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.

That is, existential claims are verifiable and not falsifiable, universal claims are falsifiable and not verifiable. — jorndoe

Universal and Existential

Universal quantifier ∀ - “All cat’s are mammals.”
Existential quantifier ∃ - “There exists a cat.”

"There is supernatural witchcraft" is a universal claim. "There is a supernatural witch" is an existential claim. The existential claim that there is a supernatural witch logically follows from the univeral claim that there are supernatural witches.

Either supernatural witches exist or they don't.

Universal claims

I can verify my statement "cats exist", because I can point to two cats. No-one can falsify my statement "cats exist", as I can point to two cats.

I cannot verify my statement "cats don't exist", because there may be two cats that I am unaware of. Someone can falsify my statement by pointing out two cats.

I cannot verify my statement "unicorns exist", because I cannot point to two unicorns. No-one can falsify my statement, as there may be two unicorns that they are not aware of.

I cannot verify my statement "unicorns don't exist", because there may be two unicorns that I am unaware of . No-one can falsify my statement as there may be two unicorns that they are unaware of.

Existential claims

I can verify my statement "a cat exists", because I can point to a cat. No-one can falsify my statement, as I can point to a cat.

I cannot verify my statement "a cat doesn't exist", because there may be a cat that I am unaware of. Someone can falsify my statement by pointing out a cat.

I cannot verify my statement "a unicorn exists", because I cannot point to a unicorn. No-one can falsify my statement, as there may be a unicorn that they are not aware of.

I cannot verify my statement "a unicorn doesn't exist", because there may be a unicorn that I am unaware of . Someone cannot falsify my statement as there may be a unicorn that they are unaware of.

Cats exist as I can point to one. The fact that I cannot point to a unicorn does not mean that they don't exist.

IE, both existential and universal claims can be i) either verifiable or unverifiable and ii) either falsifiable or unfalsifiable.

Verification

People are guilty of making unverified statements all the time: in the pub, at the bus stop, on the Forum, in the media.

It is not the case that unverifiable statements should not be made on the Forum, after all, this is philosophy, but if an unverifiable statement is presented as a fact, such as "there is no such thing as supernatural witchcraft", the author should be required to verify their use of an unverifiable statement presented as a fact

IE, it is not that an unverifiable statement should be verified, rather, it is the use of an unverifiable statement presented as a fact that should be verified.

witch-hunts — Agent Smith

Comme on dit, le terroriste des uns est le combattant de la liberté des autres.

It's quite a paradox that the Saudi ethos, by extension the entire Middle Eastern Islamic mindset, can be both so open-minded (witchcraft) and so narrow-minded (witchcraft). — Agent Smith

YouGovAmerica did a poll 2019 that contributes to this topic, including:

"YouGov asked Americans about their belief in various paranormal entities. Turns out that more than four in 10 Americans believe that ghosts, demons, and other supernatural beings do exist."

"More than one in five (22%) say that demons “definitely exist” while slightly more (24%) believe that they “probably exist.” The numbers are similar when Americans are asked about ghosts: 20 percent say they “definitely exist” and 25 percent say they “probably exist.”"

"Far less common is the belief that vampires live among us. Only 13 percent of Americans say that vampires definitely or probably exist."

"More than one-third of Americans (36%) say that they have personally felt the presence of a spirit or ghost. Once again, women (41%) are more likely than men (31%) to say that this has happened to them. Just over one in ten (13%) Americans say that they have communicated directly with a ghost or spirit of someone who has died."

Polls can be interesting, but it is not always clear what conclusions can be drawn from them.

This is a case where existential verification, not falsification, applies — jorndoe

You are right that to say that the proposition "there is such a thing as supernatural witchcraft" requires verification, but it follows that the proposition "there's no such thing as supernatural witchcraft" also requires verification.

As you made the statement "There's no such thing as supernatural witchcraft", it is your responsibility to provide a verification, not a third party's responsibility to provide a falsification.

There's no such thing as supernatural witchcraft. — jorndoe

Evidence, please.

Is there a concept — Skalidris

Perhaps two concepts: polarised and nuanced arguments.

Possibly hyperbole - deliberate exaggeration.

A kind of unspecified completeness is imagined from the beginning. — igjugarjuk

Yes, as with Kant's a priori pure and empirical intuitions, people have a historically-effected consciousness and they are embedded in the particular history and culture that shaped them. Given this, our interpretation of the world is a matter of "the give-and-take of question and answer, and our understanding of the world changes with the questions we ask of the world and the answers we get back.

It looks to me that we have an entire system here of inherited concepts, which only make sense together. — igjugarjuk

Yes, as with Kant's a priori pure and empirical intuitions, which provides the framework of the mind, as you say: "we have an entire system here of inherited concepts". Through millions of years of evolution we have an inherited framework of the brain, and consequently the mind and self, which of necessity sets limits to what we are able to reason and judge.

