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.