Again, it was your presupposition that the existence of relations must cause changes in the world. I'm asking you why that must be. — Luke

Relations must cause changes in the world if we are to know about them

If relations ontologically exist in a mind-independent world, they either cause changes in the world or they don't.

I have seen no evidence that changes in the world have been caused by relations between things. I have seen evidence that changes in the world have been caused by forces between things, but forces are a different thing to relations.

Therefore, either relations exist and don't cause changes in the world or relations don't exist.

If relations exist, but don't cause changes in the world, then we cannot know about them, and are unknown unknowns.

I cannot prove that relations don't ontologically exist, although I can justify that they don't. It is up to those who propose the ontological existence of relations to prove that they do exist, or justify that they do.

I could say, as in 3.1432, "a stands in a certain relation to b", but then again I could say "the war was raging, the Evil White Witch led an attack against Aslan, and the Unicorns joined the great battle". Why should either of these two statements be more true than the other ?

What is the relation between them? — Luke

Exactly, what is it ?

Why must the existence of relations cause changes in the world? — Luke

Exactly, if relations don't cause changes in the world then how do we know about them ?

The difference between a predicate and an individual is clear in Wittgenstein's aRb, which makes use of Frege's logic — Banno

Not lost interest, but busy as off to Vienna tomorrow for a Schnitzel and Apfelstrudel.

Did Wittgenstein treat relations as objects
In the Preface, Wittgenstein wrote "I will only mention that to the great works of Frege and the writings of my friend Bertrand Russell I owe in large measure the stimulation of my thoughts". In 4.1252 he includes examples of First Order Logic.

Traditionally, relations are internal and classes are considered as universals, but Frege treats relations and universals as objects. For Frege, a property, a special kind of function, is not part of the object possessing it, but forms together with the object a "complete whole", having as constituents the object and property.

The SEP article "Wittgenstein's Logical Atomism" sets out alternate readings to the Tractatus as to whether relations can be considered as objects or not. Anscombe argues that relations are not Tractarian objects, whilst Srenius, Merrill and Hintikka argue that they are.

Wittgenstein refers to Frege directly and includes examples of First Order Logic. As Frege treated relations as objects, this makes it plausible that Wittgenstein also treated relations as objects.

the incidental truth in RussellA's analysis is that predicates do not exist...RussellA's picture is perhaps a form of Platonism............Holding to such a picture would make understanding the Tractatus impossible.. — Banno

Relations
3.1431 The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs. The mutual spatial position of these things then expresses the sense of the proposition.

I know there is a world in my mind and I believe there is also a world that is mind-independent. I know relations exist in the world in my mind, and I believe that relations don't exist in a mind-independent world.

Badley argues that a relation C cannot exist as a particular individual in a mind-independent world, to which I agree. It would follow that if a relation cannot exist as a particular in a mind-independent world, then relations as universals cannot either, a position in opposition to Platonism.

Relations cannot exist as universals in a mind-independent world
The question is, is the statement "the relation C is an individual" true or false. The subject "the relation C" is a particular, and the predicate "is an individual" is a universal.

You wrote "predicates do not exist", in the sense that Platonic Forms don't exist and have no ontological existence in a mind-independent world

The statement "the relation C is an individual" may be compared to "the King of France is bald", whereby there is something x - such that x is the King of France (false) - and x is bald, in that there is something x - such that x is the relation C (false) and x is an individual.

Reading of the Tractatus
@Banno "The purpose here is to move beyond seeing the Tractatus in terms of idealism and empiricism. The world is all that is the case. The picture is of the world, and hence in an important sense distinct from it. Thinking of the world as either mind-dependent or mind-independent will not allow one to see that the picture shows the world."

Even though I may believe that relations don't ontologically exist in a mind-independent world, as the Tractatus may be understood independently of idealism and empiricism, my belief need not impact on my reading of the Tractatus.

This is so confused. It implies that no two things can ever be related — Luke

There are two types of relations, those in the mind and those in the mind-independent world.

I agree and believe that relations exist in the mind, but have not been persuaded that relations exist in a mind-independent world.

As regards the ontological existence of relations in a mind-independent world, I have two questions.

Q1: If relations exist in a mind-independent world, how can the mere fact of a relation between a rock on Earth and a rock on Alpha Centauri cause changes to either ?
Q2: If relations don't cause changes in the world, then why do we think that relations exist in the world ?

Words are used for communicating what is the case to someone that lacks the knowledge of what is the case — Harry Hindu

I agree, language needs both description and acquaintance. Neither is sufficient by itself.

The Rosetta Stone couldn't be deciphered without there being something external to it. As Wittgenstein wrote 5.61 Logic fills the world: the limits of the world are also its limits, We cannot say in logic: This and this there is in the world, that there is not. 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.

"Showing" is something that happens in live language use, which is what he's focusing on in the Tractacus — Tate

If aRb cannot be shown in a picture of the world because it may lead into an infinite regress, being shown the meaning of "tufaa liko mezani" will equally lead into an infinite regress, in that "Look up a word in the dictionary to find its meaning. You get more words. Look up the meaning of those words. You get more words. Since the dictionary is finite, and since word is defined in terms of other words, the definitions must be circular".

The right way to think of a relation is that "a stands to b in a certain relation"...I don't see Wittgenstein as arguing for external relations. — Luke

Relations may be the weak point in Wittgenstein's theory of showing

aRb leads into an infinite regress
Russell in his introduction gives an example of aRb: "If we say “Plato loves Socrates”, the word “loves” which occurs between the word “Plato” and the word “Socrates” establishes a certain relation between these two words, and it is owing to this fact that our sentence is able to assert a relation between the persons named by the words “Plato” and “Socrates”.

Wittgenstein introduces First Order Logic in an explanation of aRb
4.1252 Similarly the series of propositions aRb (∃x): aRx. xRb
In the case of Plato and Socrates there is something x such that Plato relates to x and x relates to Socrates, where x is "love". X is an individual, is independent of either Plato or Socrates and is an external relation

We can replace x by "relates", and get the situation there is something x such that Plato relates to x and x relates to Socrates. Again we have the situation of a relation relating, which as Bradley pointed out, leads to an infinite regress

3 The logical picture of the facts is the thought
4.121 The propositions show the logical form of reality
4.461 "Propositions show what they say"
As I understand it, the picture is of the world but distinct from the world, the world consists of facts and a thought is a logical picture of the facts. It follows that the thought is the proposition, the logical picture is the propositional sign and the propositional sign has the form aRb.
3.1431 The essential nature of the propositional sign becomes very clear when we imagine it made up of spatial objects (such as tables, chairs, books) instead of written signs. The mutual spatial position of these things then expresses the sense of the proposition.

As aRb requires a relation, aRb is not a fact, but is part of the picture. However, if a was related to b, such that aRb, this would lead to an infinite regress. Therefore, a cannot be related to b. Therefore, propositions cannot show the logical form of reality.

Showing is a problem of inference
But we know that in our thoughts, we do relate object a to b, in that we do perceive an apple on a table. We do have thoughts of relations between objects. However, these relations cannot be shown in a picture using aRb, in that if there was relation between a and b, an infinite regress would follow, Therefore our thought that a is related to b cannot be by showing, but by another mechanism.

Showing is a problem of inference, in that what a picture shows depends on who is doing the observing. I can look at a picture and see a duck, whereas my neighbour may see a rabbit. The problem of inference can be illustrated by the chess game between a Tortoise and Achilles, where Achilles tells the Tortoise that if the Tortoise wins the next game, then Achilles will pay for the Tortoise to go on a holiday in the Seychelles. The Tortoise is obviously and wisely dubious about inferring anything from such a hypothetical offer.


