ne can give an exegesis of the picture the text presents without raising the question of whether it is true or false, but if the exegesis includes the question of the truth of what is presented then it is not beside the point. — Fooloso4

Someone else has finally come full circle to my original critique. It’s this that is missing and makes it (at least on the face if it as far as I can see) not that interesting and lame duck, amongst other things.

There is a reality made of objects and their relation (bald assertion).

Well, the standard reading, after Anscombe, would maintain that elementary objects can't properly be said to even exist - they are "shown" by their relations to each other. So it's no surprise that examples are not listed...

And we know Wittgenstein himself found this problematic, too, since it led to the discussion of simples in PI.

The idea in the Early Wittgenstein is that we recognise elementary objects when we see them. This turned to the idea that we choose whatever elementary objects we wish to treat as simples, in accord with what we are doing. See PI §48.

they are "shown" by their relations to each other. So it's no surprise that examples are not listed... — Banno

So refer to Kant's transcendentalism? What is a philosophy that has no account of itself and starts in the middle and then says, "This doesn't matter"? This one does, I know. But then your language game isn't the same one I'm playing when I ask "What is a philosophy that..". It just wants you to accept it and that to me is just assertion.

At the end of the day, it is simply an internal minor squabble between Witty and Russell (and Frege). I don't see it as a major theory. The aphoristic type prose also doesn't lend itself to clear interpretation. It's like the Nietzsche of analytic philosophy.

The idea in the Early Wittgenstein is that we recognise elementary objects when we see them. — Banno

But this is the stuff of philosophy proper, not to be glossed over. His argument ONLY works if you believe the ontological framework. If anyone else just "started" and didn't explain why they started there, they would be called out. I don't see why he should get a pass.

I can predict a sort of response whereby you mention that he was demonstrating his own values whereby philosophy cannot speak of things that can't be pictured.. But BECAUSE it is the very basis for which the picture theory "hangs" (get what I did there).. it MUST be discussed otherwise, Witty garners himself right by way of never having to prove anything outside of what he himself is claiming. How convenient that works.. "I make a claim, but it would be 'nonsense' to refute its very basis". Again, real convenient.

Well, the standard reading, after Anscombe, would maintain that elementary objects can't properly be said to even exist - they are "shown" by their relations to each other. — Banno

But he does not state any elementary propositions either.

This turned to the idea that we choose whatever elementary objects we wish to treat as simples, in accord with what we are doing. — Banno

Which is a rejection of the ontology (objects), epistemology (analysis), and metaphysics (logical structure) of the Tractatus, as well as the idea that there is a final analysis.

See PI §48 — Banno

This passage mentions Plato's Theaetetus, but does not make the connection explicit. The subject of the dialogue is knowledge.

I in turn used to imagine that I heard certain persons say that the primary elements of which we and all else are composed admit of no rational explanation; for each alone by itself can only be named, and no qualification can be added, neither that it is nor that it is not for that would at once be adding to it existence or non-existence, whereas we must add nothing to it, if we are to speak of that itself alone. Indeed, not even “itself” or “that” or “each” or “alone” or “this” or anything else of the sort, of which there are many, must be added; for these are prevalent terms which are added to all things indiscriminately and are different from the things to which they are added; but if it were possible to explain an element, and it admitted of a rational explanation of its own, it would have to be explained apart from everything else. But in fact none of the primal elements can be expressed by reason;they can only be named, for they have only a name; but the things composed of these are themselves complex, and so their names are complex and form a rational explanation; for the combination of names is the essence of reasoning. (201e - 202b)

He goes on to give an example:

The elements in writing, the letters of the alphabet, and their combinations, the syllables ... (202e)

Note that Socrates does not present this as his own view. See the first sentence. Words are not derived from the combination of letters of the alphabet. He goes on to show how problematic such an analysis is.

As you point out, what we treat as simple depends on what we are doing. In §60 he considers an analysis of a broom:

Then does someone who says that the broom is in the corner really mean: the broomstick is there, and so is the brush, and the broomstick is fixed in the brush?—If we were to ask anyone if he meant this he would probably say that he had not thought specially of the broomstick or specially of the brush at all. And that would be the right answer, for he meant to speak neither of the stick nor of the brush in particular.

