I take a very different view of what Plato was up to. This is, however, not an idiosyncratic view. There are well regarded scholars whose work led me to this.

What is often overlooked is the difference between the Socrates who knew that he did not know and the Socrates of the Republic who speaks of knowledge of the whole. One key to reconciling the difference is the banishment of the poets from the Republic. Their myths are replaced by a philosophical poesis. When asked Socrates is circumspect but clear in stating that he does not actually have knowledge of the Forms:

"You will no longer be able to follow, my dear Glaucon," I said, "although there wouldn't be any lack of eagerness on my part. But you
would no longer be seeing an image of what we are saying, but rather the truth itself, at least as it looks to me. Whether it is really so or not can no longer be properly insisted on. But that there is some such thing to see must be insisted on. Isn't it so?" (533a)

The truth as it looks to him may not be the truth, and he is not insisting that it is. But he insists that there is “some such thing to see”. What he shows us is a likeness of what the beings must be, that is, an image. He too is a poet, literally a maker. 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.

What should not be overlooked is that the training of the guardians is primarily in the development of moderation - sophrosyne. Those who are picked to advance to the study of philosophy will be those who not only have the requisite intelligence but the requisite temperament.

Maybe we need an all-rounded person with many life experiences? — Drek

During the discussion of who would make the best judges Socrates suggests that it would be those who have criminal experience, for they would be better able to recognize injustice than those who have not been exposed to it.

With regard to Plato I would suggest that just as the “city in speech” is not an existing city or a city we would want to live in, the soul, which is said to be the microcosm of the city, is not the soul that emerges in the dialogue. Just as the city requires “noble lies” so does the soul. The tripartite soul of the Republic is not an accurate description of an actual soul, it is, rather, a noble lie intended to bring harmony to the conflicting desires within us. Two hints in this direction are the description of the love of wisdom as erotic and divine madness. Both are immoderate and stand in opposition to the central importance of sophrosyne (moderation). Reason may recognize the necessity of moderation, but it is not reason that makes us moderate. This is why music and gymnastics are fundamental to the education of the guardians and philosophy reserved for the few with sufficient age and maturity.

My own feeling is that I would love for akrasia not to exist because then who could then judge another for it ! — Amity

Is weakness of will is like physical weakness? Do you judge yourself for your physical limits or judge others for theirs? There are things I am not capable of no matter how much I train and try. In addition, my willingness to train and try may not be very great to begin with. Is that a lack of willpower or simply a limit of my will?

Or, it may be that the whole notion of willpower is wrong. There may only be various and sometimes competing desires. It is not weakness of will that fails to stop me from eating cake, but that at this moment the desire for cake is stronger than the desire to lose a few pounds. But this is too simplistic. The story of competing desires is not an accurate description of the complex physiological and psychological things going on within me.

Is he saying that what was referred to as a paradigm, in 55, "something corresponding to the name, and without which it would have no meaning", actually exists in memory? — Metaphysician Undercover

He starts the quoted phrase by saying: “When we forget which colour this is the name of …”. What is not remembered is what the color “greige” means, that is, what color it is. We might remember the color of the foyer but not remember that the color is called greige. So if someone asked you to paint the bedroom greige it would have no meaning. If someone asked you to paint the bedroom the color of the foyer is some house you lived in years ago that color might be the same color the person who asked you to paint the bedroom means, but that might not be the color they had in mind.

Or what does he mean by "comparable" with a paradigm? — Metaphysician Undercover

It is the situation that is comparable. Suppose the person who wanted you to paint the room found a color swatch and wanted the room painted that color, but could not find the swatch to show you. The paradigm, in this case the swatch, is lost. It would be meaningless to ask that the room be painted the color of the swatch if there is no swatch.

He seems to say at 55 that an object cannot be such a paradigm because the name can still have meaning without the object … — Metaphysician Undercover

This does not mean that the object cannot be a paradigm but that a paradigm is not necessary when the connection between the name and the thing named has been made. When the name would have no meaning for someone without an example, a paradigm is used, an example. That example might be an object, but if one already knows that this thing is called “xyz” then “xyz” still has meaning even without the presence of an object.

If the paradigm is within the memory, and the memory is unreliable, then how could we ever know the correct use of the word?

In general, the meaning of a word is determined by its use:

“For a large class of cases—though not for all—in which we employ the word "meaning" it can be defined thus: the meaning of a word is its use in the language.” (§43)

If there were no physical paradigm then the correct use of a particular word might be in dispute. In some cases a dictionary could be consulted or examples of the use of the word in literature, but such cases are rare.

Irrespective of the amount of chess knowledge Alpha Zero may have, it doesn't possess the quale of knowledge. — Inis

That may be, but doesn’t that suggest that quale is not necessary for knowledge?

OK, I see that, but then he proceeds with "what if no such sample is a part of the language..." and proceeds from here. So it is still undetermined as to the criterion for "correct". — Metaphysician Undercover

Right, if there were no sample that could be used as a paradigm then there is no way to settle whether one remembers the color correctly. It is possible that the sample has darkened but it is also possible that one does not remember the color correctly.
Such indeterminacy or uncertainty is not something Wittgenstein is attempting to overcome. See below regarding rules.

