See 4.12721. The concept of a number is a formal concept. Particular numbers are not. They fall under the concept of a number. — Fooloso4

4.1272 "The same applies to the words "complex", "fact", "function", "number", etc - They all signify formal concepts............."1 is a number", "There is only one zero" and all similar expressions are nonsensical

Why do you think that particular numbers, such as the number 1, are not formal concepts?

@Fooloso4

I now no longer believe that the x in F (x) is a formal concept, but in fact represents a concept proper.

A formal concept defines how the variables "T" and "x" are to "behave" or perhaps a better way to say it, is how they are to be understood. These aren't like "proper concepts", such as "red", "hard", etc. which settles the external properties of complex objects. — 013zen

Consider the proposition "grass is green".

If x = grass satisfies the function Green (x) then Green (x) is true.

Where grass and green are "concepts proper" (4.126)

From 4.12, a proposition can represent concepts proper, such as grass and green, but cannot represent logical form, ie "formal concepts" (4.126). A proposition can only "show" (4.121) logical form.

So, within the proposition "grass is green", where is the logical form? The logical form of the proposition must be shown by the word "is", which is a relation between concepts proper. For Wittgenstein, unlike Frege, relations are not object. Relations have no existence other than relating concepts proper, in that if the concepts proper were removed, no relation would remain as some kind of Platonic Form.

As the concept "is" can only be shown and not represented, it is a formal concept rather than a concept proper.

Similarly within the function Green (x), where is the logical form? The term "Green" infers the expression "is green", where "is" is the formal concept and green is the concept proper.

For both the proposition "grass is green" and the function Green (grass), in the first the formal concept "is" is explicit and in the second the formal concept "is" is inferred. The concepts proper remain grass and green.
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We cannot, for example, input a proper number to which corresponds the formal concept of number for say, a simple object. — 013zen

A concept proper cannot be a number.

From 4.0312, "logical constants" such as “and,” “or,” “if,” and “then” are not representatives. This makes sense, in that logical constants are not Platonic Forms.

Suppose there is a horse in a field and another horse enters the same field. We can say "horse AND horse". But if one horse left the field, the AND would not remain in the field as some kind of Platonic Form. AND only exists in the relationship between two concepts proper.

3.1432: We must not say, “The complex sign ‘aRb’ says ‘a stands in relation R to b;’” but we must say, “That ‘a’ stands in a certain relation to ‘b’ says that aRb.”

Similarly, we could "horse 2 horse". But if one horse left the field, the 2 would not remain in the field as some kind of Platonic Form. Numbers only exist in the relationship between two concepts proper.

As numbers only exist in the relationship between concepts proper, and relations in the Tractatus are not objects, they are formal concepts.
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So, while we can say: "There are two red fruits" this analyzes into:
∃x(P(x)) ∧ ∃y(P(y) ∧ (x≠y)) There is no sign corresponding to the formal concept "number" despite what appears to be a number presented in the proposition. — 013zen

However, isn't it the case that the logical symbol ∧ (which means AND), is where number is introduced into the expression. For example, "horse AND horse" by its very nature has introduced the concept of number, in that if I wanted to explain the concept of the number 2 to someone, I could say either "horse ∧ horse" or "horse AND horse" and then show them the field with 2 horses in it.

An unhappy apple is an illogical proposition not an illogical object. An apple on the table or inside the sun is not a combination of objects it is a relation of the objects apple and table (on) or apple and sun (in). — Fooloso4

An object in logical space must be a logical object, meaning that its necessary properties must be logical. For example, if an apple was a logical object in logical space, it would have the necessary properties such as weight, colour and taste. An apple having the necessary property of happiness would not be a logical object.

In a state of affairs, objects are combined, necessitating a relation between them.
3.1432 – Instead of "The complex sign "aRb" says that a stands to b in the relation R", we ought to put "That "a" stands to "b" in a certain relation says that aRb"
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I don't know if you are attempting to interpret the Tractatus or argue against it. He makes a distinction between proper concepts such as grass and formal concepts such as 'simple object'. — Fooloso4

There are proper concepts such as "grass" and formal concepts such as the variable "x".

Wittgenstein in the Tractatus never explains what a simple object is, other than there must be simple objects, and that they must exist necessarily not contingently.

As states of affairs exists in logical space, and a state of affairs is a combination of objects, this means that these objects exist in logical space. An object existing in logical space infers that it it is a logical object.

I'm suggesting that in the expression "grass is green" is true iff grass is green, objects such as grass are not referring to actual objects, which are divisible, but must be referring to logical objects, which can be indivisible, and are simples.
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Book is not a formal concept. — Fooloso4

I agree. The variable x is the formal concept, not the book.

There are no ‘logical objects’ (4.441) — Fooloso4

The expression "logical objects" may be read in two ways. It can be referring to either 1) objects that are logical or 2) logic can be an object.

As regards sense 1), in logical space are objects in combination. In order for this to be the case, these objects must be logical and their combinations must be logical. For example, a blue apple is a logical object, whilst an unhappy apple is not a logical object. An apple on top of a table is a logical combination, whilst an apple inside the sun is not a logical combination.

As regards sense 2), Frege treated relations and universals as objects. FH Bradley in treating a relation as an object concluded that relations don't ontologically exist in the world. Wittgenstein disagrees with Frege, and concludes in 4.441 that "There are no logical objects". This means in particular that relations, such as "to the left of " or "on top of" logical cannot be treated as objects, and in general that logical form, such as i) all H are M ii) S is H iii) therefore, S is M is not an object, in the sense that "grass" is an object.
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As part of a propositional analysis apples and tables can function as simples. — Fooloso4

Apples and tables as names in a proposition are concepts. Some think that concepts are simples, including myself, and fall within the theory of Conceptual Atomism.

From the SEP article on Concepts

Conceptual atomism is a radical alternative to all of the theories we’ve mentioned so far is conceptual atomism, the view that lexical concepts have no semantic structure (Fodor 1998, Millikan 2000). Conceptual atomism follows in the anti-descriptivist tradition that traces back to Saul Kripke, Hilary Putnam, and others working in the philosophy of language (see Kripke 1972/80, Putnam 1975, Devitt 1981).

If concepts weren't simple, when we thought of a concept such as grass as a set of other concepts, such as a low green plant, we would have to think of each of these concepts, such as a plant, as a set of other concepts, such as a living organism. But sooner a later a concept must be a simple otherwise our thought would be never-ending.

Therefore, thought requires that some concepts must be simples.