How is the relationship between language and reality to be understood
If showing is inadequate in enabling us to understand the relationship between language and reality because of the problem with inference, then where is the solution.

As an aside, my belief is that the solution may be found in a triumvirate combining Wittgenstein's Tractatus which establishes the gaining of knowledge by acquaintance, Wittgenstein's Philosophical Investigations which establishes the gaining of belief by description and Kant's a priori intuition which ties both of these together.

Why are you raising the issue of Bradley and external relations?...I don't see how C can be independent (external) of A or B when it is the relation between A and B; what relates A to B. — Luke

You're assuming that there is something called C

That's the question. Is there a something C that relates A to B. What is C ?

Either C is grounded in its relata or it isn't.

If C is grounded in its relata, then C doesn't exist because it is just a property.

If C isn't grounded in its relata, then it is independent of its relata, and is an individual. Bradley presents this as a problem, in that somehow the relation C needs to be related to its relata. This leads to the problem of infinite regress, meaning that C cannot exist.

Either way, C cannot ontologically exist, and if doesn't, cannot be "what relates A to B".

are you assuming that if external relations exist then they must be individuals? — Luke

An external relation is a relation that is external to the terms or things it relates, and is not grounded in its relata. For example a cherry and a strawberry are 3m apart. Some philosophers believe that if external relations did exist they would be ontological additions. An internal relation is grounded in its relata. For example, a cherry and a strawberry may both be the same shade of red. Some philosophers believe that internal relations are not ontological additions because they can be reduced to intrinsic properties.

As regards FH Bradley, what he calls "real" relations are grounded in their relata, and are what would be called in modern usage internal relations, and therefore not ontological additions. Those relations not grounded in their relata, and are what would be called in modern usage external relations would be ontological additions. It is these external relations that Bradley argues cannot exist, as their existence would lead to an infinite regress, in that this external relation would need another relation to relate it to its relata.

Therefore, if relations grounded in their relata are internal relations, and not ontological additions, then relations not grounded in their relata are external relations, are individuals, and would be ontological additions.

Relations are in the picture of the world, not in the facts. — Banno

For Wittgenstein, is there a mind-independent world ?
I follow that " the notion of a mind-independent world is not found in the Tractatus", yet he does refer to things we would expect to be in a mind-independent world, for example:
4.014 The gramophone record, the musical thought, the score, the waves of sound, all stand to one another in that pictorial internal relation, which holds between language and the world...............(like the two youths, their two horses and their lilies in the story.........)
6.3432 We must not forget that the description of the world by mechanics is always quite general
6.373 The world is independent of my will

Although Wittgenstein may not refer to a mind-independent world, I read that the existence of a mind-independent world is assumed.

Does the "world" in the Tractatus exist in the mind or is it mind-independent ?
3 The logical picture of the facts is the thought

In a mind-independent world, there are two possibilities as regards the existence of relations.

Possibility One: If relations don't exist, then facts don't exist. Therefore, as the logical picture in the mind cannot be a logical picture of facts in the world ( although it can be a representation of facts in the world), it can only be a logical picture of facts in the mind. In this case, the "world" must be read as existing in the mind.

Possibility Two: If relations do exist, then facts exist. Therefore, the picture in the mind can be a logical picture of facts in the world. It can also be a logical picture of facts in the mind. In this case, the "world" may be read as either existing in the mind or existing as mind-independent.

IE, one's reading of whether the "world" in the Tractatus exists in the mind or is mind-independent depends on one's opinion as to the existence or not of relations in a mind-independent world.

Bradley's argument cannot be given a reasonable parsing in first order logic. — Banno

Are ontological relations in a mind-independent world individuals

Terminology
In modern usage, an internal relation is not an ontological addition, such that the cherry is the same shade of red as the strawberry. An external relation is an ontological addition, such that the cherry is 1m distance from the strawberry.

Relations in logic
Grammar, first-order logic and predicates are mental things, part of mathematical and linguistic language. The relation (r) between a rock on Earth (a) and a rock on Alpha Centauri (b) may be expressed as
r (a,b), where r is a relation, not an individual.

Relations in a mind-independent world
However, Bradley is questioning the nature of relations in a mind-independent world. What exactly are relations ? Can they be individuals ? In a mind-independent world, if relations are independent of their relata, Bradley proposes that this leads into an infinite regress, which suggests that relations cannot be independent of their relata. If relations are grounded in their relata, then this is the modern usage of internal relations, and which presents no ontological addition.

Either way, Bradley is proposing that ontological relations don't exist in a mind-independent world.

Russell's Theory of Descriptions may be more suitable than Frege's First-Order Logic
However, if Bradley was being expressed using logic, perhaps RTD would be more suitable than Frege's First Order Logic, as it does not depend on the subject-predicate form. For First Order Logic, there is a relation between a and b. For RTD, there is something, a relation, that relates to a and relates to b, in which case the relation is an individual.

A relation relating leads back into Bradley's problem of infinite regression.

Two questions about the ontological existence of relations in a mind-independent world
We know that relations exist in the mind, as we talk about ghosts, unicorns, governments, ethics, the sweet smell of success, the tree swaying in the wind, tables, apples, etc. Science tells us that a world of elementary particles and forces, a world of gravity, the photo-electric effect, volcanos, rain, etc are explainable by the Laws of Nature.

Q1: If relations exist in a mind-independent world, how can the mere fact of a relation between a rock on Earth and a rock on Alpha Centauri cause changes to either ?
Q2: If relations don't cause changes in the world, then why do we think that relations exist in the world ?

I wonder if you are familiar with What the Tortoise Said to Achilles? — Banno

My attempt:

Can ignore (A) which is a hypothetical and redundant.

From (B), which is not hypothetical:

Let side one of the Triangle have length a
Let side two of the Triangle have length b

There is a length c that is equal in length to side one of the Triangle
Length c is also equal in length to side two of the Triangle

Therefore c = a and c = b
From which it follows that a = b

If a = b then (Z) follows.

The solution may be easier if shown rather than said.

What the Tortoise said to Achilles — Banno

The puzzle of the Tortoise and Achilles is what the Tractatus is trying to solve
4.1212 " What can be shown, cannot be said"
4.461 "Propositions show what they say"
As Bertrand Russell wrote: "This is perhaps the most fundamental thesis of Mr. Wittgenstein’s theory. That which has to be in common between the sentence and the fact cannot, he contends, be itself in turn said in language. It can, in his phraseology, only be shown, not said, for whatever we may say will still need to have the same structure."

The puzzle of the Tortoise and Achilles points out the main theme in Tractatus, in that what can be shown cannot be said. As you wrote "before he accepts (C) we must first show him that if A, B and C are true, he must accept Z", meaning that before the Tortoise accepts (if A is true and if B is true then Z is true) he must be shown that (if A is true and if B is true then Z is true).

In other words, before the Tortoise accepts what he is told to be true, the Tortoise must be shown that it is true.

Knowledge by description and acquaintance
This takes us back to Bertrand Russell's distinction between knowledge by description and knowledge by acquaintance. In his paper On Denoting 1918, whereas knowledge by description is something like ordinary propositional knowledge (e.g. "I know that snow is white"), knowledge by acquaintance is familiarity with a person, place, or thing, typically obtained through perceptual experience, such as "I know Sam". According to Bertrand Russell's classic account of acquaintance, knowledge by acquaintance is a direct causal interaction between a person and some object that the person is perceiving.

Wittgenstein studied philosophy under Russell at Cambridge in 1912 and 1913, and Wittgenstein's Picture Theory, completed 6 years later in in 1918, is a development of knowledge by acquaintance.

