§61-§64

§61-§64 is an extended discussion about the difference and/or similarities between the two ways of playing the ‘game’ set out at the end of §60. I’m going to treat these sections together. To recall, the game is one in which either (1) only composites have names; or (2) only parts have names and the composites are described by means of them.

Without getting too far into it, Witty basic point seems to be: the two ways of playing the game can be identified, but it is not necessary that they are. As per his modus operandi at this point, Witty makes their identification hinge upon a conditional: if certain conditions hold, then they can be identified. If not… well, there’s no reason to assume the identity of the two ways of playing the game. As to what conditions these might be, Witty basically leaves this open - those conditions cannot be specified in advance. They’re the sort of thing that require examination ‘close up’ (§51).

That all said, Witty does make the stronger point that it is important not to make any assumptions about the identity of the two ways of playing the game: doing so might ‘seduce us’ (§63) into thinking that (2) is a ‘more fundamental form’ of (1), playing an explanatory role with respect to it. But this ought to not be the case if any attempt to identify the two ways of playing the game is conditional upon certain conditions holding. Basically, its important not to be ‘seduced’ into thinking in the manner of §46 - the passage of the Theaetetus - where simples always serves to explain composites.

Note, in this connection, how a great deal of the preceding discussion between §46 and now has been about actually qualifying Socrates’ statement (in a way that changes its status drastically): yes there are some cases in which simples cannot be ‘further analyzed’ (the Paris rule is neither a meter not not a meter long; red neither can be said to exist or not exist), but this is the case only if (conditionals again!) those simples play particular roles in particular language games. The conditioning here is grammatical (and thus revisible) and not metaphysical (and thus fixed), as it were. Hence why §64 ends by simply arguing that the two ‘ways of playing the game’ can in certain circumstances simply correspond to different language-games altogether (one in which the ‘simples’ have different roles in each, I imagine).

Anyway, if what I’ve written here has the flavour of a summary, it’s because I think these parts serve to ‘end’ the discussion simples and composites began in §46. So, zooming out so far the PI has covered something like:

§1-§27: Imperatives (block! slab!)
§28-§36: Demonstratives (this, that)
§37-§45: Names (Nothung, Mr. N.N.)
—
§46-§64: Linguistic Roles (Simples, Composites, and Iterations thereof)

It is implied that red is a thing which exists when we say things like "red is a colour". So we do use red in this way, like if I were to say "I know what red is", or "red is my favourite colour", etc.. I agree that Wittgenstein's solution is to say that what this means is that there is something which has that colour.

But as per my discussion with Fooloso4 on this subject, I am not convinced of this solution. We can say "red is a colour", and "red" can have meaning, in that context of being designated as a colour, without there being anything which has that colour. We can know "red is a colour" without there being anything which has that colour. So it appears like we can give words like "red" a meaning through a definition like that, so that the word has meaning within that logical structure, without the necessity of there being a thing which has the colour red. So it seems to me that Wittgenstein's solution doesn't really capture what it means for "red" to exist in the imagination. There doesn't need to be a thing which has the colour red, for "red" to have meaning, because "red" can have meaning by definition (or context within a logical structure). — Metaphysician Undercover

I don't see what you're getting at here except that we can make up a name for a non-existent colour (when would we ever use such a name?). Anyhow, what does this have to do with the phrase "Red exists" or our preceding discussion?

I disagree. I think we commonly use "red", as well as the other colours in this way. For example: "Red is my favourite colour". "I pick red as the colour to paint my room." "What colour is it?" "The primary colours." "The colours of the rainbow." "Blue is the colour of the sky". And so on. — Metaphysician Undercover

My comments were made in response to your use of the statement "Red is a colour", not any of these other statements.

But notice that there seems to be a special requirement. "Red" is used here in the context of "colour", and it is this context of usage which gives the impression that red is an independent thing. It isn't an independent thing though, because it relies on this necessary relation with "colour" for its existence (via usage) as a thing.. This is the "essentialism", or necessity within a concept, which Wittgenstein may be trying to reject, or at least showing that it can be rejected. When red is defined as necessarily a colour, it gets existence as a thing, by being restricted to being a member of that category, "colour". — Metaphysician Undercover

I don't think anybody is questioning whether red is a colour.

In Wittgenstein's upcoming discussion of concepts, he removes all of this nonsense of a constructed necessity, (boundaries are constructed for a purpose), to get down to the bare bones of what a concept really is. — Metaphysician Undercover

I don't see it as "getting down" to any "bare bones". He just tries to describe, and urges us to "look and see" (§66), how language is actually used. §93 may also be relevant here.