But 'forever private experience' opens up an abyss of possibility. It's outside the space of reasons — igjugarjuk

However, even if I may never know your particular subjective experience when observing a wavelength of 700nm, through reason, judgment and imagination, I am able to gain an extensive understanding about it.

The tool we use is language, allowing private sensations to be publicly discussed.

For example, the start of the Universe may forever remain private to us, yet through reason scientists have developed a cosmological model explaining the existence of the observable universe from the earliest known periods through its subsequent large-scale evolution. They have understood how the universe expanded from an initial state of high density and temperature, and have offered a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure.

IE, even private experiences are not outside the space of reason, if the tool we use to understand them is language.

Hume is like an actor on a stage among other actors. His speeches are unified as his speeches..and interpreted as such a unity. — igjugarjuk

Yes, in the world is the mind and the mind-independent. Yet the mind is part of the world, so the mind must share characteristics with what is mind-independent, giving us a link between the mind and what is mind-independent.

In a sense, the mind and the mind-independent make up one unity, giving the mind the possibility of being able to understand the mind-independent, because the mind has evolved in synergy over millions of years within the world. The mind is a product of the world, as is that which is mind-independent.

IE, the mind and mind-independent are part of one greater unity, the world.

Understood correctly, Berkeley was a defender of common-sense who cannot be interpreted as saying that the world is a 'figment of the imagination — sime

Did Berkeley believe that the world is a "figment of the imagination"

Bertrand Russell The Problems of Philosophy - 1912
He then proceeds to consider common objects, such as a tree, for instance. He shows that all we know immediately when we "perceive" the tree consists of ideas in his sense of the word, and he argues that there is not the slightest ground for supposing that there is anything real about the tree except what is perceived. Its being, he says, consists in being perceived: in the Latin of the schoolmen its "esse" is "percipi." He fully admits that the tree must continue to exist even when we shut our eyes or when no human being is near it. But this continued existence, he says, is due to the fact that God continues to perceive it; the "real" tree, which corresponds to what we called the physical object, consists of ideas in the mind of God, ideas more or less like those we have when we see the tree, but differing in the fact that they are permanent in God's mind so long as the tree continues to exist. All our perceptions, according to him, consist in a partial participation in God's perceptions, and it is because of this participation that different people see more or less the same tree. Thus apart from minds and their ideas there is nothing in the world, nor is it possible that anything else should ever be known, since whatever is known is necessarily an idea.

IEP - George Berkeley
Berkeley’s famous principle is esse is percipi, to be is to be perceived. Berkeley was an idealist. He held that ordinary objects are only collections of ideas, which are mind-dependent. Berkeley was an immaterialist. He held that there are no material substances. There are only finite mental substances and an infinite mental substance, namely, God.

AC Grayling - Berkeley's Argument for Immaterialism
Berkeley's philosophical view is often described as an argument for "immaterialism", by which is meant a denial of the existence of matter (or more precisely, material substance.) But he also, famously, argued in support of three further theses. He argued for idealism, the thesis that mind constitutes the ultimate reality. He argued that the existence of things consists in their being perceived. And he argued that the mind which is the substance of the world is a single infinite mind – in short, God.

Blake Winter - Berkeley's Arguments on Realism and Idealism
Bertrand Russell credited Berkeley with being the first philosopher to show that the position of idealism may be held without contradiction (Russell, 1997). However, in addition to this, Berkeley also attempted to show that realism was absurd, because it required concepts which could not in fact be conceptualized (1977). From this, Berkeley concluded that idealism was not merely possible but necessary, or at least necessarily the only theory we could understand. That is, he concluded that we are epistemologically forced to renounce realism in favour of idealism.
We will take realism to mean the ontological position that there are things which exist that are neither minds nor ideas in minds. We will take idealism to mean the ontological position that everything that exists is either a mind or an idea in a mind.

If Realism is the belief in a mind-independent world, and Idealism is also a belief in a mind-independent world, then how do Realism and Idealism differ ?

Realism may be defined as the ontological position that there are things which exist that are neither minds nor ideas in minds. Idealism may be defined as the ontological position that everything that exists is either a mind or an idea in a mind.

From the above texts, Berkeley's position was that of Idealism, believing Realism to be absurd. Berkeley was also an Immaterialist, in that there are no material substances but only ideas in the mind and ideas in the mind of God. Berkeley may admit that the tree continues to exist when we shut our eyes, but this continued existence is due to the fact that it remains as an idea in the mind of God.

Imagination is defined as the faculty or action of forming new ideas, or images or concepts of external objects not present to the senses.

