The point being that atomism is explicitly rejected in the investigations. That has got to have some relevance. — Banno

<shrug> Whitman wrecked his early work by revising it. Later doesn't equal better.

I'm not sure we're far enough along to begin some Grand Appraisal. It's a strange book. Hard to tell what's premise and what's conclusion, or, maybe better, what's a speculation and what a consequence of that speculation.

I intend to continue trying to take it on its own terms. Insofar as I have an agenda, that's it.

We get "world" for all obtaining atomic facts; "reality" for all obtaining and not obtaining atomic facts; I think it turns out "state of affairs" is kept around for its useful ambiguity: it covers the case where you only have a subspace defined, the case where only the positive facts are defined, and the case where absolutely everything is defined. — Srap Tasmaner

Yes, this is where we differ. See:

1.13 The facts in logical space are the world.
and
2 What is the case, the fact, is the existence of atomic facts.

So,

Here's one thing I keep thinking about: can we think "state of affairs" as always short for "state of affairs in logical space"? — Srap Tasmaner

yes and no? I think once again the distinction between what obtains and not is important, and atomic facts just are, where states of affairs actually obtain in reality.

2.1 We make to ourselves pictures of facts.

In other words, states of affairs.

But, then we get this, which is just confusing:

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.

2.06 The existence and non-existence of atomic facts is the reality. (The existence of atomic facts we also call a positive fact, their non-existence a negative fact.)

2.063 The total reality is the world.

Therefore, some epsilon delta form of solipsism?

The thread seem to be going slowly — Banno

This is a Good Thing™.

The confusion only gets clarified about this whole world/reality thing in propositions 5.6, and so on, with the limits of my language being the limits of my world and so on.

See:

This remark provides the key to the problem, how much truth there is in solipsism. For what the solipsist means is quite correct; only it cannot be said, but makes itself manifest. The world is my world: this is manifest in the fact that the limits of language (of that language which alone I understand) mean the limits of my world. (5.62)
The world and life are one. (5.621)
Original German: Die Welt und das Leben sind Eins.
I am my world. (The microcosm.) (5.63)
Original German: Ich bin meine welt (Der Mikrokosmos.)
The subject does not belong to the world, but it is a limit of the world. (5.632) — Wittgenstein

And then he got rid of atomic facts - see Philosophical investigations. — Banno

As I understand it, you do believe that there's an early and later Wittgenstein. I don't think this is entirely true. After all, I think Wittgenstein wanted to publish both books side by side.

Much goes unchanged long the course of his thought. Not so atomic facts.

Or at least objects. See PI❡46 and thereabouts.

The grammar built from objects and facts would work quite well, qua grammar. Indeed, it's not at all distant from the grammar of interpreting first order language. The annoying thing was that what counts as an object changes form occasion to occasion. Hence, the grammar of the Tractatus can never be more than a special case, a sub-class of language; a language game.

Did you decide on some suitable understanding of "logical space"?

Take your pick, says Piglet:

https://en.wikipedia.org/wiki/State_space

The confusion only gets clarified about this whole world/reality thing in propositions 5.6, and so on, with the limits of my language being the limits of my world and so on. — Posty McPostface

Cool, so there's only about two thirds of the book between where we are now and that.

Sadly, or not so sadly, depending on how much you like this reading group, yes... I think so.

Haha.

My long-promised take on pictures will happen tomorrow. I'm leaning toward pushing on into 3 pretty quickly too. Stuff there that rounds out what we've been working at.

Cool, thanks!

@Srap Tasmaner

This is from the Scott Soames book I referenced above:

I think it's a good explanation...

More to the point of what we were arguing over:



So, basically he (Wittgenstein) raises the issue of 'possible worlds' but neglects to pursue the matter further. Kind of unfortunate given how popular the idea is nowadays with two dimensional ism or possible world semantics (the author does note though, that Wittgenstein first brought it up though); but, that kind of clarifies the whole issue up, yes?

Read the footnotes starting with '3', then '4'. It's all in there.

