hypothetical ways to verify — Marchesk

We could start there. "In principle" is up for negotiation.

Can you come up with a hypothetical way to verify that there really are entities you'd call universals?

Depends on what you mean by disaster... — Mr Phil O'Sophy

Anything in the answers already given you would count as a disaster and attribute to something you'd be willing to call "Western civilization"?

our inability to verify it (at least currently). — Marchesk

Nobody thinks that's a criterion for meaningfulness. Anyone who goes down the verificationist road will say, x is a meaningless proposition if it cannot in principle be verified.

you have to focus on what people feel - not what should they feel — csalisbury

Not only is that true, but, as Arlie Russell Hochschild argues in Strangers in Their Own Land, Republicans deeply resent being told by the Left how they should feel, who they should care about, what they should be outraged about and what not.

I never thought the birther movement was racist. — Hanover

Wait, really?

Here's a poll from 2015. The pollster gets a B rating from 538, and shows a tiny Democratic lean.

You can argue race is not a factor here. You could say thinking Obama was born somewhere else is just ignorance, like most Americans not being able to pick out Estonia on a map, something like that. After all, only 60% of usual Republican primary voters seem to know where Ted Cruz was born. You can say there's no pattern to the opinions of Trump's primary supporters, and I won't be able to prove you wrong. There's no proof to be had either way here.

I'm just asking, do you really look at numbers like these and see no evidence that race was part of birtherism?

I don't accept there are double standards — Baden

Isn't the disagreement precisely over whose double standard everyone should follow?

How can progress obtain for a singular "I". It doesn't. — Posty McPostface

?

That was "I" because I didn't want to speak for anyone else!

Plus I'm choosing to take Pseudo's comment in sensu diviso -- more or less against his express wishes -- and thus as a claim that I am mired in uncertainty, which I ain't.

Look at the thread currently running on the Tractatus, they can't get past the second proposition with becoming mired in uncertainty. — Pseudonym

Oy! I think I'm making progress! And the work is good for me.

Hmmm, have decided it's better to give a "no such thing" option, since partisans of the other options would also disagree with the partisans of option 3. But you can't edit the options, at least not once it's going. Look for a re-rolled poll.

Oh yeah, meant to say, "If you don't think there is such a thing, don't vote," but I forgot. I'll add that.

ADDED: Shoot! Have to amend the question again. If the proposition is "Western Civilization has been a disaster," you may choose, even considering "Western civilization" to be a vacuous description, to consider the proposition thereby nonsense or thereby false.

It isn't another fact. — Srap Tasmaner

A picture does not contain its own truth.. — unenlightened

While waiting around, I started reading The False Prison by David Pears, and within a few pages it is suggested that this little exchange is very nearly the whole point of the Tractatus. So there you go.

An atomic fact is absolutely a bit here, good call.

I don't think though that a complex has an extra bit that's on or off; either the right set of bits is on or it isn't. Calling them a set like that, treating them as a unit, implicitly adds another bit, in a sense, but it's not something that shows up on the same level. It isn't another fact.

Last last part, some of what each of us had right and wrong:

You were right that Sachlage is associated with possibility -- it's possible assignments of the value fact to atomic facts.

This assignment is in some sense "external" -- the atomic fact as a whole gets designated fact, without regard to its internal structure -- I think. But since a Sachlage is consistent, we rule out things like the same object participating in multiple atomic facts, a restriction not in place in the "big" space of all possible atomic facts.

I would expect to be able to say that a Sachlage also rules out mutually exclusive atomic facts -- and may have said so above -- but there are no mutually exclusive atomic facts! They are all independent.

I don't know quite how to take the last bit.

Last part.

We call the partition in effect, that Sachlage, "reality", so it's the complete set of obtaining and non-obtaining atomic facts. The world is all of the atomic facts that obtain, the positive "half" of the Sachlage. But I don't know yet whether there is a function over partitions that assigns one the value "true" and the rest the value "false". Maybe.

W seems instead to focus on the Sachlage itself as a function that assigns some atomic facts the value "fact" and some not. From just the ones that are assigned "fact" -- the "positive half" -- you get the whole thing. It's a partition. And focusing on this level keeps to the forefront that shifting the value of a single atomic fact (from fact to not, or vice versa) is always an option, and that switch defines the difference between one partition, one Sachlage, and another.

