So, a new way of doing business. Stir the country up with issues of racism, then watch the stock market. — Brett

The example was set by the present day American president, except the polls were being watched rather than the stock market (not much difference there though).

One thing I brought up in another thread about this is that we could say that two things "match" when they're structurally similar--for example, two shirts that we'd loosely call "the same shirt."

But when we're talking about the correlation between a proposition and a state of affairs, surely we're not saying that they're similar in that way, are we? (And beside that, extramentally, we have nothing to make a determination that they're similar.)

With the DNA example you use, we're talking about a physical process that manipulates materials in a particular way. If we're proposing this for a way that correspondence can work when it comes to something like truth value, what analogous (to DNA) physical process are we talking about? — Terrapin Station

The issue is "meaning". I think there is far more meaning in two extremely complex things like DNA which happen to match, than there is in the correlation between a proposition and a state of affairs. In comparison, the correlation between a proposition and a state of affairs is extremely simplistic, while the correlation between replicated DNA is extremely complex. Don't you think that the complex correlation is far more meaningful than the simplistic correlation?

Proposition: (1) is not logically valid, where (1) refers to the proposition (∃x)(x=x) (∃x)(x=x)(\exists x) (x=x) — Kornelius

That's the point, the law of identity is a metaphysical assumption, so of course it's not logically valid.

The Law of identity is held as a law that is logically true. — Kornelius

No, the law of identity is not held as a law which is logically valid. It is held to be true, and perhaps even sound, depending on how you define "sound", but it is not held to be logically valid. The three fundamental laws, identity, non-contradiction, and excluded middle, are all held to be true, but not one of them, on its own, is logically valid.

Does CK want to separate (somebody, himself, whoever) from the American Revolution? Maybe he feels it was an inadequate revolution? Too bourgeois? Just a bunch of privileged anti-tax whiners? Not a revolution for the slaves? Perhaps his criticism was too timid? — Bitter Crank

There was a civil war (whatever that means), and there were reasons for that war. The flag is a symbol of the political state, and there are many degrees of separation between the political state at the time of the American Revolution and now. As much as we may celebrate our independence with fireworks, military parades, or whatever the hoopla, there is separation between the political state then and the political state now. The name "Rome", carries on, and we think Rome has been around for thousands of years. There could even be a Romulus and Remus day, celebrated by some with great fireworks, but that political state is gone. The flag represents the political state, and the political state exists as the ideology, which is gone because we do not support it. Why ought we support that flag?

Hilarious over-analyzing and indignation over what is a straightforward non-issue. — Maw

Nike likes to create the sensational non-issue. It utilizes the oldest trick in the advertising book, free publicity from controversy. And since they're very careful to choose a non-issue, it can't backfire. Ever think it may have all been a setup? How many "discontinued shoes" are there going to be out there in the world, as expensive collectors items?

Got an argument, or perhaps minimal criterion for correlation(what all correlation is existentially dependent upon)? — creativesoul

Argument? If you do not believe that there's a correlation between the two distinct instances of DNA, when DNA replicates, then just say so. But I think that's a silly argument on your part.

The US dime used to bear what was a symbol of Italian fascism--the bundle of sticks and an axe called the fasces. It was an ancient Roman symbol. — Bitter Crank

The word "fascism" is actually derived from that Latin bundle word, "fasces", as is "fascine" which is a type of faggot. But the English, "fasten", is supposed to have a completely different, Germanic origin. Isn't that fascinating? The English can fasten up a faggot without being fascist. Well of course, not even if you're the fastest to fasten up a bundle, it doesn't mean you're fascist. None of this could be fastenating though, because "fasten" only sounds similar "fascin", and has a similar meaning, but they're different words. So they must be spelled differently to ensure that separation.

And, there's a reason why the American flag has fifty stars and not some other number. Though it might be history, there is a separation here. What was once an accepted symbol may not be acceptable today, if it reminds us of something we want to separate ourselves from.