And finally;

OK, and this is the last part from that chapter. Further from that the issue does not continue.

Waiting on you @Srap Tasmaner, if you have any thoughts about the above or moving onto proposition 2.1 and so on...

Here we go. Thinking I'll post bits as I get them done, then you can read and comment while I'm doing the next bit. (Here and there you'll notice me futzing with the translation a bit.)

The picture theory is presented in 2.1-2.225. It's broken into chunks as follows:

2.1-2.141 deals with facts.
2.15-2.1515 is structure, form of representation, and the representing relation.
2.17-2.182 picks up the strand of the link to reality from 2.1511-2.1512
2.19 throws in the world
2.2-2.225 is a bit of a kitchen sink summation, with some emphasis on truth and falsehood.

We have already talked a bit about 2.11: a picture presents "how things stand", "what the situation is" in logical space. There's trouble right off the bat. Why doesn't he say "how things might stand"? Or "what the situation might be"? To drive home this is not an oversight, remember 2.11 is the comment on 2.1: "We make to ourselves pictures of facts ((Tatsachen))." That's facts, not possible facts, possible atomic facts, whatever.

Sticking with 2.11: what the picture presents is the obtaining and not-obtaining of atomic facts; this is the gloss on "how things stand in logical space". And we have seen exactly this formula before, in 2.06: "The obtaining and not-obtaining of atomic facts is reality." Alright, then, a picture presents reality. (And here we remember that even though Tatsache was originally introduced simply as the obtaining of an atomic fact, we have since refined that as a positive fact, and there are also negative facts.)

Wait, so does that mean pictures are by definition "accurate" or "true" or something?

If a picture, a picture of facts, presents reality, then what are we to make of 2.01-2.02 2.201-2.202, which seems to say exactly what I pointed out he didn't say at the start: "The picture depicts ((bilden)) reality by representing ((dartellen)) a possibility of the obtaining and not-obtaining of atomic facts. The picture represents a way things might stand, a possible situation, in logical space."

Now there's a little variation in the verbs here — hard to say yet whether this is a technical usage or not. In 2.11 it's plain stellen: a picture presents, puts before you, offers maybe. In 2.202 it's darstellen, which is more like "depicts" or "represents" — it's "present or put there", so I guess it becomes "depict" or "represent" because some sense of displacement is built in.

Leaving the usage of verbs aside as uncertain, we'd have to conclude that reality is a possible situation in logical space. That doesn't seem so bad. The way things are is a way things might be. But there's more: 2.21 says "The picture agrees with reality or not; it is right or wrong, true or false."

So a picture, of facts, presents reality, by representing a possible situation in logical space. What it represents is its sense and the picture is true if its sense agrees with reality. (2.221-2.222)

Okay, so pictures and reality.

A picture represents a way things might stand in logical space. I've been calling that sort of thing a possible partition of logical space into existing, or obtaining, atomic facts and non-existing atomic facts. There are many, many such partitions possible.

Before going on, is this right? Should we think of a way things might stand in logical space as a way logical space might be partitioned into obtaining and not-obtaining atomic facts? I really can't think of an alternative. That makes some of LW's grammar seem a little weird to me, but I'm hoping that's mainly a linguistic issue. The phrase he uses in 2.06 and again in 2.11, "the existence and non-existence of atomic facts" — how are we take that if not as a partition?

Maybe we're inclined to say, no, it's not like a list of atomic facts with a check mark next to the ones that exist. But is that a partition? Or is that a representation of a partition? What is the partition "itself"? Suppose I have a collection of red marbles and blue marbles. I can make a rule to sort the marbles by color. Is that rule the partition? Or is it the rule we follow in constructing the partition? What if I get two boxes and put all the reds in one and all the blues in the other? Is that physical separation the partition? I think, again, and oddly, that's a representation of the partition, a representation that happens to use the very things it represents. If I explained to someone that I could sort the marbles by color and they didn't know what I meant, I could do the boxes and say, "I mean like that." But was physically separating the marbles into boxes necessary? I don't think so.