Perhaps it is because our readings of the text are so far removed, but I find your comments to be quite disconnected from the text. Given that we are trying to read it together, could you please provide more references to the text to support your assertions in future. This may help to reduce confusion and determine where/how you disagree.

Notice that it requires the reader "seeing" what the author means, And since an aphorism is brief, there is a need for strict passage by passage interpretation to see them all. — Metaphysician Undercover

Yeah, well you crack on with that, I don't want to sound like I'm telling people what they should do.

This is as much aimed at the other posts as yours, but, the kind of onanistic scholasticism that this whole thread has shown is not for me so I'll duck out of this one.

I mean, two pages of self-congratulatory fake 'eureka' to arrive at the basic standard Hacker and Baker interpretation of a single aphorism which I can only presume (from the level of implied scholarship) that everyone has already read. So what was the point? I just don't get it.

I mean, two pages of self-congratulatory fake 'eureka' to arrive at the basic standard Hacker and Baker interpretation of a single aphorism which I can only presume (from the level of implied scholarship) that everyone has already read. So what was the point? I just don't get it. — Isaac

I hope these interpretations are just Hacker and Baker interpretations. I know I don't use Hacker and Baker, most of my interpretations are my own.

I mean, two pages of self-congratulatory fake 'eureka' to arrive at the basic standard Hacker and Baker interpretation of a single aphorism which I can only presume (from the level of implied scholarship) that everyone has already read. So what was the point? I just don't get it. — Isaac

What drew me to Wittgenstein was the fact that there was so little agreement as to what he meant. He was an interpretative challenge. The following points to what is at issue.

In an early draft of the foreword to Philosophical Remarks:

The danger in a long foreword is that the spirit of a book has to be evident in the book itself and cannot be described. For if a book has been written for just a few readers that will be clear just from the fact that only a few people understand it. The book must automatically separate those who understand it from those who do not. Even the foreword is written just for those who understand the book.

Telling someone something he does not understand is pointless, even if you add that he will not be able to understand it. (That so often happens with someone you love.)

If you have a room which you do not want certain people to get into, put a lock on it for which they do not have the key. But there is no point in talking to them about it, unless of course you want them to admire the room from outside!

The honorable thing to do is to put a lock on the door which will be noticed only
by those who can open it, not by the rest. — Culture and Value 7-8

Secondary literature is just that, secondary. I read Hacker and Baker when I first wrestled with Wittgenstein. I did not find them helpful and found much that I disagreed with. If I struggle with the text only to arrive where Hacker and Baker or anyone else has already been then so be it.

Of all that is written, I love only what a person hath written with his blood. Write with blood, and thou wilt find that blood is spirit.
It is no easy task to understand unfamiliar blood; I hate the reading idlers.
He who knoweth the reader, doeth nothing more for the reader. Another century of readers—and spirit itself will stink. — Thus Spoke Zarathustra,

I don't see what you're getting at here except that we can make up a name for a non-existent colour (when would we ever use such a name?). Anyhow, what does this have to do with the phrase "Red exists" or our preceding discussion? — Luke

Replace "red" with the made up colour, let's call it "X". Suppose someone proposes that we combine a specified multiplicity of precise wavelengths of light, for a lab experiment or some other purpose, and we call this colour "X". The point is that "X" has meaning but it has not yet been created, and not yet been seen. So "X" has meaning even though there is nothing, not a physical object, nor in the mind, which has that colour. It's getting off track of the text, just an opinion. but I just thought I'd put that out there as a possibility. Words like "red" may be given meaning through definition. We can define things into existence, if imaginary things qualify as having existence. Isn't this like Sam26's example of "God"?

We could extend this to the proposition that "God exists," which does not derive meaning from whether or not the thing associated with the concept has an instance in reality, but how we use the concept in a variety of social contexts. We should not think that a name is only meant to be some element of reality (PI 59). — Sam26

Perhaps it is because our readings of the text are so far removed, but I find your comments to be quite disconnected from the text. Given that we are trying to read it together, could you please provide more references to the text to support your assertions in future. This may help to reduce confusion and determine where/how you disagree. — Luke

Do you not find that my quoted passages from 65-77 are a good indication of what Wittgenstein is doing in that section? https://thephilosophyforum.com/discussion/comment/243311 What do you think I'm missing, or misrepresenting?

Yeah, well you crack on with that, I don't want to sound like I'm telling people what they should do.

This is as much aimed at the other posts as yours, but, the kind of onanistic scholasticism that this whole thread has shown is not for me so I'll duck out of this one.

