Trying to clarify objects in Wittgenstein's Tractatus

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Sam26 has an ongoing thread summarizing Wittgenstein’s Tractatus. During the course of that thread, a lot of discussion regarding Wittgensteinian objects came up, and I thought it might be best to isolate talk on that topic specifically to its own thread, as to not derail the original thread's purpose. I've linked the thread, so that you can all follow along, and contribute there as well.

Before getting to objects, and what they are, I think it would be helpful to do a little groundwork, so that we can all approach from the same standpoint. I’d like to mostly stick to the primary text here, so quoting from the Tractatus directly. Any translation should suffice, although there are technical difficulties we can run into between translations, but we can do our best to avoid them.

I’d like to start with a basic assumption regarding the text, that I hope isn’t too contentious to boot - namely that the Tractatus presents a three part isomorphism between:

1. Thoughts
2. Language
3. Reality

An isomorphism is held between 1 or more structures if and only if to each of the elements of one, an analogous element is present in the other, and the form of the elements in one shares the form of the elements in another. It is a 1-to-1 correspondence which preserves the relevant form between structures.

Now, I believe that Wittgenstein starts with (1) of the isomorphism when he says:

“The world is the totality of facts, not of things” (1.1).

We know that (a) the world and (b)facts are in (1) of the isomorphism because Witt tells us that:

“The facts in logical space are the world” (1.13 ).

And also, of facts he says:

“The picture is a fact” (2.141).
“The picture is a model of reality” (2.12).

So, we know that to facts correspond reality, and facts alongside the world exist in logical space. Facts are just pictures we form in thought, to which can correspond a reality.

I say can correspond, because Witt says:

“The world divides into facts”(1.2).
“Any one can either be the case or not be the case, and everything else remain the same” (1.21).

When it is the case, to a fact corresponds an atomic fact and is called a positive fact:

“What is the case, the fact, is the existence of atomic facts” (2).

When it is not the case, to a fact corresponds the nonexistence of atomic facts, and is called a negative fact:

“(The existence of atomic facts we also call a positive fact, their non-existence a negative fact)” (2.06).

“The picture depicts reality by representing a possibility of the existence and non-existence of atomic facts” (2.201).

Everything else remains the same when one is the case or not the case because:

“Atomic facts are independent of one another” (2.061).

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

1. Thoughts

Facts>Atomic Facts

2. Language

3. Reality

Next, Wittgenstein moves to (2) of the isomorphism, telling us that

“In the proposition the thought is expressed perceptibly through the senses“(3.1).
“The simplest proposition, the elementary proposition, asserts the existence of an atomic fact” (4.21).

So, we can fill in:

1. Thoughts

Facts>Atomic facts

2. Language

Propositions>Elementary propositions

3. Reality

Now, before we fill anything else in, let’s talk more about one of these. We know what a proposition is. A proposition is the content of a declarative sentence which can either be true or false. So, in the sentences:

“The balls is red”
“La pelota es roja”
"La belle est rouge”

While the sentence is different, the proposition contained is the same. A proposition can be analyzed into an elementary proposition, and to this corresponds an atomic fact.

What is an atomic fact? Well, Witt tell us:

“An atomic fact is a combination of objects (entities, things)” (2.01).
and
“In the atomic fact objects hang one in another, like the members of a chain” (2.03).

This structure is carried over to elementary propositions when Witt says:

“The elementary proposition consists of names. It is a connexion, a concatenation, of names (4.22).
“It is obvious that in the analysis of propositions we must come to elementary propositions, which consist of names in immediate combination” (4.221).

So, an atomic fact is a combination of objects just as an elementary proposition is a combination of names.

So, we can now fill in:

1. Thought

Facts>Atomic Facts> Objects

2. Language

Propositions>Elementary propositions>Names

3. Reality

Before going any further, and saying anything substantial about what objects or names are, or what role they play, I’d like to stop and just open up for discussion regarding what’s been said.

Does this seem a reasonable outline so far, or did I miss something, or does anyone disagree? I'd also like to say that I am working through this as well, so don't take me to be saying I've definitively laid out how this works thus far. Please feel free to offer input and work through this together constructively.
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1. Thought

Facts>Atomic Facts> Objects

I would not put facts and objects under the heading of Thought. They are independent of thought. I would put them under Reality.

The following statements might lead someone to think that facts are part of thought:

:

“The picture is a fact” (2.141).
“The picture is a model of reality” (2.12).

but:

We picture facts to ourselves.
(2.01)

A painting of a tree is a fact. It hangs on the wall, but what is pictured in that picture (painting) is not another picture.