In the Tractatus picture theory, a proposition such as "grass is green" pictures the state of affairs grass is green.

The state of affairs grass is green exists in a logical space.

As concepts can be simples, the concept "grass" could be a simple, and as words such as "grass" logically picture an object such as grass existing in a logical space, this suggests that objects such as grass are also simples.

It is true that actual grass is divisible, for example into the top of the blade of grass and the bottom of the blade of grass, but objects aren't actual objects but rather logical objects, and logical objects such as grass can be simples.

Ir objects such as grass are not actual objects but logical objects, then logical objects such as grass can be simples.
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At 4.126 Wittgenstein introduces the term "formal concepts". — Fooloso4

In the function T (x), where T is on a table, the function T (x) is true if the variable x satisfies the function T (x). For example, T (x) is true if the variable x is a book.

As I understand it, the variable x is what Wittgenstein is defining as a formal concept.

4.126 (I introduce this expression in order to exhibit the source of confusion between formal concepts and concepts proper, which pervades the whole of traditional logic)...................so the expression for a formal concept is a propositional variable in which this distinctive feature alone is constant.
4.127 The propositional variable signifies the formal concept, and its values signify the objects that fall under the concept.
4.1271 – Every variable is the sign for a formal concept
4.1272 Thus the variable name "s" is the proper sign for the pseudo-concept object.

we have observed that physical processes can form complex objects without human intervention, such as trees — amber

Some think that relations don't exist outside the human mind, in which case there cannot be complex objects outside the mind.

From Wikipedia – Relations (Philosophy) -

Eliminativism is the thesis that relations are mental abstractions that are not a part of external reality.

Do we observe a complex object because the object is complex or because we think the object is complex.

How to avoid the circularity of a human observing something that is independent of being observed?

Trying to make sense of the Tractatus from the useful conversation between @schopenhauer1 and @013zen:

A picture theory, however, would allow speculation, as long as you’re positing possibilities that logically follow from experience — 013zen

If I see a shadow I picture a shadow, and have learnt nothing, because I am picturing a picture. This leads to the problem of infinite regress, what pictures the picture.

However, as you say, if I picture a shadow, from past experience I can picture possible causes of the shadow, such as a cat, or a horse, or a cloud. Though none of these pictures of possible causes by themselves can tell me the true cause, for that I need further observations. If from further observation I do see a picture of a cat and not a picture of a horse or a cloud, then I can infer that the cause of the shadow was in fact a cat.

IE, it is not possible to learn from a picture of reality, but it is possible to learn from pictures of possible realities.
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I can't think of an object in space without a shape — 013zen

Within the Tractatus an object is indivisible, a simple.

This is not what the Neutral Monist thinks of an object, a simple. They think of an elementary particle such as a fermion or boson. This is not what the Indirect or Direct Realist thinks of an object, as for them an object such as an apple can be divided into the top of the apple and the bottom of the apple.

However, if the apple is thought of as a logical object, then it can be indivisible, simple, and as a logical object it can exist in a logical space. But where does this logical space exist?

The outside world is inherently logical, in that one thing is always one thing and if thing A is to the left of thing B then thing B is to the right of thing A. If the mind pictures a logical outside world then it follows that the picture in the mind will also be logical.

Noting, however, that the logical relation in the outside world between thing A and thing B is not the same as any ontological relation between thing A and thing B.

Logical objects in logical space puts a limit on what is possible, in that because one thing being two things is not logical it is not possible. Only logical objects are possible. Logic puts a limit on what is possible.

Objects such as apples and tables as logical objects are possible and therefore simples. Relations such as to the left of, taller than, heavier than or on top of as logical relations are possible and therefore simples.

A logical object can only exist in a logical space. Within this logical space exist other logical objects. This means that a logical object cannot exist in the absence of other logical objects. The consequence is that each logical object exists in some combination with other logical objects. A logical object in combination with another logical object is called a "state of affairs".

Between each logical object and all other logical objects are possible states of affairs

If within this logical world are logical possible states of affairs, and the mind can picture this world, then the mind in picturing logical possible states of affairs of necessity also becomes logical.

4.112 “Philosophy aims at the logical clarification of thoughts.”

It is exhausting to have philosophers not explain themselves well..................I think Wittgenstein has just particularly been mythologized. — schopenhauer1

Perhaps Wittgenstein didn't think of himself as a philosopher, and was working out his ideas more for himself than others. A kind of conversational research with himself.

There are philosophers that I respect such as Kyle Banick who do say that Wittgenstein had "big ideas", so perhaps Wittgenstein deserves to have been mythologized, even if that wasn't what he wanted himself.

The problem here is where Schopenhauer (and previously Leibniz) actually laid out their reasoning for their premise and built a foundation, Wittgenstein simply asserts it to build his linguistic project of atomic facts and propositions that can be stated clearly. — schopenhauer1

Wittgenstein uses an apodictic style

On the one hand, considered by some to be the greatest philosopher of the 20th century, and on the other hand, the Tractatus is notorious for its interpretative difficulties.
(SEP – Ludwig Wittgenstein)

On the one hand, the Tractatus employs an austere and succinct literary style. The work contains almost no arguments as such, but rather consists of declarative statements, or passages, that are meant to be self-evident, and on the other hand, the Tractatus is recognized by philosophers as one of the most significant philosophical works of the twentieth century.
(Wikipedia Tractatus Logico-Philosophicus

A proposition may have value even if the words are ambiguous

It makes sense to say that what is important in the world are facts (objects in combinations) rather than objects, even if no-one can agree what an object is, and no-one can agree how objects combine.

IE, the statement "what is important in the world are facts (objects in combinations) rather than objects" has a value that everyone may agree with, even though there is no agreements as to what "object" and "combination" actually mean.

Similarly, everyone may agree with the statement "in the world postboxes are red", even if the Indirect Realist and Direct Realist don't agree where exactly does this world exist.

Even though the Tractatus uses a didactic style, everyone may agree that the remarks are of value, even if everyone disagrees with what the remarks actually mean.

Where is the value in the Tractatus

The question is what substantive philosophical lessons can we extract from the Tractatus. According to Facts, Possibilities, and the World. Three Lessons from the Tractatus, Hans Sluga:

One is the concept of fact, on which Russell and the Wittgenstein of the Tractatus relied so much, is philosophically brittle and that we must turn our attention, instead, to the broader notion of the factuality of the world.

Two is that we can and must think about the world in both factual and modal terms but that in doing so we must treat the idea of possibility, not that of necessity, as primary and we must conceive of possibilities as merely virtual, not as factual.

