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Tractatus

September 29th, 2024

Personal analysis of Wittgenstein's landmark work.

1 The world is everything that is the case.

Wittgenstein deliberates here that there exists a world and that it is self-evident, that it is "everything that is the case." That is the case implies an observation, so it is the observable phenomenon that everything is.

What I really mean here, is that the world is abstraction that absorbs the observable. That's what I think Wittgenstein is trying to establish here in his axiom.

Here he defines the world. We shall use his terminology throughout this analysis.

1.1 The world is the totality of facts, not of things.

This is an important axiom because it rejects the idea that there exists things. He's saying objects in a Platonian sense do not exist. There is no table, there is no exact chair that you can pull out. There is the existence of a chair. There is a chair in front of you. There is a chair you are sitting on. These are facts that are indisputable. However, the chair in an essence of its own does not exist.

Here, he also references the world again. He says that the world is this totality of facts, not things. This is implying that the "totality of facts" is "everything that is the case." This is a strong axiom to make, but we will go forth with it.

This idea also presupposes that with facts there must exist an observer making these facts. I don't think he has addressed it here yet, but it is clear that these facts have connection between "observer and thing".

1.11 The world is determined by the facts, and by these being all the facts.

The world is defined by facts. This is assumable from the previous statement, but I think Wittgenstein is on the spectrum and leaves no room for assumption.

"[B]y these being all the facts." I think Wittgenstein is being thorough here and saying that the world, "everything that is the case," is made up of all the facts. Not just a few, not many or majority, but ALL the facts. It is the totality.

1.12 For the totality of facts determines both what is the case, and also all that is not the case.

Here we get more information on what the totality of facts really means. It's an observation (at least, from what I assume, let's keep reading) that defines "what is the case and what is not the case." The world is defined from statements (facts) that define that that exists and that that does not.

He's justifying why the totality of facts is what defines the world, or "what is the case" because they issue statements on the negative and positive existences of our reality.

1.13 The facts in logical space are the world.

The facts, the totality of them are the world. That's the point he's trying to get at. But he brings in "logical space."

Per a reddit post, it's interpreted as:

"Logical space" is not defined in the Tractatus but, per the context, it's the set of all possible states of affairs. The logical space is not just what is the case but also what is not the case but logically possible.

"The set" of all possible states of affairs. So I imaqgine this in a mathematical sense, in that facts X, Y, and Z can exist in a logical space. Now we can negate X and keep Y and Z, so we get the set {~X, Y, Z}.

So pull all facts of the world, which may number in the trillions, and set them all on and off negation and non-negation. Combine them in every way, say each fact is either true or false, and that is the complete logical space of the world.

I'm implying here that the facts of the world are finite. There's only so many facts that exist in the world. Which I can suppose is true. As much as I'd like an infinite world, I do not believe that is the case. There are no infinite facts, it would not be possible, or would it? Would the expansion of the universe imply that the length of the set of facts that exist in logical space keeps growing? I am not sure. I don't believe so, because facts are not things.

Facts are statements, or observable phenomenon. Facts are "the case as they are."

1.2 The world divides into facts.

Sure, if the world is the set of facts that exist in logical space, then sure the world can be plucked apart fact by fact.

1.21 Any one can either be the case or not be the case, and everything else remain the same.

This is branching off what I said earlier with negation of X {~X, Y, Z}. All facts are independent of one another. I can say that the cow is red and the cow is blue. That may not be true, but the logical space exists. Does that make sense? What I'm saying is regardless if it is true, I can think of it, and that hence logical space exists, that set of facts exists in this world and I can think it. If I can think it, it is a part of the world, and it is "the case of how things are."

2 What is the case, the fact, is the existence of atomic facts.

Facts are what is the case. Atomic facts is a completely different matter. Wittgenstein is advocating that what is the case, the self-evident statements we call facts, are in fact unable to be broken down into smaller constituent parts. They are the most atomic form of a logical existence.