IE, as Berkeley's position is that all that exists in either in our minds or the mind of God, and as something that exists as an idea is part of an imaginative rather than real world, I stick by my statement that "some Idealists think the world is a figment of the imagination", including Berkeley.

There's also the problematic issue of 'private knowledge' — igjugarjuk

Private knowledge of representations
I observe an object in the world and have subjective knowledge of the colour red in my mind. As the object in fact emitted light of a wavelength of 700nm, my perception of the colour red can only be a representation of a wavelength of 700nm. My perception of red is private, in that no-one else will be able to perceive what I perceived. It is private knowledge and will forever remain private knowledge. And yet there is a public word "red" that allows me to discuss publicly what I have privately perceived.

My understanding of how this is achieved I wrote here

Universals are thoughts — RussellA

Inferentialism and Representationalism are both required within language
For Brandom, the meaning of a sentence comes from its relationship with other sentences using inferential logic. This is along the lines of Wittgenstein's "meaning is use" in Philosophical Investigations.

As I see it, both Inferentialism and Representationalism are required within language.
Inferentialism is about coherence within a given language, and Representationalism is about correspondence between the language and the world. Inferentialism allows new ideas to be discovered by finding new relationships between existing ideas and Representationalism allows new ideas to be discovered in the world.

Reason and judgement are needed by both Inferentialism and Representationalism, whether the inferential logic of Inferentialism or the discovering of concepts in the constant conjunction of events in the world. As reason and judgement are attributes of the mind, they can only be the responsibility of the individual making that reasoning and judgement.

Inferentialism uses inferential logic within language itself, but as language exists publicly within the world, there is no difference in the way in which we perceive objects in the world within Representationalism and language as an object in the world within Inferentialism.

IE, our knowledge is always of representations of objects in the world, whether the subjective colour red in the mind representing the object 700nm in the world or the subjective concept red in the mind representing the public word-object red in the world.

It's absurd to rationally question the very framework of rationality — igjugarjuk

I agree

The mind cannot change without a corresponding change in the brain

I am arguing from a position of Reductive Physicalism rather than Non-Reductive Physicalism, where mental states are nothing over and above physical states, and are reducible to physical states. For every actually instantiated property F, there is some physical property G such that F=G.
The mind exists within the brain. The brain is a physical structure and is the framework. The mind is the content. What is in the mind corresponds to what is in the brain. What is expressed in the mind must be in some way be expressed in the brain, in that the mind doesn't have a soul outside of time and space allowing it to act independently of the brain. The mind cannot change without a corresponding change in the brain.

The Self cannot inspect itself

Hume’s denial that there is an inner perception of the self as the owner of experience is one that is echoed in Kant’s discussion in both the Transcendental Deduction and the Paralogisms, where he writes that there is no intuition of the self “through which it is given as object”

On the nature of self-awareness, for example, in an unpublished manuscript Schopenhauer concurs with Kant, asserting that, “that the subject should become an object for itself is the most monstrous contradiction ever thought of”

The same can be said of the Wittgenstein of the Tractatus, who famously likens the self to the eye which sees but does not see itself.

Change cannot be spontaneous

A physical structure can be changed by something exterior but cannot spontaneously change itself, in that a snooker ball can start to move when hit by a snooker cue, but a snooker ball at rest cannot spontaneously start to move.

The brain is a set of physical parts. Each part may be changed by something exterior to the part, but each part cannot spontaneously change itself.

Even if there is nothing external acting on the brain, the brain may change because of the interaction between the parts that make it up. The brain as a whole is changed by its parts, not by the set of parts acting as a whole. The brain as a whole cannot be changed by the brain as a whole, meaning that the brain cannot change itself.

A framework consisting of a set of parts may change by the interaction between its parts, but not by the set of parts as a whole, ie, a framework cannot change itself.

IE, our rationality, our self, is not the content of the framework of the brain. Our rationality, our self, is the framework of the brain. As a framework cannot question itself, as you say, "It's absurd to rationally question the very framework of rationality."

Idealists do not think that the world is a figment of the imagination — Wayfarer

There are different kinds of Idealism.

For example, as described by the SEP - Idealism, there is Berkeley's "Ontological Idealism", where the mind is the ultimate foundation of all reality, or even exhaustive of reality, and there is Kant's "Epistemological Idealism", where Idealism is not about any existence of things but only our representation of them.

IE, some Idealists think the world is a figment of the imagination.

there is a genuine philosophical insight that I think Stove is somehow missing — Wayfarer

Berkeley's argument "the mind....is deluded to think it can and does conceive of bodies existing unthought of, or without the mind, though at the same time they are apprehended by, or exist in, itself" may be countered by common sense justifications.

