(This is rough and I’m not satisfied with it, but I have to walk the dog and teach the class.)
At the outset, this looks like a metaphysical proposition. This is a philosophy book, after all; we want to know about how things are with the world, and what kinds of things it might contain. This answer is exhilarating and perplexing: exhilarating because it promises comprehensiveness, inclusion, a world which leaves nothing out: the world is all there is. We have our frame; now on to the details!
But it is a bit perplexing too. What else, after all, could the world be? (Q: “What is there?” A: “Everything.”) Is this actually telling us anything? The world is all that is the case – ok, what’s the case? Facts. The world consists of facts – and of those facts being all the facts.
Is Wittgenstein just defining the term ‘world’ for purposes of his system here, then? That wouldn’t be very interesting: surely his definition is meant to tell us something about what worldhood amounts to. Perhaps he is maintaining something subtle: that the dependence of world-talk on facts is implicit in our ordinary ways of speaking and thinking, or that the dependence of world-talk on facts is the only ‘respectable’ or ‘sensible’ thing left over when you really think through what talk about ‘the world’ amounts to, and don’t get caught up in the kinds of mistakes that Plato, Hegel, Russell, or whoever might have made.
Following this out in one way will lead one to say things like “Aha! So Wittgenstein is committed to an ontology of facts, perhaps also to there being ‘totality facts’ which close off the world-system. Wittgenstein holds that the world supervenes on the matters of particular fact which constitute it.” Treating these as metaphysical theses, you can decide if you think they are true or not, and whether ‘totality facts’ are second-order facts about the membership of the class of first-order facts, and if so whether they count as structural facts, and whether this is the only sort of higher-order structural fact that exists (as Wittgenstein seems to hold) or whether there might not be others – perhaps set-theoretic ones?
But there’s a second kind of reading and thinking that can emerge here, pointed to in the idea of the world’s ‘supervening’ on matters of particular fact. If that’s all there is to world-talk, what is Wittgenstein saying here? Well. We talk, assert such-and-such to be the case or not, all the time. Ultimately, ‘the world’ is just the total collection of all these particular matters of fact. There’s nothing more to being a world than that: the sun is yellow, the breeze is cool, my friend is coming over, and all the other true propositions.
Now. If we want to indicate ‘the world’, how do we do it? We can’t point to it; we can only state various facts. And this isn’t a matter of the world’s size; if it was coherent to imagine a world that contained only a few facts, and which was thus thinkable-as-a-whole by an entity like us, there’s a sense in which we still wouldn’t be able to point to ‘the world,’ just to the various facts. If we were to speak like the metaphysicians, we might agree that ‘the world supervenes on matters of particular fact’; but the important thing to note there is that this is not anything like saying that there is one thing, the world, which depends in any interesting sense on these other things, the facts. Rather, there are just the facts.
So “the world is all that is the case” doesn’t exactly say anything: analyzed further it turns into something trivially true like “all the facts are all the facts,” or else nonsensical because “the world” doesn’t really signify, doesn’t really point to anything on its own. But it does, the thought goes, actually show us something critically important: what world-talk amounts to. You can’t talk about the world directly, or show how the world emerges out of matters of particular fact, since there isn’t any ‘world’ in that sense to talk about or to emerge. But you can appreciate that the sense of world-talk depends on the factual-propositional structure of thought and assertion in general, and thus come to see something about the structure of our discourse which can’t be stated directly.
At 4.461 Wittgenstein characterizes tautologies and contradictions as sinnlos, without sense. In 4.4611, his comment on this, he clarifies: “Tautology and contradiction are, however, not nonsensical (unsinnig); they are part of the symbolism, in the same way that “0” is part of the symbolism of arithmetic.”
It could plausibly be maintained, against the ‘ineffabilist’ second reading I have been laying out above, that to read “the world is all that is the case” as not telling us anything about the world and yet as showing us something about the overall structure of factual discourse, showing us something that cannot be said, is to read “the world is all that is the case” as sinnlos rather than unsinnig, as a kind of tautological higher-order appreciation of something about the overall structure of factual discourse, which can’t be stated directly (perhaps because in stating it our language has no recourse but to treat it as another matter of particular fact, which it is not), but which nonetheless one can be brought to see by careful consideration of what factual discourse as a whole amounts to.