But, this axiom seems to bother me. Can't facts be broken down further? If no objects exist, then I suppose so, in that the objects readily only exist as factual statements or observations of what is the case. In other words, we cannot break down the world any further than our perceptions and observations of "what is the case." This is what Wittgenstein is trying to allude to. The world, as the logical space we know it as, cannot be broken down any further than the observations we have of it "as is the case."

I think this is a fair statement.

2.01 An atomic fact is a combination of objects (entities, things).

This is where it gets confusing. The fact is atomic---it in unable to be broken in smaller constituent pieces---yet here he defines an atomic fact as a combination of constituent parts. "Objects" of all things, of which he has clearly defined the world not to be the totality of. He states explicity that the world is the totality of facts and not objects.

Yet here he still posits the existence of objects. I suppose the only real existence of objects exist as parts of facts. Maybe he does not mean objects and things in the traditional sense, but rather in the sense of objects as members of facts. They are building blocks of facts? Yet how can a fact be atomic then?

After sleeping a bit, I realize that he's saying that an atomic fact is atomic in that it is no the combination of other facts, it is the most reducible form of purely a fact. Facts are defined as a combination of entities.

2.011 It is essential to a thing that it can be a constituent part of an atomic fact.

The essential, I am assuming, he refers to a thing's quality. It is the quality or properties of a thing that it is a part of a fact. So what he's saying is that the essence, or the property, of say a chair, is that this chair's essence is defined by the fact it "can be a constituent part of an atomic fact."

The atomic fact being that "someone can sit down in it," that is what makes the chair's esssence. This is what I'm assuming Wittgenstein is implying.

2.012 In logic nothing is accidental: if a thing can occur in an atomic fact the possibility of that atomic fact must already be prejudged in the thing.

He's saying that atomic facts precede things. I interpret atomic facts as "that is the case" or an observation, so I assume he's saying that observations must precede entities. The observation, or the atomic fact, or that is the case, must have "prejudged," and by prejudged I assume he's saying that it must have been determined beforehand the possibility of the thing.

The fact that "it is sittable" must have preceded the entity of the chair. He's making a big argument here.

2.0121 It would, so to speak, appear as an accident, when to a thing that could exist alone on its own account, subsequently a state of affairs could be made to fit.
If things can occur in atomic facts, this possibility must already lie in them.
(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)
Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things.
If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context.

He's saying that it is often mistaken that things can exist without the context, the observation, the atomic facts surrounding it. However, a state of affairs can always be fitted on. He said it's mistaken to believe that a state of affairs is fitted on after-the-case, when in fact it must prejudge the existence of the essence or object beforehand.

"If things can occur in atomic facts, this possibility must already lie in them." Yes, he's saying that "states of affairs" precedes objects and entities. I think Plato would be a good beforehand reading.

"(A logical entity cannot be merely possible. Logic treats of every possibility, and all possibilities are its facts.)" He's saying the logical space must exist before a logical entity can exist in it, and that its probability and possibility is predetermined by the facts describing the logical space.

"Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things." In other words, everything, entity or object, must exist in a context. In this Wittgenstein describes the context as "states of affairs" or "atomic facts" or "the world as the totality of these facts." Facts being a relation between objects and objects and objects and logical space.

"If I can think of an object in the context of an atomic fact, I cannot think of it apart from the possibility of this context." Take the idea of a cow. We cannot separate the cow from the context of space and time. We cannot remove it from this context, because it is the logical space in which we observe it to exist in. If we tried to move the idea of cow to say, a mathematical space, and say that cow exists as mathematical operation, it doesn't make much sense.

I think what Wittgenstein is getting at here is that objects are inseparable from their atomic facts, and atomic facts being the relation or observations of the "state of affairs." Atomic facts are also statements about the logical space of the world.

2.0122 The thing is independent, in so far as it can occur in all possible circumstances, but this form of independence is a form of connexion with the atomic fact, a form of dependence. (It is impossible for words to occur in two different ways, alone and in the proposition.)

"The thing is independent" is saying that the object exists as a separate body since it can occur in many different atomic facts. It is dependent on the atomic fact however. He's saying that it "is impossible for words to occur in two different ways, alone and in the proposition." What this means is that I'm not sure exactly, but maybe perhaps he's implying that words have a singular definition, which I wholeheartedly disagree with.