I mean, two pages of self-congratulatory fake 'eureka' to arrive at the basic standard Hacker and Baker interpretation of a single aphorism which I can only presume (from the level of implied scholarship) that everyone has already read. So what was the point? I just don't get it. — Isaac

What can I say? If you don't enjoy it ... It's not like your parents are forcing you to go in with the Boy Scouts.



Since correct terminology appears to be important to you, just let me inform you that Wittgenstein does not use "identity" here, nor does he discuss identifying the different forms that the two distinct language games may take (according to my translation). He actually seems quite critical of their assigned identities as "analysed" and "unanalysed" forms.

What he talks about is whether the orders of the two distinct language games have "the same meaning", whether they achieve "the same" thing, whether the person who carries out the orders does "the same" thing. So he is asking whether the two distinct orders (as distinct language games) are actually two forms of the same order. He concludes that each "form" of expressing the order [misleading in this representation of mine, because it's not really one order but two distinct orders], is in it's own way deficient.
"—But can I not say that an aspect of the matter is lost on you in the latter case as well as the former?"

So what was the point? I just don't get it. — Isaac

The fun is in the exercise, not only the results; each section is like a math problem - the answers are probably out there - in the back of the book, as it were - but the exegetical engagement 'from within' is - for me anyway - alot more intellectually stimulating and rewarding.

I see that section, 61-63, could be used as a strike against Platonism. The common Platonist argument is that the same idea, concept, or information, can be presented in different physical forms; different media or even different languages can represent the very same idea. Since different physical forms represent the very same idea, concept, or information, then the idea, concept, or information represented is something distinct from the physical representation of it. Therefore the idea, concept, or information, has an independent non-physical existence. That is the Platonist argument. You'll see that Wittgenstein is here arguing that distinct representations, which some might say represent the very same "order" in two different ways, do not really represent the very same "order", they are two distinct orders. This undermines that Platonist premise.

Red itself is not the paradigm here. The paradigm is a sample, an example of a red thing, which gives meaning to the word "red". This paradigm may be a physical object, or in the mind. That is Wittgenstein's resolution to the apparent contradiction. "Red" has no meaning unless there is a paradigm to demonstrate red. So "red exists" has no meaning, because "red" has no meaning, unless there is an example of something red, be it a physical object or in the mind. The appearance of contradiction is avoided, because that's all that "red exists" means, that there is such a sample of red, to give the word "red" meaning . — Metaphysician Undercover

Maybe me using 'red' as a paradigm was wrong. The intention I had was to portray red as a facilitator of comparison rather than simply as entities subject to that comparison. As W says in §50, explicating his use of 'paradigm':

It is a paradigm in our language-game; something with which comparison is made. And this
may be an important observation; but it is none the less an observation concerning our language-game—our method of representation.

and refines this function in the parenthetical sentence at the end of §53.

(We do not usually carry out the order "Bring me a red flower" by looking up the colour red in a table of colours and then bringing a flower of the colour that we find in the table; but when it is a question of choosing or mixing a particular shade of red, we do sometimes make use of a sample or table.

but if 'sample' was the correct word to use for 'facilitator of comparison' in both the Paris meter discussion and the discussion of 'red', that's fine.

I'm not doing any of the heavy lifting here, so it's very likely that I'm play too fast and loose with the context of discussion. Regardless, though, I think the point I was making was pretty clear judging from Luke and Street's reactions, I doubt this (possible) error I made disrupts my exegesis too much.

Replace "red" with the made up colour, let's call it "X". Suppose someone proposes that we combine a specified multiplicity of precise wavelengths of light, for a lab experiment or some other purpose, and we call this colour "X". The point is that "X" has meaning but it has not yet been created, and not yet been seen. So "X" has meaning even though there is nothing, not a physical object, nor in the mind, which has that colour. It's getting off track of the text, just an opinion. but I just thought I'd put that out there as a possibility. Words like "red" may be given meaning through definition. We can define things into existence, if imaginary things qualify as having existence. Isn't this like Sam26's example of "God"? — Metaphysician Undercover

Okay, but it's just not clear to me what you're arguing for or against here. Is it something in particular that Wittgenstein has said? Something seemingly related to this is what Wittgenstein says at the end of §58:

In reality, however, we quite readily say that a particular colour exists, and that is as much as to say that something exists that has that colour. And the first expression is no less accurate than the second; particularly where ‘what has the colour’ is not a physical object. — PI 58

However, Wittgenstein is talking about the coloured object being non-physical or perhaps fictional, whereas you appear to be talking about the colour (itself) being non-physical. I don't follow why you are raising this possibility.