Three is that we must consider the world as a whole, if we are to make sense of logic, science, and ethics.

However, I need to research this further.

Edit to add — Paine

I'm sure you probably already know, but the edit facility is quite useful.

At the bottom of one's own post - left clock on three dots - left click on edit - make changes to text - save comment.

At any rate, I agree with, like 90% of your post. Its just specifics we differ on, right now. — 013zen

Conversational research. As the architect Louis Kahn said "The street is a room by agreement".

One can say that he is castigating all the metaphysicians and epistemologists that came before. — schopenhauer1

I, actually, take Wittgenstein to be attempting to break away from this tradition (epistemology and metaphysics) — 013zen

Perhaps the following is relevant.

It may not be the case that Wittgenstein was trying to break away from the tradition of epistemology and metaphysics, but rather that he didn't know much about the tradition in the first place. From IEP Ludwig Wittgenstein (1889—1951)

His early work was influenced by that of Arthur Schopenhauer and, especially, by his teacher Bertrand Russell and by Gottlob Frege, who became something of a friend.

His philosophical education was unconventional (going from engineering to working first-hand with one of the greatest philosophers of his day in Bertrand Russell) and he seems never to have felt the need to go back and make a thorough study of the history of philosophy. He was interested in Plato, admired Leibniz, but was most influenced by the work of Schopenhauer, Russell and Frege.

He was influenced by Leibniz's logical form. From The Problem of Logical form: Wittgenstein and Leibniz by Studia Philosophiae Christianae

The article is an attempt at explaining the category of logical form used by Ludwig Wittgenstein in his Tractatus logico-philosophicus by using concepts from Gottfried Wilhelm Leibniz’s The Monadology.

He was influenced by Schopenhaur's division of reality into the phenomenal and the noumenal. From Schopenhauer's Influence on Wittgenstein by Bryan Magee.

Schopenhauer was the first and greatest philosophical influence on Wittgenstein, a fact attested to by those closest to him. He began by accepting Schopenhauer's division of total reality into phenomenal and noumenal, and offered a new analysis of the phenomenal in his first book, the Tractatus Logico‐Philosophicus.

IE, it is difficult to consciously break away from a tradition if one doesn't know much about the tradition in the first place.

1. Examples of names (the simple symbols for objects) are: "x,y,z,etc.
2. Examples of elementary propositions are functions such as: "'fx'', 'ϕ(x, y)', etc. — 013zen

4.24 - "Names are the simple symbols: I indicate them by single letters (x, y, z). I write elementary proposition as function of names, so that they have the form"'fx'', "ϕ(x, y)', etc."

I believe that he is not saying that the single letters x, y, z are objects, but is saying that these single letters indicate possible objects, such that the variable x indicates the objects ball, elephant or sandwich.

In order for an elementary propositions to picture the world, it needs two parts, representatives such as grass, green, tall, mountain, velocity and logical constants such as and, not, if, then, or.

Logical constants are not objects, they are rules that determine how the objects relate.

Consider the logical function F(x), where F(x) is true if the value x satisfies the function F. But as F and x are not only unknown, don't refer to anything and have no sense, F(x) cannot picture the world, and if cannot picture the world cannot be an elementary proposition.

Consider F(x) is true if x is green, The value x = grass satisfies the function, whilst the value x = strawberry doesn't satisfy the function. As F and x are now known, F being the object green and x being the objects grass and strawberry, the world can now be pictured, meaning that we now have an elementary proposition.

4.0312 - "My fundamental idea is that the logical constants are not representatives – that there can be no representatives of the logical facts"

Logic by itself, functions such as F(x), cannot fulfil the role of representatives, and as representatives are needed in addition to logic to picture the world, functions such as F(x) cannot be elementary propositions.
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We might be able to infer that an atomic fact, for something like this, might be something like: "v=d/t". I wonder. This could also explain why Witt lists: "time" as a "form of an object". — 013zen

A fact is a state of affairs in the world that obtains. A state of affairs is objects in possible combinations

Which is the state of affairs, d/t or distance divided by time? Which is the object, t or time?

From Russell's Introduction "In Wittgenstein’s theoretical logical language, names are only given to simples. We do not give two names to one thing, or one name to two things."

Therefore, the variable t cannot be the object, as being a variable it names more than one thing, and as Russell says, t cannot be a simple as it names more than one thing, and if not a simple cannot be an object.

2.0251 Space, time, colour (being coloured) are forms of objects.

From 2.051, time is the object, not the variable t.

Therefore, a state of affairs being objects in possible combinations cannot be d/t but must be time divided by distance. If this state of affairs obtains, then the fact is distance divided by time, not d/t.

(Kyle Banick – 1/3 – Necessity and contingency)

These limits of what is said versus what is shown are a question for me in how this work is presented as solving particular issues for the future. But I think it puts 'idealism versus realism' into the diagram rejected in 5.6331. — Paine

I wrote "Unfortunately, this line of enquiry cannot be developed within the Tractatus, as the Tractatus doesn't engage with ether Idealism or Realism."

Fundamentally, I am sure that the general opinion about the Tractatus is that Wittgenstein does not engage with Theories of Knowledge, such as Idealism and Realism. For Wittgenstein, the importance of philosophy was not about developing Theories of Knowledge but helping clarify one's own thought process.

7 - "Whereof one cannot speak, thereof one must be silent"

IEP – Ludwig Wittgenstein (1889—1951)

Wittgenstein’s view of what philosophy is, or should be, changed little over his life. In the Tractatus he says at 4.111 that “philosophy is not one of the natural sciences,” and at 4.112 “Philosophy aims at the logical clarification of thoughts.” Philosophy is not descriptive but elucidatory. Its aim is to clear up muddle and confusion.

There is probably no Theory of Knowledge that hasn't been ascribed to Wittgenstein, and I am sure parts of the Tractatus can be read in support of one theory or another.

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I don't see how saying: "no part of our experience is at the same time a priori" could be an expression of idealism. — Paine

My basis understanding of the difference between Idealism and Realism is:
Idealism = the world exists in a mind. Berkeley said in the mind of God, the Solipsist says in the mind of the observer.
Realism = one world exists in the mind and another world exists outside the mind. The Indirect Realist says that these worlds are different. The Direct Realist says that these worlds are the same.