When it is the case, to a fact corresponds an atomic fact and is called a positive fact:

“What is the case, the fact, is the existence of atomic facts” (2).

When it is not the case, to a fact corresponds the nonexistence of atomic facts, and is called a negative fact:

“(The existence of atomic facts we also call a positive fact, their non-existence a negative fact)” (2.06).

I think the Pears/McGuinness translation is clearer here:

What is the case—a fact—is the existence of states of affairs.
(2)

(We call the existence of states of affairs a positive fact, and their non-existence a negative
fact.)
(2.06)

It is not "when it is the case, to a fact corresponds an atomic fact and is called a positive fact". It is that when a state of affairs exists we call it a positive fact, or, in ordinary terms simply 'a fact'. And when the state of affairs does not exist it is a negative fact, or, in ordinary terms 'not a fact'. If the state of affairs exists a proposition stating it a fact is true, and if the state of affairs does not exist then a statement stating it is a fact is false.
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An online edition of the text with side-by-side translations can be found here.
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Nice. Thanks.
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An online edition of the text with side-by-side translations can be found here.

Awesome! Thank you!

Fooloso, you say:

I would not put facts and objects under the heading of Thought. They are independent of thought. I would put them under Reality.

Because:

We picture facts to ourselves.
(2.01)

Truthfully, this is something I was uncertain of when I was typing it up, originally....yet I think that perhaps this is due to language. As you can see here:

"A propositional sign is a fact" (3.14).

Witt uses the word Fact, at that level of the isomorphism interchangeably. It seems like, to a "fact" in reality corresponds a "fact" (thought) in our mind, corresponds a "fact" contained in the proposition.

I settled on using the expression "Facts and atomic facts" at the level of thought, because at the point in the Tractatus that I was quoting, I believe that Witt was laying out the logic behind his conclusion that objects must exist. He seems to refer to "reality" at a minimum here.

I was going to reserve: "States of affairs" for reality, because alongside:

“The picture is a fact” (2.141).

in 2.201, Witt says:

"A picture depicts reality by representing a possibility of existence and non-existence of states of affairs"

I do take your point, however, and that difficulty, is why I wanted to take the time to try and settle on a common manner of referring to points in the isomorphism, since Witt doesn't always seem consistent. But, I admit this inconsistency may be due to my misunderstanding something. Does what I said make sense?
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I wonder how the "isomorphism" relates to ideas about representation. The following statements establish a connection but also a distance:

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

2.15121 Only the outermost points of the dividing lines touch the object to be measured.

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

2.1515 These co-ordinations are as it were the feelers of its elements with which the picture touches reality.
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It is a 1-to-1 correspondence which preserves the relevant form between structures.

It seems there are a number of places in the text where we do not have a way to confirm or deny that. The passages move from thinking to language in a sequence. Do you think of the "isomorphism' as a freedom to move forward or backwards in that regard?
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You can see how the above was seized upon by the Vienna Circle as grounds for their verificationism, even if Wittgenstein himself disowned them.
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the Tractatus presents a three part isomorphism between: 1. Thoughts 2. Language 3. Reality

I'm not sure that isomorphism is the right word, as it suggests that they are independent of each other.

Thought and language are two aspects of the same thing. A proposition is a thought and a thought is a proposition. As Wittgenstein says, the limits of my language is the limits of my world. The world is the content of my thoughts (ie, of my propositions)

Wittgenstein is careful to avoid giving his opinion as to where this world exists, inside the mind or outside the mind.

It is more the case that thought IS language rather than thought maps to language, and the world IS the content of thought (and language) rather than maps to thought (and language).
===============================================================================
A proposition can be analyzed into an elementary proposition, and to this corresponds an atomic fact.

You need to introduce "state of affairs" earlier on.

IE, the elementary proposition (aka atomic proposition) "grass is red" corresponds (not in the sense of represents but more in the sense of displays) with the state of affairs grass is red, but doesn't correspond with the atomic fact grass is red, as the state of affairs grass is red doesn't obtain in the world.

The Tractatus only deals with concrete objects, such as grass and apples, and concrete properties, such as yellow and red. The Tractatus doesn't deal with abstract things, such as beauty and love, and abstract properties, such as yellowness or redness. This is why the Tractatus is so limited, in the sense that Philosophical Investigations isn't.

Within the Tractatus, objects are treated as logical objects, unalterable and indivisible, not physical objects.