Language needs acquaintance with the world
As you wrote: "Look up a word in the dictionary to find its meaning. You get more words. Look up the meaning of those words. You get more words. Since the dictionary is finite, and since word is defined in terms of other words, the definitions must be circular". So language only as description is problematic. It may be coherent, but sooner or later, in order for it to be intelligible it needs some fixity with the world it is attempting to describe. It needs some correspondence with the world, it needs some direct acquaintance with the world.

Someone may tell me the colour of an object is "nyekundu", but until they physically point it out to me, I can never know what they mean.

Language needs more than acquaintance, it also needs description
A language based on knowledge by acquaintance only would be too limiting, in that I only know of the 1969 moon landing by description, as I was not personally there. A language of knowledge by description must be founded on a language of knowledge by acquaintance. Knowledge by description is imagining new combinations of things one already knows by acquaintance. I already know by acquaintance the moon, a rocket, and one object falling onto another object. I can imagine a new combination (a rocket) + (one object falling onto another) + (the moon). As an aside, knowledge by description is not knowledge of the world, as the combination exists only in my mind. If I said "I know about the 1969 moon landing", what is mean is "I believe there was a 1969 moon landing".

To be more terminologically accurate, there is knowledge by acquaintance and belief by description.

Relations are, in Kant's words, "a priori intuition"
Bertrand Russell wrote: That the world is my world appears in the fact that the boundaries of language (the only language I understand) indicate the boundaries of my world.
5.6 The limits of my language mean the limits of my world.
5.61 Logic fills the world: the limits of the world are also its limits, We cannot say in logic: This and this there is in the world, that there is not. 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.

Relations exist in the mind, in that I know the apple is green. I would argue that a belief in relations is an innate part of the structure of the brain, in the same way that Kant described time and space as a priori intuitions. We cannot observe the world independently of those beliefs that are inherent within the structure of the brain. A kettle can only do what a kettle can do. The brain can only do what the brain can do.

Whether relations exist in the world or not , we have a visceral belief in their existence as they are, in Kant's words, a priori pure intuition.

Relations in the world can only be said, not shown
Consider a table consisting of a table top and table legs. There are two kinds of relations, i)
the physical relation between spatially separated masses in the world and ii) the relation between the table legs and table top we perceive in our minds.

As regards the first kind of relation, consider an object above the Earth. The force between the object and Earth may be expressed as GmM/r2.. There is a relationship between the two masses as well as a spatial relationship between them. These relationships may be called The Laws of Nature, and exist. As Laws of Nature, they can only be inferred, as Hume noted, by constant conjunction, in that they can be said but not shown.

As regards the second kind of relation, the relation we perceive is independent of relations within the Laws of Nature. Even if ontological relations did exist in the world, such relations make no contribution to physical changes within the world. As they have no effect on the world, we can remove them from our world ontology. As they cannot be shown, they can only be talked about.

Conclusion
Achilles tells the Tortoise that "the apple is green", but the Tortoise won't accept this, as "the apple is green" means no more than "the apple is green".

Wittgenstein provides a solution is his Tractatus, pointing out that there is a distinction between what can be said and what can be shown. The Picture Theory in Tractatus is explaining language as knowledge by acquaintance, where propositions show the facts because they have the same logical form, such that "the apple is green" is true iff the apple is green.

For Bradley, it is insufficient to say that "relation C relates table top A to table legs B", it needs to be shown. The problem being that as relation C is independent of its relata A and B, a further relation D needs to be shown relating relation C with relata A and B, leading to the conclusion that relations independent of their relata are not possible.

IE, for the Tortoise, saying something is true is insufficient, for Wittgenstein's Tractatus, saying cannot show the truth but showing can and for Bradley, saying that relations are true is insufficient if it cannot be shown that they are true.

Would you care to address Bradley's regress? — Banno

FH Bradley argued against the existence of relations in the world

Wittgenstein's Picture Theory of Language requires relations in the world
4.461 The proposition shows what it says
4.023 A proposition is a description of a fact
4.012 It is obvious that we receive a proposition of the form aRb as a picture

The main theme in the Tractatus is that the sole purpose of language is to mirror reality, showing reality rather than saying what reality is. We cannot say with language what is common between language and the world, rather, it must be shown, because any language we use will also rely on the same relationship, meaning that we cannot step out of language using language itself. For Wittgenstein, propositions refer to relationships of objects in the world, sharing a logical form with reality. Logical form of language can only be shown, but not spoken about.

As Wittgenstein assumes the existence of facts, he is also assuming the existence of relations in the world. I know relations exist in my mind, in that I know the relation "the apple is green". If relations do exist in the mind, but don't exist in the world, then propositions cannot share the same logical form with reality, meaning that there is no foundation to Wittgenstein's Picture Theory of Language.

The world in the Tractatus may exist in the mind of whoever is doing the thinking
It is my belief that the Tractatus can be read such that the "world" exists in the mind of whoever is doing the thinking, meaning that the Picture Theory is relating one part of the mind to another part of the mind, rather than the mind to the world.

Forces don't establish relations
Science accepts a world of fundamental particles and fundamental forces. Taking a particular example, if relations exist in the world there is a relation between a particular rock on the Earth and a particular rock on Alpha Centauri. The rock on Earth may be hit by a photon emitted by the rock on Alpha Centauri. Whether the photon came from a rock on Alpha Centauri or elsewhere in the Universe makes no difference to the effect it has on the rock on the Earth. There is no information within the photon as to its source. Any changes to the rock on Earth is due to the photon and not its source. The relation between the rock on Earth and the rock on Alpha Centauri is irrelevant to any changes occuring to the rock on Earth.

I am not saying that I know that relations don't exist in the world, rather, that as relations have no affect on physical changes that may occur in the world, they serve no useful purpose in our world ontology.

Leibniz's Regress Argument of 1676
Leibniz pre-dated Bradley's Regress argument. He wrote: "Suppose, for example, that there is a relation between a and b, and call it c; then, consider a new relation between a and c: call it d, and so forth to the infinite. It seems that we do not have to say that all these relations are a kind of true and real ideas. Perhaps they are only mere intelligible things, which may be produced, i.e., that are or will be produced."

Bradley's questioning the nature of properties
The nature of an object's properties is problematic. Bradley starts with the example of a lump of sugar. He notes that there appears to be such a thing as a lump of sugar and this thing appears to have qualities such as whiteness, sweetness, and hardness. But, asks Bradley, what is this “thing” that bears properties? On the one hand, he thinks it is odd to assume that there is something to the lump of sugar beside its several qualities, thus implying that postulating a property-less bearer of properties is incoherent. On the other hand, he notes that the lump cannot merely be its qualities either, since the latter must somehow be united.

For Bradley, unity or “coexistence” of qualities presupposes relations, which is why he questioned our concept of relations.

Bradley's Regress Argument
Bradley’s original formulation of the regress arguments can be found in his book Appearance and Reality (1893). Bradley’s worry seems to be that if relations are conceived of as independent from the terms that they relate, they themselves will become just like the terms that need relating and this way they will lose their relating power.

He wrote in 1893: "Let us abstain from making the relation an attribute of the related, and let us make it more or less independent. ‘There is a relation C, in which A and B stand; and it appears with both of them.’ But here again we have made no progress. The relation C has been admitted different from A and B, and no longer is predicated of them. Something, however, seems to be said of this relation C, and said again, of A and B. And this something is not to be the ascription of one to the other. If so, it would appear to be another relation D, in which C, on one side, and, on the other side, A and B stand. But such a makeshift leads at once to the infinite process."