But I'm assuming what he's really getting at, in a roundabout way, is that the things can exist in many propositions/atomic facts and is independent in that nature, not affecting other things, however they are dependent on their connection with atomic facts to occur in possible circumstances.

2.0123 If I know an object, then I also know all the possibilities of its occurrence in atomic facts.
(Every such possibility must lie in the nature of the object.)
A new possibility cannot subsequently be found.

"If I know an object and its essence, I know all the possibilities of its occurence in atomic facts." This is tricky, I think what he's saying is that to really know something, you have to know all the possible configurations that it exists in logical space in its atomic facts. I know you can sit in a chair. I know an animal can sit in a chair. I could list all the configurations of atomic facts, and therefore I can say that I know what a chair (object) is.

New possibilities cannot be found is a strong statement. I do not agree with this, as we redefine things everyday. "Things" are a changing relativistic language phenomena. But sure, let us assume there is an objective definition of a chair in that it is sittable. This will never change and surely by that regard that new possibilities of its existence in different, new atomic facts cannot be found.

2.01231 In order to know an object, I must know not its external but all its internal qualities.

Sure. I think internal and external qualities are a reference to intrinsic and extrinsic properties I learned in grade school, which I think is Plato's forms or something like that. This statement seems straightforward, but might I be deceived?

2.0124 If all objects are given, then thereby are all possible atomic facts also given.

We define objects by their possibilities in atomic facts. So if X then Y seems given. Facts precede objects as stated above.

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.

Sure. Like stated before, I think what Wittgenstein is trying to describe here is that the world is a set of atomic facts that are switched on and off. These atomic facts can be negated and therefore describe things and not things. This space can also exist without atomic facts. But things are rooted in this space that is described by atomic facts. We must have a space to root these things in in order to define them.

2.0131 A spatial object must lie in infinite space. (A point in space is an argument place.)
A speck in a visual field need not be red, but it must have a colour; it has, so to speak, a colour space round it. A tone must have a pitch, the object of the sense of touch a hardness, etc.

I think the way I described it is "dimensions of existence" or "planes of existence." Wittgenstein is saying properties exist in their logical space and gives concrete examples here. So I think what he's trying to describe here is:

Object A: {color_space["red"], spatial_space:["that there"], time_space:["five o' clock"]}

Object: {space_1[fact_1, ..., fact_n], ..., space_n[fact_1, ..., fact_n]}

Now don't mix this up and say the world is the set of objects. No, facts precede objects in Wittgenstein's eyes, so objects exist only as facts. They are at the bottom of the tree of the model of the world.

World -> Facts -> Atomic Facts -> Objects

Now of course, now looking closer I think these spaces are not independent of one another. The time space for example is defined by that is the case, but it is defined by the sun's position so it related to the spatial space. Interesting way to frame the world.

2.014 Objects contain the possibility of all states of affairs.

What is a state of affair exactly? I assume he is saying "as is the case" or "that which is self-evident." Reddit offers more help:

Facts are states of affairs that are actual.

This means that a state of affair is a truthful fact. Truthful in that it is self-evident or is the case. This helps a lot.

"Objects contain the possibility of all truthful facts." What does the possibility of a truthful fact mean? I assume that he is saying something along the lines that objects must account for the possibility of all states of affairs that exist in reality. (I refer to reality as "the totality of what is the case.") The definition of an object, say a chair, must account for all possibilities of reality, that all chairs contains all realities in that they are "sittable." It doesn't matter if I'm in space, or in India, or in a different logical space of reality, this chair must be sittable.

2.0141 The possibility of its occurrence in atomic facts is the form of the object.

Let's start with "its occurance in atomic facts is the form of the object." Sure, we defined this beforehand. Object's forms, or their essence, or their defining feature (Plato's forms I assume,) is in our observations or our conception of the atomic facts that are either true or untrue for this object.

