I don't think Wittgenstein is talking about different roles for the chart. He's talking about different roles for whatever it is we see as the paradigm. He's saying that, here, it is used as part of the game, a thing we do is to read off the chart, other places it is used as a means of teaching the rules, in others players simply deduce the rule by observing others play. — Isaac

Thanks Isaac, but unfortunately I'm not satisfied with that explanation. You seem to have jumped ahead to §54. He doesn't mention paradigms at §53 (but maybe we also disagree on the meaning of 'paradigm'?). He says:

If we call such a chart the expression of a rule of the language-game, it can be said that what we call a rule of a language-game may have very different roles in the game.

He actually says that a rule may have very different roles in the game. I'm having trouble imagining how this works. He indicates that if we consider the chart as an expression of a rule, then this somehow demonstrates that a rule can have different roles in the game. This seems to imply that the chart also has different roles in the game. But what are those different roles for the chart?

§53. W here treats language game (48) as though it were in a foreign language that we are trying to understand. He states that there are "a variety of cases" in which we would consider that a sign in the game was being used to represent a particular colour or coloured square. W cites two examples in which we would make such a consideration. The first is if we knew that the users of language game (48) had been taught the use of the signs in a particular way. The second is if the relationship between the colours and their representative signs was compiled in a chart, and where the chart might be used to settle disputes.

W suggests that we can imagine a chart like this being used as "a tool in the use of the language", and gives an example in which its users each carry a copy of the chart in order to encode and translate signs. W explains how the chart could be used to describe a complex, where a user "looks up each element of the complex in it and passes from this to the sign", and then the person to whom the sign is given uses their own chart to translate the sign "into a picture of coloured squares".

This chart might be said to take over here the role that memory and association play in other cases.

W then observes parenthetically that "We don’t usually carry out the order “Bring me a red flower” by looking up the colour red in a colour chart and then bringing a flower of the colour that we find in the chart; but when it is a question of choosing or mixing a particular shade of red, we do sometimes make use of a sample or chart."

This reminds us of the strange behaviour of the shopkeeper at §1 who uses a chart/table to look up the colour red.

W ends the section by stating: "If we call such a chart the expression of a rule of the language-game, it can be said that what we call a rule of a language-game may have very different roles in the game."

I must admit that I find this obscure. Firstly, note that W considers the (whole) chart (or "such a chart") to be the expression of a rule of the language-game, rather than the individual signs or associations contained within it. In terms of its various roles, we can glean from Wittgenstein's example that the chart is used for the different roles of encoding signs and translating signs when describing complexes. I'm not sure what other roles there could be; perhaps there are different roles when using the chart for elements vs. complexes. However, perhaps just noting that the chart (and therefore a rule) can have more than one role is sufficient..?

[n.b. I've switched to using the 4th edition (2009). Earlier versions will have table instead of chart.]

A typical example is not an example of a type — Metaphysician Undercover

It literally is.

Well this is the problem isn't it? Where do we find an example or a sample of a type? — Metaphysician Undercover

Everywhere.

An object is not itself a type, and therefore cannot provide such an example. — Metaphysician Undercover

No, but an object can be an example or a sample of a type.

Perhaps a dictionary definition will help:

paradigm
/ˈparədʌɪm/
noun
1. a typical example or pattern of something; a pattern or model.

This is what is pointed at during an ostensive defintion: a typical example or examples.

I just thought it was an unusual argument.

If the meaning of "one metre" is the length of the stick, then it makes no sense to ask if the stick is one metre long.

But it makes sense to ask if the stick is one metre long.

Therefor, the meaning of "one metre" is not the length of the stick. — Banno

But what if the meaning of "one metre" is the length of the stick? :joke:

What was impossible? Making sure that the stick stayed one metre long... — Banno

How could it not? Anyway, I'm just trying to make sense of the text and of Wittgenstein's puzzling statements about the standard metre. I welcome your opinion. But I think I've said more than enough about it for now, and it's probably time to continue on...