Conclusion
Whether relations exist in the world or not has significant implications. If relations don't exist in the world, objects such as apples don't exist, properties such as greenness don't exist. These things only exist in the mind. The fact that thought requires relations does not presuppose that a world of elementary particles and forces also needs relations.

As relations in the world, even if they existed, make no changes to the physical world, they may be removed from our world ontology.

sentence tokens — bongo fury

3.143 - "For in a printed proposition, for example, no essential difference is apparent between a propositional sign and a word. (That is what made it possible for Frege to call a proposition a composite name.)"

The Eiffel tower is in Paris, is 330m in height and is made of wrought iron. I can replace "I saw the 330m tall wrought-iron structure in Paris" by "I saw the Eiffel Tower". Is this what Wittgenstein is referring to ?

Curious that you want to downplay the relational/factual/structural aspect of the artwork and stress the whole, er, feeling — bongo fury

By definition, what makes an artwork rather than a craftwork is that an artwork has an aesthetic. An aesthetic is a unity between its parts, rather than just being an aggregation of parts loosely related.

W is keen to use musical and pictorial structure to explain propositional structure — bongo fury

4.023 A proposition is a description of a fact
2.0272 The configuration of the objects forms the atomic fact
Notebooks - Musical themes are in a certain sense propositions. [40]
Music, some music at least, makes us want to call it a language; but some music or course doesn't. (CV 62)
4.001 The totality of propositions is the language

The proposition is a combination of words, music is a combination of notes, so there is a similarity in this sense. I agree that Wittgenstein used music to explain propositions, but did he say that music uses propositions, that propositions are used in music as well as language ?

The proposition "the apple is green" describes a fact in the world that the apple is green, but what fact in the world does a combination of musical notes describe ?

But that line of thinking was leading me to expect, the individual notes and combinations of notes in music express feelings not [while combinations of notes express] thoughts. — bongo fury

In great music, as with great painting, the notes, or brush marks, combine into a single aesthetic experience, which is a feeling rather than a thought.

As well, in a great novel, the words may also combine into a single aesthetic experience, which is a feeling, and is over and above the thoughts contained within its propositions.

So, yes? — bongo fury

A proposition is a relationship between words. My belief is that a thought is a relationship between feelings. So yes, as far as I know.

Are feelings to thoughts as words are to proposition — bongo fury

Admittedly, I didn't make it clear what the point of my post was.

For Wittgenstein, a thought is not a single thing, a simples, but rather involves a relationship between entities.

2.01 "An atomic fact is a combination of entities"
4 "The thought is the significant proposition"
4.012 "It is obvious that we receive a proposition of the form aRb as a picture"
4.023 "A proposition is a description of a fact"

In my post, I was trying to make the same point, that thoughts are not single things, such as feelings, but involve relationships between things.

In several places Wittgenstein refers to the language of music......................Understanding a musical theme is not simply having a feeling. — Fooloso4

Tactatus 4 "The thought is the significant proposition"

Language and music
I agree with the gist of what you are saying. Perhaps I am quibbling about definitions.

Language is defined as human communication, using words in a structured way. Words are defined as a single distinct meaningful element of speech or writing. Understanding requires thoughts, and thoughts are propositional, in that propositions are relations between parts, aRb.

I sense the colour of red, I sense the sound of a crackle, I sense the pain of heat. These individual sensations are feelings. They can only be connected by a thought. Feelings are different to thoughts. Feelings are not propositional, thoughts are propositional.

We can gain both feelings and thoughts from music, but the individual notes and combinations of notes in music express feelings not thoughts. I can subsequently think about the music, but these thoughts are external to the music, not an intrinsic part of the music. Meaning can only be expressed in a proposition, such as "the apple is on the table". Thoughts express meaning and music expresses feelings. As music is not propositional, music cannot express meaning. I can say that music means a lot to me, but any such meaning is extrinsic to the music, in that I can have the thought that I enjoy the emotion I find in some music.

Language is about transmitting thoughts, and thoughts is where meaning resides. Music is about transmitting feelings. I agree that music is like language, but to say "music is language" is a metaphor.

I know you are "experiencing red". You do not see a green Ferrari." — Banno

I agree that you know that I am experiencing the public object emitting 700nm labelled "red"
You believe that I am experiencing in my mind the colour red, but you can never know, as it is not possible to know what is in someone else's mind.

As you can never know, I may in fact be experiencing the colour green, unlikely, but possible.

He's getting out of the head, into the language. — bongo fury

There would be no public language if there were no private thoughts.

It is plain that Bradley thinks of A and B as being like two objects fastened together with a bit of string, and he thinks of R as being like the bit of string.

@Banno

Broad has a rejectionist approach, challenging Bradley' scepticism about relations' ability to relate their relata. Broad argues that it is the job of relations to relate. But how exactly do relations relate. To simply say that it is the job of relations to relate is circular and unsatisfactory.

Relation is being used in two ways, Russell's Pluralism, whereby there is a relation existent in the world that is able to give a unity to separate entities, and Bradley's Monism, whereby the only relation between an aggregate of entities is in the mind.

A tree requires a relation between its trunk and branches. The Solar System requires a relation between the Sun and Earth. Relations exist universally within the Universe, such that there is a relation between a rock on Earth and a rock in Alpha Centauri.

What exactly are unifying relations. Are they abstract in nature, as some say that numbers are. It is easy to say that they exist outside of time and space, as it is easy to say that ghosts exist, but has such a claim ever been justified using reasoned argument. Bertrand Russell may describe relations as subsisting, but this goes back to having an abstract existence. Could it be similar to the Higgs boson, giving mass to matter. Are there fundamental particles named "relations" relating matter still to be discovered by the Large Hadron Collider.

For Broad to suggest that those sceptical of relations think of the relation between a rock on Earth and a rock on Alpha Centauri as a piece of string gluing them together is setting up a Straw Man argument, putting a ridiculous idea in the mind of their debating opponent and then quite sensibly demolishing it.

The existence of elementary particles and elementary forces is scientifically well established, and events in the Universe can sensibly be explained using them, whether the birth of Solar Systems or an apple falling under gravity to the Earth.

Gravitational forces between the apple and Earth are scientifically understood, and the behaviour of the system can be explained without the need for any unifying relation. The introduction of a unifying relation would result in an over-determination, ie, where a single-observed effect is determined by multiple causes, any one of which alone would be sufficient to account for the effect.

Given the choice between i) Broad's world in which relations exist but are neither needed nor explained and ii) Bradley's world where relations don't exist, it seems the more sensible to choose ii).

I could be persuaded otherwise if some scientific method was proposed whereby unifying relations could be located, measured and described. To say that they exist outside of time and space introduces mysticism and is an inadequate explanation.

A picturial or musical language means that the claim that thinking is a kind of language is not the same as the claim that we think in words. — Fooloso4

Music is a language is metaphorical - feelings and thoughts
We talk about the language of music, but this is a metaphor, in that music is like language, not that music is language. Music is like language in that there is a relationship between the individual parts.

When I hear a single note, this is not music. Music is the relationship between notes. We get meaning from the relationship between things. A single note has no meaning. There is only meaning in a combination of notes.

When I hear music, in the first instance, I have a feeling, which I may or may not think about. Feeling is an emotional state, whereas thinking requires judgement, reasoning and intellect.

Feeling is about a single thing, I feel pain when touching a hot radiator. It is the nature of thought that it is propositional. On perceiving the colour red, I cannot have the single thought "red". The thought must be about something, such as "this is red", "red is an attractive colour", etc. Feelings are singular, thoughts are propositional. Thinking is feeling plus a proposition.