5.633 and 5.634 makes the point that we see a shape in the world, we don't see a representation of a shape in the world. But where is this world. Does this world only exist in a mind as Idealism proposes or does this world also exist outside the mind as Realism proposes. 5.633 and 5.634 says nothing about this .
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The single mention of "pure realism' probably comes from it being a thought experiment appended to saying: — Paine

5.62 "The world is my world: this is manifest in the fact that the limits of language (of that language of which I alone understand) mean the limits of my world

As before, he is not saying anything about where this world exists.
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This difference between images built up through thoughts and words and what they show is evident throughout the book. — Paine

I thought the idea of the Tractatus Picture Theory is that there is no logical difference between an elementary proposition in language and a state of affairs in the world

A thought is what it shows.

He does engage with the issue: — Paine

5.634 and 5.641 could refer to either Idealism or Realism.

In 5.64, Wittgenstein says that solipsism coincides with pure realism. However, the term "pure realism" is only used once in the Tractatus.

How does Wittgenstein explain that solipsism coincides with pure realism?

An elementary proposition in language is true if the state of affairs in the world it pictures obtains.

Elementary propositions
By elementary proposition, we naturally think of expressions such as "the apple is on the table ", "grass is red". "the Eiffel Tower is in London", "the house is next to the school". I would argue that words expressing concepts are indivisible and simples. I know that "house" may be described as "a roof over a wall over a foundation", but nevertheless, in a sense, all these words expressing concepts are simples, whether "house", "roof", "wall" or "foundation".

Kant's Unity of Apperception

2.0232 - “Roughly speaking: objects are colourless”

A name names a set of properties. A name is no more than a particular set of properties, in that if all the properties were removed from an object then there would be no object. An object doesn't "have" properties, an object "is" its properties.

Even though an object is no more than its set of properties, an object, when thought about as a concept, because of Kant's Unity of Apperception, has no properties. The unity of apperception transcends the parts in favour of the whole.

For example, as an analogy, when eating a New York Cheesecake, the enjoyment doesn't come from knowing anything about its individual ingredients, such as thinking that this flour tastes good, that I like the vanilla extract and the eggs are fresh. The enjoyment comes from the taste of the cheesecake as a unified whole, something that has transcended any particular combination of ingredients.

(Wittgenstein - Tractatus Logico-Philosophicus: Necessity and Contingency (Part 1/3) Kyle Banick)

States of affairs
A state of affairs is objects in combinations, where objects make up the substance of the world and are indivisible and simple.

As a Neutral Monist, I think that the substance that makes up the world are elementary particles, such as fermions and bosons, indivisible and simple. But Wittgenstein cannot be referring to fermions as objects, as a proposition such as "grass is green" is certainly not picturing fermions in combination.

However, Wittgenstein is talking about the world as a logical space containing logical objects. So how can grass be thought of as a logical object indivisible and simple?

Understanding Objects within Idealism and Realism
Suppose the Tractatus had been written from the viewpoint of Idealism. Then grass in the world in fact exists in the mind, and if exists in the mind, then must exist in the mind as a concept. As a concept, can be argued to be indivisible and simple, meaning that elementary propositions picturing a state of affairs becomes understandable from the perspective of Idealism.

Suppose the Tractatus had been written from the viewpoint of Realism, then how can grass be understood to be an object indivisible and simple?

On the one hand, the Direct Realist does believe that objects such as apples, tables, grass do exist in the world as objects indivisible and simple. They believe that when we perceive an apple in the world, there is truly an apple existing in the world, and would continue to exist even if there was no mind to observe it. This means that elementary propositions picturing a state of affairs becomes understandable from the perspective of Direct Realism.

On the other hand, the Indirect Realist does not believe that objects such as apples, tables, grass exist in the world as objects indivisible and simple, but only exist in the mind as concepts indivisible and simple. When we perceive an apple in the world, there is no apple existing in the world, but only in the mind of the observer. This means that elementary propositions picturing a state of affairs is not understandable from the perspective of Indirect Realism.

But the Tractatus avoids Idealism and Realism

2.02 - “The object is simple”

However, Wittgenstein in the Tractatus deliberately avoids any reference to Idealism or Realism. This leaves us with the problem of what exactly is the proposition "grass is red" picturing in the world, and how exactly can grass be thought of as an object in the world indivisible and simple?

In order to be indivisible and simple, grass cannot be a physical object in a physical world, but only can be a logical object in a logical world, and logical objects can be indivisible and simple.

If this is the case, and an elementary proposition in language is true if the state of affairs in the world that it pictures obtains, and the state of affairs in the world is not a physical world but a logical world, then language is not picturing a physical world but a logical world.

This supports either Idealism or Indirect Realism but not Direct Realism. Unfortunately, this line of enquiry cannot be developed within the Tractatus, as the Tractatus doesn't engage with ether Idealism or Realism.

The problem here is Wittgenstein's muddling of epistemological and metaphysical concepts without clear distinction or marking what is what. — schopenhauer1

There are many philosophical questions:

How does language and thought relate to the world?
How does language relate to thought?
Does the world we experience only exist in the mind, or does it also exist outside the mind, and if it does exist outside the mind, how does the world we experience in our mind relate to the world outside the mind?
Is Neutral Monism correct, that apples only exist as concepts in the mind and outside the mind are only elementary particles and elementary forces in space and time?
Do tables exist outside the mind?

Perhaps it doesn't matter, as you say:

The problem here is Wittgenstein's muddling of epistemological and metaphysical concepts
It just looks like axiomatic assertions without much explanation that one must either accept or not.
Are objects actual entities or are they simply functional as a role?
One is a "realism" whereby the world exists independently of facts, and the other is an idealism of sorts whereby the world is simply the logical coherence of the world.
Objects become denuded of any of its usual attributions, other than its function to support atomic facts.

Perhaps all that matters, as you say:

The ideas become anemic on their own (without the reader doing the heavy-lifting).

Perhaps the Tractatus is like a paper weight. As long as it does the job of keeping the papers from flying away it has done its job, in that as long as it has got people to think it has done its job.

Your claim was that about his removal of relations and properties from his ontology. If ontology is about what exists, and properties and relations are shown, then even if they cannot be described they exist. — Fooloso4

Just because a picture can show a relation doesn't mean that the relation ontologically exists. A picture can show that the Empire States Building is 113m taller than the Eiffel Tower, but this does not mean that a difference in height of 113m ontologically exists in the world.
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He is not interested in the particular state of affairs that are modeled, but the possibility that is can be modeled. — Fooloso4

He is interested in possible elementary propositions, such as "grass is red", "grass is green", "grass is purple" and "grass is orange", showing possible states of affairs, such as grass is red, grass is green, grass is purple and grass is orange.