I haven't gone back to the text, but here's my new thought:

There's the logical space of possible atomic facts. That's all of them, with no thought at all for which obtain, which don't. The only restrictions here -- I think -- would be form and logic. But again, obtaining not an issue.

Then there are the possible partitions of the entirety of logical space into atomic facts that obtain, and atomic facts that don't obtain. Such a partition is a Sachlage, a way things might stand in logical space.

There's a sense in which the Sachlage doesn't affect which atomic facts an object may participate in -- again, that's only down to form and logic. But we can still look to the partitions, and say here's a partition that includes atomic facts an object could participate in, here's one that includes atomic facts an object cannot, because of formal or logical reasons. Atomic facts here are still all possible atomic facts, but we can look at those in terms of the possible partitions of logical space, the Sachlagen.

This starts to sound right to me. And it leaves Tatsache as the obtaining or not of an atomic fact. A Sachlage is still just a partition, a possible way logical space might shake out, but I think we'll want a way to say here's a partition that obtains. But a partition is on a whole different level from an atomic fact, so we can't talk about this the same way. Such a partition actually obtaining would be a collection of Tatsachen, of facts, and now we're in a position to sort out what is meant by "reality", by "the world".

We never do in fact talk about a partition being factual. Instead, we talk about the collection of atomic facts that would be factual if a partition obtained. That leaves us with two options: list the atomic facts and say they obtain; list the obtainings, the facticities of the atomic facts, and say they -- what? Are? It seems where we want to end up is saying this or that atomic fact is a fact -- I'm just not quite sure that's what W's taxonomy does.

Thoughts?

ADDED: One further note about the big logical space: it would include, I think, atomic facts that are mutually exclusive. ((ADDED: WRONG)) It's not a consistent space at all. Everything possible is there. The partitions of this space will all be logically consistent, I think.

MORE ADDED: This would make the Sachlagen the possible worlds I had been hunting for, with the curiosity that we don't directly specify an actual world ((ADDED: mainly wrong)) -- as, for instance, an indexical, the way Lewis would have it -- instead, we shift to collections of facts. (Still haven't gone back to see how "reality" and "world" slot in here -- that's next.)

I had wanted to say that 2.11 is a little wrong -- that it should say that a picture shows how things might stand in logical space. — Srap Tasmaner

Oh yeah, we got this earlier:

2.201 The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts.
2.202 The picture represents a possible <situation> in logical space.

((Wasn't ready to be doing this.))

@MetaphysicsNow, @mcdoodle, @John Doe, @Arne, @JimRoo, @Sam26

Posty and I are still here, just about to work on the picture theory for real.

Try this link:
http://www.kfs.org/jonathan/witt/ten.html — Posty McPostface

Interesting.

Btw, I discovered something nice I hadn't noticed about the PDF available from Project Gutenberg. It presents the complete English text followed by the complete German text, and since it can't present them en face, there's a cool feature: you can click on the section numbers to jump from the English to German (or vice versa). Super handy.

I'm pretty much in agreement with everything you've said — Posty McPostface

Hopefully not this:

a picture is clearly a Sachverhalt — Srap Tasmaner

because this is obviously false. Sachervalten are combinations of objects, the primary simples of reality; pictures have elements but they're not objects -- presumably they'd be complexes.

What we can say is that there is an isomorphism between them -- that pictures have exactly the same kind of structure, the same kind of structure among their elements, that holds among the parts, the objects, in an atomic fact.

(And we can nod here at my question about how to deal with this isomorphism -- I argued that the metaphysics is specifically whatever representation needs, and so there's barely any sense in asking, say, how does W know these structures are the same?)

Also not this:

What 2.11 says is simply that the picture shows you what the situation is in logical space, how things stand -- and how things stand is which atomic facts obtain and which don't. — Srap Tasmaner

If the picture said of things that are, that they are, and of things that aren't, that they aren't, the picture would be an assertion. It doesn't and it isn't.