Now let's address the possibility. That means that we do not know all atomic facts that include and define the object. So we define the form of the object as the possibility of its occurence in atomic facts we may make in the future. This makes sense. The form of a chair is that they are sittable, so there may be atomic facts in the future that describe different things sitting in it. Sure, that is its form.

So objects have a form, they are defined by atomic facts that describe it, either true or untrue.

2.02 The object is simple.

I don't know what to think of this.

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.

What is a statement? I'll assume a fact. What is a complexes? I assume a complex fact. So a complex fact can be broken up into facts (constituent parts.) These constituent facts can completely describe the complex fact. Maybe these constituent facts can be broken recursively until they are atomic facts.

2.021 Objects form the substance of the world. Therefore they cannot be compound.

What is a substance of the world? I guess that which is the case. But we defined the world before as the totality of atomic facts. I assume by substance he refers to that which is directly observable. Substance as in relating to our senses. So our senses relate to the object.

He's saying objects cannot be compounded. Compounded in that being combined I assume. So maybe he's referring to our base senses. I'm not sure. But sure, this object cannot be combined to create more objects like we can with facts. He's saying that an actual physical sensical world exists in substance that we cannot compound and manipulate.

2.0211 If the world had no substance, then whether a proposition had sense would depend on whether another proposition was true.

Sure, I think he's trying to argue against a counterpoint here that there is no substance. He's advocating there must be of substance to observe that which is the case. Propositions cannot be cyclical in definition, or can they?

2.0212 It would then be impossible to form a picture of the world (true or false).

True. Because if all propositions depended on propositions to be true, then we could never figure out what is true or false. But that is readily not the case, as the sky is blue.

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.

He's continuing to justify why he includes objects as that which has substance in reality. He's saying that all this abstraction layer must have some real observable phenomena to it, something graspable, so he defines it here as within the objects and that which is substance.

2.023 This fixed form consists of the objects.

I was alluding to this above. But note, he says fixed form. He says fixed, as in unchanging. Why would he posit this? I think this is brash assumption that that the objects that produce the substance of the world are unchanging. It's strange. Maybe that implies that the states of affairs and atomic facts that make up these objects are also unyielding and unchanging? I am not sure. But they rely on possibilities, so that is readily not the case. I presuppose that he's implying that there exists a logical space of atomic facts that is objectively true, and that since we are only human that we are grasping at possibilities of this.

2.0231 The substance of the world can only determine a form and not any material properties. For these are first presented by the propositions—first formed by the configuration of the objects.

The reality can only determine a form---it could only determine the essence of the object. The essence, reminder, being its possibilities of occurences in propositions. Propositions being atomic facts, again. I assume this is the case. What we observe only determines the possibilities of what propositions we can make of it, and not the actual material property. I see, he's saying that we can only propose atomic facts regarding things and that is the form of it.

His reasoning is that a property of an object is formed from the proposition we make of it. Okay, so he's clearly delineating what is our definition of objects and what is actual substance that exists. He's separating language and substance here.

2.0232 Roughly speaking: objects are colourless.

To put in layman terms, objects themselves have no properties. We create propositions that give it its property. "This is blue," and not that the object is inherently blue. The big difference again being that blue on exists in the language and logical form.

2.0233 Two objects of the same logical form are—apart from their external properties—only differentiated from one another in that they are different.

This seems very... circular and self-evident. A strange proposition to make. Same logical form, in that you can make the same set of propositions about these objects, they are only "differentiated from one another in that they are different." I suppose he's saying they're only different because you say there are two objects, and that implies they must be different in that way, not different in its essence/form.

Of note, he also separates external properties from the logical form---I think external properties being propositions that live in different logical spaces, like space and color.

2.02331 Either a thing has properties which no other has, and then one can distinguish it straight away from the others by a description and refer to it; or, on the other hand, there are several things which have the totality of their properties in common, and then it is quite impossible to point to any one of them.
For if a thing is not distinguished by anything, I cannot distinguish it—for otherwise it would be distinguished.

Properties are born from our language propositions, our atomic facts. He's stating the obvious here---that if there are no propositions that we can make of these many objects that they do not share in common, then we cannot distinguish these two objects.