But if we are making or repairing brooms the broomstick and brush might be thought of as two things rather than one. The brush then might be regarded as one thing or a combination of bristles. At the atomic level (the choice of terms is deliberate) the broomstick, the brush, and the bristles are all composites. In the final analysis what serves as a final analysis depends on what we are doing. It may be, however, that there is no final analysis. An atom was once thought of as simple, indivisible, but we now know that what we call an atom is not an atom it its original sense. Whether or not there is something or things that are simple and indivisible remains an open question. It may be an a priori mythology.

So refer to Kant's transcendentalism? — schopenhauer1

Fuck no.

How many more times will you post to explain how uninteresting this all is? :wink:

There is a philosophical trap in explanation.

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. We do not get to the meaning of a word by setting out its definition using other words, because we would then never step outside that circularity. We can get to the meaning of words by using them.

Explaining a rule suffers a similar circularity. We can state the rule in ever more detail, finding ourselves in a circle or a regress. But there is a way of understanding a rule that is seen in implementing it, not in analysing it.

This is only superficially "starting in the middle".

And this is perhaps why Wittgenstein said he had entertained and exhausted what was interesting in schopenhauer.

In the final analysis what serves as a final analysis depends on what we are doing. It may be, however, that there is no final analysis. — Fooloso4

That's it.

And this is perhaps why Wittgenstein said he had entertained and exhausted what was interesting in schopenhauer. — Banno

:lol:

Realism:
"The realist wishes to claim that apart from the mundane sort of empirical dependence of objects and their properties familiar to us from everyday life, there is no further (philosophically interesting) sense in which everyday objects and their properties can be said to be dependent on anyone’s linguistic practices, conceptual schemes, or whatever." --SEP

Wittgenstein wasn't a realist, then.

We can get to the meaning of words by using them. — Banno

Fine and dandy, but now we are mixing up our language games. Are we going to explain early Witty by way of later Witty or are we going to take early Witty at face value when it was written?

Why shouldn't we do both, with care? If Wittgenstein agrees with us that there are problems with the Tractatus, let's acknowledge that.

Wittgenstein wasn't a realist, then. — Tate

In the Tractatus objects and their relations are independent of the mind. The logical structure that underlies language is also independent of the mind. Whether or not a proposition is true is determined by comparing it with reality. But:

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

5.61 Logic pervades the world: the limits of the world are also its limits.
...
We cannot think what we cannot think; so
what we cannot think we cannot say either.

5.62 This remark provides the key to the problem, how much truth there is in solipsism.

5.63 I am my world. (The microcosm.)

5.632 The subject does not belong to the world:
rather, it is a limit of the world.

5.634 This is connected with the fact that no part of our experience is also a priori.
Everything we see could also be otherwise.
Everything we describe at all could also be otherwise.
There is no order of things a priori.

5.64
Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it.

Why shouldn't we do both, with care? If Wittgenstein agrees with us that there are problems with the Tractatus, let's acknowledge that. — Banno

Ok, I wanted to make sure I was playing by the rules of this language game.

We do not get to the meaning of a word by setting out its definition using other words, because we would then never step outside that circularity. We can get to the meaning of words by using them.

Explaining a rule suffers a similar circularity. We can state the rule in ever more detail, finding ourselves in a circle or a regress. But there is a way of understanding a rule that is seen in implementing it, not in analysing it.

This is only superficially "starting in the middle". — Banno

So in Tractatus, Witt explains (pretty commonsensically) that true propositions about the world are ones where only facts of the world are stated. Facts are actual states of affairs of objects and their relations to other objects. If you want to make a picayunish point about how I'm using facts and states of affairs, be my guest, but now we are getting to pedantic-ville and not my point. My point is, behind all of these Zarathustrian-stated assumptions is a metaphysics of the world as objects. It is this claim that I am saying that reveals something about his philosophical conception. The Tractatus falls apart if the world is not objects and their relations. Atomic facts are simply "turtles all the way down", as what is truly being pictured is nowhere to be found (empty set, error, not even on the scene). Why? Because to prove this claim, something other than mere stating of asserted propositions must be accomplished (which is all he is doing).

