The Tractatus opens with the line “The world is everything that is the case.” To this, Wittgenstein adds at 1.11, that the world is made of those facts and the fact that those are all the facts. This is a “stop”-clause of sorts. Frank Jackson uses one in his From Metaphysics to Ethics, which one might see as problematic. Barwise and Perry discuss this in Situations and Attitudes and decide to reject a stop clause. They think it is alright to not have an upper limit on what constitutes the world.

Why bring this up? There is an odd part in Russell’s intro to the Tractatus. He says “We touch here one instance of Wittgenstein’s fundamental thesis, that is, it is impossible to say anything about the world as a whole, and that whatever can be said has to be about bounded portions of the world.” (p. 17 of my version) This is odd because Wittgenstein starts off saying something about the world as a whole. Then he says, no really, that is the whole world. Wittgenstein not only says something about the whole world, he adds another proposition saying that’s everything. That looks like two violations of the thesis Russell attributes to him.

One might think that there could be a self-reflexive proposition or fact in the world. This is ruled out because of what Wittgenstein sees as the “fundamental truth” of type theory (that’s from his Notes on Logic). That “truth” is that a proposition cannot contain itself, which can plausibly be understood by saying that a proposition cannot be impredicatively defined. Since reflexive propositions cannot exist by Wittgenstein’s lights, he has to add another proposition to a “complete” specification of the world saying that it is complete. But, it seems like he’d need another proposition saying that those really are all the facts, and so on.

I’m having trouble squaring what Wittgenstein says with Russell’s explanation of Wittgenstein. The quote from Russell follows up a discussion of Wittgenstein on the idea of objects in general. Short version: Wittgenstein thinks “object” is a pseudo-concept and that it is legitimate to talk about objects only in connection with another property. Interestingly, this property need not be a sortal, e.g. person, dog, cat, copy of the Moral Problem by Michael Smith. It can be a mass term or adjectival property, e.g. water, blue, red, light. There’s more to untangle in the connection between these ideas, and it is possible that Russell got the interpretation wrong, but, it does seem like this is something Wittgenstein was sympathetic to.