Not all objects can exist in the world. The world consists of a logical space. This logical space is the set of all possible states of affairs. Only those objects having a suitable logical form can exist in this logical space. If a possible state of affairs obtains then this is a fact.
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I'm not sure that isomorphism is the right word, as it suggests that they are independent of each other.

Thought and language are two aspects of the same thing. A proposition is a thought and a thought is a proposition.

I'm no Tractatus expert, but I don't think this is right -- wouldn't it be more Witt's position in the Phil. Investigations, rather than here? Leaving aside the perhaps trivial point that we can have thoughts that are non-propositional, we should take more seriously Witt's use of "picture" at so many critical points in the Tractatus. I don't read him as suggesting that language is the only picture-making tool at our disposal.

With that said, though, I agree that it's hard to fit in the "limits of language" quote. But I'm not the first to suggest that the Tractatus, for all its careful organization, is often self-contradictory.
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There is a difference between what an object is, which Wittgenstein does address, and the identification of an object. This is about the former. As will become evident, the latter is not something to be found in the world, and thus not something to be discovered by propositional analysis.

Simple objects are not like the objects we encounter in the world. Objects in the world are a configuration of simple objects. These complex objects are facts. A state of affairs. Simple objects are not the objects of empirical science. They are not physical entities. They are not what we would find if we divided physical objects to the point where further division is no longer possible. They are not something like subatomic particles.

They exist in logical rather than physical space. Simple objects are merely formal or logical. They are the constituents of the transcendental logical structure of the world.

More to follow.
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Leaving aside the perhaps trivial point that we can have thoughts that are non-propositional...I don't read him as suggesting that language is the only picture-making tool at our disposal.J

Wittgenstein wrote before the Tractatus that he thought that thinking and language were the same.

Notebooks 1914-16 – 12/6/2016 – page 82.

Now it is becoming clear why I thought that thinking and language were the same. For thinking is a kind of language. For a thought too is, of course, a logical picture of the proposition, and therefore it just is a kind of proposition.

1.1 – The World is the totality of facts, not of things
3 – A logical picture of facts is a thought

Therefore, a thought is a picture of facts in the world

4 – A thought is a proposition with a sense
4.022 – A proposition shows its sense.

Therefore, a proposition is a thought

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

Therefore, my thoughts about the world are limited by the propositions I use in language.

It seems that Wittgenstein doesn't distinguish between propositional thoughts, "snakes are reptiles" and non-propositional thoughts, "Indiana Jones fears snakes"

As Bertrand Russell writes in the Introduction to the Tractatus:

It is clear that, when a person believes a proposition, the person, considered as a metaphysical subject, does not have to be assumed in order to explain what is happening. What has to be explained is the relation between the set of words which is the proposition considered as a fact on its own account, and the “objective” fact which makes the proposition true or false.

If thinking is a kind of language, then thinking IS language rather than thinking being isomorphic to language, because for Wittgenstein, thinking and language are not two separate isomorphic objects but rather two aspects of the same object (Wikipedia - Isomorphism).
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Good citations, thanks. If I have a beef, it's clearly with Witt and not your interpretation of him!
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It is a 1-to-1 correspondence which preserves the relevant form between structures.
— 013zen

It seems there are a number of places in the text where we do not have a way to confirm or deny that. The passages move from thinking to language in a sequence.

I think it can be seen in how the text uses the terms that it employs. I can see many places which seem to confirm this.

Do you think of the "isomorphism' as a freedom to move forward or backwards in that regard?

I'm sorry, I don't completely understand. Would you be able to phrase it differently? :)

I seriousl doubt Wittgenstein understood half of what he wrong.

I think that Wittgenstein, like any philosopher - or human for that matter - is simply thinking through these problems, and gets some things right and other things wrong. We read other philosophers to try and see how these problems have been handled, and what we can learn from them.

You can see how the above was seized upon by the Vienna Circle as grounds for their verificationism, even if Wittgenstein himself disowned them.

Agreed. I don't believe that this was merely accidental. The Vienna Circle grew out of the Mach's positivism - it was in fact originally called the Ernst Mach Society. I believe that Wittgenstein was in a sense directly responding to positivism, which Witt got from Russell who finally adopted the neutral monism of Mach in the early 1900s. At this time positivism was in direct combat with another theory being put forth by Boltzmann, Hertz, and Helmholtz called the "picture" theory of theories. I believe that Witt was very aware of this debate at the time due to Russell, and a lot of those ideas lay the groundwork for the Tractatus. But, this is my own personal take that I am still formulating.

