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. — Fooloso4

Yes, but it depends on what you mean by his ontology. If you mean his analysis of how propositions connect with the world, and the limits he puts on language, then I agree. Although, in the PI he still believes there are limits to what can be said, it's probably where I disagree with Wittgenstein.

Yes, but it depends on what you mean by his ontology. If you mean his analysis of how propositions connect with the world, and the limits he puts on language, then I agree. — Sam26

It is not simply a matter of how propositions connect with the world but of the logical structure of the world from simple objects that make up the substance of the world (T 2.02 - 2.021) that combine in determinate logical ways to form the facts of the world (T 2.01).

It is not simply a matter of how propositions connect with the world but of the logical structure of the world from simple objects that make up the substance of the world (T 2.02 - 2.021) that combine in determinate logical ways to form the facts of the world (T 2.01). — Fooloso4

I don't find anything to disagree with here, at least not in this statement. I'm very familiar with the Tractatus and what it says.

We can always start a thread on the Tractatus.

There is one that I am active in now. I would like to hear what you have to say. We have covered through 3 without getting bogged down in details but now the other participants are anxious to jump ahead. I am somewhat sympathetic but think there are still some issues that need to be discussed that will shed light on the later problems.

In my Wittgenstein Commentary thread I start out by talking about the Tractatus in general terms. You can read some of my comments there.

"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. — Metaphysician Undercover

Nowhere does he say or even imply: 'There is no need for a definition or boundary of the concept "game"'.

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. (But that never troubled you before when you used the word "game".) "But then the use of the word is unregulated, the 'game' we play with it is unregulated."——It is not everywhere circumscribed by rules; but no more are there any rules for how high one throws the ball in tennis, or how hard; yet tennis is a game for all that and has rules too. — PI §68

Rules are boundaries. When the interlocutor suggests, as you do, that the use of the word or the 'game' we play with it is unregulated, Wittgenstein responds that it may not be everywhere circumscribed by rules, but this does not mean that it has no rules.

I understood Wittgenstein as insinuating that one's private experience of red, i.e. phenomenal red, is neither a necessary nor sufficient estimation of the public use of optical red. The purpose of ostensive definition is to 'set up' the estimation of optical red in terms of phenomenal red, and vice versa, without either being semantically reducible to the other, since while they conceptually overlap they are not conceptually equivalent.

Yet at the same time Wittgenstein pointed out that the meaning of physical concepts such as optical red cannot be meaningfully said to transcend the holistic totality of one's experiences, due to the meaning of utterances resting upon use and demonstration.

So I understood Witty as rejecting the epistemologies of both phenomenalism and physicalism, whilst being close in spirit to metaphysical pluralism - not in the sense of substance pluralism but in the sense of use pluralism and family resemblance.

Nowhere does he say or even imply: 'There is no need for a definition or boundary of the concept "game"'. — Luke

If you refuse to understand what is written, then I can't help you to see what you deny is there. But I'll try one more time. He starts 68 with a proposition. The concept of number is defined for you as ... such and such. He replies to this proposition with "It need not be so". He says he can give the word "number" rigid limits, (a rigidly limited concept), or he can use "number" in a way such that the extension of the concept is not closed by a frontier.

Do you understand that he is saying that he can use the word "number" in a way such that its meaning is not bounded by a definition? So he proceeds with "And this is how we do use the word 'game'." He is explicitly saying that we use the word "game" in this way, such that the extension of the concept is not bounded by a definition.

Rules are boundaries. — Luke

Not exactly, so consider that notion a misleading prejudice, and forget it. Here's the point. Boundaries are rules, but not all rules are boundaries. So he has excluded definitional boundaries as the type of rules which apply in the concept of "game". However this does not mean that the concept is unregulated. We can conclude that the concept is regulated in a different way, rules other than definitional boundaries are what govern the conception of "game".

If you look back to 66, you'll see that the concept "game" is described as a "complicated network
of similarities", which are characterized at 67 as "family resemblances". Do you see the difference between a network of similarities, and a boundary or a limit to this network? The network of similarities is necessary for the existence of a concept, a boundary to the network is not necessary.

