We want to add predication. To do this, Tarski developed satisfaction. — Banno

Quick question.

I perceive something in the world that is cold, white and frozen, and I name it "snow".
Therefore, "snow" means something in the world that is cold, white and frozen.

For Tarski, Convention T is "p" is true IFF p. Therefore, "snow is white" is true IFF snow is white.

Tarski's T convention assumes that in the object language the subject is satisfied by its predicate, in other words, the subject "snow" has the property "is white".

I perceive something in the world that is the ground and name it "the ground".

Therefore, Tarski's Convention T may be written as "snow is on the ground" is true IFF snow is on the ground.

But Tarski's T convention assumes that in the object language the subject is satisfied by its predicate. This would mean that "snow" has the property "is on the ground".

But is it true that "snow" has the property "is on the ground", as for snow, being on the ground is a contingent rather than a necessary fact ?

What am I missing ?

Yes, although the circularity perhaps only reflects the fact that definitions are unnecessary. The game asks for judgements, but not reasons.......But, as such, they all fail the sorites test, which requires some perfectly absolute intolerance, as well as tolerance.. — bongo fury

Truth rests on meaning - and meaning rests on definition

The Sorites Paradox asks that when on the removal of a single grain a heap becomes a non-heap.

In the dictionary, a "heap" is defined as a "large number of". "Large" is defined as "considerable". "Considerable" is defined as "large". In this case, circular. Does this mean that definitions are unnecessary? Society has determined that it is not necessary that a "heap" be defined within a single grain, as it has, or example, with the metre length, recorded on a bar of platinum - iridium in the Bureau International des Poids et Mesures.

The Sorites Paradox is only a paradox because it requires a definition that does not exist. It would be like asking if the proposition "a xyxxy swims in the sea" is true or false before the meaning of "xyxxy" had been defined.

The Sorites Paradox requires the definition "a heap has at least X grains and at most Y grains" without defining the meaning of X and Y.

In Tarski's terms, the proposition " a heap has at least X grains and at most Y grains" is in the object language. The truth or falsity of the proposition may only be proven in the metalanguage, whereby a heap has at least X grains and at most Y grains. Yet the meaning of X and Y has never been defined. Truth can never be proven in the metalanguage until meaning has been defined in the object language.

The Sorites Paradox shows that it is not the case that definitions are unnecessary, rather, that it is only a paradox because it is requiring a definition that doesn't yet exist.

An interesting puzzle, though, is how, relative to a language game, truth can be absolute as well as relative. — bongo fury

Given the Sorites Paradox, we have a heap of sand. A heap is defined as "a large number of". Large is defined as considerable. Considerable is defined as large. Definitions become circular.

The word "heap" is as vague as any concept - love, hate, government, the colour red, tables, etc. Yet we have one word for something that is imprecise, for something vague yet is recognizable.

I suggest that the brain's ability to fix a single name to something that is variable is fundamentally statistical. For example, I am certain I see the colour green, I believe it is green, I am probably seeing green, I think it is green, it could be green, it may be green. Such statistically-based concepts could be readily programmed into a computer. Complex concepts may be developed from a set of simple concepts.

You present an account of institutional facts, in which the direction of fit is word-to-world. and then jump to the non sequitur that all utterances are of this sort. They are not. — Banno

I agree that most of the time I accept the names given to things by society, such as ships, tables, governments, etc. However there are occasions when there are no existing words that fit the bill. For example, to make a philosophic point, two years ago I made the performative utterance: "a peffel is part my pen and part The Eiffel Tower".

I agree that most of the time the direction of fit is world to word, but there are occasions whereby word to world is also required.

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What is truth ?
I perceive in my world my pen and the Eiffel Tower. My pen and the Eiffel Tower are facts in my world.

Along the lines of the Tractatus, it is immaterial as to whether I believe in Idealism or Realism. Regardless, I know that my pen and the Eiffel Tower are facts in my world.

In a performative utterance, I name my pen and the Eiffel Tower a "peffel". A performative utterance is in a sense a christening, such as "I name this baby Horatio". I record my performative utterance in a (metaphorical) dictionary.

Before the performative utterance, in my world are the facts my pen and the Eiffel Tower. After the performative utterance, in my world are the facts a peffel, my pen and the Eiffel Tower.