But now fatigue is setting in. This second kind of reading seems to collapse under its own weight. At 6.1 and 6.11 Wittgenstein offers the view that analytic propositions are propositions of logic, that propositions of logic are tautologies, and that tautologies say nothing. Leaving aside the issue of whether there even can be any tautologies for Wittgenstein that are not of forms like (p → (q → p)), ‘the world is all that is the case’ is not like ‘it’s raining or it’s not raining.’ Neither says anything, but ‘it’s raining’ does say something, and ‘it’s raining or it’s not raining’ is something like a corner case of the ordinary ways we have of employing and reasoning from propositions like ‘it’s raining.’
‘The world is all that is the case,’ by contrast, doesn’t say anything at all. It first appears as a metaphysical claim; but upon consideration we see that it can’t be that because it’s not saying anything about the world. So then we might think, well, it’s showing us something important about what ‘worldhood’ amounts to in terms of the facts of which we can speak, but not something which can be said per se.
But: What can be said at all can be said clearly. Propositions are what is said and the thought is the significant proposition. ‘The world is all that is the case’ neither says anything nor expresses any thought; it is not sinnlos but unsinnig. It traces out a path of thought, one filled in by the comments on it and by proposition 2 and the rest of the book; but that path leads, not to a higher-level appreciation of the fact-structure of the world, not to some quasi-tautological residue of our ordinary use of ‘world’ and ‘fact’, but to the absurdity of the original claim. The thought here would be that in this statement we have not even given the sign ‘world’ any meaning in the first place (6.53), and thus that Tractatus 1 is itself, like “most propositions that have been written about philosophical matters…not false but senseless.” (4.003) Nothing at all is being said here.
Then what are we doing when we reason through to this conclusion? I suppose the thought on this style of reading would be that we are performing a kind of reductio ad absurdum on the original claim. We’re showing that the hypothesis that it has sense breaks down under scrutiny. But that’s just employing the logic that we already have and using the terms of our language as we already have them. We’re not learning anything except that the attempt to treat this particular statement as meaningful fails. It’s not a philosophical tautology, a corner-case of some minimal logical residue left over when metaphysics has failed; it’s just plain nonsense. Our reasoning isn’t showing us anything important, but only that nothing here was being said in the first place.
If that third reading is right then the Tractatus can’t be a complete or exhaustive work. There are an arbitrarily large number of ways for us to go wrong with philosophical words. (What was Wittgenstein doing when he came back to philosophy?) Rather, the thought would be that the reader of the Tractatus might come to see her own philosophical impulses and beliefs as of similar character, work through the flawed assumptions behind them, and eventually come to see that she hadn’t actually been thinking anything at all.
This is one reason that some philosophers hate Wittgenstein. It can be upsetting to suggest to someone that their whole enterprise is wrong from the get-go. On the other hand, getting upset about this seems like a failure of character, for a philosopher at least. We should just consider the arguments for and against and weigh them the best we can. Or isn’t that the deal?
It is sometimes observed, in relation to proposition 2 (“What is the case, the fact, is the existence of atomic facts”), that Wittgenstein doesn’t give any examples of atomic facts. Various discussions of why this is so are offered, and there are some standard examples of what an atomic fact might be that one hears (e.g. ‘red-at-x,y,z,t’ – this is standard metaphysics stuff, a world of properties and spacetime points).
But it may be that the search for an examples of atomic facts in the first place is just a mistake; it may be that there aren’t any and that Wittgenstein never intended there to be. If it is right that “the world is all that is the case” is not really any sort of statement at all in the end, then it should also be right that “what is the case, the fact, is the existence of atomic facts” is not any sort of statement either. And one way of thinking about this might simply be to point out that just as ‘the world’ is a sign with no meaning attached in 1, so too ‘atomic fact’ is a sign with no meaning attached in 2. After all, if nothing is being said, then nothing is being said.