So thus far we have this as what is the case with Tractatus:
1. Witty is making propositions.
2. His propositions rely on claims outside of the propositions (objects- presumably somewhere in space and time).
2a, Therefore, his claim (of objects) must be demonstrated beyond referencing the mere propositions themselves that entail the very claim being posited.
3. A claim that is beyond the propositions that entail them must be demonstrated.
3a. What counts as being demonstrated can be a number of things including scientific explanation through experimentation or results of empirical studies, arguments that show X, Y, Z about a feature of reality that cannot be disproven easily, etc. etc.
3b. Witty provides none of these for the basis of his propositions (objects).
3c. Therefore, Witty fails to prove the very claims that are the basis of his propositions. He has not done the legwork for a foundation of his claims that are necessary because of 2- his very propositions rely on claims outside of the propositions.

Whether or not a proposition is true is determined by comparing it with reality. But:

5.6 The limits of my language mean the limits
of my world. — Fooloso4

How does this work then? I compare a proposition to the state of a world that is limited by my language.

This actually sounds like empirical idealism. It's not Berkeley, but it's similar. And this is indeed a kind of realism (per the SEP article on idealism).

Logic pervades the world: the limits of the world are also its limits.

How would logic pervade the world? Because it pervades language, it pervades the world?

I am my world. (The microcosm.)

5.632 The subject does not belong to the world:
rather, it is a limit of the world.

5.634 This is connected with the fact that no part of our experience is also a priori.
Everything we see could also be otherwise.
Everything we describe at all could also be otherwise.
There is no order of things a priori.

5.64
Here we see that solipsism strictly carried out coincides with pure realism. The I in solipsism shrinks to an extensionless point and there remains the reality co-ordinated with it.

This is heavily idealistic, isn't it?

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.

How does this work then? I compare a proposition to the state of a world that is limited by my language.

This actually sounds like empirical idealism. — Tate

The language used by philosophers is already deformed, as though by shoes that are too tight — Wittgenstein Culture and Value 47

The proposition "The cat is on the mat" is true if the cat is on the mat. The limits of my language play no role here. The problem Wittgenstein is pointing to does not occur in the world, but only at the limits of the world.

How would logic pervade the world? Because it pervades language, it pervades the world? — Tate

The structure of the world is logical. It is what makes language possible. That is, propositions about how things are in the world, the propositions of science. They are not dependent on a subject.

5.632 The subject does not belong to the world: rather, it is a limit of the world.

This is heavily idealistic, isn't it? — Tate

Note that he calls it "pure realism" (5.64) This continues:

The self of solipsism shrinks to a point without extension, and there remains the reality co-ordinated with it.

5.641 What brings the self into philosophy is the fact that ‘the world is my world’.
The philosophical self is not the human being, not the human body, or the human soul,
with which psychology deals, but rather the metaphysical subject, the limit of the world— not a part of it.

The logical relationships within the world are not the only relationships. There is also a relationship between the “I” and the world, matters of ethics and aesthetics.

The limits refer to what can be said, propositions about things in the world, and what stands outside those limits. Statements about ethics and aesthetics are senseless in that they do not point to what what is the case. They are not statements of fact. But this does not mean that they are meaningless in the sense of having no significance for us.

The proposition "The cat is on the mat" is true if the cat is on the mat. The limits of my language play no role here. The problem Wittgenstein is pointing to does not occur in the world, but only at the limits of the world. — Fooloso4

What problem?

Note that he calls it "pure realism" — Fooloso4

Berkeley's idealism is a kind is realism. The SEP calls it ontological idealism to distinguish it from epistemological idealism.

There is also a relationship between the “I” and the world, matters of ethics and aesthetics. — Fooloso4

Not according to the quote you provided:

The subject does not belong to the world:
rather, it is a limit of the world.

Thank you. Can you advise a good secondary resource?

What problem? — Tate

The problem you raised about limits:

How does this work then? I compare a proposition to the state of a world that is limited by my language. — Tate

There is also a relationship between the “I” and the world, matters of ethics and aesthetics.
— Fooloso4

Not according to the quote you provided:

The subject does not belong to the world:
rather, it is a limit of the world. — Tate

The metaphysical subject is not found in the world. It is not a relation between things in the world, but, rather, between the self and "my world".

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 s — RussellA

The standard perspective is that relations are attributions. As I said, they're similar to properties. Properties are predicates. The linking verb "to be" associates objects and properties, and this association gives rise to propositions.

Now you can go neutral monism and say that propositions are states of affairs, and that the world and language have some sort of sympathy with one another.

Or there are alternatives.

The metaphysical subject is not found in the world. It is not a relation between things in the world, but, rather, between the self and "my world". — Fooloso4

Ok. That doesn't comply with the quote you gave though. Plus for some reason you have brought up the T schema.

