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?

I
Yes

No. I only have Ogden & Ramsey. We've been using German where necessary for clarity.

I have started Tractatus a couple of times and just could not get into it. Reading it in a structured way with others could make the difference. At least that is my hope. — Arne

I am in exactly this boat, fwiw.

This is the thread.

We're still working on 1 - 2.063. Haven't even gotten to pictures yet. Haven't even nailed down what the terms in the first sections mean. Jump right in! We've basically just started.

Yes. It has begun.

Welcome back! — Andrew M

It was worth the wandering just for the return. I'm still kind of stunned by the elegance of the argument that convinced me. The symmetry of it. In standard SB, on (H & Tue) our Beauty receives no information at all, is not even conscious; in Informative-SB, she receives nearly all the possible information. We gather all of it together into one box -- and then close the lid. Just like that, transforming one into the other.

It's quite beautiful. And a fine reminder to look for the general problem of which the one at hand is only a special case.

Let's see if we can put the "atomism" in "logical atomism"!

(The following are from the O&R translation.)

I'm going to pick out just a few remarks that are especially on point, but pretty much everything from 1 to 2.063 is required, and I'm leaving out a lot of local context to highlight these:

1.21 Any one ((i.e., any Tatsache)) can be the case or not be the case, and everything else remain the same.
...
2.02 The object is simple.
2.0201 Every statement about complexes can be analysed into a statement about their constituent parts, and into those propositions which completely describe the complexes.
2.021 Objects form the substance of the world. Therefore they cannot be compound.
2.0211 If the world had no substance, then whether a proposition 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).
...
2.061 Atomic facts ((Sachverhalten)) are independent of one another.
2.062 From the existence ((Bestehen)) or non-existence of an atomic fact we cannot infer the existence or non-existence of another.

(One issue I'm just a little concerned about -- maybe not much -- is that from the style it can be hard to tell whether you're reading a positive claim or simply (!) a contextual definition. I think it's actually all the former and none of the latter in these remarks, but there are a few others I lean toward seeing as contextual definitions.)

2.021 - 2.0212 jumps out as being something like an argument, when mainly we're being treated to interwoven assertions.

1.21 and 2.062-2.062 are essentially equivalent, since we've already been told (2) that a fact is the existence of an atomic fact.

Let's start with a simple-minded analogy. (Not an example of what W is talking about, but an analogy, to get us started.)

We can imagine the world being different, different ways of the world being different. If I think to myself, "If only everyone were nicer to me!" that's a difference. I imagine the rest of the world going on as it does except everyone is nicer to me. But everyone is a lot of people, and it's a class that splits readily given any predicate: "If only everyone I know were nicer to me!" (Taken together with "If only everyone I don't know were nicer to me!" you get the original wish.) Everyone I know is still quite a few people and we could continue splitting using predicates (everyone I know from work, everyone I know from work I go to the bar with, etc.). It becomes natural to expect there to be a smallest unit of difference we could eventually reach -- "If only she were nicer to me!" for some "she". (We're going to pretend to stop here for a moment, since this is just an analogy.) At each point along the way, the complementary class could be left as is, still not as nice to me as I'd like, and only the new smaller class I'm looking at changing. Once we get to a single element -- "she" -- we can imagine only her being nicer and no one else.

When we think about differences in the way the world might be, we expect to be able to find a smallest unit of difference. Must we be able to do so? Can we imagine always being able to go still smaller, never reaching something that is only a class member and not itself a class?

The analogy we used solves itself. The difference we were interested in is niceness, and there is a smallest unit to which the predicate nice applies, a person. (Okay, we're pretending again -- we could wish she were nicer to us Tuesdays, or last Tuesday around 3, etc.) Our classes of people must have people as members, and we must be able to identify individual members, else what sort of classes are these anyway? (That's quite weak, but we'll save real thinking for the text itself.)

It seems clear that any predicate will have such a smallest unit of applicability, and then the smallest unit of difference in the world we can imagine is such a predicate applying or not applying to one such a unit.

That's it for the analogy, a simple-minded view of how something like analysis might work, and of what might count as a fact.

Tomorrow, I'll have a go at what W actually says unless someone else beats me to it.

Thanks!

I believe you, Sam. But I'm under the impression you think we have already made a mistake or are in danger of making a mistake, only you haven't told us. And you haven't said what the right way would be.

We're just talking here. I'd like to hear what you have to say.

Such a distinction makes perfect sense and would be useful. Whether it tracks W's usage is something we'd want to know, just to make sure we don't misunderstand him.

Any suggestions or should we just dismiss this issue as to treating Sachverhalten as actual and obtaining to the world, and Sachlage as possible and not necessarily obtaining to the world, and Tatasche as being a composite of the previous two? — Posty McPostface

I don't understand the "composite" business.

