations and proper (external) relations.)
The holding of such internal properties and relations cannot, however, be asserted by propositions, but it shows itself in the propositions, which present the facts and treat of the objects in question.
4.1221
An internal property of a fact we also call a feature of this fact. (In the sense in which we speak of facial features.)
4.123
A property is internal if it is unthinkable that its object does not possess it.
(This bright blue colour and that stand in the internal relation of bright and darker eo ipso. It is unthinkable that these two objects should not stand in this relation.)
(Here to the shifting use of the words “property” and “relation” there corresponds the shifting use of the word “object.”)
4.124
The existence of an internal property of a possible state of affairs is not expressed by a proposition, but it expresses itself in the proposition which presents that state of affairs, by an internal property of this proposition.
It would be as senseless to ascribe a formal property to a proposition as to deny it the formal property.
4.1241
One cannot distinguish forms from one another by saying that one has this property, the other that: for this assumes that there is a sense in asserting either property of either form.
4.125
The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them.
4.1251
Now this settles the disputed question “whether all relations are internal or external.”
4.1252
Series which are ordered by internal relations I call formal series.
The series of numbers is ordered not by an external, but by an internal relation.
Similarly the series of propositions “aRb”,
“(∃x):aRx.xRb”,
“