In Searle's terms, a performative utterance is an Institutional activity. A performative utterance creates new Institutional facts, whether it is the fact that the bishop always stays on the same coloured squares, or a peffel is part my pen and part the Eiffel Tower. Institutional facts require a social obligation, whether I am obliged to move the bishop diagonally, or my listener is obliged to acknowledge the sense of the word peffel when used in conversation.

Under what conditions is the statement "a peffel is part my pen and part the Eiffel Tower" true ? Its truth value can only be known if its meaning is first known. The meaning of a "peffel" may be discovered in the dictionary, such that "a peffel is part my pen and part the Eiffel Tower". Knowing the meaning of a "peffel", and knowing that my pen and the Eiffel Tower are facts in my world, the statement "a peffel is part my pen and part the Eiffel Tower" is true.

It is said that dictionaries are not all that useful as meaning changes, but (metaphorical) dictionaries are foundational to knowing the nature of truth. It is true that definitions may change with time, in that Art as Postmodernism didn't exist before the 1960's, but as definitions change, our knowing what is true changes. Our knowledge of what is truth is not a fixed thing.

Under what conditions is the statement "A is X and Y" true. First, its meaning must be known. The meaning of "A" may be discovered in the dictionary, such that "A is X and Y". Knowing its meaning, and knowing that X and Y are facts in my world - the statement "A is X and Y" is true.

Therefore, a linguistic statement is true when, not only, the subject has been defined in a performative utterance as having the properties given in the predicate, but also, the predicate exists as facts in the world.

IE, rather than "snow is white" is true iff snow is white, I would suggest that "snow is white" is true iff not only has "snow" been defined as having the property "white" but also snow is white.

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You present an argument that language is arbitrary, which in a sense it is, then jump to the non sequitur that truth is relative — Banno

Some aspects of language can be arbitrary, and other aspects can be relative.

I perceive something white in my world. I have a free choice as to what I name it. In a performative utterance I give it a name, I christen it "X". In a sense, my choice of "X" is arbitrary.

As regards "the truth is what I say it is", truth refers to the statement "snow is X" rather than the fact in the world that snow is X.

Situation one: I christen "snow" as "white".
"Snow is white" is true iff "snow" has been defined as "white" and snow is white.

Situation two: I christen "snow" as "black"
"Snow is black" is true iff "snow" has been defined as "black" and snow is white.

In a sense, the truth of the statement is relative to my arbitrary choice of the name I use when christening what I have perceived in my world.

Sometimes something is true because you say it. You cannot apply the above reasoning to everything. — Michael

Agree. Most of the time I accept the names given to things by society, such as ships, tables, governments, etc. However there are occasions when there are no existing words that fit the bill. For example, to make a philosophic point, two years ago I made the performative utterance: "a peffel is part my pen and part The Eiffel Tower". For me, it is now true that the "peffel" is part my pen and part the Eiffel Tower.

And if the truth is what you say it is, does it follow that what you say is true, is true? Can you cast spells? — Banno

The truth is what I say it is
I perceive the world and observe something white. In a performative utterance, I name this something "black". Henceforth, for me, "something is black" is true iff something is white, and the truth for me is that "black" is white.

Unfortunately, those in authority within society had previously in a performative utterance named this something "white", such that society as a whole accepts that "something is white" is true iff something is white, and the truth for society as a whole is that "white" is white.

Truth is relative. There is no absolute truth. My truth is no more valid nor less valid than anyone else's. It may be true that I will have difficulty fitting in with society, but that is no judge as to what I know to be true. After all, in 1633, the Inquisition of the Roman Catholic Church forced Galileo Galilei, one of the founders of modern science, to recant his theory that the Earth moves around the Sun, and under threat of torture, Galileo so recanted.

Is what I say true, true
I make the performative utterance "I name this ship Queen Elizabeth".
I can then say that it is true that this ship is named Queen Elizabeth.
Is what I say is true, true ?
(What I say is true) is (this ship is named Queen Elizabeth)
So yes, (this ship is named Queen Elizabeth) is true

So yes, what I say is true is true.

Spells
A spell has magic power. Magic produces supernatural effects. The supernatural exists outside the natural world. The natural world is matter, energy, time and space. My belief is that there is nothing outside the natural world, though I don't know.