For the other issue, I'll have to wait until I can look at the text again. I don't think he distinguished Sachlage and Sachverhalt this way, but you could be right. His terminology is whatever it is, though, and we can certainly use terms he didn't to make these distinctions.

You must not think — Sam26

Not the very best way to begin a post.

If you'd like to offer a different take on the passages under discussion, I'm sure we'd all be interested.

My issue was the suggestion that something isn't a possibility if it is an actuality. That struck me as an odd way to approach modality. I just want to avoid us talking past each other -- I don't know that there's real disagreement here between me and @MetaphysicsNow.

I wasn't raising an issue of interpretation at all.

Should we move on, or do people think there is more to milk out of these first few propositions? — MetaphysicsNow

No no no, we can't move on yet!

(If there are things we think we'll be better able to address after covering more, I could see keeping a little list somewhere of what we want to come back to. That's reasonable.)

In this case, I'm not at all sure we have a common understanding of these sections and we haven't yet addressed the key issue here, which is the atomicity of atomic facts. I'd try starting on the latter, but don't we need the former first?

As for some Sachverhalten being actual rather than possible -- I'm a little puzzled by the dichotomy. S is actual entails S is possible. Do you do that differently?

arguably whatever form a collection of objects has is derived from and only from those objects, so any collection of objects has form at least in some sense — MetaphysicsNow

There's so much I want to say here but I'm at work now!

So yes, I think LW wants to say something just like this. The step I began with, of just imagining a collection of things, may be an imaginary step, a step no one can actually take. Maybe it's a step philosophers sometimes think they or others take.

Is it possible to get this wrong? I mean, is it even possible to imagine incorrectly here, or must we imagine things in their connectedness?

That connectedness, the way things participate in Sachverhalten -- couple thoughts. First, there's this strong sense of necessity everywhere. You can say that my car can just happen to be in a parking lot, but my sense is he wants to say my car can't just happen to be capable of being in a parking lot. This possibility seems to be, well, part of the essence of my car. And likewise of a parking lot, that it can have cars in it. Now one thing LW seems to walk right up to saying and not quite say is that an object just is all the possible Sachverhalten it could participate in, that these are an object's essence.

Historical-contextual note. If that's roughly the road we're on, this looks spookily like a context principle for things. Frege tells us the meaning of a word is the contribution it makes to determining the truth value of propositions in which it appears. Look familiar? W is coming really close to saying the essence of an object is the contribution it makes to ("the actuality of"?) the Sachverhalten in which it participates.

((Various autocorrect fixes.))

Thanks. We've moved on here, but I appreciate your thoughts. You've addressed a lot of the gaps in my understanding of this stuff, and I especially appreciate you taking the time to do that.

Your scheme for removing the time element is pretty cool, and I'm going to spend some more time looking at it.

In terms of your M&M example, if two people guess tails and they are correct, they both get an M&M. To reflect Sleeping Beauty, the experiment is set up such that only one person gets to guess when the outcome is heads. If the person conditions on the fact that they are getting to guess at all, then they will know that they are more likely to be in the tails track. — Andrew M

One more point.

If you take a step back, SB looks a bit like a fucked up way of doing two trials of a single experiment. (No worries about the single coin flip -- the trial is asking different subjects for their credence.) But whichever way you split, by toss outcome or by day, it's not two trials: it's one trial each for two different experiments and which experiment is being run is determined by the coin toss, and is thus the source of Beauty's uncertainty.

Still thinking about how to properly score this thing.

The Lewis table is what you get if you try to compensate for SB's structure by treating the coin itself as biased 2:1 heads:tails. You start with this table
drop (H & Tue) and conditionalize on P(H1 ∨ T1 ∨ T2) = 2/3 to get
So it's true that the Lewis does represent an attempt to "discount" the overabundance of tails, but it does it in the wrong place. You can't mess with the coin.

The only thing to do, to get a better measure of success rate, is to score the results at 2:1, so that you can get a payoff table like this:
I'm not sure this is sophisticated enough though. What if instead of going all heads/tails, you use a mixed strategy? The payout events (W and L) have the right ratio, but the payout values are still screwy.

Not sure I even need to worry about mixed strategies here though. The coin being fair gives a lower bound to failure of 50% and an upper bound to success of 50%.

Thought I was done, but I'm going to keep thinking about the scoring problem.

Here's a variation of the experiment. Suppose that for Tuesday and Heads Beauty is also awakened and interviewed. At every interview she is informed whether or not it is a Tuesday and Heads interview. She knows these rules prior to the experiment. Naturally if she is informed that it is Tuesday and Heads at the interview, she can conclude with certainty that she is in a state associated with heads.

