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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.

4.122

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, betwen 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.

4.123

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 intern al property of this proposition.

It would be as senseless to ascribe a formal property to a proposition as to deny it the formal property.

4.125

The existence of an internal relation between possible states of affairs expresses itself in language by an internal relation between the propositions presenting them.

4.126

In the sense in which we speak of formal properties we can now speak also of formal concepts.

(I introduce this expression in order to make clear the confusion of formal concepts with proper concepts which runs through the whole of the old logic.)

That anything falls under a formal concept as an object belonging to it, cannot be expressed by a proposition. But it is shown in the symbol for the object itself. (The name shows that it signifies an object, the numerical sign that it signifies a number, etc.)

Formal concepts, cannot, like proper concepts, be presented by a function.

For their characteristics, the formal properties, are not expressed by the functions.

The expression of a formal property is a feature of certain symbols.

The sign that signifies the charcteristics of a formal concept is, therefore, a characteristic feature of all symbols, whose meanings fall under the concept.

The expression of the formal concept is therefore a propositional variable in which only this characteristic feature is constant.

4.127

The propositional variable signifies the formal concept, and its values signify the objects which fall under this concept.

4.128

The logical forms are anumerical.

Therefore there are in logic no pre-eminent numbers, and therefore there is no philosophical monism or dualism, etc.