I had wanted to say that 2.11 is a little wrong -- that it should say that a picture shows how things might stand in logical space. But what 2.11 actually says is that the picture shows the obtaining and the not obtaining of atomic facts. We're at one remove from the atomic facts themselves. In this sense, the picture doesn't show, doesn't present the atomic facts themselves at all. So that bears looking at.

*

So we're doing the picture theory now. I make that 2.1-2.225. If you'd like to have a run at summarizing and interpreting, have at it. If not, I'll put something together over the next day or so.

I really think we need to go back — Srap Tasmaner

Or we could just blunder on into the picture theory -- the main thing we skipped was the stuff about form, and we can pick that while doing the picture theory.

Let's stick with this for just a bit, then I really think we need to go back.

One thing that's really noticeable is the parallelism between the descriptions of Sachverhalt and picture:

2.031 In the atomic fact the objects are combined in a definite way.
2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.
2.033 The form is the possibility of the structure.

2.14 The picture consists in the fact that its elements are combined with one another in a definite way.
2.141 The picture is a fact.
2.15 That the elements of the picture are combined with one another in a definite way, represents that the things are so combined with one another.
This connexion of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation of the picture.
2.151 The form of representation is the possibility that the things are combined with one another as are the elements of the picture.

(German below -- you can see the same phrases being used.)

So a picture is clearly a Sachverhalt, but what it pictures is presents is, near as I can tell, never a Sachverhalt, but a Sachlage. Now that's interesting.

There's something that seems vaguely to support what I was saying before:

2.173 The picture represents its object from without (its standpoint is its form of representation), therefore the picture represents its object rightly or falsely

That "from without" I could make go with my "external" view -- a picture will present atomic facts from the outside, thus as Sachlagen. It's not much.

What I was wondering about was whether the key to reading 2.11 was that the picture presents the obtaining and non-obtaining of atomic facts in logical space, emphasis there, and thus as Sachlagen, that seeing atomic facts as possibilities -- possibilities that are actualized, but no matter -- is seeing them as Sachlagen.

But I think that's wrong. "Situation", "how things stand", that's not bad here. What 2.11 says is simply that the picture shows you what the situation is in logical space, how things stand -- and how things stand is which atomic facts obtain and which don't. In other words. Sachlage seems to be used in just its ordinary sense in 2.11.

-----------------------------------------

2.031 Im Sachverhalt verhalten sich die Gegenstände in bestimmter Art und Weise zueinander.
2.032 Die Art und Weise, wie die Gegenstände im Sachverhalt zusammenhängen,ist die Struktur des Sachverhaltes.
2.033 Die Form ist die Möglichkeit der Struktur.

2.14 Das Bild besteht darin, dass sich seine Elemente in bestimmter Art und Weise zu einander verhalten.
2.141 Das Bild ist eine Tatsache.
2.15 Dass sich die Elemente des Bildes in bestimmter Art und Weise zu einander verhalten stellt vor, dass sich die Sachen so zu einander verhalten.
Dieser Zusammenhang der Elemente des Bildes heisse seine Struktur und ihre Möglichkeit seine Form der Abbildung.
2.151 Die Form der Abbildung ist die Möglichkeit, dass sich die Dinge so zu einander verhalten, wie die Elemente des Bildes

I'm going to rethink my position in view of

2.11 Das Bild stellt die Sachlage im logischen Raume, das Bestehen und Nichtbestehen von Sachverhalten vor.

2.11 The picture presents the facts in logical space, the existence and non-existence of atomic facts. ((O&R))

2.11 A picture presents a situation in logical space, the existence and non-existence of states of affairs. ((P&M))

I think I've been wrong not to look harder at logical space, the world, and reality.

Maybe there will be other answers as well. I do worry sometimes about getting the German wrong, connotation, usage, and so on, do it's good to get input on that. Of course we'd need to know what was typical usage was asking Viennese elite about a hundred years ago for our baseline. More work than I'm willing to do.

https://thephilosophyforum.com/discussion/comment/190476 — Posty McPostface

I've read that quote, and it is not obvious to me that the underlined statement is true. I remain confused.

ADDED: Besides which, I think "states of affairs" there is Sachverhalten.