So a partition is purely logical, formal. In most usages it is simplest to identify the partition as the rule you use to create it, but that's slightly abusive. We need something like the rule and the application to a given space, or the rule applied to a given a space. It is a function, defined on a specific domain, and assigning to each member of that domain some single value from some finite list.

Now, Wittgenstein says that what a picture represents is its sense, a possible partition of logical space, and that its sense, this partition, can agree or disagree with reality. If the sense of the picture corresponds with reality, then the picture is true. It is the picture itself that is truth-apt, not its sense. He does not say that the sense of the picture is true or false but the picture itself. Agreement with reality would appear to consist in representing the partition "actually in effect" — I don't have handy another way to say this.

Next installment: structure, form of representation and all that.

There are facts that represent other facts. They do this, roughly, by their elements being arranged the same way the elements of the facts represented are. This is pretty intuitive. But it also leads directly to the point that a representing fact, a picture, cannot have as an element any of these: something that indicates it is a picture, something that indicates what fact it is a picture of, something that explains how it represents what it represents, any indication that it is a picture at all. None of those are present in the fact represented, so there is no element in what is represented for any such element of the picture to correspond to. (If there are such things, they will have to be immanent in the picture, but not an element.)

Thus we get 2.172: "The picture, however, cannot represent its form of representation; it shows it forth." (More below.)

We're still working through whether and how pictures are veridical. We begin with pictures tied to facts and reality. Thus at 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." That's are. No question that the elements of a picture are combined in a definite way. Of course they are. So what does a picture represent? Obviously a veridical picture shows things combined as they are. What about a non-veridical picture? Doesn't it show things combined in a way that they aren't? (More on this in a moment.)

We get the rest of the terms we need in the remainder of 2.15: "The connection of the elements of the picture is called its structure, and the possibility of this structure is called the form of representation." Structure makes perfect sense, but form of representation is the possibility of this structure? And then in 2.151 he says: "The form of representation is the possibility that the things are combined with one another as are the elements of the picture."

So this is what 2.172 says the picture cannot represent. It represents a possible situation in logical space, atomic facts existing or not, and it represents (vorstellen this time instead of darstellen) that things are combined the way its elements are, but it does not represent the possibility of itself having the structure it shows the things it represents having.

The form of representation is the possibility of this fact, the picture, having a certain structure; what's notable about this structure is that its elements can be coordinated with the things it represents. This is the representing relation. The representing relation is what makes a fact a picture, and this relation is immanent in the picture. (Evidently pictures are not signs at all, are not arbitrary — that will come later. Pictures are models.)

All this leads up to 2.17: "What the picture must have in common with reality in order to be able to represent it after its manner — rightly or falsely — is its form of representation." So its form of representation — the possibility of the picture having the structure that it does, its elements being combined as they are — this possibility is what the picture has in common with reality.

So now we can come back to the true and false problem. We can look at this backwards: what the picture does not represent, it cannot get wrong; what no picture represents is its own form of representation. This it cannot help but get "right". But what is it?

((Timeout. Possible that "form of representation" is not the best translation here. P&M use "pictorial form" which is scarcely better. The key word here is Abbildung which seems to cover lots of stuff related to projection — reproductions (as of pictures), mappings and such in mathematics. As a matter of fact, it seems likely that this idea of projection — from what is represented to the picture — is exactly what's missing here. LW has all these descriptions that run from the picture to reality — the feelers and all that — but almost nothing in the other direction, which is quite strange.))

It seems like he was on the verge of saying that a picture has the same structure as what it represents, but he doesn't — he says it has in common with what it represents this form of representation, or projection or mapping. So we can conclude that this possibility of the structure the picture has is also a possibility found in what is pictured.

Remember my marbles? Physically sorting the red and blue marbles into separate boxes is a way of physically representing the logical partition of the marbles by color, using the marbles themselves. The physical arrangement of them into separate boxes creates a correspondence, a systematic correspondence like a mapping or a projection, between how the marbles are combined or separated and the logical partition. This is a physical model of a logical possibility. That's suggestive anyway.