It's impossible that the paradigm is an archetypal object, because according to 55, it is impossible that the paradigm is an object. An archetypal object is an object, and therefore cannot be the paradigm. — Metaphysician Undercover

I've tried my best to explain my understanding of Wittgenstein's use of 'paradigm', MU, but it seems I've failed. A paradigm is more like a type than a token, if that helps.

But the point is that the name is more than just a label affixed to the object. — Metaphysician Undercover

Is it?

The name maintains meaning when the object is destroyed. — Metaphysician Undercover

Yes, because the name is not the object. If an object is destroyed, we can still use the name. "When Mr. N. N. dies one says that the bearer of the name dies, not that the meaning dies." (§40) Or: "In a sense, however, this man is surely what corresponds to his name. But he is destructible, and his name does not lose its meaning when the bearer is destroyed." (§55) What is in question at §51 is: what is the correspondence relation between name and object?

So the "paradigm" by which the name is taught must be something other than the object. — Metaphysician Undercover

Yes, the paradigm is the archetypal object. Wittgenstein gives an approximate definition of 'paradigm' at §50:

What looks as if it had to exist, is part of the language. It is a paradigm in our language-game; something with which comparison is made.

Colours are an example of a paradigm for Wittgenstein. I would say that it is something which is used in the giving/learning of an ostensive defintion, e.g. "That colour is green". This appears to be what he means when he says at §51 that signs would be taught by "pointing at paradigms". At §56, Wittgenstein challenges the notion that paradigms can be mental rather than public.

Agreed. I only wanted to highlight that the literal reading of Wittgenstein on the standard metre has some scholarly support.

Firstly, it needs to be emphasised that Wittgenstein draws a distinction at §49 between words and propositions or, that is, naming and describing:

But whether it 'is a word or a proposition' depends on the situation in which it is uttered or written. For instance, if A has to describe complexes of coloured squares to B and he uses the word "R" alone, we shall be able to say that the word is a description—a proposition.

W here depicts 'describing', or using "R" as a proposition. Another example of this is the 'block-pillar-slab-beam' language-game (2), where the words/signs are being used within the language-game as orders for person B to bring a particular stone to person A.

But if he is memorizing the words and their meanings, or if he is teaching someone else the use of the words and uttering them in the course of ostensive teaching, we shall not say that they are propositions. In this situation the word "R", for instance, is not a description; it names an element——.

W here depicts 'naming', or using "R" as a word. We would not expect that person B in language-game (2) would automatically know how to use the words 'block', 'pillar', 'slab' and 'beam'. They would need to be taught how to use these words, and we would presuppose "that the use of the signs in the language-game would be taught in a different way, in particular by pointing to paradigms."

What do you expect the paradigms would be in the case of language-game (2)? I assume that the name of each stone would be taught via ostensive definition, by being associated with a pattern; with 'stones that look like this'. For other objects, it may not be about what the object 'looks like'; it might be what it smells, tastes or feels like, or something else.

Wittgenstein points out the distinction between naming and describing:

...but it would be queer to make that a reason for saying that an element can only be named! For naming and describing do not stand on the same level: naming is a preparation for description.

For a more informed opinion, Baker and Hacker offer this reading of the opening remarks at §51:

The words of §48 ‘correspond’ to colours, but what does the correspondence consist in (‘what does “the name-relation” consist in?’)? The description of §48 merely set up this connection, but did not say what it was. The first response is that ‘R’, ‘W’, etc., would be taught by pointing at paradigms. This is correct. But this is to say something about the ‘preparation’ for the language-game. We want an explanation of what correspondence consists in in the practice of the language; i.e. we want to know how the teaching relates to the practice of using the signs. In particular, we must reveal the normative component of teaching that provides a standard of correct use. — Baker & Hacker, Understanding and Meaning Volume 1, Part II

I've found an online copy of the book, for those interested. The article I've been citing is Chapter 3 of the book.

Thanks for the clarification, so no one's trying to to say that one can 'never' say that the Standard Metre is or is not 1m long, — Isaac

Actually, Wittgenstein is. At least, that's how I read it (at §50). More precisely, it makes no sense to say either that the standard metre is or that it is not one metre long.

Hi Isaac, welcome.

I understand (I think) the references you're making, but I'm not clear what it is you're actually arguing against.