Do you not find that my quoted passages from 65-77 are a good indication of what Wittgenstein is doing in that section? https://thephilosophyforum.com/discussion/comment/243311 What do you think I'm missing, or misrepresenting? — Metaphysician Undercover

Yes, your quoting of Wittgenstein gives a good indication of what Wittgenstein is doing. I'm more trying to understand what you are doing, which is why I have requested you to support your assertions/questions with textual references.

§65

§65 serves as something like a transitional discussion, which both picks up from the previous section (i.e. sections §46-§64), and serves to introduce a new line of inquiry. If §51 implored us to look at what happens 'in detail' across various cases, and if §53 spoke of 'various possibilities' of how language-games make signs correspond to things, and if alot of the discussion so far has been iterating through the various and variable roles that words and can take on in language games - in short, if what has been so far focused on is difference and variety, §65 begins to broach the question of similarity - it asks about the 'general form of the proposition', and of what can be said about this general form (of which, one imagines, the various 'cases' have been 'species', as in genera-species).

And to this Witty simply says: there's nothing invariant across all the different cases taken under consideration so far - there are 'affinities', but not some hard core in common between them all. The proceeding discussion will elaborate on this.

in short, if what has been so far focused on is difference and variety, §65 begins to broach the question of similarity - it asks about the 'general form of the proposition', and of what can be said about this general form (of which, one imagines, the various 'cases' have been 'species', as in genera-species). — StreetlightX

Maybe I'm just misreading, but this seems to overlook that one of Wittgenstein's main motivations in the Tractatus was the discovery/development of the general form of the proposition (e.g. TLP 4.5, TLP 5.47, TLP 6).

Yeah, it's no accident that that Witty reprises the vocabulary of the TLP when he speaks of the 'general form of the proposition' - italicised in the PI - only to repudiate it in the latter book. This is one of the more clear moments of discordance between the two Witty's.

I agree. The fundamental point of the rejection of the Tractatus is that W. had sublimed the logic of language (PI 38, PI 89). That there is a general form of a proposition is based on assumptions regarding the fixed logical structure that underlies language (and the world).

However, Wittgenstein is talking about the coloured object being non-physical or perhaps fictional, whereas you appear to be talking about the colour (itself) being non-physical. I don't follow why you are raising this possibility. — Luke

Right, so what I was pointing out, is that I thought that Wittgenstein's representation of the imaginary "red" was not quite correct (I had a slight disagreement). Notice that at 58 he wanted to replace "red exists" with "the word 'red' has meaning", but the attempt appeared to contradict itself. He resolves the contradiction, by admitting that "In reality, however, we quite readily say that a particular colour exists", with the following qualification as to what this means, "and that is as much as to say
that something exists that has that colour".

So let me explain my disagreement. He has allowed that "exists" can refer to imaginary colours. But when he says this means "something exists that has that colour", and allows that "'what has that colour' is not a physical object", I think that he doesn't properly represent how an "imaginary colour" really exists. It is not a case of a non-physical object having the colour red, it is a case of a definition. So the colour "red" is defined into existence, as an object, just like the mathematical objects are defined into existence. They exist as objects so long as the definition is adhered to

This relates directly to his description of concepts at 68-80. Notice at 68-69, there is no defined boundary to the concept "game". We can however draw a boundary (definition), for a specific purpose. At 70, he describes the concept of "game" as "uncircumscribed". This word relates right back to #3, where he talks about producing a definition for a specific purpose. The definition circumscribes the area.

Then at 75, he's back onto this idea, asking if to know what a game is, but not be able to say what it is, is like an "unformulated definition". But this is problematic because at 76, if someone draws a boundary (formulates a definition) it wouldn't be the same boundary that I would draw.

So, in all of this, right back to that point at 58, he is removing the need for a definition from the existence of a "concept". To know what red is, or what a game is, does not require that one knows a definition. He is presenting the concept as something other than requiring a definition. Accordingly, I know what 'red' is if I can point to a red thing. And, he has completely separated this from "I know what red is if I can recite a definition of 'red'".

As expressed by my disagreement above, I am not yet convinced that this separation, and the way it's expressed at 58, is accurate. It is implied that if I can recite the definition of red, yet cannot point to a red thing, then I do not know what red is.

Yes, your quoting of Wittgenstein gives a good indication of what Wittgenstein is doing. I'm more trying to understand what you are doing, which is why I have requested you to support your assertions/questions with textual references. — Luke

So what I am doing is attempting to understand what Wittgenstein is doing. When his way of doing things is inconsistent with, or clashes with, what is customary for me, then understanding what he is doing becomes difficult. This is where disagreement crops in, I want to go this way, as is my habit, and Witty says no, go that way.