§69

§69 does some clarification work about the role of boundaries with respect to games (which we can also read as: 'rules with respect to language-games'). As with §68, the point is that the inability to exhaustively 'draw boundaries' around games is not some kind of incapacity or 'ignorance'. We are not failing at something that could, in principle be done - if only we were more intelligent, had better powers of conceptual discernment, etc etc. That we "can't tell other exactly what a game is ... is not ignorance".

And yet again, Witty iterates that this in turn does not mean that boundaries cannot be drawn: "we can draw a boundary - for a special purpose." - but we don't need such a boundary for us to understand what a game is - unless we have a 'special purpose' in mind for it: "Does it take this to make the concept usable? Not at all! Except perhaps for that special purpose". To summarize in point form:

(1) Games (and concepts/words) are not necessarily exhausted by their rules/boundaries.
(2) [Which means]: An inability to exhaustively define a game by means of rules/boundaries is not a deficiency on the part of us or the concept of games.
(3) Which doesn't mean we can't draw boundary if we want to for the sake of some purpose.

---

Since this is a small section, I wanna take the opportunity to go over the motivating context of these remarks. Specifically, it's important to keep in mind the discussion in §60-§64, about whether or not we should 'analyse' compound things into simple things. Recall there that while Witty said that lots of compound things (like broom) could be 'analyzed' into simple things, certain aspects of the compound could be lost in the analysis into simples. So we can't take for granted that the analysis of compounds into simples is guaranteed a priori as an unproblematic operation.

The questions dealt with here are of a similar problematic: can makes be 'analyzed' into their rules? Is there a straightforward, 1:1 correspondence between a game and rules/boundaries that 'compose' it? (just like: is there a straightforward, 1:1 correspondence between a compound and the simples that 'compose' it?). If the discussion of simples and complexes are anything to go by, the answer will be: not necessarily.

I understood Wittgenstein as insinuating that one's private experience of red, i.e. phenomenal red, is neither a necessary nor sufficient estimation of the public use of optical red. The purpose of ostensive definition is to 'set up' the estimation of optical red in terms of phenomenal red, and vice versa, without either being semantically reducible to the other, since while they conceptually overlap they are not conceptually equivalent.

Yet at the same time Wittgenstein pointed out that the meaning of physical concepts such as optical red cannot be meaningfully said to transcend the holistic totality of one's experiences, due to the meaning of utterances resting upon use and demonstration.

So I understood Witty as rejecting the epistemologies of both phenomenalism and physicalism, whilst being close in spirit to metaphysical pluralism - not in the sense of substance pluralism but in the sense of use pluralism and family resemblance. — sime

Hi sime. I had to replace your use of 'optical red' with 'the word "red"' to make sense of this. It was unclear to me which section you were referring to with your comments, or whether you were commenting on the text as a whole, but it sounds like a reasonable summary of PI 58. (I think!)

Do you understand that he is saying that he can use the word "number" in a way such that its meaning is not bounded by a definition? — Metaphysician Undercover

No, I don't see him saying that the concept has no definition whatsoever, as you claim; only that the concept is not everywhere circumscribed by rules. Therefore, this leaves some rules/boundaries/definition to the concept.

Boundaries are rules, but not all rules are boundaries. — Metaphysician Undercover

For example?

So he has excluded definitional boundaries as the type of rules which apply in the concept of "game". However this does not mean that the concept is unregulated. We can conclude that the concept is regulated in a different way, rules other than definitional boundaries are what govern the conception of "game". — Metaphysician Undercover

What do you mean by "definitional boundary", and how is it different from a rule?

Do you see the difference between a network of similarities, and a boundary or a limit to this network? The network of similarities is necessary for the existence of a concept, a boundary to the network is not necessary. — Metaphysician Undercover

That's fine, except your claim was that no boundary or definition is required for the concept of a game whatsoever. This implies that the word, in this context (of "board-games, card-games, ball-games, athletic games, and so on"), can mean anything at all. But the word "game" (in this context) has a circumscribed meaning/definition/usage, even though it is not everywhere circumscribed.