Is it the idea, made earlier I think, that there are games in which the expression "the Standard Metre is 1m in length" may be meaningful? — Isaac

The statement we have recently been discussing is the seemingly paradoxical and/or law-of-excluded-middle-defying:

There is one thing of which one can say neither that it is one metre long, nor that it is not one metre long, and that is the standard metre in Paris. — Wittgenstein, PI §50

If so, how do you square that with Wittgenstein's later discussion about holding the colours as samples in our memory at some times, yet at still other times we might refer to expectation (such as mixing chemicals). It seems clear to me that he is making the point, not that there is some absolute rule about a sample such as the Standard Metre, but rather that its rule depends on the language game? — Isaac

Good question. This is apparently a common objection. However, as the author of the previously cited article notes, the standard metre plays a unique role, along with other standards such as colours:

Insofar as we find it necessary to begin testing and checking the size of the standard metre bar, the bar is thereby deprived of its special epistemic status. It is de facto no longer functioning thereafter as fulfilling the language-game criteriological role of a standard of unit length. A standard or criterion, whether of metric length, colour, or of identity conditions for an individual private sensation, is never treated in such a way while its language-game role continues, but rather with something amounting to respect for the dignity of its exceptional responsibility. — Dale Jacquette, Measure for measure? Wittgenstein on language-game criteria and the Paris standard metre bar.

Could we not follow exactly Wittgenstein's later example I mentioned above to say "the standard metre is not 1m long" and mean by it "the standard metre must be broken because it is nowhere near my memory of how long a metre is". That seems to me to be a perfectly coherent use of the expression consistent with what Wittgenstein seems to be saying. — Isaac

Fair enough, but I think in the context of Wittgenstein's use in the text, he is referring to the standard metre in its 'criteriological role' as a standard, and in this role/context it can neither be said that it is or that it is not one metre long. But perhaps this is a dodge.

To be honest, the cited article offers a defence against the type of argument you have outlined, but I didn't find it entirely convincing, so I will concede that this may be a possible context in which it could be said that the standard metre is/not one metre long. However, I wonder whether the same argument would hold against the current standard metre, defined in terms of the speed of light

So what's going on at 51 when he says the following?

Well it was presupposed that the use of the signs in the language-game would be taught in a different way, in particular by pointing to paradigms.

This is in the context of describing the language game of (48) in which there is a pattern of coloured squares, which are given signs. So how is this a "different" way? That language game of (48) is an exemplar, sample, or standard. It is a matter of pointing to a paradigm. Is he now saying that to understand that paradigm, we must refer to a further paradigm? Of course this would be just a recipe for infinite regress.

Or, is it the case that he is trying to lead us away from this idea of pointing to a paradigm? He hasn't yet answered what "correspondence" consists of, and maybe he has a different explanation, something other than pointing to a paradigm. — Metaphysician Undercover

The way I read it, after posing the initial question of how signs and colours correspond, W states that it was presupposed that the correspondence associated with the use of the signs in the language-game would be different from the correspondence associated with the teaching of those signs. W indicates that the teaching of the signs consists of pointing to paradigms, where the paradigms here are the colours (or the coloured squares), and associating those colours with the signs/words/letters "R", "B", etc. However, how is this correspondence maintained in the use of these signs? We would presume that it consists of something other than pointing to paradigms (i.e. something other than ostensive definition). We can presume this because naming and description are on a different level; ostensive definition is only a precursor to playing the game. Wittgenstein then goes on to question how the correspondence is maintained within the language game (in use) after the terms have been defined: are mistakes possible, and what counts as a mistake? Is it a mental correspondence between sign and colour? etc.

Without quoting the entire article, I think that the author of the article on the polarity principle sums up the (or my) main point as:

"To say that the standard metre bar is neither one metre nor not one metre in length is to say that the predication and its negation are both equally philosophically ungrammatical."