In the first instance, music is feeling. We may think about these feelings, and in thinking about them, we express our thoughts in propositional form. Language is thoughts expressed in propositional form. It is not that the music is language, rather, our feelings about about the music may be expressed as thoughts in language.

W wants to talk in technical terms (worthy of a diagram) about the propositions and their reference, not so much about thoughts as such: as items in their own right. — bongo fury

But as Wittgenstein is identifying thought as proposition, in talking about propositions, he is also talking about thoughts.

Like the teacher, he probably didn't mean "thoughts" to refer to identifiable brain events that correspond or fail to correspond to propositions. It was more a matter of putting the reference of symbols in the perfectly realistic context of our deliberate efforts to make sense of them. — bongo fury

2.0272 The configuration of the objects forms the atomic fact
4 The thought is the significant proposition
4.023 A proposition is the description of a fact
4.1252 Similarly the series of propositions "aRb"..............
Bertrand Russell - If we say “Plato loves Socrates”, the word “loves” which occurs between the word “Plato” and the word “Socrates” establishes a certain relation between these two words.............3.1432: “We must not say, the complex sign ‘aRb’ says that ‘a stands in a certain relation R to b’; but we must say, that ‘a’ stands in a certain relation to ‘b’ says that aRb”

Agree, Wittgenstein is defining "thought" as where meaning resides. If I walked into a room and said "dog", I would be treated as eccentric. If I walked into the room and said "My dog has fleas", everyone would appreciate the meaning of what I had said.

I guess the metaphysics he presents would be compatible with Kant. It would be compatible with some kind of mystical view. — Tate

Kant's belief was Scientific Realism rather than mysticism.

A thought is expressed in language. This does not mean that a thought is language. The expression, language, is not what is expressed, the thought. — Fooloso4

Wittgenstein wrote in his Notebooks 1914-16: "Now it is becoming clear why I thought that thinking and language were the same. For thinking is a kind of language."

His Tractatus was completed 1918.

This notion of a "private, subjective experience" permeates your writing. It is not used in the Tractatus. — Banno

True, in that Wittgenstein is using the word "thought" - 4.116 "Everything that can be thought at all can be thought clearly". The problem with Wittgenstein's "thought" is that he has redefined it as a proposition, which is not common usage. I was trying to get the word back into ordinary language, reinforcing the distinction between the public and the private, between the subjective and the objective, and between the unthinking experience rather than cognitive intellect.

The public use of the word "red" and my private experience of the colour red. A subjective fact or truth would be that I like apples, whilst an objective subjective fact or truth would be that the apple is a fruit. My visceral rather than intellectual response.
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So you are not here setting out the tractatus in its own terms — Banno

True, in that the Tractatus writes: 4 "A thought is a proposition with a sense", whilst I wrote " A thought is linked with a proposition". I am probably muddling up my exegesis with my critique.
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language is inherently public.............Language is not moving information from one head to another. — Banno

I agree that language can only evolve within a group of people, and so is inherently public.
However, if language isn't about moving information from my head into the Barista's head, then what is language for.
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any thought can be put into propositional form. — Banno

This is a bit circular, along the lines of known unknowns.

As I can only communicate using language, I can only communicate thoughts that I can put into propositional form, in that I cannot communicate using language thoughts that I cannot put into propositional form.

So , it is true that any thought that can be put into propositional form can be put into propositional form.
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the word "red" has a public and not a private use. — Banno

When I look at a red sunset, I am looking at a wavelength of 700nm. Inside my head, I may have the private subjective experience of a particular colour. No-one apart from myself will ever know what particular colour I am experiencing, it may, for example, be the colour green. Similarly for yourself, you may be experiencing the colour yellow.

We both publicly agree that the colour experienced by whoever observes it shall be named "red". The word "red" has a public and not a private use.

It is true that we may be both talking about the same thing, the "red" light emitted from the sunset, but we may not be thinking of the same thing. I may be thinking of the green sunset and you may be thinking of the yellow sunset.
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Why, indeed, must there be a something to which "red" refers? — Banno

I can see different wavelengths and still have the feeling of seeing the same colour. For example, I can see a sunset with a wavelength of 650nm and say to you that it is red. I can see a postbox with a wavelength of 700nm and say to you that it is also red.

There are two aspects, the public aspect, where red is defined as a wavelength between 625 and 750nm, and the private aspect, the actual colour that I experience in my mind, which could be green for me and yellow for you.

As a noun, we can say that the sunset is red, and as an adjective, we can say that there is a red sunset.

We use the word "red" for a wavelength of 650nm, and we use the word "red" for a wavelength of 700nm. The wavelengths 650nm and 700nm are different, yet we use the same word "red".

Object A has the wavelength property of 650nm and the colour property of red. Object B has the wavelength property of 700nm and the colour property of red. Objects A and B have different wavelengths but the same colour. Objects A and B are not the same, in that their wavelength are different, and so in that sense are different objects.

However, the word "red" can refer to different objects, as long as they have the same property of redness. The word is referring to the property of the object, not the object which may have a set of properties.
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Yet the components, "is blue' and "the postbox", while they might be part of a thought, do not form a thought, a proposition, until brought together. — Banno

4 The thought is the significant proposition
4.023 A proposition is the description of a fact
2.0272 The configuration of the objects forms the atomic fact
4.25 - If the elementary proposition is true, the atomic fact exists; if it is false the atomic fact does not exist

For Wittgenstein, a thought is a proposition, a proposition is a description of a fact, and facts are combinations of objects. Wittgenstein within Tractatus is defining thought as a proposition, "the postbox is red".

However, in common usage, I can think of a thing, such as a postbox, independently of any proposition that it may be within.

Yes, one should be aware to separate the exegesis from the critique.
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Would you care to address Bradley's regress? As i said, I do not understand the argument. Since you rely on it, perhaps you might explain it. — Banno

I will try. That will be my next immediate project, though I will be hard pressed to clarify in a post a debate that started in 1893, involved Bertrand Russell and still continues.

I like Kyle Banicks' 12 minute video British Idealism with FH Bradley that sets the scene.

Thought is linguistic for Wittgenstein. — Tate

I think so.

This is not Kant. There is no a priori knowledge. It's all just a world put together with the same logic that is the backbone of language. — Tate

Critique of Pure Reason - A239 - "We can only cognize objects that we can, in principle, intuit. Consequently, we can only cognize objects in space and time, appearances. We cannot cognize things in themselves."

No system can function without some degree of an innate, a priori, pre-existing structure. I can see the colour red because I have the innate ability to see red. I cannot see the colour ultraviolet because I don't have the innate ability to see ultraviolet. A kettle functions as a kettle because it has a particular structure. A kettle cannot function as a toaster.

Without an innate, a priori, pre-existing ability to know something, we could never make sense of the world.

Of course for Wittgenstein, if we construe the grammar of sensation as object and designation, then the object - the "private subjective experience"-drops out or consideration. — Banno

The "beetle" plays an important role in the language game

Wittgenstein in Tractatus proposed that thought is language
4 "The thought is the significant proposition".

If it is true as Wittgenstein proposes that thought is language, the thought of the private subjective experience the postbox is red is also the proposition "the postbox is red". In which case, the statement (propositions represent private subjective experiences, and it is these private subjective experiences that show the logical form of reality) is equivalent to the statement (propositions show the logical form of reality).

The question is, is Wittgenstein correct in proposing that thought is language.

Thought existed before language
There are two main theories as to how language evolved, either i) as an evolutionary adaptation or ii) a by-product of evolution and not a specific adaptation. As feathers were an evolutionary adaptation helping to keep the birds warm, once evolved, they could be used for flight. Thereby, a by-product of evolution rather than a specific adaptation.