However if Beauty is told that it is not Tuesday and Heads at her interview, should she condition on that information or not? — Andrew M

I really like this argument. I meant to ask about it myself -- I saw a variation of it on StackExchange a few days ago while I was digging around for other approaches -- but I forgot.

Maybe an even cleaner version is for the additional rule to be: if and only if it's a (Tue & Heads) interview, you will be told at the start that it's a (Tue & Heads) interview; then when Beauty is not told this, she infers ¬(Tue & Heads). Now when you delete the (Tue & Heads) interview, absolutely nothing else changes. You could even run standard Sleeping Beauty by having the experimenter lie, tell her it's Informative-SB, but then never do the (Tue & Heads) interviews. This looks like the perfect way to solve SB by treating it as a special case of something more obviously solvable.

Still some things to puzzle through, but I'm convinced. My sojourn in the land of halferism is at its end.

I do still disagree about how to interpret this thing though. The failure rate of my tails-guessing Beauties is still 1/2, no matter how much they pat themselves on the back. The argument you give here totally justifies conditioning on being interviewed, so the epistemic issue isn't there; it's in this conflict between the two ways of measuring success. Michael (this is my 8 year old, not TPF's Michael) gets 1 M&M and a fatherly lecture on how to measure the success of predictions.

Thanks for hanging so long, @Andrew M (weird, the Andy in my story is my 10 year old, not you). Think I learned some things. Going to take a long break now from Sleeping Beauty.

Well, yeah, it would be quite a coincidence. I didn't see the need to labor the point. What you say here is what I was saying, so long as you take "tends to successfully predict" as the meaning of "justified". I think you probably should, because what else is there?

I don't know that you can make much more of this.

Yeah, we're not nearly there yet!

I'm going to wait for MN to chime in.

See y'all tomorrow.

The world is all that is the case and what is the case is the Bestehen of a Sachverhalten. One way of thinking about this is that the world is "how stuff hangs together". And it is holding together particular ways the facts might lie together--Sachlage — John Doe

This sounds good, except it's the possibility of things lying together, not facts.

What's the stuff about sense?

ADDED: Maybe don't -- it sounds like maybe we'd be getting way ahead of ourselves.

I don't think so. He uses the word "possible" a lot in the first couple pages, and with both.

2.0122 is another:
"The thing is independent, in so far as it can occur in all possible Sachlagen, but this form of Independence is a form of connection with the Sachverhalt, a form of dependence."

I think it's facts that are the actuality of either.

Very nice.

Yeah, good point. I totally forgot about Sachlage, which O&R render as "state of affairs".

At a glance, he seems to use Sachlage where there's a sense of the relation to other objects being "external", accidental. 2.0121 reads that way.

2.014-2.0141 repeats this same pattern of pushing the possible Sachlagen into the object as Sachverhalten.

It looks like maybe a rhetorical distinction.

The relationship of facts to atomic facts is pretty much that the former are just collections of the latter — MetaphysicsNow

I don't read it that way at all. A fact, Tatsache, is the Bestehen of a state of affairs or atomic fact. Bestehen is in O&R as "existence", but I don't know. I think of it as obtaining or holding. It can even be persistence or insistence, though that's not much better in context than "existence". It's, at root, an emphatic version of "stand", if that helps anyone.

((BTW, does anyone here have better German than I do? he asked hopefully.))

Anyway, I think states of affairs are more or less by definition possibilities, and a fact is such a possibility obtaining. Thus the world (i.e., the actual world) is fully determined by which possibilities happen to obtain.

My reading here is colored by my sense of the TLP as the link between Frege and Tarski, and then eventually PWS as the fulfillment of this whole approach. Facts are the on/off switches of states of affairs because we'll eventually define a possible world by running down a list of propositions and assigning truth values (Frege's contribution).

Sorry, I'm not getting your experiment, or its equivalence to SB.

One thing I'm generally uncertain about is how strongly to lean on "what day today is" being random. There are some things we can say about their equivalence for Beauty, but Elga and Lewis are both pretty cautious about that. I don't think we can just throw a big principle of indifference at "what day today is" and be done.

Here's how I converted from thirderism to halferism. Heads interviews are red marbles, tails interviews are blues.

If you select a marble from an urn with 1 red and 2 blues, sure, chances of getting the red are 1/3. But that is not Beauty's situation. Instead we have two urns, red in one and blue in the other. A coin is tossed to determine which urn to select from. It doesn't even matter how many marbles are in each; your chances of getting red are 1/2. Beauty cannot tell the difference between one interview on heads and any number of interviews on tails, but she knows that each procedure has a 1/2 chance of being followed.

I don't know what you're talking about. "Picture" is "Bild".

Does anyone have P&M handy? I thought, as @JimRoo says, that "states of affairs" was their translation of what O&R do as "atomic facts".