All things are identical to themselves. Which is exactly the formulation I discussed and exactly the principle that implies nothing with respect to the number of existant objects. — Kornelius

Do you not recognize the difference between "a thing", and "all things"?

The law of identity states that a thing is the same as itself. What justifies you formulation, that all things are the same as themselves, other than induction? The law of identity is not an inductive principle.

The whole is the interdependent things, there is no sense in saying that these interdependent things are independent, independent from what? — leo

Doesn't "whole", as a complete unity, signify to you, an independent thing?

All talk about information being within cells, rna, dna, etc. dubiously presupposes meaning where there is no creature/agent capable of drawing correlations between different things. — creativesoul

When DNA replicates, it's quite clear that something is making a correlation between distinct things. If there was no correlation, it would not be a replication. So if agency is necessary to draw correlations between distinct things, then agency must be involved in DNA replication.

Push hard enough on the notion of information and a conflation between causality and meaning takes place — creativesoul

What are you saying, that information is meaning with causal power? But you wanted to remove agency, that's what I objected to. Meaning cannot be causal without agency. The form of causation here is commonly called "final cause", what you refer to as "the intent to acquire a desired result", and agency is implicit within this concept of "intent". Clearly, when we speak of "information" in this way, the assumption of agency is warranted, and cannot be overlooked.

Call it however you want, my point is nothing interacts with nothing, rather a thing interacts with other things which themselves interact with other things and so on, so there is an interacting whole, and so if instead of considering the whole we single out a thing, and model how it appears to interact with some other things, and then say that the whole is governed by these interactions, then we're not actually modeling the whole, we're modeling a world we made up that matches the whole in some limited ways but not at all in some other ways, we're missing essential parts of the whole, and that's the issue I'm pointing out, fundamental physics does not model our world, it models a world physicists made up. — leo

You haven't justified your assumption of a "whole". Just because things interact doesn't mean that there is a whole. You proceed from the observation that things interact, to the conclusion that there is a whole. But why, what makes you believe in a whole? Isn't the "whole" just the concept of "independent thing" transposed, to include all other things as parts of that thing? So the assumption of a "whole" is just the disguised assumption of an independent thing, which is what you were trying to get away from in the first place. Dismissing "independent thing" for "whole" does nothing for you because a whole is necessarily an independent thing.

I would take issue with him on one point: he held seemingly contradictory views. On the one hand he argued against the existence of the Actually Infinite and on the other he argued for eternal time (which is a form of Actual Infinity). Aristotle’s arguments for Eternal/Infinite time: — Devans99

Actually, in relation to "the eternal", what Aristotle argued is that anything eternal must be actual. So the infinite is argued to be potential, and the eternal is argued to be actual. This produces a separation between "infinite", and "eternal", as categorically distinct, and lays the ground work for a conception of "eternal" which is other than infinite time. This is the sense of "eternal" which is more commonly expressed in metaphysics, meaning outside of time.

God cannot have a temporal start or end to his existence. He would just 'be' with no tense. God would be both finite and eternal - which is only possible outside of time. — Devans99

Right, this is that sense of "eternal", "outside of time".

I cannot overlook the backdoor smuggling of agency when there is none warranted. All talk about information being within cells, rna, dna, etc. dubiously presupposes meaning where there is no creature/agent capable of drawing correlations between different things. — creativesoul

Actually, agency is warranted. How do you think DNA could replicate without agency?

I am not sure where you are getting this and why you think it is true. Could you clarify? In no suitable formulation of the law of identity would it be valid only in a model with exactly one and only one object. How would you even formulate this? I take it something like this: — Kornelius

The law of identity states that a thing is the same as itself.

But this is no law of logic, and certainly not a law of identity. It is fairly simple to provide a model for which the statement is false. Therefore, it is not a law of logic. Logical laws are true in every model, not just some models. — Kornelius

That is our point of disagreement. My claim is that the law of identity is not a law of logic, it's a metaphysical assumption. You think it's a law of logic. Because of this disagreement, I do no think we will ever find an expression of the law of identity which we both agree with.