I'm not sure that isomorphism is the right word, as it suggests that they are independent of each other.

I don't believe that an isomorphism necessarily suggests a certain independence between each structure, but in practice I admit it is used to talk about independent structures. I take your point, but I believe that isomorphism is the best word, since it gets across the salient points without being a mouthful. You're point is taken, though.

Thought and language are two aspects of the same thing. A proposition is a thought and a thought is a proposition.

I would be careful here. A proposition in some sense contains a thought, but a thought is not identical with a proposition. A proposition is a string of words with a definite syntax and semantic content; a thought of a red ball is not a series of words in my mind. But, I understand your point - a proposition contains a thought; the form of the proposition mirrors the form of the thought.

You quote:

Now it is becoming clear why I thought that thinking and language were the same. For thinking is a kind of language. For a thought too is, of course, a logical picture of the proposition, and therefore it just is a kind of proposition.

Which is both a really interesting quote, so thanks for that, but also note a couple of things in it. Wittgenstein says it is becoming clear to him why he thought that thinking and language were the same. He didn't say that its become clear that they are the same, but rather why he used to think that they were the same thing. Thinking IS a kind of language but it is not identical with our natural language that we use everyday. It is its own kind of language, which is translatable into many many different natural languages.

IE, the elementary proposition (aka atomic proposition) "grass is red"

First of all...why did you say grass is red and not green? xD Secondly, I don't take "Grass is red" or "Grass is green" or anything of the sort to be representative of an elementary proposition for Witt. These are examples of propositions.

It seems that Wittgenstein doesn't distinguish between propositional thoughts, "snakes are reptiles" and non-propositional thoughts, "Indiana Jones fears snakes"

Whether or not "Indiana Jones fears snakes" is a non-propositional or propositional is first of all a modern debate characterized by either being a propositionalist or objectualist. I would argue that while I'm certain this topic has come up in one form or another throughout history, that where Wittgenstein falls on either side of this debate is not directly articulated in the Tractatus. Witt could have very easily fancied himself a propositionalist and considered internal states to be captured by propositions.

It is clear that, when a person believes a proposition, the person, considered as a metaphysical subject, does not have to be assumed in order to explain what is happening. What has to be explained is the relation between the set of words which is the proposition considered as a fact on its own account, and the “objective” fact which makes the proposition true or false.

We can't appeal to Russell's interpretation of the text either, because we know that historically Wittgenstein thought that Russell didn't understand a word of it.
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Simple objects are not like the objects we encounter in the world. Objects in the world are a configuration of simple objects. These complex objects are facts. A state of affairs. Simple objects are not the objects of empirical science. They are not physical entities. They are not what we would find if we divided physical objects to the point where further division is no longer possible. They are not something like subatomic particles.

I agree with everything up until the last point, and not for a technical reason, but perhaps due to phrasing. I believe that you are right, Wittgenstein is not concerned with those simple entities out in the world to which correspond his objects. But, by setting up the isomorphism, we know that there must be simple physical entities to which correspond our simple objects, right?

But, based on everything else you said, I'm definitely interested in hearing more! Looking forward to it. Good luck.
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we know that there must be simple physical entities to which correspond our simple objects, right?

I don't think so. As I understand it, or perhaps misunderstand it, there are no simple physical entities or objects. Every physical object is complex. The problem is to explain how a configuration of simple non-physical objects results in a physical object. It may be that this indicates that I have got something wrong, but it may simply be that Wittgenstein would have said that such problems are a matter of science not logic.

He says only:

The substance of the world can only determine a form, and not any material properties. For it is only by means of propositions that material properties are represented—only by the configuration of objects that they are produced.
(2.0231)

I will hold off saying more for the moment. This should not be taken to mean that an explanation will be forthcoming. To the extent I can address it it will be in terms of what an object is.
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I think that Wittgenstein, like any philosopher - or human for that matter - is simply thinking through these problems, and gets some things right and other things wrong. We read other philosophers to try and see how these problems have been handled, and what we can learn from them.

I agree. Wittgenstein, though, is not treated this way by the majority of his adherents.

Plus, I was being a little bit more negative - I think he makes less sense than 'some right, some wrong'. He's mostly senseless, making htings up.
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I agree. Wittgenstein, though, is not treated this way by the majority of his adherents.

I would say this is generally true of adherents :P
I've never met a Kantian that thinks Kant is wrong, or a Humean that thinks Hume is wrong. lol

Plus, I was being a little bit more negative - I think he makes less sense than 'some right, some wrong'. He's mostly senseless, making htings up.