One of the things you seem to have a hard time with, is that rule-following is intrinsic to the actions associated with linguistic activities. — Sam26

Indeed, language requires being able to follow the rules/logic/grammar of the language game. This is not something that is grasped all at once as a whole in a moment of insight. It often involves some form of correction and mimicry as the language game is learned. This applies to other rules as well. When, for example, one is learning the rules of chess, the pieces are identified and how they move is shown. When the player who is learning makes a move that violates the rules how the piece is allowed to move she is shown again. A more astute learner may learn simply by watching others play.

But not all games are played by rules that are set and clearly defined. Sometimes the rules are made as we go along by some kind of consent and agreement. There are no rules that stand as the rules for making rules. In addition, the existing rules may no longer be adequate when something new is learned, as in the case of quantum mechanics, where the Newtonian rules do not apply.

I follow, but clearly the point Wittgenstein is making at 54 is that there are different senses of "following a rule". On what basis would you choose one over the other as the correct sense? — Metaphysician Undercover

§54 is about the different functions or ways in which a rule is used in a game. In each case there is no confusion as to what rule is to be followed.

All I see is that it is stated, I do not see him rejecting it. — Metaphysician Undercover

There is a reason why it is in parentheses. The next paragraph begins -

“One might, of course, object at once …”

And concludes:

“An example of something corresponding to the name, and without which it would have no meaning, is a paradigm that is used in connexion with the name in the language-game."

The example serves as a paradigm for something that corresponds to the name.

I do not see where Wittgenstein makes this claim. In fact, if this were the case, then we'd have to rely on memory. But he explicitly rejects a reliance on memory at 56. — Metaphysician Undercover

If we are not in agreement that something is red we must rely on a paradigm that can be pointed to rather than what each of us remembers. If you do not know what “greige” is you can look it up and find that it does have a meaning, that it is a color, but since there are many colors greige is still meaningless unless you are shown a sample - from a paint color card or the color of the foyer, for example. They serve as a paradigm. The sample can be destroyed, the foyer can be destroyed, but there must be something that you can be shown that is used as a paradigm. “An example of something corresponding to the name …” (§55)

Do you not recognize that as blatantly contradictory? — Metaphysician Undercover

Two different senses in which one can follow a rule. The first means to understand what the rule is. You have indicated that you can follow the rule to fetch a red apple but choose not to. Do you follow?

How is that the rule? "Fetch a red apple" is the statement, what is said. — Metaphysician Undercover

It is grammatically in the imperative mood. It is an order or command or request. If you understand the grammar (the rule) you know it is telling you to fetch an apple. It is part of the language game of giving orders, and obeying them. (§23)

You should read the thread from the beginning, we covered that already. — Metaphysician Undercover

Well then you should know that it is not my “imaginary scenario”. Others pointed to the centrality of action, you disagreed.

Wittgenstein explicitly states that the name must have meaning even if everything is destroyed. — Metaphysician Undercover

Are you referring to the statement in §55 in quotes? If so, that is not Wittgenstein's position, it is one that is said that he rejects.

Once the connection between the name and the thing named is made the paradigm is no longer needed, but without the paradigm the connection cannot be made. If we read in an ancient text that someone took the “x” and threw it, the object named would have no meaning unless we knew what it was. If no “x” exists and nothing else is said about it then the name no longer has any meaning.

So it is clear that he is not thinking about a multitude of objects acting as the paradigm. — Metaphysician Undercover

What is the paradigm of a horse or a cat or a table? Where do we find the paradigm?

So we can conclude that "a paradigm" does not refer to any object, or a multiplicity of objects. — Metaphysician Undercover

Then what do you think it refers to? What are the examples that correspond to the name? What serves as a paradigm depends on that is being named. The paradigm of a rule will not be an object but the paradigm of a table will be.

Right now if someone said "fetch a red apple", I would not be in the least bit inclined to go to the store and get a red apple. — Metaphysician Undercover

Following a rule does not mean that one must follow it, but rather that one knows how to follow it.

So despite the fact that acting in a certain way may indicate that I know the rule, if there is such a rule, it's not a reliable way of indicating whether I know that rule. — Metaphysician Undercover

There may be cases where we cannot tell whether or not you know the rule, but if you consistently follow it that is a reliable way of indicating that you do know it.

And so it doesn't suffice as a premise, whereby we could conclude the existence of such a rule, because in each and every particular case when someone says "fetch a red apple", people behave differently. — Metaphysician Undercover

In this case it is not a matter of whether or not there is such a rule. “Fetch a red apple” is the rule. Those who consistently fetch a red apple understand the rule and how to follow it. Why some don’t follow it requires further investigation into the particulars of that case to determine whether they choose not to follow it or if there are circumstantial reasons that prevent them from following it or if the cannot follow it because they do not understand what to do.