But this of necessity means that he is also interested in particular elementary propositions, such as "grass is purple", showing a particular state of affairs, such as grass is purple.
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It is the substance of the world not the facts in the world that prevents this: — Fooloso4

Yes, the world wouldn't exist without substance (ie, unalterable objects, simples) and there would be no propositions.

But on the other hand, as a proposition is not a single world, such as "grass", but words in combination, such as "grass is red", a proposition can only show in the world objects in combination (ie, states of affairs) such as grass is red.

One can perhaps understand Wittgenstein as a coherentist and not a correspondent theorist — schopenhauer1

In the Tractatus, Wittgenstein was trying to avoid a pure Coherentism, where one proposition gets its meaning from another proposition etc, by ultimately founding propositions on states of affairs that exist in a world outside these propositions.

He doesn't. — Fooloso4

4.122 is saying that propositions cannot describe properties and relations, but can only show them. This is the difference between what is said and what is shown.

It is impossible, however, to assert by means of propositions that such internal properties and relations obtain: rather, this makes itself manifest in the propositions that represent the relevant states of affairs and are concerned with the relevant objects.

4.022 – A proposition shows its sense.

FH Bradley treats relations as objects, and if relations were objects, this would lead into an infinite regress problem. This is why Bradley concludes that relations don't ontologically exist.

Anscombe believes that relations are not objects, and therefore cannot be nameable. 3.1432 should be read that in aRb, it is not the case that a stands in relation to b, where R is an object, but rather that a stands in a certain relation to b.

However in a picture of a and b, as a relation is not an object, the relation between a and b cannot be shown.

For the Tracatus, relations are just objects coming together. This relation cannot be described in a proposition but can only be shown by the proposition itself. However, remembering to avoid any infinite regress by thinking that the proposition shows a relation by showing a relation by showing a relation, etc.

The Tractatus is not about universal concepts describing a world, but about particular propositions (which are particular thoughts) showing particular states of affairs.
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Every object in the world is composed of simple objects. These simple objects are in this sense universal. — Fooloso4

In the Tractatus, in the world are logical objects in logical configurations. These logical objects are simples, indivisible. There are many of them.

A Platonic Form is a universal of which each particular object is an instantiation.

The Tractatus is not a proponent of Platonic Forms, but treats each object as a particular, even if there are many of them.

And yet, the meaning is often not understood. Your reading of Wittgenstein is a case in point. If we must infer what is meant then it is not evident from the outward form. — Fooloso4

Yes, that's the nature of language, where the meaning of a word often depends on context.

Where Wittgenstein writes in 4.002 "Language disguises thought", according to the Merriam Webster Dictionary, "disguise" can mean "to change the appearance of", "gives a false appearance to" and "obscures".

But as Wittgenstein points out, knowing what is the case also means knowing what is not the case.

So we know that "disguises" doesn't mean "jumps", "thinks", "stands", etc, etc.

Therefore we have some good idea as to the possible meanings of "Language disguises thought".

But as the Tractatus must be read as a whole, we can further narrow down its meaning by reading it in the context of the whole.
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Objects are particulars. A universal property of objects is to combine with other objects. — Fooloso4

However, one feature of the Tractatus is Wittgenstein's removal of relations and properties from his ontology. Another feature is his removal of universals in favour of particulars.

For the Tractatus, objects combine as particulars not as universals.

From the outward form, how the thought is expressed, we do not see the logical form that underlies it. — Fooloso4

It is clearly the case that from the outward form of clothing we can infer the form of the body beneath it.

It is also clearly the case that from the outward form of language we can infer the form of the thought beneath it, otherwise language would be meaningless.

What use would language be if when someone said "please pass the sugar", no-one knew the thought behind these words.

From the outward form of language we clearly do know the form of thought beneath it.

Wittgenstein in the Tractatus does away with universals in favour of particulars, where the form of language maps directly not only with the form of thought but also with the form of states of affairs in the world.

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1.13 - The facts in logical space are the world — Fooloso4

The world is a logical space.
In this logical space are possible states of affairs.
A state of affairs consists of logical objects in logical configurations
If a state of affairs obtains, then it is a fact

Here Wittgenstein draws an analogy between "clothes" and "a body" with "language" being the clothing and "thought" being the body that is clothed. So, there is a distinction that is made between the two — 013zen

4.002 may be correct that language disguises thought, but is not inconsistent with the idea that language is thought.

I see a one-storey brick building, think one-storey brick building and say "house". I see a two-storey stone building, think a two-storey stone building and say "house".

It is true that the word "house" has disguised the thoughts, but this does not detract from the fact that the word "house" is the thought of a one-storey brick building and the word "house" is also the thought of a two-storey stone building.
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These are examples of propositions, not elementary propositions, though. — 013zen

As I understand it, for the Tractatus:

The world is a logical space in which can only exist logical objects in logical configurations.

A state of affairs is a logical configuration of logical objects. A state of affairs may or may not obtain. If it obtains then it is a fact. For example, grass is green and grass is red are possible states of affairs. Grass is green obtains and grass is red doesn't obtain.

All states of affairs are independent of each other, in that either grass is green or grass is red. It cannot be the case that grass is both green and red at the same time.

An elementary proposition stands for a state of affairs

A name stands for an object.

Therefore an elementary proposition will be an arrangement of names.

An elementary proposition will be true if the state of affairs obtains.

For example, the elementary proposition "grass is green" is true if the state of affairs grass is green obtains.

All elementary propositions are independent of each other, in that either "grass is green" or "grass is red". It cannot be the case that "grass is both red and green at the same time".

That an elementary proposition is conceivable does not mean that it is true, for example "grass is red". In the same way, because a state of affairs is possible it doesn't mean that it obtains, for example grass is red.

For Wittgenstein, propositions are truth-functions of elementary propositions, for example,
"grass is green and the sky is blue"

(The Theory of elementary propositions, Jeff Speaks, Phil 43904, 8 Nov 2007)

Wittgenstein's objects are "simples"

Tractatus 2.02 Objects are simple.

From Wikipedia - Simple (Philosophy)

In contemporary mereology, a simple is any thing that has no proper parts. Sometimes the term "atom" is used, although in recent years the term "simple" has become the standard.

From Jeff Speaks Wittgenstein on facts and objects: the metaphysics of the Tractatus

What does it mean to say that an object is simple? One thing Wittgenstein seems to mean is that it cannot be analyzed as a complex of other objects. This seems to indicate that if objects are simple, they cannot have any parts; for, if they did, they would be analyzable as a complex of those parts.