Therefore, I believe that I cannot cast spells, but I cannot say that I know that I cannot cast spells.

What is truth? — Pie

Consider the propositions "snow is white" and "the bird is blue". To know whether they are true or false, one must first know what they mean. We cannot decide whether a proposition is true or false until we know what it means.

There are two kinds of propositions
"Snow is white" is analytic necessary, as snow is white by definition. "The bird is blue" is synthetic contingent, as we need to observe the world.

The example of the Rosetta Stone
Ancient Egyptian was a coherent language that described the world in which the ancient Egyptians lived, yet couldn't be understood for thousands of years until the discovery of the Rosetta Stone. In Tarski's terms, ancient Egyptian is the object language. Something external to the object language was needed to give the object language meaning. In this case the Rosetta Stone was needed. In Tarski's terms, a metalanguage.

The meaning of "snow is white"
Go back to the beginning. I perceive in the world something that is cold, white and frozen. I name this something in a performative act "snow". I could equally well have named it "schnee". I record my performative act in a dictionary, where white is described as one of the properties of snow, in that white is a necessary property of snow. Austin discusses performative acts.

I utter the proposition "snow is white". In Tarski's terms, utterances are uttered in the object language. In Tarski's terms, performative acts are carried out in the metalanguage. Therefore, what does the utterance "snow is white" mean. It only has meaning if snow is white has been established during a performative act in the metalanguage. It has no meaning if snow is white has not yet been established by a performative act in a metalanguage.

Is "snow is white" true or false
The utterance in the object language "snow is white" is true if the predicate "is white" has been established as a property of the subject "snow" during a performative act in a metalanguage. The utterance in the object language "snow is white" is false if the predicate "is not white" has been established as a property of the subject "snow" during a performative act in a metalanguage.

Meaning of "the bird is blue"
For "the bird is blue" to have meaning as an utterance in the object language, the properties of the subject "bird" and properties of the predicate "is blue" must have been established during performative acts within a metalanguage. A bird, for example, having several colours, ability to fly and being an animal

Is "the bird is blue" true or false
The utterance in the object language "the bird is blue" is true if, first, the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage and second, if it is perceived in the world that the bird is blue. The utterance in the object language "the bird is blue" is false if, first the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage, and second, if it is perceived in the world that the bird is not blue

The analytic T-sentence "snow is white"
Under what conditions is the utterance "snow is white" true ? The T-sentence is "snow is white" is true iff snow is white. "Snow is white" is an utterance in the object language.

"Snow is white" is true if the predicate "is white" has been established as a property of the subject "snow" during a performative act in a metalanguage.

An analytic T-sentence may be generalised as "A is B" is true iff the predicate "is B" has been established as a property of the subject "A" during a performative act in a metalanguage.

The synthetic T-sentence "the bird is blue"
Under what conditions is the utterance "the bird is blue" true ? The T-sentence is "the bird is blue" is true iff the bird is blue. "The bird is blue" is an utterance in the object language. "The bird is blue" is true iff not only the predicate "is blue" has been established as a possible property of the subject "bird" during a performative act in a metalanguage but also if it is perceived in the world that the bird is blue

A synthetic T-sentence may be generalised as "A is B" is true iff not only the predicate "is B" has been established as a possible property of the subject "A" during a performative act in a metalanguage but also if it is perceived in the world that the A is B.

Quine and the analytic-synthetic divide
Quine wrote Two Dogmas of Empiricism 1950. He argued that analytic truths are problematic. He distinguished between logical truths, "no not-x is x" and truths based on synonyms, such as "a bachelor is an unmarried man". Synonyms are analytically problematic, in that although bachelor is a synonym for unmarried, they have a different senses, different meanings.

Consider the analytic proposition "snow is white", which is analytic because by definition snow is white. But note that the word "is" has different possible meanings. As a metaphor, "cheese is heavenly". As irony, "spinach is delicious". As identity, A is A. As description, "the Eiffel Tower is a wrought-iron structure erected in Paris for the World Exhibition of 1889 with a height of 300 metres". As definition, "a unicorn is a mythical animal typically represented as a horse with a single straight horn projecting from its forehead". As assumption, "drinking a lot of water is good for you".

The word "is" in "snow is white" is not used as an identity, but as a definition.