"RussellA - Transcendental Idealism" should be treated as a figure of speech.............That's really not the case — Wayfarer

"Transcendental Idealism" does not address Stove's problem

Kant's "transcendental" is about a priori pure and empirical intuitions. Kant's "Epistemological Idealism" is not about any existence of things but only our representation of them.

The expression "transcendental idealism" can only be a figure of speech as it is about more than the transcendental and idealism, in that it does not include any reference to the world of the noumena, an important part of Kant's theory.

Experiencing certain phenomena through my senses, I have subjective knowledge of the colour red. I was born with the innate ability to perceive the colour red. "Transcendental idealism" is the combination of my innate ability to perceive red and my perceiving the colour red.

Using reason, understanding and imagination, I arrive at the belief that my perception of red was caused by light in the external world having a wavelength of 700nm. This light having a wavelength of 700nm is Kant's noumena.

IE, Kant's "Transcendental Idealism" does not address the problem of how we are able to know what precedes, if anything, our phenomena.

However, Kant then grants that you can be both a transcendental AND an empirical realist: — Wayfarer

As you wrote about Kant's theory of "Transcendental Idealism": "you can be both a transcendental AND an empirical realist", this indicates the phrase "Transcendental Idealism" should be treated as a figure of speech rather than something to be taken literally.

In my terms, Kant's phrase "Transcendental Idealism" includes both Epistemological Idealism and Ontological Realism. The problem is, how to link them ?

For the Ontological Idealist, ie for those not believing in the ontological existence of a mind-independent world, this is not a problem, as there is no "Ontological Realism".

However, for the Ontological Realist, it does remain problematic.

We can only ever have knowledge of representations in our mind. The belief that something mind-independent caused them we can justify in various ways. However, if we can never have knowledge of what caused these representations, we can never know that our belief is true.

For example, I have subjective knowledge of the colour red. I believe it was caused by a wavelength of 700nm. I can justify this using scientific procedures, but as science itself is founded on representation, a science founded on representation is incapable of getting behind the representations themselves.

David Stove's Discovery of the Worst Argument in the World addressed this problem, raising the inevitable conclusion that there is no way to get out.

IE, many justifications can be made for our belief in a mind-independent world, but none
as far as I know beyond doubt. One can only say that from the weight of evidence there is most likely a mind-independent world, and perhaps pragmatically that is all one needs.

even the most apparently-obvious scientific hypotheses are mental constructions — Wayfarer

As my belief is that of Indirect Realism, I agree.

That's because you have in your mind the firm belief in an external reality. I understand that questioning that belief is difficult. — Wayfarer

It is true that I find it impossible to question the ontological existence of a mind-independent world.

Otherwise I would find it difficult to fill the kettle with water, switch on the kettle and put a tea bag into my cup if I didn't think these things were real and not a figment of my imagination.

Otherwise I would be diagnosing myself as schizophrenic, hallucinating about things that are not really there.

Otherwise, I would be diagnosing myself as having Dissociative Identity Disorder, in having long conversations about science and philosophy with myself, between two distinct personalities both existing in my mind.

IE, my sanity requires me to believe that I am interacting with a world that is mind-independent.

Kant.......His philosophy is described as transcendental idealism — Wayfarer

The term "Transcendental Idealism" is more metaphorical than literal

A better description than "transcendental idealism" could be "justified belief within Indirect Realism" in that we hypothese the cause of representations discovered in phenomena from the senses using justified belief.

A wave function collapses when a wave function reduces to a single eigenstate due to an interaction with the external world. The fact that this interaction is called an "observation" does not mean the observer has to be a conscious being. It can be a particle of light, a molecule of air, a wall, a ceiling, a window, etc.

"Observation" is being used as a metaphor in that only conscious beings can observe. A rock cannot observe the air, the tree cannot observe the wind, etc. That wind howls does not mean that wind is in anguish. That a wave of terror washed over him does not mean that terror is a wave. That to say that Jess is dynamite does not mean she is made of dynamite.

It is true that Kant as an Indirect Realist believed in Epistemological Idealism, but it is certainly not true that he believed in Ontological Idealism.

IE, the fact that Kant's philosophy is called "transcendental idealism" does not of necessity mean that it can be described as either transcendental or Idealism.

abstracts.........But the subject of the analysis are purely intelligible in nature, i.e. they can only be grasped by a mind, so they don't exist in the way that sensory objects exist. — Wayfarer

I agree that abstracts can only be grasped by the mind.

The question that remains to be answered is how can something exist in a mind-independent world outside of time and space ?

(See Does the Universe Exist if We're Not Looking?, Discover Magazine.) — Wayfarer

Can anyone make a valid argument that a mind-independent world did not exist in the 13 billion years before the arrival of human observers ?

There is an interview with John Wheeler Does the Universe Exist if We're Not Looking

We inhabit a cosmos made real by our own observation

John Wheeler has a gut feeling that we inhabit a cosmos made real by our own observation.