I'd like to make a modest proposal about post formatting, namely that we split our posts into three sections.

1. Interpretation of the sections we're currently working on.

2. (Optional) Upshot of the proposed interpretation for understanding the book so far.

3. (Optional) Upshot of the proposed interpretation of the book so far for the philosophical issues it addresses.

Here's the thing: it sure does look like the design of the experiment involves conditioning heads on ~Tuesday, so you get (1/4)/(1/2) = 1/2 for heads -- heads ends up by definition (heads & Monday). I'm tempted to say that since this is baked into the design of the experiment, this bit of conditioning has the status of background knowledge, more or less. At any rate, I consider it an open question whether this bit of restricting the space can or should be treated differently from the conditioning that Beauty might do in considering her personal situation.

Lots more to say, but first I want to ask you two about another quickie alternative experiment, which we might have done before, I've lost track.

I toss fair coin twice. I ask for your credence that the first toss landed heads only on {HH, TH, TT}.

My question is this: do you think this is equivalent to SB? And why or why not?

So we're going? @Posty McPostface you should change the thread title!

((I have a week of vacation coming up, so good timing! My intention is just to read and work and talk -- if we hit some stumbling block or something really really interesting, I'll figure out which box has Cora Diamond and David Pears in it. The Notebooks are in there somewhere too.))

First incautious thoughts.

You can imagine a collection of things, but even if you imagined a collection of everything, you would not be imagining a world. A collection of things is only the substance of a world, and it must also have form to be a world. The collection must be structured. Do we say here that it must be structured in a particular sort of way to be a world? Are there ways of structuring a collection that are not world-forming ways? I think the answer to that is "yes". (We'll see. What I am thinking of is structuring the collection conceptually, i.e., by a hierarchy of predicates and class membership, that sort of thing. That's a structured collection, but it's not a world.) There is a special sort of form we're looking for, the arrangement of objects into states of affairs*. A collection of objects arranged into states of affairs is a possible world; the actual world is one of these, the one in which a particular collection of states of affairs is the case.

Need to go back there a moment. You can have
(1) A collection of things;
(2) A collection of things arranged into states of affairs;
(3) A collection of states of affairs;
If you add that some states of affairs are the case and some aren't, then you can also have
(4) A collection of states of affairs that are the case;
(5) A collection of the holdings of states of affairs.
And we should go back again, and note
(2a) A collection of things arranged into possible states of affairs;
(3a) A collection of possible states of affairs;

I think we take two steps away from things. We consider them as they could be arranged into states of affairs (logical space), and shift our interest from the things themselves to these possible arrangements. Then we consider whether any individual possible state of affairs is the case; if it is, this is a fact (Tatsache). Now we're looking at collections of facts, not states of affairs, not things -- and this is a possible world, a collection of facts. How the "lower levels" get dragged along is a point of interest.

Is there anything gained in talking about possible facts? What would that be? A state of affairs is already a possible arrangement of things -- what would be the possible holding of a possible arrangement be except a possible arrangement?

I'm going to stop right here, so we can nail down how to understand facts. (I've been doing some of this by looking and some by not looking, so maybe I've made a hash of it.)

There's lots of stuff I haven't gotten to yet -- the gesture toward picturing in 2.0212, which explains why we're doing all this. Geez, why didn't he start here?

And we need to get to the biggy, which is @MetaphysicsNow's question about the atomicity (!) of facts states of affairs.


No, I don't think LW is building a sort of phenomenalist world like Goodman in The Structure of Appearance, or like Russell might have been doing around this time. (Don't know Russell well enough to know what he was doing right before the TLP.)

I would guess color turns up as a key exemplar of the way logical space works. (Hume noticed this with the "missing shade" business, and LW returns to issues of color throughout his work.) When he says in 2.0251 that "Space, time, and colour (colouredness) are forms of objects", I don't think this is meant to be an exhaustive list such as Kant might have given. They are examples of how objects are tied to a particular subspace of logical space, how what states of affairs they can be part of is prejudged.

I think I see what you're getting at -- the comparison to Kant, rationalism and empiricism -- but it doesn't quite feel true to the text. There's only the one mention of knowledge, at 2.0123-2.01231, and the suggestive variation in 2.0124, where instead of me knowing an object, objects are given. If anything, it seems like LW is specifically avoiding the tradition of starting with a perceiving subject. Instead we're going to start with how representation is possible and get to who does this representing later.

What do you think?

* This is Sachverhalt. Pears & McGuinness "state of affairs", Ogden & Ramsey "atomic fact". ((I only have Ogden & Ramsey, but we all have the German, right? I'm happy to follow the P&M terminology.))

EDIT: Dang it! Wrote "facts" for "states of affairs".