Where does meaning and truth exist
Consider the proposition in an object language "snow is white". To know whether it is true or not first requires knowing what it means. As with the example of Ancient Egyptian, meaning cannot be discovered within the language itself, no matter that the language is coherent, no matter that it describes the world within which it exists. Meaning is discovered external to the language itself, whether the Rosetta Stone, or a dictionary created in a performative act within a metalanguage.

The meaning of the object language exists within the metalanguage, not in the object language. Similarly, the truth of the analytic proposition "snow is white" exists not in the object language but in the metalanguage.

Consider the proposition in the object language "the bird is blue". The meaning of the object language exists within the metalanguage, not in the object language. The truth of the synthetic proposition "the bird is blue" requires not only its meaning which exists only in the metalanguage and not the object language but also a perception of the world that the bird is blue

Where is the world
I perceive something in the world. If I believed in Idealism, the world would exist in a mind. If I believed in Realism, the world would exist mind-independently.

My argument so far requires that I perceive a world, but whether this world exists in my mind or exists mind-independently makes no difference to either the meaning or truth of the analytic "snow is white" or synthetic "the bird is blue". As an aside, Wittgenstein's Tractatus may also be read independently of any belief in Idealism or Realism.

The creation of meaning and truth
I perceive in the world something that is cold, white and frozen. In a performative act I name this something "snow". Subsequent to this performative act, "snow" means something cold, white and frozen and it is true that "snow" is something cold, white and frozen.

Meaning and truth have been created in a performative act.

The problem of the nature of objects and properties
I perceive something in the world that is cold, white and frozen, and in a performative act name it "snow". Later I may discover that "snow" is not only cold, white and frozen but also H2O. How can the same object have different properties ? This raises the question of what "snow" is exactly. It raises the question of what any noun is, whether it be snow, table, the Moon, the Eiffel Tower, etc.

Bradley, for example, questioned the nature of objects and their properties. He 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, leading to questioning the ontological existence of relations.

IE, "snow" is not an object existing in the world. "Snow" is a name given to a set of properties that exist in the world.

A solution to the Liar Paradox
Consider the statement "this statement is false". Tarski diagnosed the paradox as arising only in languages that are "semantically closed", and to avoid self-contradiction, it is necessary to envisage levels of language, the object language and the metalanguage. The metalanguage is where truth and meaning are created in performative acts.

When I name this ship the Queen Elizabeth, the ship only has the name Queen Elizabeth at the conclusion of my performative act. At the conclusion of my utterance "I name this ship" it is not yet true that the words "I name this ship" refer to the proposition " I name this ship Queen Elizabeth".

Similarly, the statement "this statement is false" only has meaning at the conclusion of my performative act. At the conclusion of my utterance "this statement", it is not yet true that the words "this statement" refer to the proposition "this statement is false".

IE, within the performative act, "this statement" doesn't refer to the statement "this statement is false".

Summary
Truth is a creation of a performative act, in that, in naming this ship the Queen Elizabeth, it becomes true that this ship is named Queen Elizabeth.

My conclusion may be summed up by a line from that great film "The Shooter" - The Truth is what I say it is

Anyway, I agree that there must be "something deeper than mathematics". — Gnomon

:smile: :smile: :smile:

Perhaps those mathematical ratios & regularities tell us only that whatever happens is natural & logical — Gnomon

Given G as 6.67 * 10-11 Nm2/kg2, whatever follows is natural and logical, agreeing in this respect with Max Tegmark that the universe is mathematical.

The question remains, why is G the value it is in the first place. Either mathematics spontaneously caused itself, which I cannot accept, or there is something deeper than mathematics, meaning that the universe is not, at its core, mathematical.

"snow is white " is true iff s..........All we need to do now is work out what s might be. — Banno

My attempt:

I believe that I am observing something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer

Rather than keep saying "I believe that I am observing something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer" it is more convenient to say "I believe that I am observing snow"

Where "snow" is defined as "something that is atmospheric water vapour frozen into ice crystals and falling in light white flakes or lying on the ground as a white layer".

In other words, "white" is part of the definition of "snow".

I need no knowledge of the world to know that "snow is white", only knowledge of language.