To follow up on my last post about subliming language, according to the Tractatus:

Logic is transcendental. — T 6.13

Right, so what I was pointing out, is that I thought that Wittgenstein's representation of the imaginary "red" was not quite correct (I had a slight disagreement). — Metaphysician Undercover

Where does Wittgenstein speak of an "imaginary red"?

He resolves the contradiction, by admitting that "In reality, however, we quite readily say that a particular colour exists", with the following qualification as to what this means, "and that is as much as to say that something exists that has that colour".

So let me explain my disagreement. He has allowed that "exists" can refer to imaginary colours. — Metaphysician Undercover

As I explained in my previous post, and as is clear from the quote, he does not speak of imaginary colours:

In reality, however, we quite readily say that a particular colour exists, and that is as much as to say that something exists that has that colour...particularly where ‘what has the colour’ is not a physical object. — PI 58

If I speak of a white unicorn, that doesn't make the colour imaginary. Also, red is not an imaginary colour.

But when he says this means "something exists that has that colour", and allows that "'what has that colour' is not a physical object", I think that he doesn't properly represent how an "imaginary colour" really exists. — Metaphysician Undercover

Probably because he is not talking about imaginary colours or how they exist. It is the coloured object which is imaginary (actually, "non-physical" is Wittgenstein's description).

It is not a case of a non-physical object having the colour red, it is a case of a definition. So the colour "red" is defined into existence, as an object, just like the mathematical objects are defined into existence. They exist as objects so long as the definition is adhered to — Metaphysician Undercover

What about all of Wittgenstein's talk of ostensive definition? How do you account for that? If I point at a red object to explain the meaning of the word "red", is that defining "red" into existence? Firstly, I didn't invent the word, so no. Secondly, our ability to sense and distinguish red as a colour is, for the majority of us, part of the human experience. I would have a hard time explaining the meaning of the word in this way if nobody else could distinguish the colour. Therefore, I wouldn't consider it entirely as "defining the colour into existence". Anyway, this seems to be taking us far from the text.

So, in all of this, right back to that point at 58, he is removing the need for a definition from the existence of a "concept". — Metaphysician Undercover

No, he is pointing out that the concept of a game or a number (and probably many more concepts) is not "everywhere bounded by rules" (§68). The concept can be made more rigidly bounded or defined for some purpose if we desire, but it is otherwise not so exactingly defined (§69). However, this doesn't mean that (until we make the definition more exact) it is not defined, or that "he is removing the need for a definition".

To know what red is, or what a game is, does not require that one knows a definition. He is presenting the concept as something other than requiring a definition. Accordingly, I know what 'red' is if I can point to a red thing. And, he has completely separated this from "I know what red is if I can recite a definition of 'red'". — Metaphysician Undercover

He is not "presenting the concept as something other than requiring a definition". An ostensive definition is also a definition. Are you suggesting that the only true definition is in (numerical) terms of wavelength, or what did you have in mind?

As expressed by my disagreement above, I am not yet convinced that this separation, and the way it's expressed at 58, is accurate. — Metaphysician Undercover

I don't see this as being expressed anywhere at §58.

It is implied that if I can recite the definition of red, yet cannot point to a red thing, then I do not know what red is. — Metaphysician Undercover

A strange way to put it: "I do not know what red is". If you mean by this that you do not know some of the ways to use the word "red" (in this example), then that would be correct.

Where does Wittgenstein speak of an "imaginary red"? — Luke

It's what you called "fictional", I called it "imaginary". Wittgenstein referred to it in this way: "'what has the colour' is not a physical object". When he says that there is something which has the colour red, but this thing is not a physical object, doesn't this imply "imaginary red" to you? Or do you hold a difference between a fictional object which is red, and an imaginary red? I think you're trying to make something out of nothing.

As I explained in my previous post, and as is clear from the quote, he does not speak of imaginary colours: — Luke

Of course he speaks of imaginary colours. Look at 56-57. He speaks of bringing the memory of the colour before "the mind's eye", and he even says the "memory-image". "And don't clutch at the idea of our always being able to bring red before our mind's eye even when there is nothing red any more."

If an image of red in the mind's eye is not an "imaginary colour", then what is? I'll tell you what is. We can create an "imaginary colour" by definition, as I described. Notice that these two senses of "imaginary colour" are quite distinct. That's my point.