And in summary:

"The fact that it makes no sense to attribute the property of being one metre long to the standard metre bar, because it makes no sense by virtue of its language-game criteriological status to deny that the standard metre bar is one metre long, is supposed to be analogous to the fact that it makes no sense to attribute existence to elements because it makes no sense to deny that elements exist. As a point of philosophical grammar, now that Wittgenstein has moved beyond the picture theory of meaning, it is as meaningless now for different reasons to say that the elements exist or do not exist as it would be to say that the elements as simplest parts have ceased to exist because they have been destroyed, where to be destroyed means nothing other than to be broken down into simpler parts."

The author also cites another example of the same principle at work, where Wittgenstein (later in the book) rejects the claim "I know that I am in pain" because there is no "established practical role for the complementary or conceptually-grammatically polar expression, ‘I doubt that I am in pain’."

I also searched through OC for something similar, and the stretch of passages from OC 35 to 60 also touch on the same example of knowledge (unsurprisingly); in particular 35-37 and more specifically 58-60.

I thought there were more examples, but perhaps more will come up later in the text. Something to test and/or keep an eye out for, anyway.

Paradigms, exemplars, samples, standards: all have a similar meaning.

I don't think Wittgenstein really believes that we can't say a meter stick is 1 meter long, — fdrake

I think he does really believe it. The standard metre's only role is to set the naming convention; to use its length to define the "metre" unit. It makes no sense to say that the standard metre is not one metre long, and it therefore makes no sense to say that it is one metre long. This 'polarity principle', that I referenced in an earlier post, is something W will raise again in various forms through PI and On Certainty (as a principle, not a paradox).

Furthermore, it is not only absurd to say that the standard metre is not one metre long, but also, the question or proposition of the standard metre's length-in-metres means that we are now playing the description (i.e. measuring) game, instead of the naming game. However, the naming game is, conventionally, the standard-metre's only game/purpose.

I'm viewing my attempt to neuter the paradox... — fdrake

You've used this term more than once. What do you consider to be the paradox? I don't think Wittgenstein views it or intends it as a paradox.

Thanks for the clarification, . I think I agree (but maybe I still don't get it?). In relation to the reading of the text, I think you pretty much nailed it in one of the opening paragraphs of your original post:

The issue we're discussing arises, then, when we interpret the meter stick as an thing to be measured using itself; the problem being, how can it make sense to say that the meter stick is a meter long when we're using comparison to the meter stick to measure? The alleged problem with this is that the length of the meter stick will always be a the length of the meter stick, so it's not appropriate to say we measure any length using it in the game of measuring using the meter stick as a standard.

The Paris metre represents the word "metre", but there is still a need to signify which aspect of it represents "metre"? — Metaphysician Undercover

Don't we already know that?

Hi . At first, I thought I was in agreement with your post, but something doesn't sit right, so I hope you can clarify.

The key thing, it seems to me, is bound up with what it means to compare an item in our game of measuring with the meter stick. If we grant that a comparison takes place between distinct elements, then it is inappropriate to measure the meter stick with itself. If we constrain 'comparison' to mean 'must be done between distinct units in the language game, one of which is the meter stick itself', then applying the meter stick to itself is not a comparison in the sense of comparison at work in the language game. But I believe it is a comparison in the broader language game of length measurement, standardisation and unit ascription.

Is the C1 comparison simply comparing the metre stick to itself (somehow)?

Also, I don't understand what the 'broader' type of comparison (referred to in your last sentence above) is supposed to include. Is this 'broader' comparison also included in C1?

The comparison which occurs between the meter stick and itself is not a comparison in sense C1, but it is nevertheless a comparison of length/extension.

What is "a comparison in sense C1"? What type of comparison is being made in the C1 sense if it is not a comparison of length/extension?

It is required that a length is the same as itself as a constitutive rule of of the broader length comparison language game, because the game operates on its items as token length representations rather than as actual objects for measurement. Precisely, then, comparisons in this broader game are comparisons of lengths relative to lengths and not lengths relative to the meter stick. Call this comparison sense C2.

Are you saying that 'token length representations' are abstract units of measurement? Therefore, C2 comparisons are not made relative to the metre stick, but to the metre unit?

So in terms of C1 comparisons, the meter stick can't be held up to itself - this is not an appropriate move in the language game, but in terms of C2 comparisons it absolutely is; C2 comparisons operate on lengths.