This is from your wiki quote:

the law of identity states that each thing is identical with itself

So we seem to agree at this point. My question to you is how do you proceed from the proposition "each thing...", to your formulation "for all x...."? Notice that the former refers to particular, individual things, and the latter refers to a group of things. Your formulation appears to have a veiled inductive conclusion, inherent within. You must apply inductive logic to "each thing is identical to itself, to derive "all things are identical to themselves". Therefore your formulation is one which has been polluted by inductive logic.

At this point, we need to recognize and respect the difference between learning an order (memorizing it), and applying a principle to create an order (application). One can learn, memorize, the numerals from 0 to 9, and reproduce them, over and over again correctly, without having grasped the principle of application. Knowing the principle of application is what enables the person to proceed in recreating the same order in higher numbers. Wittgenstein is now proceeding to emphasize this distinction, the difference between learning something through memory, therefore being able to repeat it from memory, and knowing how to apply a principle, whereby the person might take what has been learned from memory and proceed through application of a principle, to use what has been memorized, in completely new situations. Only when the person is capable of proceeding in application, has the person "understood the system". Now he will proceed to investigate, what signifies to us, that the person has understood the system.

Shannon's equation quantifies information, which he defined as the reduction of uncertainty. — Galuchat

This definition of "information" just begs the question. Certainty is subjective (of the subject), so a change to the degree of certainty, "information", must also be subjective. How can we account for any naturally occurring information with a definition like that?

So then it appears that the very concept of independent thing is flawed. — leo

As independent things is the simple way of looking at the world. And there is much empirical support for this. We see things as distinct from each other, and we can take these distinct things and move them in different directions, separate them and do different things with them. There is good empirical evidence to suggest that things really are distinct from each.

When we talk about these distinct things interacting with each other, this is based in observations of past interactions, and the possibility of future interactions. We do not observe that all things are necessarily interacting with each other, but we have seen interactions, and we propose that there is the possibility for all things to interact. So your conclusion "it's all an interacting whole", isn't quite right, because all interacting is just a possibility.

To designate what we see of reality as "a whole", requires a unifying principle. We do not see this unifying principle, and there is no empirical evidence for it, because it is the "possibility" of interaction. So to reify your whole, we need to validate this "possibility". In the past, this was accomplished through the concept of "time". The entire visible universe was assumed to share the very same present, "now". This was the principle by which the universe was assumed to by a unity, one whole. "Possibility" was validated by the division between future and past, created by the present. Modern principles of physics have removed the reality of the present, "now", thereby dismissing the principle which provided for the unity of "the universe". Speculators now attempt to re-establish a principle of unity in various ways, like a theory of everything.

I apologize: I should not have assumed you were familiar with this; that is completely on me. I am employing standard first-order logic notation. The statement (∀x)(x=x) (∀x)(x=x)(\forall x)(x=x) says "for all x, x is identical to x." — Kornelius

This is the problem then. That is not the law of identity. The law of identity does not allow that there is more than one X. When you say "for all X...", you have already allowed the possibility of more than one X, thus breaking the law.

Please let me know if there is any step that isn't clear! — Kornelius

What is not clear is how you get from the law of identity, as commonly stated, to your formulation of it. And I'm sorry to be the one to inform you of this, but your example fails because it utilizes a formulation of the law of identity which is already itself in violation of the conventional law of identity.

It's the "information in the head" situation. We located it there because we didn't want knowing to be an activity that's smeared across the universe. Too mind-of-Goddish. — frank

You know there's a difference between information and knowledge, don't you? That there is information all over the universe does not mean that there is knowledge all over the universe. I seek information so that I can have knowledge. When I find the information which I am looking for, it does not go into my head and become knowledge. Other people can find the same information which I find, and produce their own knowledge which is not the same as my knowledge, based on that same information. Clearly the information does not go into my head, if others have equal access to it. How could the same information go into all those different heads at the same time?