In Tarski's terms, I can say "snow is white" and a German can say "schnee ist weiss". These are said within the object language

The metalanguage is where words are defined, in that "white" is part of the definition of "snow", "white" means "weiss" and "snow" means "schnee"

Therefore, we can replace "snow is white" is true iff s by "snow is white" is true iff "white" is part of the definition of "snow", "white" means "weiss" and "snow means "schnee"

Therefore s = the linguistic declaration that "white" is part of the definition of "snow", "white" means "weiss" and "snow" means "schnee".

Metaphorically, what we call "Logic" is simply mathematics with Words (Gk. logoi). And words are merely encapsulated & portable commonly-relevant meanings. — Gnomon

Mathematics tells us that the gravitational force between any two objects is F = GmM/r2, where G = 6.67 * 10-11 N m2/kg2. But mathematics does not tell us why G = 6.67 * 10-11 N m2/kg2, rather than 1 * 10-11 N m2/kg2, for example. Mathematics tells us what will happen, not why it will happen.

Mathematics is based on making logical inferences from observed regularities. If we measure the gravitational force between two objects numerous times and discover that G = 6.67 * 10-11 N m2/kg2, we believe that it is true that G = 6.67 * 10-11 N m2/kg2.

It is true that mathematics tells us that G = 6.67 * 10 -11 N m2/kg2, but mathematics doesn't tell us why G = 6.67 * 10 -11 N m2/kg2 is true. If mathematics cannot explain why something will happen, then in order to understand the nature of reality, we need to know more than mathematics.

IE, what does the mathematical symbol G mean to us ? It means that we can predict what will happen, it does not mean that we know why it will happen.

“the existence of consistent patterns that can intuitively be discerned and from which accurate deductions can be made which emulate the state of things as they are”. — Benj96

Consistency
If there was no regularity in what we observed, there would be no logic in what we observed.

For example, if one morning the sun rose in the east, the next day it rose in the west, and the following day it did not rise at all, we would say that there is no logic in the behaviour of the sun. We expect regularity in the laws of nature. If today 1 + 1 = 2, then we expect that tomorrow 1 + 1 = 2.

If we observe the sun has risen in the east for the previous 1,000 days, we logically infer that the sun rises in the east, where such an inference is based on an assumption of regularity in what we observe, an assumption of the regularity in the laws of nature.

Perhaps, rather than logic depending on regularity, perhaps logic "is" regularity.

Where is this regularity
We observe regularity, but where is this regularity - in the mind of the observer, or observer independent ?

Regularity requires the existence of a relation between two things or two events. But there can only be regularity in an observer independent world if relations ontologically exist in an observer independent world. As I have never come across a persuasive argument that relations do ontologically exist in a observer independent world, my belief is that relations don't ontologically exist in an observer independent world.

If relations don't ontologically exist in a observer independent world, then regularity, which depends on relations, cannot exist in an observer independent word. This means that regularity can only exist in the mind of the observer, meaning that logic can only exist in the mind of the observer

In fact, the world is only comprehensible to an observer because the observer imposes themselves on what they observe. We observe the world, and after observing regularities in the world, we logically infer that regularity exists in the world. Such logical inference is in the mind of the observer, not in what is being observed.

Therefore, logic doesn't exist independently of any observer.

The phrases "observer independent" and "observer dependent" should be treated as figures of speech rather than taken literally.

"Observer independent" refers to a conscious person having free will. "Observer dependent" refers to a non-conscious thing not having free will. Searle's inferred assumption is that free-will is a consequence of consciousness.

Consider two unobserved rocks on the moon. We have examples of i) information, in that there is a particular arrangement of things ii) numbers, in that 1 + 1 = 2 and iii) computation, as that of an abacus, in that 1 + 1 = 2.

In Searle's terms these are "observer dependent", in that there cannot be information, numbers or computation without a conscious observer, meaning that information, numbers and computation only exist in the mind, not in a mind-independent world.

Searle's observer independent refers to an animate system (such as a person) which, when experiencing identical inputs, may result in alternate outputs because it has consciousness.

Searle's observer dependent refers to an inanimate system (such as a calculator) which, when experiencing identical inputs, must result in the same output because it doesn't have consciousness.

However, the assumption that an animate system with consciousness (such as a person) when experiencing identical inputs may result in alternate outputs is unproven and needs to be justified.

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.