2.024 Substance is what exists independently of what is the case.

What? This turns my understanding of what's on my head. I suppose here he's separating substance (observable) from what is the case (proposition.) What is the case, or the states of affairs, being a part of language and logical space, and substance being a part of what I define as reality.

2.025 It is form and content.

He's saying objects are form and content. What is content?

2.0251 Space, time and colour (colouredness) are forms of objects.

Now I'm more confused. I assumed that these logical spaces were just logical spaces, now he's saying they are forms of objects. Is he saying they are a type of object (form of object) or is he saying they are the forms of objects? I assume the latter. He's saying that form is "the possibility of [an object's] occurrence in atomic facts" So space and time are examples of forms, he's saying that objects can inherit part of this logical space and therefore spawn possible atomic facts they can partake in?

Let's go with this: an object's form is its dimensions.

2.026 Only if there are objects can there be a fixed form of the world.

2.027 The fixed, the existent and the object are one.

The object exists. And what exists is fixed. I think that's what he's saying here.

So to summarize, objects are the existent and substance of the world, of which atomic facts and states of affairs (true atomic facts) can be propositioned which exist in logical spaces, and the totality of these atomic facts make up the world.

I think to put forms in a more blunt way, I think forms are the true portions of logical space that involve a single object.

2.0271 The object is the fixed, the existent; the configuration is the changing, the variable.

The configuration being its properties. I think I caught onto this earlier, that the language and propositions we make of objects can be malleable.

Like a lightbulb, we can flick on and off these atomic facts that exist in the world.

2.0272 The configuration of the objects forms the atomic fact.

Yes, the configuration being the properties of an object. But these properties change, and so do the atomic facts we make of the world. I recognize this especially with our language. Our language defines and interprets the world, but importantly Wittgenstein argues here that there exists a phyiscal world that must exist to base our language off of.

I understand now why he did this, because I want to argue against the idea of a fixed substance world he speaks of. I feel it is all subjective and of perspective and of interpretation through our language. I do not know how to exist other than through the means of language.

2.03 In the atomic fact objects hang one in another, like the links of a chain.

Atomic facts are links of objects. I assume each object interlinking one another to form a proposition. "The sky is blue."

2.031 In the atomic fact the objects are combined in a definite way.

Definite as opposed to infinite. I assume he's saying there is a limit to how many objects can exist in an atomic fact. There must be a fixed number of words in every meaningful sentence after all.

2.032 The way in which objects hang together in the atomic fact is the structure of the atomic fact.

Sure, I think we commonly refer to this as semantics and grammar from a language perspective.

2.033 The form is the possibility of the structure.

Hm... he defines the form as another thing again. I think its the same. I think I'm starting to understand what he means by form. An object can exist in many different finite number of atomic facts. I assume it as a set of possibilities. The form is the set of all these possibilities. It is the pattern recognized that is true for all the set of possible atomic facts, or shall I say states of affairs.

It is the possibilities provided by the structure. Hopefully, he clarifies a little more later on.

2.034 The structure of the fact consists of the structures of the atomic facts.

It's compositional in nature. Sounds good.

2.04 The totality of existent atomic facts is the world.

He redefines the world... this guy is kind of getting on my nerves. But okay sure, yes to reclarify his original statement, the totality of existent atomic facts is the world.

And I was wrong in my definition of states of affairs. States of affairs belong in the side of substance. It is "as is the case" side of things. A truthful atomic fact is just that.

2.05 The totality of existent atomic facts also determines which atomic facts do not exist.

That which exists defines what does not exist. I like that.

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.)

Okay, a clearer picture is being made here. Yes, reality belongs on the side of the logical now. It is not the substance of which I have been referring to.

2.061 Atomic facts are independent of one another.

2.062 From the existence of non-existence of an atomic fact we cannot infer the existence or non-existence of another.

Just because "the sky is blue" does not mean "the sky is red" is false.

2.063 The total reality is the world.

Definition here, makes sense.

2.1 We make to ourselves pictures of facts.

Pictures is a new terminology. Let's take a look.