I don't see how "having information scattered all over the environment", which appears to me to be an accurate description, (imagine if you could see microwaves, the pollution! - out of sight, out of mind), leads to behaviourism, or panpsychism. That's quite the stretch.

I agree, the distinction between description and reality is relevant here. The law of identity attempts to get right to reality, independent of what we say about it, by placing the identity of the thing right within the thing itself. There's a critical point which needs to be understood though, and that is that anything we say about the thing is always going to be something said about it, and not part of its real identity, what's within it. So the law of identity itself is always going to suffer that problem of being something said about reality (descriptive), though its intent is to say something true, real. That is why it is an "assumption". The formulators of the law have looked for the most fundamental, the most widely applicable principle in relation to "reality". So, recognizing that anything we say about reality will necessarily be descriptive, the law of identity is an attempt to say the most important thing about reality which can be said, and that is to emphasize this separation, and put the real identity of the thing within the thing itself, rather than within what we say about it. The assumption is that this separation is true, real. That's what the law of identity gives us, is an indication of the separation between the true identity of the thing, which is within the thing itself, and the identity which we assign to the thing. The thing itself is an object, but in grammar the object is represented as the subject, and this is that separation, predication is of the subject. And that separation must be maintained.

To be able to properly apply the law of identity requires that one understand the law. Leibniz's "identity of indiscernibles" is an application. Simply put, it tells us that if there are two distinct things, then they are not identical (i.e. not the same thing), and conversely, if there is no difference between what appears like two distinct things, then it is actually one thing (the same thing).

but what the people here think about Aristotle work? It's outdated, or have much more to say that all modern philosophy? — Gilliatt

Good philosophy is never outdated.

What's wrong with that? The detective goes looking for clues, relevant information.

I can't see that the law of identity makes any ontological claim at all other than that 'objects' might have static fixed identity rather than dynamic continued functionality. But that is the essence of the OP and the basis of the pseudo-problem of the Ship of Theseus. If that is what you are driving at then I agree. — fresco

No, it's not really what I'm driving at at all. To think that the law of identity states that an object has a static fixed identity is a misunderstanding of the law. What the law does is place the identity of the object within the object itself, rather than within a description or a name. Therefore the identity of the object is just as dynamic as the object itself is, because an object's identity is the same thing as the object. "An object is the same as itself". But what the law does, which requires a metaphysical assumption, is to state that there is something there with a temporal continuity, an object. This is required in order that it may actually have "an" identity, rather than a multiplicity. And, despite all the changes which are occurring, there is something which is remaining the same, which has an identity as "the object". This is why it is an ontological principle.

The Ship of Theseus is a pseudo-problem because it starts with the ontologically based premise that there is an identified object called the ship of Theseus, and that this thing has some sort of temporal extension. Once you recognize that there is no necessity by which such an assumption is produced, the problem disappears because the name could be applied arbitrarily.

Really, I'm afraid that the Trump phenomenon is just a symptom of the social disease which has infected us. Check the man's approval ratings. As it appears that very little is being done to diagnose the disease, let alone cure it, we're probably in this degenerative condition for the long term.

Kornelius os correct as far as logic based on 'set theory' irrespective of whether an 'object' or ' member of a set' can be said to 'exist in the world'. Indeed 'existence' is a whole other ball game transcendent of the one we usually call 'formal logic' — fresco

Yes, but my point is that the law of identity transcends formal logic as well as the notion of 'existence", and that is why it is an ontological principle rather than a principle of logic. It is evident that the law of identity transcends logic by the fact that there are two incompatible forms of identity, what is referred to as qualitative and numerical identity. That these two are incompatible, and cannot be synthesized into one, is demonstrated by the riddle of The Ship of Theseus.