A proposition in some sense contains a thought, but a thought is not identical with a proposition............................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 — 013zen

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. — 013zen

It all depends on whether, in the Tractatus, for Wittgenstein, language and thought are the same thing.

If not, then isomorphism may be the suitable world. If they are, then as an object such as an apple cannot be isomorphic with itself, isomorphism may not be the suitable word.

A starting position to determine whether in the Tractatus language and thought are the same thing could be the article The Thought (Gedanke): the Early Wittgenstein, written by Sushobhona Pal

His conclusion is " Apart from this, apparently, the Tractatus implies that the realms of thought and language coincide", or as he says elsewhere " are "coextensive".

As he writes:

Wittgenstein writes in unequivocal terms that we cannot think what we cannot think and therefore what we cannot think we cannot say either. It means what cannot be thought cannot possibly be spoken about either. These entries suggest that thinking and language (speaking) are coextensive.

For Wittgenstein, if a thought is a picture of the world and a proposition is a picture of the world, then how can a thought not be a proposition?
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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. — 013zen

In Wittgenstein's terms (as I understand it), grass is red, grass is green, not grass is red and not grass is green are States of Affairs.

The elementary propositions "grass is red" "grass is green" "not grass is red" and "not grass is green" may be true or false

If the elementary proposition "grass is green" is true, then grass is green is a fact. Alternatively, if grass is green is a fact, then the elementary proposition "grass is green" is true.

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).

the Tractatus presents a three part isomorphism between: 1. Thoughts 2. Language 3. Reality — 013zen

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).
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A proposition can be analyzed into an elementary proposition, and to this corresponds an atomic fact. — 013zen

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.

it is impossible to directly receive that which is not real, for we would never be aware of an affect. — Mww

Seeing a beautiful sunset affects an observer differently to seeing a sunset.

Does this mean that abstract concepts such as beauty are real?

@Michael

NOTES ON INDIRECT REALISM

Chain of events

Everyone seems to agree that there is a chain of events prior to perception. For example, light from the sun hits an object, part of the light is absorbed by the object and part reflected, a wavelength then travels though space to the eye of an observer, this causes an electrical signal to travel along the optic nerve from the eye to the brain where it is somehow processed, thereby enabling the mind to perceive the colour red.

There is a chain of events going back in time prior to my perceiving the colour red, which if disrupted, would have prevented the perception of the colour red

It is a fact that I directly perceive sensations, such as the colour red, an acrid smell, a bitter taste, a sharp pain or a screeching noise. These sensations are sometimes called qualia.

The expressions "I see the colour red", "I perceive the colour red", "I am aware of the colour red", "I am conscious of the colour red" and "I sense the colour red" seem synonymous.

It is accepted that each link in the chain can be of a different kind, in that an electrical signal up the optic nerve is of a different kind to a wavelength of 700nm that precedes it. It is also a fact that there is no information within a subsequent link in the chain that can determine the preceding link in the chain, in that the wavelength of 700nm could have been equally caused by light reflecting off a rose, a strawberry, a lizard, a frog, a painting, a television screen or a Christmas light. Each link in the chain is an intermediary between sunlight hitting the rose and the perceiver perceiving the colour red

There is the question of terminology regarding mapping, presenting and representing. We perceive the colour red because light was reflected off a rose. We can say that "the colour red represents a rose", "the colour red is mapped to the rose" or "the perceiver is presented with a rose and perceives the colour red", but as with most words in language, all these are figures of speech rather than literal descriptions.

The Perceiver and what the perceiver perceives

It is important to note that the "I" that is perceiving the colour red is not separate to the colour red that is being perceive, but rather the perceiver and perceived are one and the same thing. If otherwise, would lead into the infinite regress homunculus problem.

It cannot be the case that what the perceiver is perceiving is external to the perceiver, such as sense data or an intermediary, because sooner later, in order for there to be perception at all, what is being perceived must be internal to the perceiver. The perceiver and what is being perceived are two aspects of the same thing.

As John Searle explains in The Philosophy of Perception and the Bad Argument

The relation of perception to the experience is one of identity. It is like the pain and the experience of pain. The experience of pain does not have pain as an object because the experience of pain is identical with the pain. Similarly, if the experience of perceiving is an object of perceiving, then it becomes identical with the perceiving. Just as the pain is identical with the experience of pain, so the visual experience is identical with the experience of seeing.

The cause of the perception

So the perceiver and the thing being perceived are two aspects of the same thing and neither external to the other. But something cannot come from nothing. The perception cannot have been spontaneously self-created out of nothing. There must have been a cause, even if the cause is unknown. As my perception of the colour red cannot have been caused by the colour red being perceived, because these are two aspects of the same thing, the perception must have caused by something external to not only the perceiver but also the thing being perceived. The cause can only have been a prior link in the chain of events going back in time.

The relation between what is perceived and the unknown cause of such perception

Humans commonly name the unknown cause of a sensation after the known effect. For example, the cause of seeing a red colour is described as a red object, the cause of a bitter taste is named as a bitter food, the cause of an acrid smell is named acrid smoke, the cause of hearing a loud noise is named a loud noise and the cause of a painful sting is named a sting. Although the sensation is real, the named cause is fictive.

We can only know about an object from its properties. If an object had no properties we would not know about it. For example we may describe a rose as having the properties of being red in colour, being circular in shape and being sweet in smell, yet as Bertrand Russell pointed out in his Theory of Descriptions, it is more correct to say that there is something that has the properties of being red, being circular and being sweet. There is no Platonic thing that is a rose that exists independently of its properties. The rose is no more than its set of properties. Therefore, to say "I see a red rose" is a figure of speech for the more literal "I see something that has the colour red, has a circular shape and a sweet smell, and that this something with these properties has been named "a rose"".

In the expression "I see a red rose", red is an intrinsic part of what a rose is, not an extrinsic property. We may say that red is an adjective qualifying the noun rose, but must remember that this is a linguistic convenience, not a literal description of the relationship between the object rose and its property redness.

Adverbialism

Therefore, as regards the Adverbialist, rather than say "I perceive a red, circular and sweet rose", it is more correct to say "I see something that has the properties of red, circular and sweet and that this something has been named rose".

Therefore, for the Adverbialist, as the perceiver of the sensation and the sensation are two aspects of the same thing, the expression "I see a red, circular and sweet rose" may be replaced by "I perceive redness, circularness and sweetness" and "this something having the properties of redness, circularness and sweetness" has been named "a rose"". For the Adverbialist, redness, circularness and sweetness are adverbs qualifying the verb "to perceive".