Interestingly Lewis Carroll's paradox concerning the meaning of logical deduction in "What the Tortoise said to Achilles" came 50 years earlier than Wittgenstein's remarks concerning the relationship between rule-based definitions and language use.

https://en.wikipedia.org/wiki/What_the_Tortoise_Said_to_Achilles

Whilst this is slightly jumping the gun, later on in PI Wittgenstein expresses a similar logical refutation of the idea that the use of language can be grounded in rule-based definitions or explicitly expressed conventions, because in a nutshell the very meaning of rules and conventions is grounded in their use! - For otherwise our definitions lead to infinite regress.
As an example, just try to define the logical operators non circularly.

Also, regarding the question of 'exactness' with respect to the specification of rules, Wittgenstein had questioned earlier in his career (i think during his middle period in Philosophical Grammar), whether the notions of exactness, identicalness etc were a priori in the sense of being phenomenological aspects of experience. The significance being whether or not exactness is empirically reducible. For if it isn't, then the notion of exactness is well, inexact, it's meaning only being demonstrable as a family resemblance of uses across different language-games.

No, I don't see him saying that the concept has no definition whatsoever, as you claim; only that the concept is not everywhere circumscribed by rules. Therefore, this leaves some rules/boundaries/definition to the concept. — Luke

Well, I don't see how you can miss it, because. he clearly states that a concept may be bounded by a definition but "it need not be so". Then, we can use the concept in a way so that it "is not closed by a frontier". And, the concept of "game" is like this. Further, at 69 he says of the concept "game", "We do not know the boundaries because none have been drawn."

For example? — Luke

Look at 85, Wittgenstein compares a rule to a sign-post. A sign-post is not a boundary. They are fundamentally different. A sign-post encourages you to proceed, a boundary prevents you from proceeding.

That's fine, except your claim was that no boundary or definition is required for the concept of a game whatsoever. — Luke

Let's be clear, this is not my claim, it is Wittgenstein's claim. And, he's very explicit about this point. You ought not deny it, or you'll misunderstand what he's showing us.. I am still undecided as to whether I agree or not, I'll see where it leads. However, I see no reason to reject this claim, at this point. If this means that the word "game" can mean anything at all, then what's wrong with that? We are fundamentally free to use words however we please, This is very obvious with the youngsters who make up new uses for words every day.

This implies that the word, in this context (of "board-games, card-games, ball-games, athletic games, and so on"), can mean anything at all. But the word "game" (in this context) has a circumscribed meaning/definition/usage, even though it is not everywhere circumscribed. — Luke

Hold on, you've added an extra condition "in this context". The context acts as a boundary, it bounds the word, as a particular instance of use, therefore with a particular purpose. Notice that Wittgenstein says that the concept itself is unbounded, but it may be bounded for a particular purpose. So putting a word into a particular context is an instance of limiting the concept for a particular purpose.

And yet again, Witty iterates that this in turn does not mean that boundaries cannot be drawn: "we can draw a boundary - for a special purpose." - but we don't need such a boundary for us to understand what a game is - unless we have a 'special purpose' in mind for it: "Does it take this to make the concept usable? Not at all! Except perhaps for that special purpose". To summarize in point form: — StreetlightX

I see a possible paradox here. We may draw a boundary for a special purpose. In this case the concept is being used for a specific purpose. However, Wittgenstein says that the concept is "usable" without such a boundary. As Luke points out, this would mean that there are no restrictions to the possible uses of any such concept. If this is the case then there is nothing which distinguishes one concept from another, each is infinitely usable. Each concept is usable in an infinite number of ways, having its use defined by the particular instance of usage.

The problem being that the usefulness of a tool is created by having a particular purpose for that tool, not by having an endless number of uses. Usefulness is created by conforming the tool to the specific use. A "tool" which has no particular use, like a piece of matter, may be infinitely usable, but it has little if any usefulness, and can't really be called "a tool". So we really need a distinction between "useful" and "usable" to bring the concept from the category of usable into the category of useful.