Whichever of the two forms of identity that you choose to employ in your logical endeavours, will determine the outcome of your logic, like a premise. Sure you can take "what a thing is", without that thing having existence (like a symbol which represents nothing), and proceed to apply logic to this "what a thing is", but then you necessarily use qualitative identity. However, the law of identity clearly deals with numerical identity, the thing itself. So all you do in this case is separate "what the thing is", from the thing itself, and circumvent the law of identity. Therefore this logic which you refer to, does not actually employ the law of identity, it avoids the force of the law by hiding behind the illusion that qualitative identity is identity in the sense of the law of identity. But it is not, so it violates the law of identity by choosing qualitative identity as a principle, instead of numerical identity, which is required by the law.

But we know now, because of mathematical advances in logic, that this principle does not assume the existence of anything. The statement (∀x)(x=x) (∀x)(x=x)(\forall x) (x=x) is made true by any model that assumes no objects: it would be vacuously satisfied, and therefore true. — Kornelius

I'm not familiar with your use of symbols, but there is an object assumed, or else there is nothing identified. The object need not be a physical object, are you familiar with mathematical objects? If your statement identifies a mathematical object, then this is an ontological statement, it gives reality to that mathematical object, as an identified object. Perhaps your symbol is the object itself, I don't know what your symbol symbolizes. And a model with no objects makes no sense to me, because the model is itself an object.

It is simply incorrect to say that the statement that every object is identical with itself implies (or presumes) that an object exists. It does not. — Kornelius

That's true, the law of identity itself, does not give existence to any objects. But when the law of identity is used, when an object is identified, then the object necessarily exists, as the object which it is. Otherwise the law of identity is violated. You cannot claim that a specified object is identical to itself, and also say that there is no such object, without launching yourself into nonsense.

I am sorry to be blunt, but this is simply incorrect. As I said: every model validates it, no matter whether no objects, some objects or infinitely many (countable or uncountable) objects exist. — Kornelius

You can say that, but your claim is wrong. Try to demonstrate it, why don't you? Show me a model with no objects which validates the law of identity.

That's basically what I was trying to tell Kornelius. It's an ontological principle because it produces the logical necessity that there is such a thing as what is being referred to with "A", or else the principle is just nonsense. If there was not a particular thing which is referred to with "A" you could refer to anything as A. So the law of identity necessitates the existence of the thing identified.

The law of identity is a law of logic; it is not an ontological principle. Perhaps you mean Leibniz's law of indiscernibles? — Kornelius

No, I mean Aristotle's law of identity, which is an ontological principle. It states that a thing is the same as itself. It is ontological because it assumes the existence of the thing. Without the existence of the thing the principle makes no sense. So if any logicians make use of this principle, they are making use of an ontological principle.

The law of identity is most certainly a principle of logic, not of metaphysics. — Kornelius

It may be the case that logicians make use of the principle, but to classify the principle itself, we need to see what validates it, and that is an ontological assumption about the existence of a thing. So it is a metaphysical principle. For example, there are many "scientific principles", and this means that the principles are verified by scientific methods. But when some scientists speculate about metaphysics, and employ metaphysical principles, we cannot call these principles scientific principles just because scientists are using them. Likewise, when logicians employ the law of identity, they are employing a metaphysical principle not a logical principle. It is ontology which states that a thing cannot be other than itself, not logic. What sort of logic do you think one could use to determine that a thing could not be other than itself?

145: The imaginary pupil is supposed to have learned to write the series 0 to 9 in the way which we call correct, consistently, numerous times. Wittgenstein now proposes that he teach the pupil the recurrence of this series in "the tens". At some point, we can decide that the student has the capacity to continue the series independently. We can say that he has "mastered the system". But how far must he be able to produce the series, before we can draw such a conclusion? "Clearly you cannot state a limit here".