The article notes that "When physicists look at the basic constituents of reality— atoms and their innards, or the particles of light called photons— what they see depends on how they have set up their experiment."

In addition "Our observations, he suggests, might actually contribute to the creation of physical reality. To Wheeler we are not simply bystanders on a cosmic stage; we are shapers and creators living in a participatory universe."

IE, from the standpoint of Epistemological Idealism within Indirect Realism, I agree with the above, and I am sure that not only Kant but also Schopenhauer would as well.

Are humans necessary for the existence of the universe

The article also asks "Does this mean humans are necessary to the existence of the universe? While conscious observers certainly partake in the creation of the participatory universe envisioned by Wheeler, they are not the only, or even primary, way by which quantum potentials become real. Ordinary matter and radiation play the dominant roles.........In this case the mica, not a conscious being, is the object that transforms what might happen into what does happen."

IE, the article raises the question "Does the Universe exist if we're not looking", and its answer is yes.

Philosophical idealism can accept that material objects and forces have a degree of reality — Wayfarer

Some have said that "definitions are not all that helpful", but it has also been said about Ordinary Language Philosophy that traditional philosophical problems are rooted in misunderstandings philosophers make by distorting or forgetting how words are ordinarily used to convey meaning in non-philosophical contexts. Such philosophical use of language creates the very philosophical problems they are employed to solve.

Idealism may be simply defined as a belief that there is no mind-independent external world. Realism that there is a mind-independent external world. Within Realism is Direct Realism and Indirect Realism. Direct Realism may be simply defined as the belief that we directly observe objects in the external world as they really are. Indirect Realism may be simply defined as the belief that we only observe representations of objects we believe to be in the external world. Kant was an Indirect Realist.

IE, it is true that Idealism accepts that material objects and forces have a degree of reality, but that reality is in the mind, not in a mind-independent world.

The view that abstract objects are real is generally associated with Platonism or scholastic realism. But you've already indicated that you reject this with reference to F H Bradley's argument. — Wayfarer

The Platonist believes in the existence of abstract objects, where abstract objects exist outside time and space, are not causal and are necessary. The Nominalist believes in concrete objects, where concrete objects exist in time and space, are causal and are contingent.

It is still possible for the Nominalist to reject the Platonism of abstracts while still believing in the ontological existence of relations.

I personally reject the Platonism of abstracts because I find the idea of objects existing in the external world outside of time and space incomprehensible.

For a similar reason, I also reject the ontological existence of relations, as they also exist in the external world outside of time and space.

My belief that elementary particles and elementary forces do ontologically exist in a mind-independent world — RussellA

This is just what has been called into question by 20th Century physics — Wayfarer

The age of the universe is about 13.8 billion years, and human intelligence has been on the Earth for about 7 million years. That a mind-independent world existing 13,793 billion years before the arrival of human observers has been called into question makes no sense to me. It brings to mind the belief of Young Earth Creationism, whereby lifeforms were created in a supernatural act about 6,000 to 10,000 years ago.

I am also sure that most contemporary philosophical interest in the quantum world is comparable to that of medieval discussion about the philosopher's stone and its relevance to alchemy.

Yeah, no. Not buying. Aren’t you the one supposed to be defending realism? — Wayfarer

Luckily, my livelihood is not dependent on my selling.

I believe in Realism
Idealism is the view that things exist only as ideas, with no reality of material objects outside of the mind. Realism is the view that objects exist in themselves, independently of our consciousness of them. My position is not that of Idealism, as I believe objects exist in themselves, independently of our consciousness of them. It comes down to exactly what "objects" are. My belief that elementary particles and elementary forces do ontologically exist in a mind-independent world, though relations don't, is consistent with Realism.

Do you believe in Realism or Idealism ?
As you wrote on page 3: "Ever since I began to think about it, I've held that numbers and basic geometrical principles and the like are real, in that they're the same for anyone who can grasp them. So they're not dependent on your or my mind, but can only be grasped by a rational mind." It would follow from your position that if numbers are real and not dependent on your or my mind, then there must be a mind-independent world." This is a belief in Realism.

Yet you also wrote on page 3: "I question the coherence of the idea of a 'mind-independent world'. This is a belief in Idealism."

Are these positions compatible ?

I can't see how Newton's equations of motion are metaphorical, — Wayfarer

Newton's second law F=ma is a metaphor, not a literal fact.