Recall Wittgenstein's analogy for verbal definitions in terms of occasional sign-posts that are placed to guide walkers along a route. The sign-posts tend to be laid down only at the points where they are useful, namely at the places where walkers frequently become lost or confused.

The route is analogous to the implicit conventional use of a word, whereas the sign-posts are analogous to the explicit conventional definition of the word. Needless to say, individual walkers will walk idiosyncratically , regardless of whatever the sign posts say.

And is it necessarily the case that a walker who frequently follows the route could give an accurate verbal account of it without him actually following it?

Isn't a word itself a sign?

§69
Wittgenstein keeps saying the same things, only from different angles. It seems that philosophers and others get hung up on the form of the proposition/statement, as opposed to the function of the proposition/statement, word, or concept. Clarity of thought is not about some very precise definition, which as it turns out is generally impossible. This is clearly observed in our use of the word game, which doesn't have clearly defined borders. On the other hand, clearly defined borders may be drawn if we're talking about a particular kind of game, say chess. However, the tendency for philosophers is to look for unifying principles, or some theory that sums up the concept in some neatly defined idea.

As Wittgenstein points out, someone might say that before we come to understand these unifying principles or theories, we didn't have a very exact definition or an exact measure, but then the problem raises it's ugly head again, what do you mean by exact. So, the problem continues because we aren't seeing the social nature of language in the stream of life.

There are similarities in the Tractatus and the PI in that Wittgenstein is still trying to mark out the limits of sense. In the Tractatus he sets out the limit of language, but in the PI he speaks of the limits (plural) of language, which are found in how we use language. These limits (in the PI) are seen in the various uses of propositions, words, and concepts, they are open to view. They are not hidden, as in the Tractatus, but open to view in the stream of life.

Another similarity between the Tractatus and the PI, is that Wittgenstein is still trying to understand the function of language. In the PI there is no absolute method of determining sense from nonsense, no formal boundary as he set up in the Tractatus. Something only makes sense (in the PI), or is nonsense in a particular language-game. Even the term make sense is vague, just as the term game is vague. Just as the word game would alter its meaning from context to context, so making sense would alter its meaning from context to context, or from language-game to language-game.

This is an expanded version of PI 69, pulling together a general overview.

Hold on, you've added an extra condition "in this context". — Metaphysician Undercover

The point of this thread is to discuss and understand what Wittgenstein is saying in the text. Therefore, I'm not adding an "extra condition" by talking about context; this context has been created by what he is talking about in the text and, in particular, in the section of the text that we are currently discussing. I didn't make up these examples for context:

Consider, for example, the activities that we call “games”. I mean board-games, card-games, ball-games, athletic games, and so on. — PI 66

Likewise with numbers:

cardinal numbers, rational numbers, real numbers, and so forth. — PI 68

This is what Wittgenstein is talking about. So, if you take Wittgenstein to be saying here that the words "game" or "number" can mean anything at all, then you are misreading him.

§70

§70 continues to emphasise how boundaries (read: rules) are inessential to the workings of concepts (to the concept of concepts, if you will). This is, as I mentioned earlier, analogous to the claim that the analysis of composites into simples is itself inessential for the composites to function as composites. In §70 this is cashed out in the claim that language works perfectly well without the need for definitions - hence the rhetorical question: "do you want to say that I don’t know what I’m talking about until I can give a definition of a plant?” (Witty's answer is clearly: “Obviously not”).

As usual however, Witty leaves space for boundaries to nonetheless have a place, where, in conceding to his imaginary interlocutor that the picture of the leaves is not ‘exact’, it is only not ‘exact’ in the particular sense that his interlocutor wants. Which means of course, that ‘exactness’ is only as specific as what is demanded of it. Which itself explains the closing of §69: "Though you still owe me a definition of exactness”.

§70 [Boxed Note]

The question sustained in this is something like: is the understanding of not-a-gambling-game ‘contained’ within the imperative to ‘show the children a game’? Or in other words: does the compound ‘show the children a game?’ ‘contain’ within it the simple ‘not a gambling game’? Or is there always an irreducible gap between the two, so the the complex cannot be so straightforwardly resolved into the simple. I’m not sure the question Witty asks here is really ‘meant’ to be answered - it’s meant to simply keep alive that dissonance between complex and simple.