As an aside, which may or may not be relevant, it may be useful to note that there is a significant difference between learning to count the numbers verbally and learning to write the series of numerals. In writing, we learn the digits, 0 to 9, and all the following numbers can be represented infinitely, from repeating these digits in distinct patterns. In counting verbally, we need to learn new names as we go "twelve", "thirteen", "twenty", thirty", "hundred", thousand", "million", etc.. So, whereas the writer of the symbols may obtain the capacity to continue the series indefinitely, independently, the speaker of the numbers cannot continue independently because one must always learn new words continuously, as one gets to the higher and higher numbers. There is no formula for creating the words for the numbers, which would allow one to continue indefinitely, as there is for creating the written symbols, because we must learn distinct conventions as we go.

There may be a hidden reason why Wittgenstein's example consists of learning written numerals rather than consisting of learning the numbers we count verbally. He may be trying to reveal this problem to us. In real educational situations, we learn to count verbally first, because aural training is much more efficient. When we proceed in our education, to the point of writing the numerals, as in Wittgenstein's example, we already have an understanding of how to count. So we do not really proceed simply from this process of learning how to write the symbols, to mastering the system, because there is another important ingredient which is learning how to count, which we learn through the aural process. There is an important synthesis, as we pass from learning spoken orders to learning written symbols, which is somewhat neglected here.

This may become more evident later when he discusses "reading" . Reading is completely sound oriented. The symbol represents a sound, whether imaginary or aural, and orderings are learned through verbal demonstrations. We are able to discern that M comes after L in the alphabet, by saying this part of the alphabet within our minds.

I believe you are importing metaphysical claims into the law of identity. The law itself is completely neutral with respect to whether or not an object is the same (or different) after undergoing certain change. — Kornelius

I think the law of identity is itself a metaphysical claim. So it's not a matter of me importing metaphysical claims into the law of identity, it already is a metaphysical claim.

We could take a radical metaphysical position and insist that objects can only be self-identical for any given time slice t tt. But here too, the law of identity would apply at any given time slice. The law is completely neutral here. — Kornelius

Are you familiar with the two distinct forms of identity, sometimes called qualitative identity and numerical identity? Qualitative identity allows that two distinct things, with the very same description, are "the same". Two cars off the same production line may be called "the same". In this case, identity is a function of the thing's description, "what" the thing is. Two human beings are "the same", by virtue of being within the same category, human. I call this logical identity, or formal identity.

Numerical identity, on the other hand, distinguishes one distinct thing from all other things. So the two cars from the same production line are not really "the same" car according to numerical identity. But numerical identity is based in the material existence of the thing, it is not based in a description of "what" the thing is, nor is it based in any particular logical formula whatsoever. I would say that it's based in an observed temporal continuity of existence. This is why the same car can get scratches and dents, new parts and new paint job, and still continue being the same car. This type of identity, which I call material identity, is based in the ontological assumption, "that" the thing is (an existing thing), it is not based in "what" the thing is. Are you familiar with "The Ship of Theseus"? This ancient riddle conflates the two distinct forms of identity (which were not well distinguished at the time), to pose an interesting question.

OK, so let's assume it's as you say, it's only the reader being referred to with "he" here at 144. The reader says "I can imagine that too", and this means that the reader imagines this as well as something else, and so, the reader's way of looking at things has been changed. What changed the reader's way of looking at things is understanding the phrase "And here too our pupil's capacity to learn may come to an end."

What is required then, is that we, as the readers, imagine that the student's capacity to learn has come to an end. Has anyone here, other than me offered an explanation of (i.e. an imaginary scenario) within which the pupil's capacity to learn has come to an end? I have produced this imaginary scenario, which Wittgenstein asks for, this other way of looking at things, in which the student's capacity to learn has come to an end. Regardless of what "he" refers to, I have explained how the student's capacity to learn has come to an end. Do you understand this? Do you have an imaginary scenario within which the student's capacity to learn has come to an end?