Adverbialism is consistent with Bertrand Russell's Theory of Descriptions.

The trees are in the Mississippi delta backwaters.................I could take you there and show you in person..................None of those things and none of those places are in my mind. — creativesoul

Suppose we are both in Mississippi.

I agree that in a mind-independent world are real things, in that they can physically affect me. They can cause in my sensations sharp pains, acrid smells, sweet tastes, loud noises and colours.

You say that the place Mississippi does not exist in the mind, and yet the original Mississippi Territory was only created by the U.S. Congress in 1798.

Are you saying that the place Mississippi existed before the US Congress named it in 1798?

How did the US Congress know the extent of the territory of Mississippi before the extent had even been written down?
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What I'm saying is that it is possible for a capable creature to directly perceive green cups but because they do so by means of ways that they are completely unaware of, they're not conscious of perceiving. They're just doing it. — creativesoul

I think that the expressions "I see a green cup", "I perceive a green cup". "I am aware of a green cup" and "I am conscious of a green cup" are synonymous.

As an Indirect Realist, I agree that in the first instance I directly perceive a green cup. I don't perceive myself perceiving a green cup, I am not perceiving an image of a green cup and I am not perceiving a representation of a green cup.

Subsequently, however, I can begin to apply reason about what I have perceived, and ask myself what exactly was it that I had perceived. Had I perceived a green cup as it was in the world, had I perceived an image of a green cup, had I perceived a representation of a green cup or had I perceived a cup greenly. However, I agree that all these all philosophical questions don't detract from the point that in the first instance I directly perceive a green cup.
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House cats can see green cups in cupboards and have no idea that they're called "green cups". — creativesoul

How do you know what is in the cat's mind, that the cat sees the cup as green, rather than red or blue?
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If the object has no inherently existing mind-independent property of color to speak of, then it makes no sense to accuse either one of you of not seeing the object 'as it really is'(whatever that's supposed to mean). It's appearing green to you and blue to them makes no difference - if the object has no inherently mind independent property of color. — creativesoul

As an Indirect Realist, I agree that objects in the world don't have the mind-independent property of colour, but the object must have some property otherwise no-one could see it. It could well be the property of being able to reflect a particular wavelength of light, such a red rose has the property of being able to reflect the wavelength of 700nm when illuminated by white light.

I agree that the wavelength of 700nm may have different effects on different people, in that, for example, I may perceive the colour green whilst another person may perceive the colour blue. But no-one will ever know, as it is not possible to look into another person's mind.

The question is, if I perceive the object as having the property green, but in fact the object has the property of being able to reflect a wavelength of 700nm, in what sense am I directly perceiving the object?
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Trees are in the yard. Concepts are in the language talking about the yard. Both are in the world. Concepts are in worldviews. Cypress trees are in the backwaters of the Louisiana delta. — creativesoul

If Cypress trees exist in the world independently of any human mind, then it should be obvious to someone who doesn't know the concept of a Cypress tree, that A and B are the same thing and A and B are different to C

Yet that is obviously not the case.

I don't understand why you don't understand what I'm asking and I don't know how to explain it in any simpler terms. — Michael

I generally agree with what you say, so I apologise if I'm missing something. Perhaps I'm thinking of my glass of red wine over dinner.

it's literally impossible to describe one's experiences to another person coherently in adverbial language — Count Timothy von Icarus

True, but then again it's literally impossible to describe one's subjective experiences to another person coherently using any language, in that how would it be possible to describe the experience of the colour red to someone who has never had the ability to see colour.
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Could an adverbial description do the same thing? — Count Timothy von Icarus

One advantage of an adverbial description is that it negates the homunculus problem.
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In general though, the adverbial view tends to apply adverbs only to the perceiver, e.g., to people "seeing greenly," but not to plants "reflecting light greenly." — Count Timothy von Icarus

Yes, because it is the perceiver who perceives things. If I perceive the colour green, it could have had numerous causes, a traffic light, grass, a plant, a bird, etc, My perception of the colour green will be identical even though it could have have multiple possible causes.

It is the nature of language to mix the literal with the figurative, in that "I perceive the colour green" is a figure of speech for the more literal "I perceive greenly".

Which is like saying "one difference could be that bachelors exist and unmarried men don't". — Michael

Not really, as that statement is factually untrue. Both bachelors and unmarried men exist.

Why do you think that sense data exist?

So if I'm wrong and there is a difference between sense data and qualia then what is that difference? — Michael

One difference could be that qualia exist and sense data don't. I directly know the "qualia" of the colour red, a sharp pain, an acrid smell, etc. But I don't know where my sense data are. Has any scientist discovered the site of sense data in the brain?

As I understand it, sense data and qualia are the same thing. — Michael

Only if sense data exist. The Adverbialist doesn't need them. Why do you think sense data exist if they are not needed?

According to the SEP article adverbialists accept qualia. If sense data and qualia are the same thing then according to the SEP article adverbialists accept sense data. — Michael

The Adverbialist may accept qualia but don't need sense data. For the Adverbialist, qualia exist but sense data don't, so they cannot be the same thing.

From SEP article The Problem of Perception

Part of the point of adverbialism, as defended by Ducasse (1942) and Chisholm (1957) is to do justice to the phenomenology of experience whilst avoiding the dubious metaphysical commitments of the sense-datum theory. The only entities which the adverbialist needs to acknowledge are subjects of experience, experiences themselves, and ways these experiences are modified.

From Philosophy 575 Prof. Clare Batty on Adverbialism

1. Against the Sense Datum View
The adverbialist rejects the Phenomenal Principle, that if there sensibly appears to a subject to be something which possesses a particular sensible quality then there is something of which the subject is aware which does possess that quality.
According to the adverbialist, statements that appear to commit us to the existence of sense data can be reinterpreted so as to avoid those commitments. In doing so, the adverbialism rejects the act/object model of perceptual experience—the model on which sensory experience involves a particular act of sensing directed at an existent object (e.g., a sense datum).

Adverbialist Indirect Realism seems the way to go.

I don't get the distinction between sense data and qualia. — Michael

The Adverbialist rejects sense data. Sense data should go the way of the aether, of historic interest only.

But indirect realists generally say we experience pain "directly," — Count Timothy von Icarus

The Adverbialist Indirect Realist might say in general conversation "we experience pain directly", but only as a figure of speech, not in a literal sense.

For the Adverbialist, it is not that "I see white", but rather "I see whitely". It not that that "I feel pain", but rather "I feel painly".