As regards Wittgenstein's Tractatus, the word "world" can be read as being either inside or outside the mind of the observer. — RussellA

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. That's why I'm intrigued to learn more. I've never had any interest in the Tractacus before. :grin:

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. — RussellA

Likewise saying that numbers exist outside of time and space (which just means they're not the kind of thing that ages or moves) doesn't explain anything. Nevertheless, number don't age, and are still independent of any particular mind.

That doesn't comply with the quote you gave though. — Tate

How so? No single quote can capture the whole of the steps of his interrelated argument.

Plus for some reason you have brought up the T schema. — Tate

Do you mean this?

Whether or not a proposition is true is determined by comparing it with reality. — Fooloso4

To compare a proposition with reality means that reality is not a mental construct. The facts, what is the case, is not a matter of how we conceive things to be.

Ha! I called it!

"Tractatus Logico-Philosophicus was first published in German in 1921 and then translated—by C.K. Ogden (and F. P. Ramsey)—and published in English in 1922. It was later re-translated by D. F. Pears and B. F. McGuinness. Coming out of Wittgenstein’s Notes on Logic (1913), “Notes Dictated to G. E. Moore” (1914), his Notebooks, written in 1914–16, and further correspondence with Russell, Moore, and Keynes, and showing Schopenhauerian and other cultural influences,". -- SEP on Wittgenstein

The Tractatus falls apart if the world is not objects and their relations. — schopenhauer1

So your argument is, if the Tractatus is wrong, then it is wrong.

Sure.

As for your points 1-3, you are making exactly the point made in the tractatus, that names cannot be specified, that words and explanations must come to an end, that the ladder must be thrown away.

You are agreeing with Wittgenstein.

And this is the point Wittgenstein returns to in his discussion of rule-following in PI, around §201.

I'm not going to let you get away that easily :wink:.

So your argument is, if the Tractatus is wrong, then it is wrong. — Banno

The Tractatus is wrong if it fails to prove the very foundation it stands on. It never even set out to do that. It's more that he never proves himself right, as he skips the foundation, assumes it, and goes from there. And if you're going to rebut with the whole

he was demonstrating his own values whereby philosophy cannot speak of things that can't be pictured.. — schopenhauer1

I will answer again:

But BECAUSE it is the very basis for which the picture theory "hangs" (get what I did there).. it MUST be discussed otherwise, Witty garners himself right by way of never having to prove anything outside of what he himself is claiming. How convenient that works.. "I make a claim, but it would be 'nonsense' to refute its very basis". Again, real convenient. — schopenhauer1

As for your points 1-3, you are making exactly the point made in the tractatus, that names cannot be specified, that words and explanations must come to an end, that the ladder must be thrown away.

You are agreeing with Wittgenstein. — Banno

Names cannot be specified? What do you mean about that? He specified that atomic facts are objects.

I make a claim:
Reality is the Will.

You say, "Prove it!"

I say, "Words can never get to what the foundation is, so don't worry about it. Let's discuss the conclusions that might arise if we take this very foundational claim as a basis.".

No, if that's the case, why should I take his claim as true? Why can't I see the world as really "Will and representation"? Why can't I believe the world is some sort of variety of processes that cannot be individually defined like a point in space-time?

I am not a fan of taking a really good post and ignoring most of its contents to then state somewhat vague things like:

As for your points 1-3, you are making exactly the point made in the tractatus, that names cannot be specified, that words and explanations must come to an end, that the ladder must be thrown away. — Banno

Can you attach any of that to my actual points? If it's too much then so be it. A conversation has to have two willing participants otherwise one person is doing most of the legwork. I can see why you like Wittgenstein if that's the case :razz:

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.

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 — RussellA

At first glance it looks like W is justifying correspondence theory by saying the world is linguistic in form. If the backdrop is Schopenhauerian, W's cosmology is pretty astonishing. I'm still looking for a good source. Gordon Baker?

Yet he mentions none of them, not even a “See Russell. See Schopenhauer. See Kant for the foundations of what I mean by object”. Objects are just assumed. Not even an “IFF objects are the basis for the world”..Why are you doing more work than him at his own argument?

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

He does not say that the world is linguistic in form. He says that the world is LOGICAL in form. It is this logical form that makes it possible for language to REPRESENT things in the world.