The problem here is that Wittgenstein has given us an example which cannot be related to anything real, therefore we cannot make sense of the example. The fact is that we learn to count through verbal training (repeat after me), not through the use of written symbols. So he has given us problems which are completely unrealistic, and cannot be comprehended, because they could not occur in they reality of education. In reality, the student learns the order of numbers through hearing them, so the mental image is an aural image, and not a "picture" at all. The order is a temporal order, (two comes after one) and is acquired by the learner through a process of memorizing. We do not learn orders by observing right to left, or left to right on a paper, (though we might learn them with a progression of flash cards, but speaking is more efficient and natural). We learn orders through memorizing a temporal progression of sounds, not a temporal progression of visual images. So Wittgenstein's example, of learning an order through written symbols does not make any sense to us.

You're reading too much into "he". — Luke

It's not a matter of what I'm reading into "he", it's a matter of determining the proper referent of "he". If "he" refers to the pupil in Wittgenstein's example, who requires having our method taught as an offshoot, or variant of his method, and may therefore have his capacity to learn come to an end here, instead of what you claim, that "he" refers to the reader of the text, this is a substantial interpretational difference.

Furthermore, what alternative picture does Wittgenstein put before the student (other than the "picture" of the series of numbers which are written down and placed before him)? What "way of looking at things" is required in order for the student to copy the numbers on the page in front of him? — Luke

Remember, the "picture" here is in the mind, a mental picture. that is how Wittgenstein has described understanding words, as associating them with mental pictures. Teaching the pupil would constitute changing the pupil's mental picture. If the pupil's capacity to learn has come to an end, then our capacity to change his mental picture, (his way of looking at things), has come to an end. It really doesn't make sense to assume that Wittgenstein is talking about changing the reader's way of looking at things.

There is a dichotomy between we and he at 144. We have a normal way of looking at things, and do not make systematic mistakes in counting numbers. He, the theoretical student has an abnormal way of looking at things, and needs his systematic mistakes corrected. Correcting a person's propensity for a systematic mistake requires changing one's way of looking at things.

Furthermore, what alternative picture does Wittgenstein put before the student (other than the "picture" of the series of numbers which are written down and placed before him)? What "way of looking at things" is required in order for the student to copy the numbers on the page in front of him? — Luke

Having the appropriate "picture" associated with the appropriate words is how Wittgenstein has been describing "understanding". So, for the person to properly understand the "formation rule" involved in counting the numbers, it is required that the person has the appropriate "picture". If the person is making systematic errors, it is necessary to change that individual's way of looking at things.

This is not intended to be some sort of theory of developmental learning. — Luke

Oh, then what is it? He distinguishes random from systematic mistakes in a theoretical way, and says that there is no sharp distinction between the two. How is this anything other than theory?

The second line of the above quote relates to the first, as he then asks whether it was his objective to draw our attention to the fact that we could imagine that. — Luke

Sorry, to have to reiterate, but he doesn't say "we", he says "he", referring to the theoretical student.

Isn't that a very odd (or oddly phrased) question? Why would Wittgenstein ask it? — Luke

I think it's poorly phrased, yes, that whole little section 144 is, that's why it's so hard to understand, but if understood properly it's not odd at all. He's explaining why we come to the end of the person's capacity to learn, if we have to correct his systematic mistakes by teaching him our methods of procedure as an offshoot or variant of his own.

There's two options given for correcting a systematic mistake. One is to wean him off a bad habit, the other is to teach him our way as an offshoot or variant of his way. If we correct his systematic mistakes in the way of correcting a bad habit, then we change his way of looking at things, he sees his old way as a bad habit which must be broken. This demonstrates that he is open, and accepting of having his way of looking at things changed. He is therefore capable of further learning.

If we can only correct his mistake by having him learn our method as an offshoot of his own, we do not change his way of looking at things. He does not see his way as a bad habit. This is because he is not open and accepting to having his way changed, and so his capacity to learn from us is limited by this. If he proceeds in doing it our way, it is what I called above, a pretense (and Wittgenstein will get into pretending later). It's as if he is saying I'll do it your way, just to please you, and get past this step, but I do not agree with you, and you will never get me to see things your way.