I'll stop here and wait for your input, @Posty McPostface. Need clarity on the form of representation, and then we'll make some sense of the true and false business. Maybe that won't be clear until we push into 3 and propositions.

This, I think, is what the Tractatus is doing.




Some interesting mathematical messing with the picture here, but probably a side issue, except to note that they manage to fill in the blank spot, and it contains the whole picture again, twisted upside-down, and so ad infinitum.

There is a sense in which this is an impossible picture, and thus 'meaningless' in Witty-speak, and another sense in which it is a necessarily incomplete and distorted representation of the reality that we we see that we are part of. I think this goes some way to explain the difficulty of pinning down the relation of world and logical space - gallery and picture.

I'll have to get back to you in a while Srap, that's a lot to cover, and really hope someone else can chime in also...

=]

No problemo.

@Srap Tasmaner, before we move on, I feel as though it's important that we still need to cover one important topic to understand the importance of the picture theory and everything else that follows. Namely, I want to delve a little more deeply into 'logical space' and the possible configurations that can be obtained from the arrangement of objects in it. In fact I would want to go as far back and cover some more of Frege, just to give some more backdrop on everything that follows from it, which is a lot. But, that might be too much to ask for, so I'm just going to stick with logical space until I feel that we've adequately covered it to entertained where and how pictures derive their meaning from, in logical space.

Just to start out in case anyone is interested, here are some useful links:

http://www.autodidactproject.org/other/wolniewicz1.html
https://www.quora.com/What-is-Wittgenstein-s-Logical-Space


I'll read up on it, and delve more into this aspect as time allows me to. I should have everything ready by the end of this week, as I'm still composing everything.

Sorry for this snag, although an important one we ought to cover.

Any input from you, Srap, welcome. If you think it's not worth doing, let me know and we can brush this aside.

I highly recommend the following to read. Let me know what you think about it @Srap Tasmaner.

Thanks.

http://www.autodidactproject.org/other/wolniewicz1.html
https://www.ontology.co/pdf/wolniewiczb.pdf

http://www.autodidactproject.org/other/wolniewicz1.html — Posty McPostface

I see that Wittgenstein regards only one possible world as actual. Does he also explain what makes a possible world actual?

It is already apparent that Wittgenstein's idea aims at the construction of a geometrical representation for the logic of propositions, and that his "logical space" is an abstract space like the "phase‑space" of physics or the "sample‑space" of the theory of probability. And this leads immediately to the next and most essential question: what are to be the points of this abstract logical space?

The right answer: to this question has been already given by Stenius (Wittgenstein's 'Tractatus', 1960): every point in logical space is the representation of a possible world! (Stenius' answer is not the only one that has been suggested, but none of the others will do as an interpretation of Wittgenstein's position.) Let's call these worlds "logical points". We have thus:

Logical space = the totality of logical points,

The logical the set of logical points which
place of “p" = would make the proposition "p" true.

One point in logical space is designated: it represents the actual world. (Since each possible world is incompatible with every other the designated point is unique.) Of course, we do not know its exact position; but if we know a proposition "p" to be true, we know the designated point to lie in that area of logical space which is the logical place of "p". Thus we have:

"p" is true = the designated point is contained in the logical place of "p".

According to Frege the denotation of a proposition is its truth‑value; according to Wittgenstein the denotation of a proposition is its logical place (= a set of possible worlds). And 'this makes clear, why formula (F) has to be rejected.

I believe the answer is presented in the above quote from the website you referenced. I see now that I'm going to have to delve into Stenius' interpretation of the Tractatus. Dang...

I believe the answer is presented in the above quote from the website you referenced. I see now that I'm going to have to delve into Stenius' interpretation of the Tractatus. Dang... — Posty McPostface

Well, it just says that the actual world is represented by a designated point in logical space. But why is this point designated?