I tend to think, that what obtains is the actuality of a state of affairs although both can exist in possibilities, made apparent by atomic facts. — Posty McPostface

I just don't see how to square this with 2.04-2.06. Some atomic facts obtain and some don't. If "atomic fact" means "state of affairs that obtains", then an atomic fact that doesn't obtain is a state of affairs that obtains that doesn't obtain. So it's not that. Second try: an atomic fact is "the obtaining of a state of affairs", and the obtaining of something is now something that can obtain or not. I can have an obtaining that obtains or an obtaining that doesn't obtain.

Facts I can deal with. Even in ordinary usage we can distinguish between "The vase is on the table" and "That the vase is on the table", the former a proposition and the latter a fact it expresses. Now we're in the realm of possible facts (I think?!) and it just looks confused to me.

I think the difference is, when speaking of objects, whether it's appropriate to call an object a "part".

If it is combined with other objects in a definite way, we have an atomic fact, and it is surely appropriate to call the object a "part" of this atomic fact. But what about all the possible atomic facts which it could be a part of, the possibility of being a part of which is prejudged in the object? Would you say it is a "part" of those? That seems wrong. So 2.013 has that little "gleichsam" in it.

So there's a distinction near the one you're talking about: an object isn't part of something that's only possible; that appellation we'd reserve for being so combined in something actual.

Where does that leave states of affairs? I read "state of affairs" as a way of looking at atomic facts, possible or actual, in which we still only consider the objects so combined as objects, rather than as parts. It's, as I've said before, a slightly more "external" view -- you have to take the "internal" view to see an object as a part. It can be two different ways of seeing the same thing: a grape can be a grape and at the same time a part of a bunch; a bunch of grapes is a thing, and it's partly made up of grapes, not "bunch-parts". (LEGOS would probably be a better analogy.)

Here's what really puzzles me about treating atomic facts themselves as always only actual and never possible: what about facts? There's all this business about facts being the existence, the obtaining, of atomic facts. The world is all the atomic facts that obtain. What's the point of all that if atomic facts are by definition actual? Doesn't that just make facts redundant? And how do we make sense of some atomic facts existing and some not? What could a non-obtaining atomic fact possibly be?

someone else — Posty McPostface

"If we build it, they will come"???

Wittgenstein does talk about möglich Sachlage — Posty McPostface

Sure, and he also wrote this:

2.013 Jedes Ding ist, gleichsam, in einem Raume möglicher Sachverhalte. Diesen Raum kann ich mir leer denken, nicht aber das Ding ohne den Raum.

2.013 Every thing is, as it were, in a space of possible atomic facts. I can think of this space as empty, but not of the thing without the space.

Why don't we just table this until we finally move on to the picture theory.

Why are you asking me? Suit yourself.

Is there something in the text I've misread or overlooked? Wouldn't be a huge surprise. Just point me in the right direction. Or post what you think is the key passage and show me how I should be reading it.

A little fill-in argumentation, cleaning up what I've posted so far.

That is to say, we can define a way of logically partitioning the world into units that are independent, the smallest unit of difference between one way the world might be, or is, and another. — Srap Tasmaner

If the actual world is partitioned into independent facts, then there can be no smaller unit of difference between this world and any other. If there could, then that difference would be independent of the rest of whatever partition it was included in. So they are the same.

2.0211 If the world had no substance, then whether a proposition ((Satz)) had sense ((Sinn)) would depend on whether another proposition is true.
2.0212 It would then be impossible to form a picture of the world (true or false).

We should be able to do some of this reasoning forward now.

Suppose the world has no substance -- no "substrate" that is the same no matter how things happen to be. Then for a proposition to have sense, it would presumably have to be about actual atomic facts -- is there an alternative? In which case a proposition asserting the actuality of what the proposition is about would have to be true.

Now why would we be unable to form a picture of the world if the sense of a proposition depended on the truth of another? That will have to wait until we get to the picture theory.

(1) It is possible to form a picture of the world (true or false);
(2) Therefore whether a proposition has sense does not depend on whether another proposition is true.
(3) Therefore the world has substance. — Srap Tasmaner

I just want to call attention to the shape of this argument. There's metaphysics here, but it's a metaphysics implied by what we understand about representation.

What that last means can play out differently: is this metaphysics implied by the fact of representation, or by our ideas, possibly mistaken, about representation?