Are you saying that C2 comparisons involve the use of the metre unit, and so here comparisons can be made between the metre unit and the metre stick?

§51. Wittgenstein reminds us of his description of language game (48) where the words "R", "B", etc. correspond to the colours of the squares. He asks "what does this correspondence consist in; in what sense can one say that certain colours of squares correspond to these signs?" Wittgenstein notes that the account given in (48) "merely set up a connexion" between the signs ("R", "B", etc.) and the colours. He states that it was presupposed that the use of signs in the language-game would be taught via "pointing to paradigms". "Very well", Wittgenstein says, but of what does the correspondence consist in with the "technique of using the language" (i.e. in use, not in preparation)? He queries whether the person describing a square always uses the appropriate sign. W asks: what if an error is made? Furthermore, "what is the criterion by which this is a mistake?" Or, does the correspondence between sign and colour consist in some mental connection made by the people using the sign, such that when using "the sign "R" a red square always comes before their minds"? Wittgenstein suggests that to discover the answer in this case, we "must focus on the details of what goes on; must look at them from close to."

§52. Anticipating resistance to his therapy, Wittgenstein states that "we must learn to understand what it is that opposes such an examination of details in philosophy."

I also think you're right that Witty's presentation of the issue is confusing because he doesn't make this narrow application clear, and it can come across as a general purpose statement about the Paris meter as such. But a close reading will dispel any such reading I think. — StreetlightX

Right, and I also think it's important to note the following section of §50, which possibly shows that the application is to much more than just the standard metre:

In this language-game it is not something that is represented, but is a means of representation.—And just this goes for an element in language-game (48) when we name it by uttering the word "R": this gives this object a role in our language-game; it is now a means of representation.

W's extension of the standard metre example to the word/name "R" here could indicate that the preparation/use distinction applies to all names in our language... I think?

It makes no sense to assert that the standard metre is one metre long, because this proposition implies that the standard metre might not be one metre long, which is absurd. Therefore, the standard metre is the one thing of which we can say neither that it is, nor that it is not, one metre long.

This relates to my 'verification' comments to Banno.

Is this an adequate reading? — StreetlightX

Yes, I think so.

ETA: although I think the standard metre is a special case as its purpose is only to set the convention.

I feel as though I've fallen behind, but things are getting serious (and more difficult) now. I've also spent a little longer on §50 to try and get clear in my own thinking.

§49. What does it mean "to say that we cannot define (that is, describe) these elements, but only name them?" Referring to his example of the 3x3 colour matrix at §48, W proposes the "limiting case" of a (one square) 1x1 matrix having a definition or description that is "simply the name of the coloured square". He states that "a sign "R" or "B", etc. may be sometimes a word and sometimes a proposition. But where it 'is a word or a proposition' depends on the situation in which it is uttered or written." W states that the word "R" might be a description or a proposition if it is being used within a language-game to refer to a coloured square. Alternatively, the same word "R" might be a word or a name if its use is being taught to others or to oneself, and where it is, therefore, only being prepared for use within a language-game. As Wittgenstein states:"...naming and describing do not stand on the same level: naming is a preparation for description. Naming is so far not a move in the language-game..."

§50. "What does it mean to say that we can attribute neither being nor non-being to elements? One might say: if everything that we call "being" and "non-being" consists in the existence and non-existence of connexions between elements, it makes no sense to speak of an element's being (non-being)..."

That is, if being (and non-being) consists in (or is defined as) the connections between elements, then it makes no sense to speak of the being (or non-being) of the elements themselves. This is clarified by his next statement:

"...just as when everything that we call "destruction" lies in the separation of elements, it makes no sense to speak of the destruction of an element..."

That is, if destruction consists in (or is defined as) the separation of elements, then it makes no sense to speak of the destruction of an element.

"One would, however, like to say: existence cannot be attributed to an element, for if it did not exist, one could not even name it and so one could say nothing at all of it."

It's hard to see the problem here, since it sounds perfectly sensible to say that if a particular element did not exist then we could not name it or talk about it. But this will become clearer with Wittgenstein's remarks on the standard metre which immediately follow, which he calls "an analogous case".