Andrew May makes a strong point that even Newton's second law is a metaphor, in that that when a body is acted upon by a force, the time rate of change of its momentum equals the force, in that F=ma,

Andrew May Metaphors in Science 2000
"In his article on the use of metaphors in physics (November issue, page 17), Robert P Crease describes several interesting trees but fails to notice the wood all around him. What is a scientific theory if not a grand metaphor for the real world it aims to describe? Theories are generally formulated in mathematical terms, and it is difficult to see how it could be argued that, for example, F = ma "is" the motion of an object in any literal sense. Scientific metaphors possess uniquely powerful descriptive and predictive potential, but they are metaphors nonetheless. If scientific theories were as real as the world they describe, they would not change with time (which they do, occasionally). I would even go so far as to suggest that an equation like F = ma is a culturally specific metaphor, in that it can only have meaning in a society that practices mathematical quantification in the way that ours does. Before I'm dismissed as a loopy radical, I should point out that I'm a professional physicist who has been using mathematical metaphors to describe the real world for the last twenty years!"

The equation F=ma cannot be literal because of Hume's problem of induction. Through logic and reason and the empirical observation of constantly conjoined events, we hypothesise that F=ma. Through further empirical observation we discover that this equation proves to be effective in the prediction of future states of affairs. We believe the equation to be literal, but this belief is only a hypothesis.

We believe, we hypothesise, that there is a regularity in what we call the "laws of nature", and accordingly create a mathematics also founded on regularity in the expectation that the regularities in our mathematics will correspond with the regularities in the "laws of nature". That our mathematics are effective in predicting future states of affairs in the world infers that our hypothesis that there are regularities in the laws of nature is correct, is true. But, this is not knowledge, as our hypothesis can never be proved, only a justified belief.

A metaphor may be defined as i) a figure of speech in which a word or phrase is applied to an object or action to which it is not literally applicable and ii) a thing regarded as representative or symbolic of something else.

IE, as the equation F=ma can never be proved to be a literal description of states of affairs in the world, and must always remain a hypothesised representation, it falls within the definition of metaphor.

My point remains -- the metaphor works for believers in ultimate truth. — Moliere

I agree that as a metaphor, the "ultimate truth" works for atheists in their belief of an "ultimate truth".

The language he uses is deeply religious throughout. — Moliere

There is no indication in the article that Wigner proposes the mystical or religious to explain why our theories work so well.

Wigner wrote - "The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve".

Metaphors are commonly used in science, such as: evolution by natural selection, F = ma, the wave theory of light, DNA is the code of life, the genome is the book of life, gravity, dendritic branches, Maxwell's Demon, Schrödinger’s cat, Einstein’s twins, greenhouse gas, the battle against cancer, faith in a hypothesis, the miracle of consciousness, the gift of understanding, the laws of physics, the language of mathematics, deserving an effective mathematics, etc.

IE, it would be more true to say that the language he uses is deeply metaphorical rather than religious.

:smile:

I think before going further, you should explain further what you mean by your term 'ontologically exist'. — Wayfarer

The mind is of a different kind to the mind-independent world

Realism is the belief that the world comprises the mind and a mind-independent world.

Although the mind is part of the world, my belief is that the the nature of the mind is different to the nature of the mind-independent world. FH Bradley's Regress Argument persuades me that relations don't ontologically exist in the mind-independent world, whilst the Binding Problem and Kant's Unity of Perception do persuade me that relations do ontologically exist in the mind.

Although everything in the mind-independent world exists in the mind, such as matter and the forces between them, there are some things that exist in the mind but not the mind-independent world, such as concepts, unicorns, apples, numbers, universals, abstracts, love and hate, ethics, pain and pleasure, fictional characters, ghosts, gods, relations, etc.

Therefore, there is a set of things that ontologically exist in the mind, and a different set of things that ontologically exist in the mind-independent world, though the sets do overlap.

IE, in the mind-independent world, quarks and the weak nuclear force do ontologically exist, but love and hate don't.

My point is that dead matter seems to obey many mathematical structure — Landoma1

Mathematics obeys matter, rather than matter obeys mathematics

From observations of the world, we arrive at the belief that there is a regularity in what we call "the laws of nature". We are able to justify such a belief through further experimentation.

In order to model what we believe to be the intrinsic regularity discovered within the "laws of nature", we invent mathematical systems also having intrinsic regularity.

If our intrinsically regular mathematical systems prove to be effective in predicting future states of affairs, then we can infer that the "laws of nature" are also intrinsically regular. We can never prove that the "laws of nature" are intrinsically regular, as this leads into Hume's problem with inductive reasoning. We can never know that the "laws of nature" are intrinsically regular, as knowledge requires a justified true belief, and the truth is beyond what we can inductively reason.

The "unreasonable" effectiveness of mathematics is a strong indication that within the "laws of nature" there is an inherent regularity.

The main issue is Eugene Wigner's The Unreasonable Effectiveness of Mathematics in the Natural Sciences

As regards the unreasonable effectiveness of mathematics, it is initially truly amazing that from sitting on a train using Richard Hamming's thought experiment, I can disagree with Aristotle and agree with Galileo that heavy objects should fall at the same speed at lighter ones, not only on the train but universally on the far side of the universe.