Also, when it comes to talking directly about representation, we'll have to be careful. We have derived our metaphysics from the fact of representation, let's say: this is how things must be for representation to be possible, for us to be doing what we think we're doing by forming representations of the world. We cannot then come to representation and say: given that the world is this way, here's how representation works, is possible, is the way we think. That would be patently circular. This is the metaphysics required by our ideas about representation; of course it will work out as the underpinnings of representation, if representation is what we think it is.

TL:DR:

In terms of a bunch of objects, and maybe even how exactly they're combined: Sachlagen. The thing objects are combined into: Sachverhalt.

is the difference between "states of affairs" and "atomic facts" reconcilable? — Arne

Once more into the breach -- assuming "states of affairs" here is Sachlagen.

It jumps ahead a little but illustrates my trifle... — Posty McPostface

And Max Black notes that Sachverhalten and Sachlagen are really hard to distinguish.

Let's look at it this way. What can objects "do"? What sorts of things happen to objects?

Here's one way of thinking about this. Suppose your domain of discourse has two objects called a and b. (This is an analogy, using math.) You can make a set {a, b}. This possibility is intrinsic to a and b being in your domain. There might also be some relation R that holds between a and b: aRb is true. Part of the formalization of aRb might be something like {a, {a, b}}.

When we look at a, we could say it might find itself in something like {a, b}, or in something like {a, {a, b}}. In the first a is "combined" with another element; in the second it is "combined" with another element in a more particular way. If there are other relations possible between a and b, the latter may not be specific enough to distinguish R from any other relation or function. At least it's distinct from {b, {a, b}}.

Roughly speaking, I think of Sachlagen as the possibility of an object coming together, being combined, with other objects in some way, perhaps not precisely specified. But W says that in Sachverhalten, objects are combined in a definite way.

Of an object participating in a Sachverhalt, we could say: it is combined with other objects, it is combined with other objects in a particular way. We could also not look at the other objects and just say it is part of a Sachverhalt -- which implies other objects that are also parts. All of these different ways of looking at a Sachverhalt and an object combined in it will be true. I think of Sachlage as being a way of thinking about it in terms of other objects, coming together with them, maybe even coming together with them in a specific way -- looking at the whole thing with a focus on the elements. I think of Sachverhalt as the totality, like a set of objects together with a relation defined on that set. An object can be part of such a totality, and here we focus on the relation between the object-member of and the totality, not between the object and the other objects that are also there.

I think it's just a perspective switch, but it does leave room for applying Sachlage where the way the objects are combined is unspecified or less specified. Both can be possible or actual, but there is a natural way to take not specifying the "how" as leaving wider usage for Sachlage, more possibilities. Of course, given a set and a lot of different relations defined on that set (analogy again) there would be more specific set-with-a-relation things than just the set thing -- same way there are usually more permutations than combinations -- so a term for sets arranged in some specific way would have the wider usage.

I've probably not been clear -- too many words -- but this is my sense of how the terms are used, and it doesn't line up at all with actual and possible.

It is also my understanding we are using the Ogden translation? — Arne

The quotes I've posted are from Ogden & Ramsey. It might be simplest just to settle on this as the official version -- it's available free (and legally) from Gutenberg.

In chitchat I've freely alternated between their rendering of Sachverhalten as "atomic facts" and the Pears & McGuinness rendering as "states of affairs".

is the difference between "states of affairs" and "atomic facts" reconcilable? — Arne

Maybe? I honestly don't know how much is riding on whether W makes a consistent distinction between the two words and what that distinction is.

and if the facts in logical are the world, then there can be no other space within the world that is not subsumed by logical space? — Arne

Certainly.

What is logical space? — Arne

That's a good question. I've been using the phrase to designate the vasty realm of possibilities. You can define a subspace of those possibilities that obtain and that's the world, our world, reality, actuality -- however that works, might depend on what level you're defining from.

some understanding of logical atomism is necessary — Posty McPostface

If by "logical atomism" you specifically mean Russell's views around this period, see below.

