4.1211 Thus one proposition ‘fa’ shows that the object a occurs in its sense, two propositions ‘fa’ and ‘ga’ show that the same object is mentioned in both of them.  If two propositions contradict one another, then their structure shows it; the same is true if one of them follows from the other.  And so on.

4.1212 What can be shown, cannot be said.

4.1213 Now, too, we understand our feeling that once we have a sign-language in which everything is all right, we already have a correct logical point of view.

4.122 In a certain sense we can talk about formal properties of objects and states of affairs, or, in the case of facts, about structural properties:  and in the same sense about formal relations and structural relations.  (Instead of ‘structural property’ I also say ‘internal property’; instead of ‘structural relation’, ‘internal relation’.  I introduce these expressions in order to indicate the source of the confusion between internal relations and relations proper (external relations), which is very widespread among philosophers.) It is impossible, however, to assert by means of propositions that such internal properties and relations obtain:  rather, this makes itself manifest in the propositions that represent the relevant states of affairs and are concerned with the relevant objects.

4.1221 An internal property of a fact can also be bed a feature of that fact (in the sense in which we speak of facial features, for example).

4.123 A property is internal if it is unthinkable that its object should not possess it. (This shade of blue and that one stand, eo ipso, in the internal relation of lighter to darker.  It is unthinkable that these two objects should not stand in this relation.) (Here the shifting use of the word ‘object’ corresponds to the shifting use of the words ‘property’ and ’relation’.)

4.124 The existence of an internal property of a possible situation is not expressed by means of a proposition:  rather, it expresses itself in the proposition representing the situation, by means of an internal property of that proposition.  It would be just as nonsensical to assert that a proposition had a formal property as to deny it.

4.1241 It is impossible to distinguish forms from one another by saying that one has this property and another that property:  for this presupposes that it makes sense to ascribe either property to either form.

4.125 The existence of an internal relation between possible situations expresses itself in language by means of an internal relation between the propositions representing them.

4.1251 Here we have the answer to the vexed question ’whether all relations are internal or external’.

4.1252 I call a series that is ordered by an internal relation a series of forms.  The order of the number-series is not governed by an external relation but by an internal relation.  The same is true of the series of propositions ‘aRb’, ‘(d :  c) :  aRx . xRb’, ‘(d x,y) :  aRx . xRy . yRb’, and so forth. (If b stands in one of these relations to a, I call b a successor of a.)