No, he is pointing out that the concept of a game or a number (and probably many more concepts) is not "everywhere bounded by rules" (§68). The concept can be made more rigidly bounded or defined for some purpose if we desire, but it is otherwise not so exactingly defined (§69). However, this doesn't mean that (until we make the definition more exact) it is not defined, or that "he is removing the need for a definition". — Luke

I think you misunderstand. He clearly removes the need for a definition. Reread 68-69. He says that we can give a concept boundaries, close the frontier, but this is not necessary. It is done for a particular purpose. Nevertheless, for Wittgenstein this does not mean that there are not rules involved. What this means is that the rules at play here are other than definitions or boundaries. If we want to look for the rules involved with the concept of "game" we must look for something other than a definition or a boundary.

He is not "presenting the concept as something other than requiring a definition". An ostensive definition is also a definition. Are you suggesting that the only true definition is in (numerical) terms of wavelength, or what did you have in mind? — Luke

Hasn't he already rejected ostensive definition as insufficient for learning types? Didn't he demonstrate that we must already know how to distinguish types before ostensive definition can be successful? We don't learn concepts of types, like "game" through ostensive definition. There must be some other form of rule, other than a rule of definition, which is at play here.

Part of the problem with philosophers and probably with thinkers in general is that we want exactness, we want some final analysis that will answer our questions. And analysis can be useful when done properly, or when seen aright. Part of the problem of the Tractatus was that Wittgenstein was trying to give propositions clarity of meaning or sense. In the Tractatus this is done via elementary propositions in terms of the simple and complex, i.e., propositions are complex until we break them into their constituent parts, viz., elementary propositions and still further into names. So, by understanding the simple parts of propositions (names), and correlating these simples to the simplest parts of facts in the world (objects) we come to some final analysis. For Wittgenstein it's objects, for Russell it was individuals, in terms of the simplest components of reality (facts).

His talk about the broom and the table in terms of some final analysis should be seen in light of his former thinking, as some of you have already pointed out. And isn't this our tendency, as philosophers especially, we seem to think that if we can get to the bottom of what is meant by this or that term or concept, then we have a more exact sense of meaning. It seems to be the case that the more exact we are with a word, for example games, the more inexact we become, i.e., we exclude many other uses of the word.

Wittgenstein still believes in the logic of language in the PI, but it's the logic of use, and not the a priori logic found in the Tractatus. The PI is more of an a posteriori investigation, or a pragmatic investigation of language usage. There is clarity in the PI, but it must be seen in terms of use and context, and one must be careful about being too dogmatic, and not to overgeneralize as is seen in many philosophical theories.

It's what you called "fictional", I called it "imaginary". Wittgenstein referred to it in this way: "'what has the colour' is not a physical object". When he says that there is something which has the colour red, but this thing is not a physical object, doesn't this imply "imaginary red" to you? Or do you hold a difference between a fictional object which is red, and an imaginary red? I think you're trying to make something out of nothing. — Metaphysician Undercover

There is a difference between real horses and fictional horses. But is there a similar difference between real unicorns and fictional unicorns? No, because horses are real, whereas unicorns are not. You are conflating this distinction with your use of the term 'imaginary', only to muddy the waters. You have not yet named an imaginary (i.e. fictional) colour; you have only named the memory-image of a real colour. Besides, I fail to see what your talk of fictional colours has to do with the text.

Also, as I explained earlier, Wittgenstein does not preclude physical objects and is not speaking exclusively about non-physical objects at §58. Therefore, he is not talking about an "imaginary red". That is a very distorted reading and I think you are putting too much emphasis on the final sentences of this quite difficult section to be drawing any specific conclusions from it.

Of course he speaks of imaginary colours. Look at 56-57. He speaks of bringing the memory of the colour before "the mind's eye", and he even says the "memory-image". "And don't clutch at the idea of our always being able to bring red before our mind's eye even when there is nothing red any more." — Metaphysician Undercover

At §56-57, he raises the putative possibility that a memory-image could play the role of a paradigm or sample, but he raises this possibility only to reject it: "we do not always resort to what memory tells us as the verdict of the highest court of appeal" (§56) and "If we forget which colour this is the name of, the name loses its meaning for us; that is, we’re no longer able to play a particular language-game with it." (§57)

I think you misunderstand. He clearly removes the need for a definition. Reread 68-69. He says that we can give a concept boundaries, close the frontier, but this is not necessary. It is done for a particular purpose. Nevertheless, for Wittgenstein this does not mean that there are not rules involved. What this means is that the rules at play here are other than definitions or boundaries. If we want to look for the rules involved with the concept of "game" we must look for something other than a definition or a boundary. — Metaphysician Undercover

Where is your textual support for these claims?

Hasn't he already rejected ostensive definition as insufficient for learning types? — Metaphysician Undercover

Where does he do this? Again, support your claims with textual references.