2.11 The picture presents the facts in logical space, the existence and non-existence of atomic facts.

I'll say that pictures are groupings of facts that exist in logical space. But then he says existence and non-existence. Let's say for a second there exists two dimensions atomic facts can exist in: true or false, and existing or non-existing. Fair?

So the picture encompasses the logical space of facts that may be true or false and exist and don't exist. A little hard to concretely imagine, but it makes sense. If you're making a bet with Schrodinger's cat, the non-existence of the cat is part of the logical picture, no?

2.12 The picture is a model of reality.

"Model of reality" is a phrase I've used before. Sure, we lasso together a portion of logical space and use it to model reality. Model in say, simulating or describing or explaining it in some form or another. Right, since atomic facts are formed from the substance and are still malleable, so are the models of reality we come up with.

2.13 To the objects correspond in the picture the elements of the picture.

When you lasso in logical space like this, these atomic facts, you grab the chains of objects that form the atomic facts. The set of objects that are chained within the atomic facts are the elements of the picture. Sure.

2.131 The elements of the picture stand, in the picture, for the objects.

Stand is a strange choice of word, but I guess this makes sense. He's saying that elements are different than objects in that they stand in the context of the picture only, instead of objects existing in the context of "substance" and "existence."

2.14 The picture consists in the fact that its elements are combined with one another in a definite way.

Okay... so we talked about chaining objects (elements) with one another. I guess he's saying we combine elements in the context of the picture, in the logical space the picture encompasses. He says again here, definite way as opposed to infinite. There are only so many ways the elements of the picture can combine with one another.,

2.141 The picture is a fact.

Not an atomic fact! A combination. A conclusion to come to from a grouping of atomic facts. Or not quite? I suppose it is an all-encompassing fact that is the conclusion of all atomic facts.

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.

This seems very circular and mystical, I'm not sure what he's saying here. Okay, so maybe he's saying that beyond objects chaining with objects to form atomic facts, that objects of different atomic facts chain together to form a picture. Is that what he's trying to get at here?

Okay, he says a picture's structure (not a logical form's structure, same word yet a different thing yet again), and he uses the word "form of representation" to describe the possibiility of this structure. So a form of a picture is its structure's possibilities. Okay, sure, so you can organize the atomic facts that exist or do not exist within a logical picture in different ways, and the sum of all these possibilities is its form of representation of 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.

The possibility that the things are combined with one another... as are the elements of the picture... Not sure yet again.

AI to the rescue: This statement means that the way something is represented, whether through a picture, language, or other means, is essentially determined by how its constituent parts are combined with each other[.]

I'm guessing the meaning of a picture is the possibility of how the things are combined with one another... sure.

2.1511 Thus the picture is linked with reality; it reaches up to it.

Pictures are linked to reality through the elements (the objects) that comprise of it.

2.1512 It is like a scale applied to reality.
2.15121 Only the outermost points of the dividing lines touch the object to be measured.

A scale in that it measures reality and separates the objects, it says a proposition about reality. I think that's what he's hinting at here. It's the connection point between the objects.

"The leaf is green." is an atomic fact. "The bush is green" is an atomic fact. "Chlorophyll is green" is an atomic fact. "The bush and leaf have chlorophyll" is a picture, a combination of these atomic facts.

2.1513 According to this view the representing relation which makes it a picture, also belongs to the picture.

The combinatorial portion of the picture that links different objects of different atomic facts is also belonging to the picture, its possibilities of combinations or its form of representation belongs to the picture and is contained within.

2.1514 The representing relation consists of the co-ordinations of the elements of the picture and the things.

Sure, the relation depends on how the elements of the picture and things are "touching" one another. I kind of get it. He's building up logic and a foundation of thought based on relations of objects from first principles.

The Tractatus is about defining the world as relations between objects, and argues for factualism that it is by these relations existing do we see the objects that comprise it.

2.1515 These co-ordinations are as it were the feelers of its elements with which the picture touches reality.

The elements, the objects of the picture, it is how it touches reality, or the totality of the existence and non-existence of atomic facts. This is interesting because this is not a first principles thing, he's saying that a higher layer of organization is a defining point of reality, and not just the totality of atomic facts making up the world. Unless, these connections he speaks of are in fact atomic facts in themselves?

