4.122 We can talk in a certain sense of formal properties of objects and states of affairs or of properties of the structure of facts, and in the same sense of formal relations and relations of structures.
(Instead of structural property I say also “internal property;” instead of structural relation, “internal relation.”
I introduce these expressions in order to show the basis of the confusion between internal relations and proper (external) relations, which is very widespread among philosophers.)
The holding of such internal properties and relations, however, cannot be asserted through propositions, but rather it shows itself in the propositions which present the states of affairs and deal with the objects in question.
The last sentence here seems patently absurd (cf. 4.116: there is no excuse for trying to get something out of ‘impermissible’ sentences). And if internal relations are not proper relations, what are they? Not relations at all, one is tempted to think. And perhaps internal properties are not really properties at all, although LW does not say so here. Haven’t we seen already how hard it would be to think what external properties of objects, etc. might be? If now their internal properties and relations go up in smoke, what can be left of the objects and states of affairs themselves? Black (p. 195) points out that, by 3 and 4, formal properties are not really properties at all and cannot be talked about. Hence, in the first sentence, the expression “in a certain sense.” Of that sentence, Black says: “The sentence should be put into apposition with 4.12a, where we are told that logical form belongs to the unspeakable.”
On p. 57 McManus says that “the intent of the qualification ‘internal’ seems to be that it taketh away what the word ‘relation’ giveth.”