Look, I'm not going to rehash everything that we've already gone over. Anyway, I would only be repeating the points that Fooloso4 made earlier. If his comments didn't convince you then I doubt that mine will either. Besides, I don't have the patience to try and correct what appears to me to be your deliberate misreadings. If you have textual support for your claims that are not blatantly taken out of context, then I look forward to seeing them. Otherwise, this is just derailing the discussion.

We don't learn concepts of types, like "game" through ostensive definition. There must be some other form of rule, other than a rule of definition, which is at play here. — Metaphysician Undercover

He's not saying that you can't learn how to use certain words by referring to things or objects. We teach children all the time by pointing to things (cups, houses, trees, etc). He's saying that meaning or sense is not derived in this way, i.e., not by pointing to some object. So, ostensive definition can be part of the learning process. Learning meaning or sense involves a wide variety of uses that may include pointing to this or that in social contexts, but is not dependent on this or that object.

§66. What is common to all the activities that we call "games"? Wittgenstein urges the reader not to automatically assume the answer, but to "look and see" whether there is anything common to them. Wittgenstein notes that some games might be played for competition while others are played for entertainment, and that some require more skill or luck than others. However, the important point is that "if you look at them, you won't see something that is common to all, but similarities, affinities, and a whole series of them at that. To repeat: don't think, but look!"

I find the current sections so iconic that it is difficult to provide a summary and not to simply quote them in their entirety.

I find the current sections so iconic that it is difficult to provide a summary and not to simply quote them in their entirety. — Luke

I largely agree with this, especially with §66 and §67, which are about as clear as Witty gets. So on to

§68:

The first thing that stands out about §68 is that it harkens back to an early early discussion back in §3, in which Witty was objecting to Augustine that his conception of language held true only for a "narrowly circumscribed area", and in fact then expressly invoked games as a further example. To recall:

§3: "It is as if someone were to say, “Playing a game consists in moving objects about on a surface according to certain rules...” - and we replied: You seem to be thinking of board-games, but they are not all the games there are. You can rectify your explanation by expressly restricting it to those games".

In §3 it might have seemed as though what was missing was a more complete or more general conception of a game. §68 in fact makes clear that this is not the case - the problem isn't that there ought to be a more complete conception of a game, but that no such complete or general conception could be forthcoming, even in principle. Instead, what can count as a game has, as it were, an indefinite extension, which can nevertheless be made provisionally definite by 'drawing a boundary'. Such a boundary will not exhaust what counts as a game, but will, like Augustine, 'circumscribe it' within a certain area.

One 'technical' note here is that §68 marks the reappearance of 'rules' as an object of discussion (they've been 'missing' since §54). With respect to them, the point made seems to be something like: rules function as constraints - they mark, like 'boundaries', lines beyond which one cannot go, without for all that exhausting the range of what can be done within a game. Hence: "No more are there any rules for how high one may throw the ball in tennis, or how hard, yet tennis is a game for all that, and has rules too."

§66
This paragraph reminds me of the courts trying to come up with a definition of pornography. A definition should be seen more as a guide than some absolute measure of meaning. Although, many definitions try to show how a word is used in a variety of contexts. However, most people use the dictionary as some absolute arbiter, and in some sense it can be used as an arbiter. And although there are not always clear boundaries around the definition, as seen in W. idea of family resemblances, there are still uses of the word that fall outside normal usage. This in turn may give rise to the idea that there is some way of setting limits, or of being more exact in our talk of games. This desire is so powerful that even after understanding what W. is saying, we are still drawn to the idea that we can describe the game more precisely.

§68
It's interesting that even the concept number, which we tend to see as more rigid, is not necessarily bounded. It too can have uses that are unbounded, just as the concept game has unbounded uses.

The question is: Why does this trouble us? It seems to be our desire for exactness, but even the concepts of being exact or being precise is not subject to a strict boundary. So, it seems we are fooled into thinking a certain way due to our lack of understanding of just how language works. Hence, Wittgenstein's method of showing us the way out of this kind of thinking.

Finally, although there are rules that govern the uses of concepts, concepts are not everywhere bounded by rules. There seem to be just enough rules to allow us to say this or that is correct or incorrect, but also enough elasticity to leave room for expansion or growth in terms of what we say, and how we say it.

That is a very distorted reading and I think you are putting too much emphasis on the final sentences of this quite difficult section to be drawing any specific conclusions from it. — Luke

Well, the first part of 58 is where he lays out the conditions for the apparent "contradiction". At the end, he offers a resolution. So it's only natural that after understanding the conditions of the contradiction, I would focus on his proposed resolution.