I'd be interested to hear more. I wouldn't say that he's making things up, but he does take himself to be doing something creative.
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I think it can be seen in how the text uses the terms that it employs. I can see many places which seem to confirm this.

I was thinking the following was an obstacle to 'equality of shape' or 'isomorphism':

2.0121 Just as we are quite unable to imagine spatial objects outside space or temporal objects outside time, so too there is no object that we can imagine excluded from the possibility of combining with others.

2.173 A picture represents its subject from a position outside it. (Its standpoint is its representational form.) That is why a picture represents its subject correctly or incorrectly.

4.0641 The negating proposition determines a logical place with the help of the logical place of the negated proposition. For it describes it as lying outside the latter’s logical place.

4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it—logical form.

4.121 Propositions cannot represent logical form: it is mirrored in them.

5.61 Logic pervades the world: the limits of the world are also its limits.
So we cannot say in logic, ‘The world has this in it, and this, but not that.’
For that would apparently presuppose that we exclude certain possibilities, and this cannot be the case since otherwise logic must get outside the limits of the world: that is, if it could consider these limits from the other side also. For that would appear to presuppose that we were excluding certain possibilities, and this cannot be the case, since it would require that logic should go beyond the limits of the world; for only in that way could it view those limits from the other side as well.
What we cannot think, that we cannot think: we cannot therefore say what we cannot think.
We cannot think what we cannot think; so what we cannot think we cannot say either.

The difference between what is said versus what is shown becomes a limit to what can be regarded as equal or the same. In that way, Wittgenstein is challenging what most have taken for granted.

Do you think of the "isomorphism' as a freedom to move forward or backwards in that regard?
— Paine

I'm sorry, I don't completely understand. Would you be able to phrase it differently?

The order of the statements in the text begins with conceptions before introducing propositions. Is that order important to understanding what is presented?
.
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I don't think so. As I understand it, or perhaps misunderstand it, there are no simple physical entities or objects. Every physical object is complex. The problem is to explain how a configuration of simple non-physical objects results in a physical object. It may be that this indicates that I have got something wrong, but it may simply be that Wittgenstein would have said that such problems are a matter of science not logic.

As you point out, every physical object is a complex. If I'm understanding you correctly, I take this to mean that what we might call "classical objects" are all complex. These are not Wittgenstein's objects, nor are they what correspond to his objects. You're right about this, I'd say.

The problem is to explain how a configuration of simple non-physical objects results in a physical object.

I don't think it is Wittgenstein's problem in the Tractatus to try and explain how a configuration of simple non-physical objects results in a physical object. I think he dips his toe into the problem, but its a tangential problem to his overall objective. I actually believe that the history surrounding the Tractatus is much more focused on this problem, and if you're interested in that then you have a solid foundation for the problem that you're seeing. I definitely think its a problem that greatly influenced the Tractatus, and I am very interested in talking about that.
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The order of the statements in the text begins with conceptions before introducing propositions. Is that order important to understanding what is presented?

I don't believe so. I think that, perhaps, Wittgenstein started with what was most accessible to him during the war, namely his thoughts. So he begins by deconstruction thoughts in logical space before moving to propositions.

The difference between what is said versus what is shown becomes a limit to what can be regarded as equal or the same. In that way, Wittgenstein is challenging what most have taken for granted.

I am still having trouble completely seeing how this precludes the possibility of an isomorphism. A proposition's literal form is not identical with its logical form. As Witt says:

"Russell's merit is to have shown that the apparent logical form of the proposition need not be its real form" (4.0031).

This form is what's mirrored in thought. All the accidental features of the proposition fade away, so to speak, but this losing of accidental features does not suppose a loss of fundamental features which are mirrored in the picture in thought.
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Wittgenstein, though, is not treated this way by the majority of his adherents.

I will leave them to stick together.

By own approach is to assume that when an important philosopher says something that seems wrong to begin with the assumption that the fault is my own. That is not to say they are not wrong. It is a matter of interpretive humility.

Having said that, in the case of the Tractatus, there are things that he himself admits he got wrong. One might then wonder why anyone bothers trying to make sense of it. My response is that even if it is in some ways wrong it is still a powerful demonstration of logical thinking and an interpretive challenge that serves as an fine exercise for our own thinking that keeps scholars working on it to this day.
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I am still having trouble completely seeing how this precludes the possibility of an isomorphism

What do you make of:

4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it

Citing this is not an argument for 'precluding a possibility', as you put it. On the other hand, maybe this would be a good time for you to provide what supports your view of the text.
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These are not Wittgenstein's objects, nor are they what correspond to his objects.