—

I was going to write something about §71, but the whole thing is straightforward enough, so I’m going to skip it.

—

§72

§72 doesn’t so much make a point as set a scene for what’s to come: its a question of finding what is common (a color) in (1) A series of multicolored pictures; (2) Various shapes of the same color; (3) Various shades of blue. In all these cases, the question to keep in mind is something like: how does one pick out similarity among these difference cases of difference? Note also how the question of ostension is creeping its way back in here.

The point of this thread is to discuss and understand what Wittgenstein is saying in the text. Therefore, I'm not adding an "extra condition" by talking about context; this context has been created by what he is talking about in the text and, in particular, in the section of the text that we are currently discussing. I didn't make up these examples for context: — Luke

You're right, "game" has a context within Wittgenstein's use here. Therefore it is being used for a special purpose, and there is likely a boundary implied by that usage. That's why I see a probable paradox in what Witty is arguing. He's saying that the concept "game" has no boundary unless someone gives it a boundary by using it for a specific purpose. However, whenever the word "game" appears, it's an instance of someone using the concept for a specific purpose. So he's really created an imaginary, and most likely impossible situation (unless platonic realism is the case) , in which the concept "game" exists, but it is not being used by anyone for any specific purpose.

However, what I think is important in Wittgenstein's description, is that the boundary is created by the context of usage, (the purpose), it is not inherent within the concept. So instead of conceiving of a concept as something which necessarily has boundaries (boundaries are essential to a concept), we conceive of a concept as providing the possibility for boundaries. This puts concepts into a different category from boundaries.

I think it's important, as we think about what Wittgenstein is saying, to think about how we as individuals make these kinds of mistakes in our own thinking. So, where have we gone wrong in our thinking by making the mistakes that Wittgenstein points out. It's one thing to grasp what he's saying, but it's another to actually apply it as we do philosophy.

What if someone happened to believe that Wittgenstein is the one making a mistake? Such a person might believe that boundaries are inherent within, and essential to any concept itself, rather than a product of how the concept is used for specific purposes. How would we ever determine which position is the correct one? Maybe if we proceed Wittgenstein will provide us with a demonstration to help us decide.

If you think Wittgenstein is incorrect, then it doesn't apply.

That's why I see a probable paradox in what Witty is arguing. He's saying that the concept "game" has no boundary unless someone gives it a boundary by using it for a specific purpose. — Metaphysician Undercover

Wittgenstein is referring to the conventional use of the word, not to a special purpose use. ("To repeat, we can draw a boundary - for a special purpose.") The conventional use does not have a definite, precise or "rigid" boundary. ("For how is the concept of a game bounded? What still counts as a game, and what no longer does? Can you say where the boundaries are? No. You can draw some, for there aren’t any drawn yet.") But this is unproblematic. ("...this never bothered you before when you used the word “game”.")

Perhaps this is where our confusion started (mine as well as yours): you initially claimed that Wittgenstein was "removing the need for a definition from the existence of a concept". This may be seen as partly right, but only if we take "definition" to mean precise definition (which I wasn't). Because what Wittgenstein is saying is that an inexact, non-rigid, vague definition works just as well in many cases.

This relates to his comments in the following/concurrent sections relating to inexactness and vagueness, and his signalling that words/sentences do not require a precise meaning/definition to be useful (e.g. "stay roughly here"). A boundary can be given to a term to make it more precise ("for a special purpose"), but it is not required for the conventional use/usability of a term.

§68. The interlocutor summarises what he takes to be Wittgenstein's position: the concept of number is "the logical sum" of all the different kinds of numbers. W says that "This need not be so". The concept can be given a definite boundary, but we can still use the concept without giving it this precise definition (and we normally do not). There is no need to clearly demarcate once and for all what counts and what does not count as a "number" for our everyday usage of the word. Wittgenstein states that this kind of imprecise definition also applies to the word "game". "For how is the concept of a game bounded? What still counts as a game, and what no longer does?" A boundary can be drawn (if we want), although none has so far been drawn; and yet this lack of precision never bothered us before. However, Wittgenstein's interlocutor worries that without a precise definition "then the use of the word is unregulated - the 'game' we play with it is unregulated." Wittgenstein responds that the use of the word still involves rules, despite the fact that it is not "everywhere bounded by rules".