2.16 In order to be a picture a fact must have something in common with what it pictures.

I am hella' confused. I thought facts were pictures, what is the defining difference? I assume the picture has elements and forms and relations in the the atomic facts they encompass? So then, a fact must have something in common with what it is proposing, therefore it becomes a picture? So strange.

2.161 In the picture and the pictured there must be something identical in order that the one can be a picture of the other at all.

Okay, maybe "the pictured" is of the substance layer. So that the picture must relate to the pictured in some way. Okay, sure.

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.

Reality, being that which is the combination of both existent and non-existent atomic facts. Maybe he means reality in the common way, I'm not sure. This translation is unclear. However, we will assume that its form of representation, or its form, is the pattern recognized in the array of logical facts that make up the logical picture that ties it to reality.

I'm assuming forms are these patterns that exist within these logical spaces that bring to light conclusions and tie it to reality.

That the things we think, logically, have some pattern inherent in reality. That is its form.

2.171 The picture can represent every reality whose form it has.
The spatial picture, everything spatial, the coloured, everything coloured, etc.

The spatial picture can represent every reality whose form it has... I'm not sure that I understand anymore. I thought that logical spaces were of the spatial variety?

Hmm.. I'm confused more than ever before.

I'm getting bored. I'm going to read through this and skip to the interesting propositions.

3.032 To present in language anything which “contradicts logic” is as impossible as in geometry to present by its co-ordinates a figure which contradicts the laws of space; or to give the co-ordinates of a point which does not exist.

Language cannot contradict logic, because it is formed by logic. The very flow of our grammar dictates a logical flow. Interesting idea.

3.031 It used to be said that God could create everything, except what was contrary to the laws of logic. The truth is, we could not say of an “unlogical” world how it would look.

Very interesting. We cannot think unlogically... that is... we cannot come to a conception of a thought which is not rooted to a picture of reality.

3.221 Objects I can only name. Signs represent them. I can only speak of them. I cannot assert them. A proposition can only say how a thing is, not what it is.

We have propositional signs, which I assume is language. Objects I can name and cannot assert. That is true, I think he's referring to the idea that Augustus referred to long ago, in which symbols of language (names) were mere pointers to reality.

4.003 Most propositions and questions, that have been written about philosophical matters, are not false, but senseless. We cannot, therefore, answer questions of this kind at all, but only state their senselessness. Most questions and propositions of the philosophers result from the fact that we do not understand the logic of our language.
(They are of the same kind as the question whether the Good is more or less identical than the Beautiful.)
And so it is not to be wondered at that the deepest problems are really no problems.

...

That good is identical to the beautiful. This is no elementary proposition grounded in atomic facts---in some sort of reality. I think that's what he's proving here.

4.116 Everything that can be thought at all can be thought clearly. Everything that can be said can be said clearly.

I'm not sure about this one. Doubt. Is fuzzy thinking not a phenomenon? I guess the "can" keyword here deliminates that possibility.

5.6 The limits of my language mean the limits of my world.

6.53 The right method of philosophy would be this. To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy: and then always, when someone else wished to say something metaphysical, to demonstrate to him that he had given no meaning to certain signs in his propositions. This method would be unsatisfying to the other—he would not have the feeling that we were teaching him philosophy—but it would be the only strictly correct method.

I will reread this again having read the conclusitory statements. I think the gist of it is this: what can be said is many and of the logical world, but what can be sensical must be grounded in atomic facts. We can only speak of what we know---and that of philosophy, ethics, and good and evil, it is not something grounded in reality. Therefore:

7 Whereof one cannot speak, thereof one must be silent.

The Meaning of Life

An ethical problem, a value attribution issue, say, do we know what you mean by meaning and life? Can you point to the object that they are referring to? If not, we are trying to relate these two non-existences.

Perhaps what this phrase really means... is an emotion. I will read Wittgenstein's other landmark work.