At 144, he asks: "What do I mean when I say “the pupil’s ability to learn may come to an end here”? ...what am I doing with that remark?" — Luke

Right, he asks that question and answers it with this:

:

Well, I should like you to say: "Yes, it's true, you can imagine that too, that might happen too!"—But was I trying to draw someone's attention to the fact that he is capable of imagining that?

Notice, he begins by speaking to "you", "you can imagine that too". Then he proceeds in this way. "But was I trying to draw someone's [a reader's] attention to the fact that he [the fictional pupil] is capable of imagining that?"[No, he's not.] And then he proceeds to talk about that fictional pupil. "I wanted to put that picture before him, and his acceptance of the picture consists in his now being inclined to regard a given case differently: that is, to compare it with this rather than that set of pictures. I have changed his way of looking at things."

You, the reader are capable of imagining what Wittgenstein asks, the fictional pupil is not. Wittgenstein says "I wanted to put that picture before him...", and "his acceptance of the picture" would incline him to look at the case differently, thus Wittgenstein would "have changed his way of looking at things. However, Wittgenstein could not change the fictional pupil's way of looking at things, the best that could be done according to what is stipulated by the example, is "to teach him ours as an offshoot, a variant of his" way of doing things. So the pupil's ability to learn may come to an end here. His way of looking at things has not been changed, and it may well be that it cannot be changed.

We have two distinct sets of circumstances in which the pupil's capacity to learn the formation rule comes to an end. One is when he is making random mistakes, and the other is when he learns what appears to be the correct way, as an offshoot or variant of his own way (pretends). In the latter, he is incapable of imagining the correct way because he will not release his own way of imagining things. We cannot change his way of looking at things. because he has found a way to incorporate, or subsume, our way of looking at things within his own way.

Ultimately, he says, he wants the reader to "regard a given case differently"; that is, he wants to change the reader's "way of looking at things". — Luke

I don't agree with that at all. He's talking in the third person, referring to "him", "he is capable of imagining that?", "put the picture before him", "his way of looking at things".

He is clearly talking about the pupil who's capacity to learn has come to an end, not the reader. He is saying that the person whose capacity to learn has come to an end is incapable of recognizing that his own capacity to learn has come to an end. "But was I trying to draw someone's attention to the fact that he is capable of imagining that?" In this sentence, "he" refers to the pupil of 143, not to the person whose attention Wittgenstein might be trying to draw. He already said he would like "you" to imagine that, in the prior sentence, now he is asking whether the pupil ("he") is capable of imagining that, what he wants you to imagine.

Consider that he has distinguished between teaching him the correct way (what is accepted by us, "our way"), and teaching him the correct way as an offshoot of his own way. "His way" remains the principal way for him, and his way is not the correct way. However, we manipulate him, and "his way", until he produces an acceptable facsimile of our way. This is a sort of pretense. He pretends to be doing it our way, when really he's doing it his way and making a representation of our way. His capacity to learn "our way" comes to an end here because the teacher has no way to distinguish the pretense from the real, to bring him around to doing it the correct way, and the pupil has no way of imaging the other way, and the fact that his way is not the correct way.

In the section where Wittgenstein describes reading, he will elaborate on such pretense, pretending to read.

The Forms are, ironically, images. Those who read Plato and think that they have ascended the cave because the Forms, the eidos, the things themselves as they are in themselves, have been revealed, are simply seeing new images on the cave wall, images created by Plato. — Fooloso4

That's a load of crap. Plato is pointing our minds toward the Forms, he is not claiming to reveal them to us. We cannot see them, we can only apprehend them with our minds, so there is nothing for him to reveal, you must grasp them directly with your mind. Nor is Plato creating images.