As Wittgenstein demonstrates, there are problems with this imaginary scenario of yours. — Metaphysician Undercover

That was a direct quote from the text (§6). What problems are there?

You seem to missing the fact that it is made explicitly clear by Wittgenstein at 55, that this so-called "paradigm" cannot be a physical object, because the name must be allowed to have meaning after the physical object is destroyed. — Metaphysician Undercover

The object serves as a paradigm. It is something that serves as an example of what red means. If someone does not know what red means I cannot tell them to remember what it means or to look in my memory. The particular object I point to can be destroyed but there are others that can serve as the paradigm.

What the name signifies must be indestructible … — Metaphysician Undercover

What cannot be destroyed is what gives the words their meaning, it “is that without which they would have no meaning” (§55) A paradigm can be destroyed but then word would no longer mean anything . If you were the last remaining member of a tribe and everything owned by the tribe was destroyed a “rel” would mean something to you but not to anyone else. Since no “rels” exist there is nothing that can serve as a paradigm by which “rel” means anything for anyone else, and if you forget or die then it would no longer have any meaning. The paradigm would be destroyed.

First, we would have to say that there is a correct response, one which is according to the rule, because simple response is insufficient to demonstrate the existence of a rule. — Metaphysician Undercover

If you fetch a red apple whenever you are asked to then you know the rule. It is as simple as that. Fetching the apple is sufficient. What more do you think needs to be added? What is missing? Whether or not one is following the rule is determined by an action:

“We could imagine that the language of §2 was the whole language of A and B; even the whole language of a tribe. The children are brought up to perform these actions, to use these words as they do so, and to react in this way to the words of others.” (§6)

So in this sense, memory would be the "highest court" because it determines whether something has meaning or not. — Metaphysician Undercover

The paradigm is the highest court.

"An example of something corresponding to the name, and without which it would have no meaning, is a paradigm that is used in connexion with the name in the language-game." (§55)

A physical example is in general a more reliable paradigm provided it does not change. In addition, we are able to compare the sample with the name. I do not need to consult a sample of the color red each time I fetch a red apple, but if you fetch a yellow apple and say that this is how you remember the color red, then we can consult the sample to settle the matter of what red means.

Also, it suggests that meaning is not indestructible as was earlier suggested, because when the memory is gone, so is the meaning. — Metaphysician Undercover

I may forget what red means, but there are still samples or examples that serve as the paradigm. The physical sample is not indestructible but more durable and reliable than a memory. It would only be the case that red had no meaning if there were no paradigm, either physical or mental, that connected the name to the color.

I do wonder about the poetic description of chess as having some kind of 'truth'... — Amity

That was my first reaction as well, but after doing a search for “truth in chess” I found several articles, many of which also discuss beauty. The truth is the search for the best move or position, the one that proves superior to all possible countermoves. The player who can do this in every game knows the truth of the game.

I use the term ‘know’ deliberately because it challenges the assumption that to know entails some kind of subjective state. Alpha Zero has not been programmed to win, it has been programmed to learn, to teach itself how to win.

From an article in the December 26th issue of The New York Times about Alpha Zero:

… a machine-learning algorithm that had mastered not only chess but shogi, or Japanese chess, and Go. The algorithm started with no knowledge of the games beyond their basic rules. It then played against itself millions of times and learned from its mistakes. In a matter of hours, the algorithm became the best player, human or computer, the world has ever seen ...

By playing against itself and updating its neural network as it learned from experience, AlphaZero discovered the principles of chess on its own and quickly became the best player ever …

Most unnerving was that AlphaZero seemed to express insight. It played like no computer ever has, intuitively and beautifully, with a romantic, attacking style. It played gambits and took risks …

Grandmasters had never seen anything like it. AlphaZero had the finesse of a virtuoso and the power of a machine. It was humankind’s first glimpse of an awesome new kind of intelligence …

By discovering the principles of chess on its own, AlphaZero developed a style of play that “reflects the truth” about the game rather than “the priorities and prejudices of programmers,” Mr. Kasparov wrote …
https://www.nytimes.com/2018/12/26/science/chess-artificial-intelligence.html

First, I would like to compliment the participants for their courteous and respectful behavior.

As has been mentioned, Wittgenstein’s discussion should be viewed against the background of the Tractatus. The basic assumptions of the Tractatus is that there are simple objects and simple names that correspond to them. Underlying the relations between simple objects and simple names is a logical scaffolding that determines how they can be combined. In the PI he rejects each of these assumptions - simple objects, simple names, and the underlying logic of relations.

Instead of a transcendental, invariant logic that underlying both language and the world it pictures he is now investigating rules - rules of games and rules of language games. Rules do not exist independently of the game of which they are the rules. There are no rules for rules - that is, no rules that allow or disallow what can be a rule of a game, and no rules for how rules are to be followed. Games do not simply follow rules they can create rules as the game is being played. Language is not simply a rule following activity, it is also a rule making activity, an activity determined by the activities we are involved in.