John Searle's quote from The Philosophy of Perception and the Bad Argument develops this idea.

The term "Direct Realism" is misleading.

Direct Realism can refer to either a causal directness, aka Phenomenological Direct Realism or a cognitive directness, aka Semantic Direct Realism. I imagine today that most Direct Realists are Semantic Direct Realists, in that Phenomenological Direct Realism would be hard to justify.

There are two separate aspects to the word "Direct" in Direct Realism, linguistic and cognitive.

As regards linguistics, inferred knowledge cannot be direct knowledge.

For example, hearing a noise next door I can infer from knowing my neighbours holiday plans that my neighbours were the cause of the noise. I have no direct knowledge that they were the cause of the noise, as such knowledge was inferred.

As regards cognition, although a subsequent effect can be directly known from a prior cause, the prior cause of a subsequent effect cannot be known because there is a direction in the flow of information in a chain of events between cause and effect.

For example, if I hit a billiard ball on a billiard table, I can directly know its final resting position, but if I see a billiard ball at rest on a billiard table, it is impossible to know its prior position.

For the linguistic aspect, as inferred knowledge cannot be direct knowledge, the term "Direct Realism" is misleading.

For the cognitive aspect, as information cannot flow from a subsequent effect to a prior cause, the term "Direct Realism" is misleading.

Adverbialism replaces the Sense-Datum Theory

Within Indirect Realism is the Sense-Datum Theory and Adverbialism. Today, the Sense-Datum theory has generally been replaced in favour of Adverbialism, which rejects the Sense-Datum Theory.

Some of our knowledge is direct involving our senses. Such as seeing the colour red, smelling something acrid, feeling a sharp pain, tasting something sweet or hearing a grating noise.

Some of our knowledge is indirect. Such as the cause of seeing the colour red was a post-box, the cause of an acrid smell was a bonfire, the cause of the sharp pain was a bee sting, the cause of the sweet taste was an apple or the cause of the grating noise was a gate closing .

The words direct and indirect have value in language.

In language it is normal to say that "I feel a sharp pain". If taken literally, this suggests that the pain I feel is external to the I that is feeling it and leads to the homunculus problem. However, even the ordinary man knows that there is a difference between language that is literal and language that is figurative. Even the ordinary man knows that if I say to someone "I see that you have a bright future", they know they are not talking to a seer, but someone using the language figuratively. The expression "I feel a sharp pain" is figurative, not iteral.

John R Searle in The Philosophy of Perception and the Bad Argument makes the point that an expression such as "I feel a sharp pain" cannot be taken literally but only figuratively, when he wrote:

The relation of perception to the experience is one of identity. It is like the pain and the experience of pain. The experience of pain does not have pain as an object because the experience of pain is identical with the pain. Similarly, if the experience of perceiving is an object of perceiving, then it becomes identical with the perceiving. Just as the pain is identical with the experience of pain, so the visual experience is identical with the experience of seeing.

This is why the Sense-Datum Theory has probably fallen out of favour to be replaced by Adverbialism. Adverbialism explicitly does not treat the pain I am feeling as external to the I that I am feeling it. Adverbialism avoids any homunculus infinite regress problem, where I perceive myself perceiving myself perceiving..................

Adverbialism does justice to the phenomenology of experience whilst avoiding the dubious metaphysical commitments of the sense-datum theory. (SEP - The Problem of Perception)

Wittgenstein was a major influence on adverbial theories. — Count Timothy von Icarus

Both the Indirect and Direct Realist believe that we directly perceive a hand, and both are Adverbialists in the sense that what is being perceived cannot be separated from the process of perceiving. IE, if nothing was being perceived, then there would be no process of perceiving, in that what is being perceived is an intrinsic part of the process of perceiving.

The adverbialist view of Wittgenstein is more relevant to thoughts. Consider "I hope you come" or "I hope X". The traditional philosopher would say that "I hope" is a process and X is separate to "I hope". But Wittgenstein as an adverbialist would say that X is the manner in which one hopes, such as "I run quickly". (Wittgenstein on Understanding as a Mental State - Francis Y Lin)

Adverbialism is a form of Indirect Realism (SEP – Epistemological Problems of Perception).
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Since cause, matter, energy, and information appear to flow across this boundary in the same manner as any other, I am not sure how movement across the boundary is supposed to be more "indirect."...Is this logical necessity or causal? — Count Timothy von Icarus

On the world side of the boundary is the wavelength of 500nm and on the mind side of the boundary is the perception of the colour green.

I am sure that both the Indirect and Direct Realist would agree that the chain of events from the object in the world to the perception in the mind is direct, being determinate. However, there is no causal necessity as the chain of events could be broken at any moment.

Indirectness enters the picture because of inference. Inferences are made about a new situation using reasoning based on prior knowledge .

Toni never eats sushi, so I infer Toni doesn't like sushi. That man is running towards the bus, so I infer he wants to catch the bus. I see red dot in the night sky and from my knowledge of astronomy infer that it was caused by the planet Mars. As I know my neighbours moved in last week, I infer they are causing the noise.

In none of these real life cases does my inference lead to direct knowledge. I have no direct knowledge that Toni doesn't like sushi, or the man wants to catch the bus, or the red dot was caused by the planet Mars or my neighbours are making the noise. IE, there is no logical necessity that my inference leads to direct knowledge.

The Indirect Realist would say that they infer that the red dot has been caused by the planet Mars. The Direct Realist would say the red dot is the planet Mars, assuming a knowledge that they can never have.
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Is there any knowledge that doesn't involve inference?...We don't see various shapes and hues and then, through some concious inferential process decide that we have knowledge of a chair in front us. We just see chairs. — Count Timothy von Icarus

I perceive the colour red. This is a direct perception and doesn't involve inference as it is within my mind. Is this knowledge? Probably, as one Merriam Webster definition of "knowledge" is "the fact or condition of being aware of something".

I go back to my diagram. Within the diagram we see dots, analogous to parts in the world. I agree that parts ontologically exist in the world as primitives, ignoring the exact nature of these parts.

The question is, do wholes ontologically exist in the world?

Within the diagram we may see the shape X, the shape L or the shape of a chair. Because we see the shape of an X, L or chair in the diagram, does it of necessity logically follow that the shapes X, L or chair must exist in the diagram independently of any observer?

As my belief is that relations have no ontological existence in the world, it follows that neither do I believe that wholes ontologically exist in the world.

We both may see a chair within the diagram. Why do you think that just because we both see the shape of a chair in the diagram, the shape of a chair must exist in the diagram independently of any observer?