However, the starting position is the amazing regularity and invariance of what we call "the laws of nature". Given such regularity, the "laws of nature" applicable on the train will also be applicable on the far side of the universe.

The fact that I can codify and quantify using reason, logic and mathematics the "laws of nature" that I observe on the train, and still be applicable on the far side of the universe, is not a measure of success of my reasoning, logic and mathematics, but rather is a measure of the regularity and invariance of the "laws of nature".

Without such regularity and invariance in "the laws of nature", our reasoning, logic and mathematics would count for nothing.

IE, mathematics is only effective because of the unreasonable regularity in the "laws of nature"

An associated issue is the question as to whether universal concepts such as "north of" and "whiteness" are or are not dependent on thought. Are they discovered in the external world or invented in the mind ?

Wayfarer - page 2 - The second, and crucial, point, is that such qualities or relations or whatever they are, (Bertrand Russell's "north of", "whiteness") are not dependent on thought, but they can only be perceived by thought.

RussellA - page 2 - If universals don't exist in a mind-independent world, yet we can perceive them in our minds, then they must have been created in the mind. As universals have been created by thoughts in the mind, they must be dependent for their existence on thoughts in the mind.

IE, not agreed yet.

You're defending the empiricist view that all concepts are derived from experience — Wayfarer

Yes. In the sense that concepts are created in the mind based on observations of the external world, not that concepts ontologically exist in a mind-independent world.

Quite right! That is the point at issue, which here you appear to be conceding. — Wayfarer

I agree that the mind uses the inventive power of intellectual reasoning, and part of its inventive power is in the invention of universal concepts, such as "north of".

The 'law of the excluded middle' didn't come into existence when it was discovered by h. sapiens; it would be true in all possible worlds — Wayfarer

SEP - Disjunction - The law of excluded middle (LEM) states that any proposition of the form (ϕ∨¬ϕ) is logically valid. The semantic principle of bivalence states that every proposition is either true or false (and not both).

SEP - Structured Propositions - For example, when a German speaker utters the sentence ‘Schnee ist weiss’ and an English speaker utters the sentence ‘Snow is white’, they have said the same thing by uttering the sentences they did.
The proposition is taken to be the thing that is in the first instance true or false

IE, as propositions don't exist in a mind-independent world, and as the "law of excluded middle" is based on propositions, the "law of excluded middle" doesn't exist in a mind-independent world.

This is the point of the a priori nature of the pure concepts of reason in Kant — Wayfarer

Exactly, a priori in the mind.

So universal concepts are not created by thought, but can only be discerned by a rational intellect — Wayfarer

If universal concepts were not created by thought, then the universal concepts of love and hate could be discovered in a mind-independent world.

If relations do not exist, then it is not the case that something is to the west of something else.
Glasgow is to the west of Edinburgh.
Therefore (at least one) relation exists. — Cuthbert

This leads to:

Statement 1 = If relations do not exist, then it is not the case that Glasgow is to the west of Edinburgh

Statement 2 = Relations exist, and It is the case that Glasgow is to the west of Edinburgh.

The conclusion that "therefore (at least one) relation exists" of necessity follows from statement 2 rather than prove anything about the ontological existence or not of relations.

But you don't know that. It's quite feasible that the wheel was invented because some Cro-Magnon discovered that you could roll a big rock on logs. Basic empiricism. — Wayfarer

Concepts are invented not discovered

One day, a Cro-Magnon on a walk through the forest happened to observe a big flat rock that had fallen from the side of a mountain rolling along on some logs on the ground. Let us call the Cro-Magnon George.

George had made a particular empirical observation and discovered something in the world, in that a flat rock can continue to move freely along the ground as long as it is supported by round logs.

George was able to make the intellectual leap from the particular to the general, and reason that any flat object may move more freely along the ground as long as it is supported by round objects. George using reason was able to use a particular observation to arrive at a universal concept, the concept of the wheel.

If concepts existed in a mind-independent world then they would be "out there somewhere"
and discoverable. However, if that were the case, two people independently observing an object, for example a rock, should be able to write down all concepts discoverable within the object, in which case, when compared, their lists should be the same. Concepts in objects cannot be discovered by observation alone, but require the inventive power of reasoning using the intellect.

IE, because the concept of the wheel does not exist in either a mind-independent rock, log or relation between the two, George could not have discovered the concept from an empirical observation. But as the concept of the wheel exists in George's mind, and because it cannot have been discovered from an empirical observation, it must have originated in George's mind, been invented in the mind of George.