Similarly for language, the development of language is relatively recent, between 30,000 and 1000,000 years ago. As the first animals emerged about 750 million years ago, this suggests that language is a by-product of evolution rather than an evolutionary adaptation.

It therefore seems sensible to propose that language is a by-product of evolution and uses pre-existing thoughts.

The relationship between propositions and thoughts
The proposition "the postbox is red" is linked to my thought that the postbox is red. But my private subjective thought of the colour red cannot be described in words to someone else, in that I cannot describe the private subjective experience of the colour red to someone born blind. My private subjective thought that it is unethical to kill spiders can be justified but not described to someone else.

All propositions are linked to thoughts, but not all thoughts are linked to propositions.

Representationalism and Isomorphism
In a computer, a picture of a house may be labelled "house", but it does not follow that the word "house" is isomorphic with the picture of the house. The word "house" represents the picture house. Similarly, in the mind, the word "red" is not isomorphic with our thought of red. The word "red" represents the thought red.

The word "red" represents the thought red, and the thought red is isomorphic with red in the world.

Description and acquaintance
The proposition "Rembrandt is a painter" is a description of Rembrandt as a painter. By seeing a picture of a Rembrandt painting, which is isomorphic with the person Rembrandt, we gain an acquaintance with Rembrandt. Similarly, the proposition "the postbox is red" only describes a state of affairs, and without giving us a picture of the state of affairs, it doesn't allow us to become acquainted with the red postbox.

Words describe whilst pictures give us acquaintance.

Conclusion
If Wittgenstein was correct that thought is language, the statement "language represents thoughts and thoughts are isomorphic with reality" can be reduced to "language is isomorphic with reality".

However. I have argued that whilst language may represent some thoughts, all thoughts are isomorphic with reality. In such a case, the expanded statement "language represents some thoughts and all thoughts are isomorphic with reality" cannot be reduced to "language is isomorphic with reality".

IE, Wittgenstein is incorrect in para 4.01 that "The proposition is a picture of reality", rather, "the proposition represents some thoughts, where all thoughts are isomorphic with reality".

A diagram may show the correspondence between language and thought.



Public language and private thoughts
Person A when observing the world has the private subjective experience X. They link their private subjective experience X with the public word object "red". Person B when observing the world has the private subjective experience Y. They link their private subjective experience Y with the public word object "red"

Persons A and B can sensibly discuss the public object red, even though Person A's subjective experience X may be different to Person B's subjective experience Y.

Wittgenstein's "world"
1. The world is everything that is the case
3.03 We cannot think anything unlogical, for otherwise we should have to think unlogically.

The Tractatus may be read that Wittgenstein's "world" exists in the mind of whoever is doing the thinking.

Wittgenstein's "beetle"
Para 293 Philosophical Investigations - Here it would be quite possible for everyone to have something different in his box................... The thing in the box has no place in the language-game at all.........for the box might even be empty.

The private subjective experience X is a fact, is knowledge, for person A, and the private subjective experience Y is a fact, is knowledge, for person B.

Without these facts, this knowledge of X and Y, Persons A and B would not be able to engage in any language game using the public word object "red".

"The postbox is red" is true iff the postbox is red
As X may or may not be the same as Y, it follows that for each observer there will be one truth, although each observer may have a different truth.

At first glance it looks like W is justifying correspondence theory by saying the world is linguistic in form — Tate

The world is not linguistic in form.

Public language and private experience

When looking at the public objects such as post box, a sunset, a strawberry, a tomato, I notice that I have a common private subjective experience X.

Also, when looking at the same public objects, I notice that alongside them is the public word object "red".

I link my private subjective experience X with the public word object "red".

Similarly, someone else will link their private subjective experience Z with the public word object "red".

I can have a sensible discussion with the other person about the public word object "red", even though my private subjective experience X may be different to their private subjective experience Z.

The public word object "red" is part of a language common between me and someone else.

For Wittgenstein, Language doesn't represent reality, it mirrors it

4.121 Propositions cannot represent the logical form: this mirrors itself in the propositions. That which mirrors itself in language, language cannot represent. That which expresses itself in language, we cannot express by language. The propositions show the logical form of reality. They exhibit it.

For Wittgenstein, language contains irreducible "atomic propositions" that picture reality, mirror the world, because they both have the same structure, the same logical form. Language doesn't represent reality (it cannot be said), it mirrors it (it must be shown).

The term "logical form" itself was introduced by Bertrand Russell in 1914.
Argument = All humans are mortal - Socrates is human - therefore, Socrates is mortal.
Logical form of argument = All H are M - S is H - therefore, S is M.
Proposition = Socrates is mortal
Logical form = S is M
S represents Socrates

Private experiences and public objects

When looking at a public object such as a red postbox, I notice that I have the private subjective experience of X associated with the public object red and the private subjective experience of Y associated with the public object postbox.

When looking at the public object red, I notice alongside is the public word object "red", and when looking at the public object postbox, I notice alongside is the public word object "postbox".

My private subjective experiences X and Y show the logical form of reality, ie, the public objects red and postbox. My private subjective experiences X and Y are represented by the public word objects "red" and "postbox".

In other words, the proposition "the postbox is red" represents my private subjective experiences X and Y, and X and Y show the logical form of reality, ie, the public objects red and postbox

Conclusion
It is not as Wittgenstein said that propositions show the logical form of reality, rather propositions represent private subjective experiences, and it is these private subjective experiences that show the logical form of reality.

Can you advise a good secondary resource? — Tate

I'm not the best to advise. I use the obvious sources, such as the SEP and IEP, but I never tell anyone I also use Wikipedia.

The use of the word "subject" and the way he uses the word "world" sounds like he's riffing on Schopenhauer, especially of the third book of WWR. — Tate

SEP -Arthur Schopenhauer
Kant posited as knowledge a mind-independent object that is beyond all human experience. Schopenhauer concurs with his teacher Schulze that hypothesizing a thing-in-itself as the cause of our sensations cannot be legitimate knowledge. Schopenhauer therefore denies that our sensations have an external cause in the sense that we can know there is some epistemologically inaccessible object – the thing-in-itself – that exists independently of our sensations and is the cause of them.

A source that shall not be named - The World as Will and Representation
Schopenhauer argues that the world humans experience around them - —the world of objects in space and time and related in causal ways—exists solely as "representation" (Vorstellung) dependent on a cognizing subject, - not as a world that can be considered to exist in itself (i.e., independently of how it appears to the subject's mind). - One's knowledge of objects is thus knowledge of mere phenomena rather than things-in-themselves.

In the Tractatus, I don't believe that Wittgenstein's meaning of the term "world" is made explicit and remains ambiguous. The "world" may be read as something existing outside the mind, but I read it as something existing inside the mind. However, in a sense, whether Wittgenstein's world exists inside or outside the mind is not relevant to his main thesis that 2.12 "The picture is a model of reality". Once the concept that the picture is a model of reality has been made, the subsequent question of does reality exist inside or outside the mind can then be tackled.

In a sense, progress is most effective as an iterative process.

Nevertheless, number don't age, and are still independent of any particular mind. — Tate

One could say that numbers weren't born one million years ago before there were minds to observe them. 2,000 years ago, Aristotle could not accept one as a number. Today, we have complex numbers, irrational numbers, etc. Numbers do change, do age.

What we know as numbers depend on their existence because of language, and humans have a language that is fundamentally the same between different peoples. Therefore, it is true that numbers are independent of any particular mind, but are not independent of all those minds sharing a fundamentally common language.