Where is your textual support for these claims? — Luke

I told you, read 68-69. "'"All right: the concept of number is defined for you as...' ---It need not be so.". Read this as not necessary. "For how is the concept of a game bounded? What still counts as a game and what no longer does? Can you give the boundary? No.You can draw one; for none has so far been drawn." It's all right there, a boundary or definition is not necessary. There is no need for a definition or boundary of the concept "game", yet the word still has meaning and is useful.

He's not saying that you can't learn how to use certain words by referring to things or objects. We teach children all the time by pointing to things (cups, houses, trees, etc). He's saying that meaning or sense is not derived in this way, i.e., not by pointing to some object. — Sam26

Since meaning is use, then you would just contradict yourself if you said that we learn how to use words this way, but we don't learn their meaning in this way.

So, ostensive definition can be part of the learning process. Learning meaning or sense involves a wide variety of uses that may include pointing to this or that in social contexts, but is not dependent on this or that object. — Sam26

Yes, of course ostensive definition is part of the learning process, but look at what he's focusing on in this section of the book, the capacity to recognize similarities, "family resemblances".

And the result of this examination is: we see a complicated network of similarities overlapping and criss-crossing: sometimes overall similarities, sometimes similarities of detail. — 66

What he's starting to focus on is this, the recognition of similarities. It's not the existence of similarities, but the recognition of similarities, and this is what he is pointing to as the fundamental aspect of conception. And, notice that he is deliberately separating this from what he seems to think is the faulty representation of conception, as the creation of a boundary or definition. You could say he is separating the material aspect, as the capacity to recognize similarities, from the formal aspect, as the existence of definitions and boundaries, and he is arguing that it is this material aspect which provides the basis for existence of a concept. The formal aspect is shown as not necessary.

One 'technical' note here is that §68 marks the reappearance of 'rules' as an object of discussion (they've been 'missing' since §54). With respect to them, the point made seems to be something like: rules function as constraints - they mark, like 'boundaries', lines beyond which one cannot go, without for all that exhausting the range of what can be done within a game. Hence: "No more are there any rules for how high one may throw the ball in tennis, or how hard, yet tennis is a game for all that, and has rules too." — StreetlightX

I believe there's a bit of a trick to understanding the use of "rules" here. His use of the term will take a sharp turn at 81, and this is a sort of preparatory usage at 68, so it might be good to read it a couple times.

The premise is, we cannot state the boundary to the concept "game". So the consequent proposition (I interpret the phrases within quotes as propositions to be analyzed) is "But then the use of the word is unregulated, the game we play with it is unregulated." The reply is that "It is not everywhere circumscribed by rules...". And this is how we play games, some activities within the game are regulated, others are not, as his example shows. Now, the concept "game" has been shown to be unbounded, but this does not force the conclusion that there are no rules. It just means that the rules which are there, are not such limits of boundary. What I intuit, is that if we want to find the rules which govern conception, we must release the notion that these rules are constraints such as boundaries, or limits of definition. So if we restrict our understanding of "rules", such that the rules of conception must be limits of definition, boundaries, we will never find the rules of conception.

Wittgenstein still believes in the logic of language in the PI — Sam26

It is not the logic of language but the logic of the language-game, different games different logics, that is to say, different grammars or rules.

It is not the logic of language but the logic of the language-game, different games different logics, that is to say, different grammars or rules. — Fooloso4

Your point seems to be a distinction without a difference. When I speak of the logic of our language I'm talking about grammar, rules, use, and finally meaning or sense, which would obviously include how words and concepts are used in language, and thus language-games. This expression is used not only in the Tractatus, but in the PI (PI 93, 345,).

The difference is that W. had in his own words sublimed the logic of language in the Tractatus (PI §38, PI §89).

Logic is transcendental. — T 6.13

It is not just the relationship between logic and language that he comes to reject.

The facts in logical space are the world. — T 1.13

Logic pervades the world: the limits of the world are also its limits. — T 5.61

Logic, according to the Tractatus underlies and is the scaffolding of both language and the world.

In the PI logic is not prior to, independent of, or determinate for the language game.

Logic, according to the Tractatus underlies and is the scaffolding of both language and the world.

In the PI logic is not prior to, independent of, or determinate for the language game. — Fooloso4

I'm not saying that it's the same method or the same kind of logic. His understanding of the role of logic in language is much different in the PI.

Sorry, I missed the clarification you made between them:

Wittgenstein still believes in the logic of language in the PI, but it's the logic of use, and not the a priori logic found in the Tractatus. — Sam26

I still think it is important to emphasize that the rejection of Tractarian logic is as much a rejection of an ontology as it is a rejection of a view of language and the activity of analysis.