He complicates this by using the term 'object' in both cases without always making the distinction clear.
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What do you make of:

4.12 Propositions can represent the whole of reality, but they cannot represent what they must have in common with reality in order to be able to represent it
— Ibid.

That there is a distinction between the form of a proposition and the logical form of a proposition. The form of a proposition, which re-presents reality, and its logical form, which can only be shown I believe. Propositions don't represent the logical form that they share with reality, but it is mirrored by the proposition.

Citing this is not an argument for 'precluding a possibility', as you put it. On the other hand, maybe this would be a good time for you to provide what supports your view of the text.

Which aspect of my view specifically? The belief that there even is an isomorphism displayed between thoughts, propositions, and reality? Or something else?
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How does the equality of form relate to the reluctance on Wittgentein's part to assemble a world on that basis.
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What do you mean by:

assemble a world
?
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I thought you were doing that by means of asserting Wittgenstein's project to be an alignment of some kind.
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He complicates this by using the term 'object' in both cases without always making the distinction clear.

I don't think that this is necessarily a bug, as much as a feature. Part of the work seems to be dealing with the idea that the meaning of a word or proposition is dependent upon how its being used.

"The sign determines a logical form only together with its logical syntactic application" (3.327).

It's an idea that stems from Frege's elucidations, and I don't think its any accident that Wittgenstein uses the idea of elucidations in the Tractatus.

"The meanings of primitive signs can be explained by elucidations" (3.263).
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I would say this is generally true of adherents :P
I've never met a Kantian that thinks Kant is wrong, or a Humean that thinks Hume is wrong. lol

I'd be interested to hear more. I wouldn't say that he's making things up, but he does take himself to be doing something creative.

He seems to have basically invented his own use of things like "language" "reality", "thought" and "object" and then run with it, in the same manner he apparently taught his student - everyone else is wrong.

One might then wonder why anyone bothers trying to make sense of it.

I feeel this might be the most apt statement in this thread :P
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He seems to have basically invented his own use of things like "language" "reality", "thought" and "object" and then run with it, in the same manner he apparently taught his student - everyone else is wrong.

I don't actually take this to be entirely true. Wittgenstein is clearly writing within a tradition, and what I mean is I don't believe it was written in a vacuum.

For example, Frege wrote a paper called, "On Concept and Object", wherein he both explained that a commentator of his had misunderstood how we was using the word "concept" in a previous text, and also defended his using the expression that way. He says:

"It seems to me that Kerry's misunderstanding results from his unintentionally confusing his own usage of the word 'concept' with mine. This readily gives rise to contradictions, for which my usage is not to blame. Kerry contests what he calls my definition of 'concept'" (1).

He goes on to say:

"On the introduction of a name for something logically simple, a definition is not possible. There is nothing for it but to lead the reader or hearer, by means of hints, to understand the words as is intended" (2).

Frege thought that if logical analysis lead a logician, or mathematician, to conclude that there is a meaningful distinction for a particular category that has yet to be identified, that instead of inventing a new word, the person should use a familiar word in particular ways that showed its meaning; the word chosen pointed the reader in the right direction. He called these elucidations.

"When we begin science, we cannot avoid using words from ordinary language. But these words are for the most part not really appropriate for scientific purposes, because they are not sufficiently determinate and are fluctuating in their use. Science needs technical expressions that have entirely determinate and fixed references, and in order to make these references understood and to exclude possible misunderstandings, one gives elucidations".

Besides 'Concept', Frege uses the word 'object' in a stipulative way as well. And in a manner not unlike Witt.

https://philosophy-science-humanities-controversies.com/listview-details.php?id=224693&a=t&first_name=Gottlob&author=Frege&concept=Object#:~:text=Object%2FFrege%3A%20locations%2C%20times,the%20meaning%20of%20a%20subject.

The Tractatus makes references to many other concepts and manners of thinking that were present during his time.

His breaking down reality into nonphysical elements was what Ernst Mach was doing in the 1900s in direct opposition to the atomic theory of reality.

There is a reason that positivism became logical positivism and logical positivists and the vienna circle, all prominent mathematicians and scientists including Einstein (He was at least initially a positivist, although not directly a Wittgensteinian. He agreed with some of the public literature the positivists released) largely adopted the Tractatus initially. There's a reason Russell developed his atomism in response to the tractatus.
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