Relations, like properties, are constituents of propositions. The ontology should just follow whatever you think of propositions. Do you agree? — Tate

For a Direct Realist and Idealist, the ontology of the external world would follow from their propositions. For the Indirect Realist, it wouldn't.

What in the world are objects, properties and relations
In my mind, I could have thoughts about things and thoughts about propositions. For example, I could name the object comprising my pen and the Eiffel Tower a "peffel". The "peffel" has the property of being extended in space, with the pen at one end and the Eiffel Tower at the other. The proposition "the peffel is north of Lyon" describes a relation.

The question is, is there an external world, and if there is, do these objects exist in it. Assuming there is an external world, an important question would be, do relations exist within it. Because, if relations don't exist in the external world, then neither do properties, and neither do objects such as peffels, Eiffel Towers, trees, apples and tables.

Wittgenstein
1 The world is everything that is the case.
1.1 The world is the totality of facts, not of things
2.01 An atomic fact is a combination of objects (entities, things)
4.123 A property is internal if it is unthinkable that the object does not possess it
As regards Wittgenstein's Tractatus, the word "world" can be read as being either inside or outside the mind of the observer. As Wittgenstein states that the world is everything that is the case as a fact, as knowledge, and not a justified belief, and as our only knowledge is within the mind, I read Wittgenstein's world as also being in the mind of the observer.

The Tractatus therefore does not address the question of whether relations exist outside the mind. For Wittgenstein, "the peffel is north of Lyon" is a proposition in the mind with the same logical form as the fact in a world existing in the mind that the peffel is north of Lyon.

Bertrand Russell
As regards Bertrand Russell, I read Russell as a believer in Realism, a believer in the existence of a world outside the observer's mind, in the existence of a mind-independent world and where relations do exist. Therefore, his thoughts on relations in the world are relevant to the current topic. For Russell, atomic facts exist in a world independent of minds, and where mathematical and logical truths such as 2 + 2 = 4 - must be unconditionally true. For Russell "the peffel is north of Lyon" is an atomic proposition in the mind that corresponds with the atomic fact in the world that the peffel is north of Lyon.

Internal and external relations
As regards an internal relation, a given property, such as being a house, entails another property, such as being a place for living. As regards an external relation, the property being a house is external to the property being a mode of transport

FH Bradley
Famously, Bradley brought a vicious regress argument against external relations. In his original version of 1893, Bradley presented a dilemma to show that external relations are unintelligible: either a relation R is nothing to the things a and b it relates, in which case it cannot relate them. Or, it is something to them, in which case R must be related to them.

Bertrand Russell's counter-argument
However, in the journal Mind 1910-1911, Bertrand Russell argued against Bradley's Regress Argument, rejecting internal relations in favour of external relations. He argued that what distinguishes a complex from a mere aggregate is that relation in a unified complex relates whereas a relation in an aggregate does not relate, and is just a member of the aggregate.

Bradley's response
Bradley found Russell's reply unsatisfactory, asking Russell to elaborate further of the difference between an aggregate of entities and a unity of those entities. However, Russell did not feel that there was anything more to be said in that the difference between relating and non-relating relations is a primitive which cannot be further explained.

Bertrand Russell's The Problems of Philosophy 1912
Russell wrote: "Consider such a proposition as "Edinburgh is north London." Here we have a relation between two places, and it seems plain that the relation subsists independently of our knowledge of it. When we come to know that Edinburgh is north of London, we come to know something which has to do only with Edinburgh and London: we do not cause the truth of the proposition by coming to know it, on the contrary we merely apprehend a fact which was there before we knew it. This conclusion, however, is met by the difficulty that the relation "north of" does not seem to exist in the same sense in which Edinburgh and London exist. If we ask "Where and when does this relation exist?" the answer must be "Nowhere and nowhen." There is no place or time where we can find the relation "north of." It does not exist in Edinburgh any more than in London, for it relates the two and is neutral as between them. Nor can we say that it exists at any particular time. Now everything that can be apprehended by the senses or by introspection exists at some particular time. Hence the relation "north of" is radically different from such things. It is neither in space nor in time, neither material nor mental; yet it is something."

The problem with Russell's explanation
Russell wrote that the relation subsists rather than exists, is neither in space nor in time, neither material nor mental; yet it is something.

Subsist means to have timeless or abstract existence, as a number, relation, etc. To say that relations exist outside of time and space is no more an explanation that saying that they have magical powers.

Does Bradley's argument fail by logic
@Banno pointed out the belief that Bradley's argument fails because he used Aristotlean rather then Fregean logic. However, Bradley's debate with Russell in 1910 to 1911 was more than 30 years after Frege's breakthrough “Begriffsschrift, eine der arithmetischen nachgebildete Formelsprache des reinen Denkens” of 1879, which Bradley must have been aware of as it marked a turning point in the history of logic, using the ideas of functions and variables.

Aristotle's subject-predicate was limited by the propositions all S is P, all S is not P, some S is P and some S is not P, whilst Frege borrowed from Boole and de Morgan the idea that propositions can be considered as variables that can have the values true or false. It could be argued that Bradley's regress argument - either a relation R is nothing to the things a and b it relates, in which case it cannot relate them. Or, it is something to them, in which case R must be related to them - is more Fregian than Aristotlean.

Relations problem with limiting the number of possible objects
If relations exist, the "peffel" is a complex object being a composite of the simple objects "pen" and "Eiffel Tower". These simple objects become complex objects when their individual parts are related. But the pen is also legitimately in relation with the Empire States Building, another complex object that can be named. In fact, as the pen is in relation with every other object existing in the Universe, each of these complex objects may also be named. But in addition, each atom in the pen is also in relation with every other atom in the universe, each of these complex objects may also be named.

For example, given four objects A, B, C and D, there are 14 possible complex objects, each of which can be named, for example the complex object ABD. If relations exist, then starting with 4 real things, we end up with 14 real things.

The question for relations is, if relations exist, where did these 10 new things come from.

Relations problem with information
Given the pen, for example, where exactly is the information that the pen is in a relation with the Eiffel Tower, or the Empire States Building, or even a particular rock in the Andromeda Galaxy. Can any investigation of the pen ever reveal this information. Can any investigation of the space between the pen and a particular rock in the Andromeda Galaxy ever reveal that there is a pen at one end an a rock at the other. Can an investigation of the rock in the Andromeda Galaxy ever reveal this information.

The question for relations is where exactly is the relation, if it doesn't exist in either each thing it relates or the space between the things it relates.

Relations problem with time
Are relations instantaneous, or is time required for the establishment of a relation between two objects spatially separated, for example, the pen and the rock in the Andromeda Galaxy. If the relation is instantaneous, how does this fit in with our scientific knowledge to date that noting can travel faster than the speed of light. If the establishment of a relation between two objects is limited by the speed of light, by what mechanism does the information travel between the two objects.

Are there "relatons" still to be discovered by the Large Hadron Collider ?

Conclusion
There are practical issues if relations do exist outside the mind of an observer, and until answered, the belief that relations do exist cannot be fully justified.

If the world is an abstract object, it would be independent of my will and mind, but still not a physical thing. — Tate

Wittgenstein wrote 6.373 The world is independent of my will.

It is said that an abstract object such as a number exists outside of time and space and is not a physical thing, whereas a concrete object such as a tree exists in time and space and is a physical thing.

Realism
Within Realism, the world may be independent of my will and mind-independent.

Idealism
There are different types of Idealism.

For example, in Berkeley Idealism, there is a world of time, space and trees, not physical, and which only exists in the mind, and continues to exist even when not observed as exists in the mind of god.