I thought there were a lot of people who took TLP itself to be one of the definitive statements of something called "logical atomism" though, so reading it ought to do the trick. Then again, this is just labeling, and I don't care. We're reading TLP and that's enough for me.

given that Russell so heavily influenced the early Wittgenstein — Posty McPostface

I'm no scholar, so I can't speak to that. I think there's plenty of textual evidence that Frege greatly influenced Wittgenstein, early and late, and Frege I know a bit about. That's a dodgy way of saying I'm slightly skeptical of "Russell's influence on Wittgenstein" being a thing.

If Wittgenstein wanted to avoid the ambiguity he could have just stuck to one term instead of convolution the whole thing with both terms. I doubt Wittgenstein would have done this unintentionally — Posty McPostface

I think there is a distinction suggested -- I just don't think it's actual vs. possible.

As for terminology in general -- this is frustrating, as I've noted. The way he rings the changes on world, reality, fact, etc., I'm not quite sure what he's up to. Is every noun he uses used in some specific technical sense? (I forget whether I posted the thought that it can be hard to tell whether you're reading a thesis, an actual claim, or a contextual definition sometimes -- if I didn't, I have now.) I don't know. I have never believed, for instance, that he was using the phrase "forms of life" as a technical term, but the commentariat have made it one. I don't know where to draw the line. I guess we have to draw it as we go.

Are facts observer independent? — Posty McPostface

Yes. In the Tractatus and in reality.

the quoted text — Posty McPostface

Ah, so that's Russell. I feel like reading that would only confuse matters. Does that seem crazy? I mean, it's hard enough to get a handle on what W is saying. Maybe more historical context would help, but there's also that danger of substituting a view that's easier to grasp for W's. Do you see what I mean?

Let me put it this way: if we need, say, Russell to understand Wittgenstein, then okay. If Wittgenstein cannot be understood on his own, then bring on the comparisons. But I'm not particularly interested in an historical approach just to be historical -- I don't care if Russell thought A, but W thought B.
.

I mean to say the latter. I feel that the difference between Sachlage and Sachverhalte is crucial here. I might be wrong. — Posty McPostface

Obtaining per se -- I can't even imagine having anything to say about that.

As for the Sachverhalt/Sachverlage thing -- I don't see this splitting as one's actual and the other's possible. There's some distinction in the text but I don't see it as that, so I don't want to assign the terms those meanings.

On the other hand, we can make such a distinction. If the words W uses obscure that distinction, then so much the worse for his chosen terminology -- unless there's an argument in the text, explicit or implicit, that we ought not be distinguishing this way.

So if the point were that one's actual and the other's not -- that's not much help is it?

As for my opinion, I think atomic facts are what constitute the world, and reality is constituted by states of affairs, speaking as an observer of the world. — Posty McPostface

I also don't see anything in the text about the way the world is versus the way we observe it. Maybe that'll come out later, but I'm not reading ahead.

Btw, do you mean this is in fact your view, or it's your understanding of LW?

Also, this might help: — Posty McPostface

Did I write something that conflicts with this quote? (And where's that quote from?)

I think this needs to be expanded a little more, although I agree with it. — Posty McPostface

Expanded how? At this point anyway, I'm guessing, because we don't have anything yet on propositions or truth.

how does it obtain in reality, not the world. — Posty McPostface

Do you mean here, how one and not the other, or how does obtaining work?

If you mean the difference between reality and the world -- I can go back to the text, but it's just going to be a question of how he's chosen to use these words. Just a technical question, important for interpretation maybe, but I don't think anything else is riding on it. I don't think he ever quite lands on something that jumps out as a "possible world" -- if he had that might help. Maybe he's deliberately avoiding that, but I'm not sure why.

If it's the latter, that would seem to be a pretty deep mystery.

((I had hoped to get this up earlier, but better late than never.))

2.021 Objects form ((bilden)) the substance of the world. Therefore they cannot be compound.
2.0211 If the world had no substance, then whether a proposition ((Satz)) had sense ((Sinn)) would depend on whether another proposition is true.
2.0212 It would then be impossible to form a picture of the world (true or false).

My last post took predication as an analogy and followed the process in one direction, and reached a less than satisfying conclusion. Mainly I think LW is reasoning backward. For my analogy, that would be a claim something like this: If there were not a unit of predication, then we could not form classes in the first place. That's certainly quicker.