§69. W asks how we would explain to someone what a game is. He suggests we would describe games (maybe provide some examples) and then perhaps add "This and similar things are called 'games'." The important point: it is not ignorance which prevents us from providing a precise definition or explanation; it is the vague nature of the concept itself. Again: "We don't know the boundaries because none have been drawn". "[W]e can draw a boundary - for a special purpose", but a boundary is not necessary to the use of the concept. Wittgenstein wryly adds that the same also applies to the concept of exactness, which itself remains vague unless we decide to define it more precisely for a special purpose: "you still owe me a definition of exactness".

Wittgenstein is referring to the conventional use of the word, not to a special purpose use. ("To repeat, we can draw a boundary - for a special purpose.") The conventional use does not have a definite, precise or "rigid" boundary. ("For how is the concept of a game bounded? What still counts as a game, and what no longer does? Can you say where the boundaries are? No. You can draw some, for there aren’t any drawn yet.") But this is unproblematic. ("...this never bothered you before when you used the word “game”.") — Luke

No, he does not refer to "conventional use" nor does he distinguish an instance of special use from an ordinary instance of use. He says at 68 that there is no boundary, but that never troubled you before, when you used the word. Then he says that this does not mean that the use of the word is unregulated. Then at 69 he says this:

We do not know the boundaries because none have been drawn. To repeat, we can draw a boundary—for a special purpose. Does it take that to make the concept usable?

Clearly he is saying that the concept is usable without a boundary.Then he proceeds at 70 to explain the difference between describing something "roughly", and describing something "exactly". He is questioning whether an "exact" description is even possible.

So he never introduced the notion of "conventional use", as you are claiming. You are adding that, and it distorts what Wittgenstein has actually said. He has distinguished between having a boundary and not having a boundary. The boundary is produced when the word is used. Each instance of use being for a particular, or "special" (besondern) purpose.

Perhaps this is where our confusion started (mine as well as yours): you initially claimed that Wittgenstein was "removing the need for a definition from the existence of a concept". This may be seen as partly right, but only if we take "definition" to mean precise definition (which I wasn't). Because what Wittgenstein is saying is that an inexact, non-rigid, vague definition works just as well in many cases. — Luke

He seems to be saying that an "exact" definition is impossible, but this just means that all definitions are to some extent vague or ambiguous. Wittgenstein is saying that the word "game" does not need any definition whatsoever to be usable. It receives its meaning (and therefore becomes definable) through use. In whatever way that you or I, or any other person uses the word, a definition might follow from the way that it was used, for that particular purpose.

This relates to his comments in the following/concurrent sections relating to inexactness and vagueness, and his signalling that words/sentences do not require a precise meaning/definition to be useful (e.g. "stay roughly here"). A boundary can be given to a term to make it more precise ("for a special purpose"), but it is not required for the conventional use/usability of a term. — Luke

So, what I think he is arguing now, in this section, is that all designated definitions, boundaries, and "places", are inexact, vague. You appear to think that he is categorizing and distinguishing between two types of definition, the precise and the vague. I see that he has already established his two categories as having a definition, and not having a definition, and now he is proceeding to argue that all instances of definition are to some extent ambiguous, vague and inexact.

The boundary is produced when the word is used. Each instance of use being for a particular, or "special" (besondern) purpose. — Metaphysician Undercover

For I can give the concept of number rigid boundaries in this way, that is, use the word “number” for a rigidly bounded concept; but I can also use it so that the extension of the concept is not closed by a boundary. — PI 68

Now your catching on.

What? You said that the use produces a boundary. Wittgenstein says it can be used without a boundary, so you're wrong. Also, W says it's the boundary which can be drawn for a special purpose, not an instance of use.