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".

Pfft. I was only using Gary Larson to support (!) to @unenlightened's point.

((Need clones! Would love to be here in this thread more, but I'm still trying to deal with Sleeping Beauty,
and I've promised to participate in the Tractatus thread, which is now starting. Oh, and I have a job.))

2. is unacceptable because P is possible through mere coincidence. — TheMadFool

True. It's also true that "If its predictions are accurate, then logic is justified" sounds more like a definition than anything else, that it says this is what we mean by "justified". Your syllogism, seen that way, is just figuring out whether the word "justified", so defined, applies to logic. And it does, despite the possibility that every test of logic has succeeded by the merest coincidence rather than because This Is How The World Is. Justification is for us, isn't it? Or were you thinking of some other meaning for "justification"?

1. If logic is justified then predictions it makes must come true
2. Predictions it makes are true
Therefore
3. Logic is justified

The fallacy the argument commits, per logic itself, is that of affirming the consequent. — TheMadFool

Are you quite clear what you want to argue here and what you don't?

How would you feel about this same argument with the first premise replaced by its converse? Or replaced by a biconditional? The one would be valid, but maybe not what you want to say. The other only "partially" valid.

It looks to me that the dog knows when the cat is angry sans a common language. — unenlightened

Probability is about expectations. Success should be measured not by what proportion of your predictions were accurate, but by what proportion of outcomes you successfully predicted. That won't usually make much of a difference, but SB is skewed so that you get twice the credit when you're right about tails but are only singly penalized for being wrong about heads. If you guess heads all the time, in our guessing version of SB, you get exactly the same proportion of outcomes right as guessing tails, but you get doubly penalized for being wrong so that only 1/3 of your predictions were right.

Because the SB scenario doubles tails outcomes, it is difficult, or at least unnatural, to express your confidence about the outcome through wagering. For instance, suppose the coin is biased 2:1 in favor of heads. You have inside information and are thrilled to be given even money odds. Then we get these results:
100 tosses, 67 heads, 33 tails, 133 interviews.
Betting heads consistently on a biased coin at even money, you break even. WTF?
The sucker who was betting tails, who didn't know the coin was biased? He breaks even too.

ADDED:
Here's the spontaneous version of guessing-SB:
Suppose I'm going to teach Andy & Michael a little about probability. I'm going to flip a coin a bunch of times, but before each flip, they each guess. When they're right they get an M&M, and when we're done we'll count the M&M's and stuff. Now suppose before one toss, Michael guesses "Heads! Heads heads heads heads heads!!!!" If the coin lands heads, do I give him 1 M&M or 6?

What happens on Tuesday&HEADS is a part of the HEADS protocol, so you excluded part of it. — JeffJo

(a) No it isn't. From the OP:

A fair coin will be tossed to determine which experimental procedure to undertake: if the coin comes up heads, Beauty will be awakened and interviewed on Monday only. If the coin comes up tails, she will be awakened and interviewed on Monday and Tuesday. In either case, she will be awakened on Wednesday without interview and the experiment ends.

I personally think it's slightly cleaner to describe the experiment as immediately sending her home at the conclusion of her final interview, whether that's Monday or Tuesday -- it reduces the temptation to argue about Tuesday and Wednesday -- but this is a standard presentation and it works just fine.

There's also little difference if you modify the experiment as @Michael suggested and push the tails interviews back a day to Tuesday & Wednesday, and give Monday entirely to heads. Or do them all at different times of day on Monday, as some internet poster (on one of the LW threads, I think) has suggested.

The only thing that matters is one for heads and two for tails.

(b) If it were part of the heads protocol, by eliminating it, you would be eliminating heads as an outcome. Simply being interviewed would tell you the coin landed tails.

If that seems like a tendentious interpretation, consider what happens as you increase the number of tails interviews: whatever the ratio, that's your odds it was tails. Do a thousand tails interviews, and it's a near certainty -- according to thirders -- that a fair coin lands tails.

The "help" I am trying to offer — JeffJo

I was speaking as Beauty there. I appreciate your input very much -- my point was that Beauty reasoning in this way makes no progress.

you won't address my "four volunteers" proof that the answer is 1/3. — JeffJo

I'll look at it. After 18 days now in this thread, I had grown weary of alternative presentations that require analysis to figure out if they're even equivalent to SB. But I'll look at it.

it is a sophistication to de-animate the world, rather than a struggle to animate others — unenlightened

This is straight-up brilliant.

((Hey @frank -- remember that thread about whether we do in some sense "talk" to the world, ask it questions and listen for an answer, etc.))

Suppose we really were asking Beauty to guess the result of the coin toss, rather than give her credence. We'll do this with 100 Beauties and tally the results.

100 tosses, presumed result of 50 heads and 50 tails, 150 interviews.
If the Beauties all guess tails all the time, they will get 100 right out of their 150 answers.

That looks like a 2/3 success rate, right? But is it?

Out of the 100 tosses, they got 50 of them wrong. Looked at this way, that's a 50% success rate.

There's an element to committed tails-guessing of over-performing in districts you're sure to win, if you see what I mean. That extra interview, the one that tips that the result was tails, it happens in the tails track. If you're guessing tails, you've already guessed it. You're not "extra right" about tails just because you get to be right twice about the same event.

Some of the math puzzles me. Figuring out how to formalize it puzzles me. It's not a situation there's an off-the-shelf model for. Getting the math to work in a satisfying way is a chance to learn. None of that makes me at all uncertain about 1/2 being the right answer though.