Following up on what I wrote here, the content of section 2 through 2.063 is going to be deep stuff.
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He talks a lot about “objects”. Now, since “facts” do not exist in our Universe, but in “logical space”, as he wrote earlier [see above link], and he claims that objects are parts of facts [=2.01 An atomic fact is a combination of objects (entities, things)], then of course the apple I am about to take a bite out of is not the kind of object he is talking about. That apple exists in the physical universe, not in “logical space”. Also, that apple does have an existence independent of any facts about it, it would seem to me. An apple is an apple. But the objects he is going to talk about live in “logical space”, not in the physical Universe, and he is going to show that they are pretty strange creatures.
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Let’s talk a little about this “logical space”. He says some odd things about it. For one thing, he used two different phrases, “logical space” and “the world”. A fellow on Witt’s level would not use two phrase for the same thing unless he made it quite clear that they are indeed the same thing. So that we must conclude that the world [=the set of all true facts] is a proper subset of logical space. There are more things hanging around logical space than just facts and just “the world”. What else is there remains to be seen.
First of all, not just truths hang around in logical space. Falsities do also. Socrates being American is a falsity, and it also is sitting in some pub in logical space, drinking a beer. He says this quite clearly in 2.06:
(The existence of atomic facts we also call a positive fact,
their non-existence a negative fact.)
The “facts” that are true, that “exist”, that are positive [“true”, “exist”, and “positive” are three ways of saying the same thing], are the elements of the set he calls “the world”. He states this explicitly in 2.04:
2.04 The totality of existent atomic facts is the world.
Just to be absolutely clear, “existence” [as used by Witt] for a fact means the idea it conveys is true in our real physical universe. But non existent facts [=facts that convey ideas that are false in the real world, such as Socrates being American], are “facts” as well; they are negative facts. They are fair game for logic to study, and so they exist in logical space [to the extent anything exists there], although they would not be said to “exist” in the very special and technical sense of "exist’ [=true in our physical world] that Witt gave to that word.
So I’m beginning to think that the inhabitants of this twilight zone he calls logical space are the concepts and ideas that logical thinking thinks about.
[Again, it doesn’t really matter whether there really “is” a logical space out there somewhere, or if it’s all in our heads. Just as it doesn’t really matter to a mathematician whether there really is such a thing as a set, or a number, so too everything Witt says about logical space remains valid whether that space is “real” in any sense or not.]
More on logical space later.