Berkeley's world is not an abstract world. Berkeley rejected the concept of an abstract. While he admits that he can abstract, for instance, the smell of a rose without thinking of the rose itself, Berkeley wants to maintain that it is impossible to conceive "any sensible thing or object distinct from the sensation or perception of it".

Within Berkeley's Idealism the world may be independent of my will yet not mind-independent.

Was Wittgenstein an Idealist or a Realist
IE, within both Realism and Idealism, the world can be independent of my will. It depends on Wittgenstein's approach to Idealism and Realism.

For example, there is an article elaborating on Wittgenstein’s anti-sceptical ideas, and based on On Certainty argues for his refutation of Idealism.

Yet there is another article that argues Wittgenstein was neither a Realist nor an Antirealist.

It seems that Wittgenstein conceived philosophy to be an activity rather than a belief.

Did he (Wittgenstein) specify or imply mind independence? — Tate

From 6.3 onwards he discusses Newtonian mechanics and physical laws, and includes in 6.373: "The world is independent of my will."

I don't think relations "reside" somewhere. They're properties, aren't they? The apple's property of redness doesn't have a location. If the apple is red, that's a fact. It's a true proposition. It's an abstract object. Abstract objects are not residents of time and space. They don't move or age. — Tate

Relations are not of necessity properties
I can say "there is a relation between my pen and the Eiffel Tower", but this does not mean the relation between my pen and the Eiffel Tower is a property.

I can say "the apple has the property red". A property needs relations, but a property is not of necessity a relation.

Properties cannot exist without relations existing, but relations can exist without properties existing.

In a mind-independent world, what are properties ?
A Realist about Universals believes that Universals can be present at various distinct locations in space at the same time while particulars are restricted to one location at a time. For example, a tomato and a strawberry are two particulars that exemplify the universal redness.

A concrete thing, such as a rock, exists inside time and space, is causal and is contingent (in that it may or may not exist). An abstract thing exists outside time and space, is not causal and is necessary (in that mathematical truths are necessary)

As regards a mind-independent world, if relations don't exist, then neither do Universals. As I have never come across a persuasive argument that external relations do exist, my belief is that Universals don't exist.

As regards a mind-independent world, as I have never come across a persuasive argument that it is possible for things to exist outside of time and space, my belief is that Abstracts don't exist.

Terminology
In the mind is the proposition "the apple is red" and the thought that the apple is red. In the world is the (believed) fact that the apple is red.

The proposition "the apple is red" both represents and corresponds with the thought that the apple is red, but is not isomorphic.

The thought in the mind that the apple is red corresponds to, is isomorphic with and represents the (believed) fact in the world that the apple is red.

2.18 What every picture, of whatever form, must have in common with reality in order to be able to represent it at all—rightly or falsely—is the logical form, that is, the form of reality.
Logical form includes representation, correspondence and isomorphism.

The expression ("The apple is red" is true iff the apple is red) is about knowledge in the mind, not (believed) facts in the world.
Light hits an apple, most of the light is absorbed, and light of a wavelength of 700nm is reflected back to the observer. We perceive light of a wavelength of 700nm as red.

We say the apple has the property of redness, but what we mean is that the apple reflects red light. If we looked at the reflection of a person in a mirror, we would not say that the mirror is that person. Similarly, if we looked at the reflection of red light from an apple, we should not say that the apple is red. When we say the apple is red or the apple has the property redness, the expressions "the apple is red" and "the apple has the property of redness" are metaphors.

In the expression "The apple is red" is true iff the apple is red, the clause the apple is red does not exist as a (believed) fact in the world but only as a thought in the mind, in that the (believed) fact in the world is that the apple reflects light of 700nm. The expression links the proposition "the apple is red" with the thought that the apple is red, both only existing in the mind. The expression does not link the proposition "the apple is red" with the (believed) fact in the world that the apple reflects light of 700nm.

IE, the expression does not link the mind with a mind-independent world, but does link one part of the mind to another part of the mind, propositions to thoughts.

I suggest the solution is found, again, in Philosophical Investigations — Banno

Wittgenstein is the Elon Musk of philosophy, pushing the iterative process in order to go fast. Accepting setbacks and failures, but driven by the aspirational goal of discovering new and important philosophic insights.

Where exactly are Wittgenstein's facts

1.1 The world is the totality of facts, not of things
1.13 The facts in logical space are the world
1.2 The world divides into facts
2 What is the case, the fact, is the existence of atomic facts
2.01 - An atomic fact is a combination of objects (entities, things).
2.0121 - Just as we cannot think of spatial objects at all apart from space, or temporal objects apart from time, so we cannot think of any object apart from the possibility of its connexion with other things
2.021 - Objects form the substance of the world

Do external relations exist in a mind-independent world

Wittgenstein's "facts" depend on the reality of external relations in a mind-independent world. If external relations don't exist in a mind-independent world, neither can Wittgenstein's "facts".

The proposition "the tree is 3m tall" exists in the mind.

If external relations do exist, it could be a fact that there is a 3m tall tree existing in a mind-independent world, thereby allowing the expression "the tree is 3m tall" is true iff the tree is 3m tall.

If external relations don't exist, the proposition "3m tall tree" still exists in the mind, as well as the thought that the tree is 3m tall. The expression "the 3m tall tree" is true iff the tree is 3m tall is then analytic rather than synthetic.

I have never come across a persuasive argument that external relations do ontologically exist in a mind-independent world, and am persuaded, in particular, by F H Bradley's regress argument against external relations.

IE, for me, the main argument against Wittgenstein's theory of "facts" is the fact that they cannot exist in a mind-independent world in which external relations don't exist.

Or that there are numerous/infinite worlds? — Merkwurdichliebe

Negative Facts

I observe the world and notice "the apple is not red"

From Tractatus:
2.06 The existence and non-existence of atomic facts is the reality (the existence of atomic facts we also call a positive fact, their non-existence a negative fact)
2.1 We make ourselves pictures of facts
2.202 The picture represents a possible state of affairs in logical space
3 The logical picture of the facts is the thought
4.023 A proposition is a description of a fact

Given the proposition "the apple is not red", there are several possible states of affairs in logical space, for example, the apple is green, the apple is brown, the apple is yellow, etc.

Because the particular state of affairs, the apple is not red, obtains, we have the fact that the apple is not red.

As the apple is not red, the proposition "the apple is not red" is true.

Bertrand Russell argued that there must be negative facts, such as the apple is not red, meaning that negative propositions are true, such as "the apple is not red".

However, Wittgenstein rejected negative facts, and argued that negative propositions describe reality. However, the apple does have a colour, for example green. This means that, if negative propositions exist, the apple can be described as being in several states of affairs obtaining contemporaneously. For example, the apple is not yellow, the apple is not brown, the apple is not red, etc. For each of these obtaining states of affairs will be a fact.

IE, the consequence of Wittgenstein's negative proposition describing reality will be a single situation being describable by several obtaining contemporaneous states of affairs each with its own fact.

“facts” — Art48

Following Wittgenstein's line of thinking, if "my dog has fleas" obtains in the world, then my dog has fleas is a fact.

Even if "my dog has fleas" doesn't obtain in the world, it is still a possibility, and therefore exists in a logical space.

As the world consists of logical possibilities, and as the world is a totality of facts, does this mean that even though "my dog has fleas" doesn't obtain in the world, because it is a possibility, it is still a fact ?

As he wrote in 3. "A logical picture of facts is a thought", this allows us to think of facts that may or may not obtain in the world, such as unicorns and their habitats.

On the other hand, Wittgenstein's move from objects in traditional philosophy to facts, where it is not the object that is important but the relationship it is in, does raise other problems.