Here the chain of reasoning seems to run like this:
(1) It is possible to form a picture of the world (true or false);
(2) Therefore whether a proposition has sense does not depend on whether another proposition is true.
(3) Therefore the world has substance.

There's not much we can do about (1) as a premise. We're about to get to the picture theory, so we'll have more meat on these bones soon. At the moment, we're in no position to evaluate (1).

(2) we might also not be in a position to judge -- having been told nothing about propositions and their sense yet. I would like to think I can makes sense of it, but -- infuriatingly -- the remark right before this, which seems to set it up, uses a completely different set of terms:

2.0201 Every statement ((Aussage)) about complexes ((Komplexe)) can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.

If this were not so we might just say this: the sense of a proposition is the states of affairs (or atomic facts) it describes, actual or not; the truth of a proposition is the obtaining of such a state of affairs. Naturally we want to keep those separate somehow. Why, specifically, should the sense of a proposition not depend on the truth of another? Because truth simply has no place here. If states of affairs are independent, they can obtain or not, without regard to whether other states of affairs obtain or not. We are essentially defining a "state of affairs" as the smallest unit of difference between one (possible) world and another. Such a difference belongs to logical space. If some state of affairs does obtain, it is part of reality, the actual world; there is in logical space another world, exactly like the actual world except that this state of affairs does not obtain.

We're not done, but I want to stop here to note the interpretative problem: 2.0201 is not about propositions but statements. It's also not about states of affairs, but about complexes. "Complexes"? And this is the commentary on 2.02: "Objects are simple." I think we're still on roughly the right track, but there are some intermediate steps, and I think it's what we need to get from (2) to (3).

To get from (2) to (3), we're going to jump ahead a little:

2.024 Substance is what exists independently of what is the case.
2.025 It is form and content.
2.0251 Space, time and colour (colouredness) are forms of objects.
2.026 Only if there are objects can there be a fixed form of the world.

(Starting to feel like I'm going to end up quoting the whole book.)

We should by now be able to recognize what 2.024 is about. There's the vast logical space of possibilities, some of which obtain here in reality. There is something that can be the way it is or another way. That something is substance, what abides whether it is this way or that, what it is that is either this way or that. (More in a minute.)

Now let's go back to the sense of propositions. Because the sense of a proposition "has to do with" (I don't really know how to put this) the (possible) states of affairs it describes, as distinct its truth or falsehood, which "has to do with" whether those states of affairs are factual -- because of this, the sense of a proposition is about substance. And since substance is independent of factuality, there is no place here, in the determining of sense, for the truth or falsehood of any proposition.

2.022 It is clear that however different from the real one an imagined world may be, it must have something -- a form -- in common with the real world.
2.023 This fixed form consists of the objects.

Reasoning backward again, we might say this: a proposition that describes a different world from ours, or describes our world different in some way, perhaps different only in respect of a single fact, is clearly still about something, even though that something is not actual. I think W goes even further: what such propositions are about is exactly the same thing that propositions about the actual world are about.

Continuing to work backwards in this way, I think it's not crazy to view substance, objects, as in some sense theoretical posits. They are simply that thing that propositions are about -- I suppose really we should say what propositions are ultimately about, since it takes analysis to get there.

*

I really only meant to address independence, but I've dragged in substance too. The last little bit about independence was @MetaphysicsNow's question from before:

2.04 The totality of existent atomic facts is the world.
2.05 The totality of existent atomic facts also determines which atomic facts do not exist.

vs.

2.061 Atomic facts are independent of one another.
2.062 From the existence or non-existence of an atomic fact we cannot infer the existence or non-existence of another.

I think the way to take 2.04-2.05 there is that if you're not on the existent list, you're on the non-existent list, and it's one or the other. There is no dependence between atomic facts, or between existent atomic facts.

Again, I think we can get this independence reasoning backward.

1.2 The world divides into facts.

That is to say, we can define a way of logically partitioning the world into units that are independent, the smallest unit of difference between one way the world might be, or is, and another.

*

Stopping here. To do:

• talk about form, the forms of objects;
• fix whatever I've gotten wrong;
• fill in whatever I skipped.

Then I guess we'd be ready to move on to the picture theory and see how things start to fit together.

Has there been any progress?