I won't rehash the standard metre discussion, except to re-quote Fogelin who interprets Wittgenstein here as saying that it makes no sense "to use something as a standard and simultaneously judge its accordance with that standard."

Wittgenstein then asks us to imagine a similar case to the standard metre in which a sample of "standard sepia" is kept hermetically sealed in Paris. W states that it will likewise "make no sense to say of this sample either that it is of this colour or that it is not".

Wittgenstein's reference to this being "an analogous case" makes clear that when he earlier said that existence cannot be attributed to an element, what he implied was that neither existence nor non-existence can be attributed to an element.

In the reference work 'Wittgenstein's Philosophical Investigations' edited by Dr Arif Ahmed, Dale Jacquette identifies a principle at work which connects the opening lines of §50 (regarding the existence of elements) with the standard metre and standard sepia examples. Mr Jacquette calls it the "polarity or complementarity principle" such that whenever "the predication or its negation or complement serve no purpose in a genuine language-game, the predication and its negation or complement are judged to have violated a rule of philosophical grammar". In the case of the standard metre, since it makes no sense to say that the standard metre is not one metre long, then it likewise makes no sense to say that it is one metre long.

Wittgenstein goes on to say that a standard or sample, such as the standard metre, "is not something that is represented, but is a means of representation". A 'means of representation' is a way of representing something. The standard metre is an example of this since it introduces, or prepares the way for, our use of the metre (as a length) in our language-games. However, once introduced, our use of the metre as a length is 'something that is represented'; something that is used within our language-games. The parallels of this distinction to the distinction drawn between names and descriptions at §49 are now apparent: preparation for use in the language-game vs. use in the language-game.

Hence: "And to say "If it did not exist, it could have no name" is to say as much and as little as: if this thing did not exist, we could not use it in our language-game.—What looks as if it had to exist, is part of the language. 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."

Stop pretending then. What do you think Wittgenstein means when he says that the standard metre is the one thing of which we can say neither that it is, nor that it is not, one metre long?

What happened to your latest post?

Have you even read the book? If you'd like to join in, then follow along. If all you have to offer are grand pronouncements about the book as a whole, then nobody's interested - at least, not yet. We're currently up to about section 50 where Wittgenstein talks about the standard metre, among other things, in case you have anything relevant to say about that. We didn't have a discussion beforehand about how we're going to discuss it, so I can't help you there.

Do you know why we're discussing the standard metre?

I never said anything about "more real".

Wittgenstein is talking about the stick, the standard measurement, the yardstick; not "one metre".

No, the tape measures metre was defined by the Standard Metre. Who know what havoc temperature and humidity have wreaked on either in the meantime, but who cares? You certainly don't when you're building your shed. You're not continually referring back to the Standard Metre. What you are calling a metre is that which 'approximately' reaches the 1m mark on your tape measure,and that is sufficient. If you are concerned that some damage has befallen the Standard Metre, you might use your tape measure to help determine whether that is the case — Ciaran

I'm sure that some people care about precision of measurement other than shed-builders. Also, who knows what havoc the elements have likewise wreaked on your tape measure? But, anyway, your tape measure is not the standard. If the standard metre were damaged, then we might agree to use some other standard measurement instead, but for now the standard metre remains the standard.

Are you talking about "one metre" or the standard metre? The standard metre is a stick which has the sample/standard length that defines "one metre".

Kripke's suggestion that the length of the standard metre may change over time does not alter Wittgenstein's insight. Perhaps the length of the standard metre (stick) in Paris does change over time, but as long as we use it as our yardstick, or as our sample against which all others are defined, then it makes no difference. Or maybe we change to some other more sturdy material and then use that as the new standard metre, and from then on all metres will be defined with reference to that new standard.

The tape measure's metre is defined by the standard metre "stick", the same as all other metres. Which other metre are you thinking of?

But it's the yardstick! (The metre-stick, but you get my drift.) How could it "might not have been" a metre? It's the definition of a metre!

The point is, you're simultaneously saying that it is a metre long (because it was baptised as such) and that it is questionable whether it is a metre long.

I typically measure them with a ruler.

I'm trying to change your mind, but you didn't answer my question: how will you verify whether it is really one metre long?