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. — Bertrand Russell, The World of Universals

"North of" and London exist in exactly the same way

The object Edinburghlondon has the related parts i) Edinburgh and ii) London
London has the related parts i) north of the Thames and ii) south of the Thames
South of the Thames has the related parts i) built up areas and ii) trees and grasslands
Built up areas have the related parts i) buildings and ii) roads
Roads have the related parts i) paving and ii) junctions
Paving has the related parts - etc

Russell writes that " the relation 'north of' is radically different from such things" as London, in that "north of" subsists whilst London exists. Yet London only exists as a relation between its parts north of the Thames and south of the Thames.

IE, the object London depends on its existence on relations between parts - the area north of the Thames and the area south of the Thames. If, according to Russell, relations don't exist in a mind-independent world, then it follows from Russell's own argument that neither can London exist as a mind-independent object.

That which many different thoughts of whiteness have in common is their object, and this object is different from all of them. Thus universals are not thoughts, though when known they are the objects of thoughts. — Bertrand Russell, The World of Universals

Universals are thoughts

A group of people may agree to share a common language. It may be agreed within the group that white objects are linked with the word "white". In the world being observed by the group, not only do white objects physically exist, but also and the word "white" physically exists as an object.

Each individual may develop their private concept of "whiteness" by observing white objects in the world. But also each individual may also link their private concept of "whiteness" with the associated public word "whiteness"

It is true as Russell writes "One man's act of thought is necessarily a different thing from another man's" - in that my concept of "whiteness" is of necessity not identical to yours.

But it is not true as Russell wrote that "if whiteness were the thought as opposed to its object, no two different men could think of it", as one person's private concept of "whiteness" is linked to everyone else's private concept of "whiteness" through the public linguistic object "whiteness".

IE, universals, such as the concept of "whiteness" not only exist in the mind as a private thought, but also are universally understood by a group sharing a common public language.

One is the distinction between the existence of universals and of sensable objects. — Wayfarer

Universals and sensables are of the same kind

There are sensable objects such as Edinburgh and London and universals such as "north of" and "whiteness".

IE, a sensable object such as London is no more that a relation between its parts, and if relations are universals, then sensable objects cannot be argued to be of a different kind to the universals from which they are comprised.

such qualities or relations or whatever they are, are not dependent on thought, but they can only be perceived by thought — Wayfarer

Universals are dependant on thought

It has been well-argued that universals such as whiteness, apples, houses, governments can not be explained as Platonic Forms that exist in a mind-independent world.

Universals can be perceived by thought, in that we can discuss them.

If universals don't exist in a mind-independent world, yet we can perceive them in our minds, then they must have been created in the mind. As universals have been created by thoughts in the mind, they must be dependent for their existence on thoughts in the mind.

IE, universals are dependent on thought and can be perceived by thought.

You wrote:
We have to show that relations exist.
Glasgow is west of Edinburgh - so we are told.
It could mean that if we turn over the whole universe item by item we will find at least one thing that is to the west of another thing.
There is a case - at least one case - of something being to the west of something else.
From which if finally follows that relations exist...........we can see that relations have ontological existence.

As regards the ontological existence of relations, there are two possibilities - either i) relations don't exist and after turning over the whole universe item by item we won't find at least one thing that is to the west of another - or ii) relations do exist and after turning over the whole universe item by item we will find at least one thing that is to the west of another

However, the problem with your statement "There is a case - at least one case - of something being to the west of something else" is that the statement can only be made on the assumption that relations do exist.

It is equivalent to saying that if relations exist then relations exist.

Amazing that inventions work so well, then. Or maybe they're all in the mind as well? — Wayfarer

Take the wheel as an example. As with all inventions they were invented in the mind, and then made into a physical thing of perhaps wood and steel, a circular rim supported by spokes revolving around an axle.

The parts of the wheel physically exist in the world, and once created, exist independently of whether anyone is thinking of them or not. This is compatible with Realism, in that there is a mind-independent world of matter and forces.

For the Naive Realist, our sense provide us with a direct awareness of the wheel as it really is.

For the Indirect Realist, we do not perceive the external world as it really is, but are only aware of a representation of the external world. Our awareness is of the concept of the wheel, not the "wheel" itself.

The concept of a wheel definitely exists in the mind, otherwise we would not be having this conversation. The question is, do wheels ontologically exist in the external world ? A wheel is a spatial relation between its rim, spokes and axle. Whether wheels ontologically exist in the external world depends on whether relations ontologically exist in the external world.

I am persuaded by FH Bradley's Regress Argument that relations don't ontologically exist in the external world, meaning that wheels don't ontologically exist in the external world.

If one is going to argue that wheels do ontologically exist in the external world, then this will require a justification that relations also ontologically exist in the external world.

Is there any reasoned argument that relations do ontologically exist in the external world ?