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.

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

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.

I think that "paradigm" in Wittgenstein's use, refers specifically to examples, or samples of use, rather than an example like the chart of coloured squares, and this is why I associate it with "grammar". Further, "paradigm" seems to imply more than just a simple example, but a pattern of use which consists of a repetition of the word being used numerous times in a similar way.

I read that post and agreed with it.

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

I agree that it makes no sense for C1 comparisons. What I've been trying to show is that there are language games in which it makes sense to say that the Paris meter stick is 1 meter long!

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.

I've just read through this thread with interest. I've found a number of points I'd like to clarify with their respective authors, but I think it would be disruptive to do so for points made way back, so I'll just limit my query to this one.

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?

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? 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.

Or is your objection to something else entirely that I have missed? If so, I'd be grateful if you could clarify.

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.

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

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, only that such a statement would be meaningless in the context of it's being used as a criteria for what a metre is. That ties in a lot better with my understanding of the text than what I thought you might be saying.

I wonder whether the same argument would hold against the current standard metre, defined in terms of the speed of light — Luke

I think it probably would. Imagine someone claiming to reference 1m using the speed of light (I'm really not sure about how this is done) came up to you with a stick taller than you and said "this stick is a metre long, I've just measured it by the speed of light". I think I'd still be inclined to say "no it isn't" based on my memory of the sort of length a metre is (ie shorter than me). Supposing that this person could demonstrate to me conclusively that they had indeed measured this stick by the new speed of light standard, I'd still be inclined to consider that I must be hallucinating, maybe some weird anomaly had taken place that I can't get my head round. Pretty much anything but agree that my entire memory of everything a metre is has been wrong, it's just too invested in too many language games now to be represented by just once source sample.

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.

OK, but in the context of what we've just discussed about Wittgenstein's reference to the many ways in which we check our use against samples, what is it about the text that makes you think Wittgenstein is being so categorical about this issue? It would be quite out of character with the rest of the argument, which seems to be entirely saying that there is no one way in which a sample is used, but rather a variety of ways depending on the context.

I don't want to jump ahead, but consider his later discussion of what it means to 'know' a paradigm or rule. Saying that the only way to 'know' what a metre is is to have access to the Standard Metre, would seem to be in contradiction to these later sections.

The trick is this: in its role as the standard meter, one can 'never' say that the Standard Metre is or is not 1m long. But the lump of metal that is the standard meter, does not always play that role in our discussions. Keep an eye on roles, and you can't go wrong here.

Yes, that's certainly how I understand it. I think that in the same way one can take "the lump of metal" and say that it does not always play that role, one can take the expression "one metre" and say it is not always (anymore) referring to "the lump of metal", at least not contemperaneously.

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

Considering we both agree when talking about the context of the discussion in the PI we should table the discussion for later I imagine. We could probably go back and forth about it for a long time, which would just derail this marvellous thread.

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). — Luke

I don't think I agree with this. The nature of a "paradigm" must be other than a physical object which plays the role of a sample. Look at what follows, 52-55. He says we must look at this situation up close. Then he discusses a variety of different possible ways which people could learn the language-game of 48. So what he is doing is casting doubt on that statement of 51, the presupposition that the language-would be taught by pointing to paradigms. Now, when looking up close, he sees numerous ways in which the language-game might be learnt.

So even when he introduces the idea of "a rule" at the end of 53, he goes on at 54 to discuss different possible ways of learning how to play according to rules.

54 Let us recall the kinds of case where we say that a game is
played according to a definite rule.

When he says "recall", I believe that this is a reference back to the same principle discussed at 31. So "learning how to play according to a rule" is not necessarily a matter of learning the rule. He again (like at 31) states the possibility of learning to play by the rule, simply by observing the play of the game, without actually learning the rule. In this case there would be no paradigm pointed to, in the sense of a sample pointed to as the rule.

Then, at 55 he returns to the idea expressed in the 40's, that even when the object which corresponds to the word is destroyed, the meaning of the word persists. So there is a sense in which the meaning of a word is indestructible. And he ends 55 with this statement:

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

Consider what this means. He has already explained that there is no such thing as a named object which is necessary for the name to have meaning. The name lives on, with meaning, after the object is destroyed. So names always have meaning even when there is no corresponding object. But now he is saying that there is something which corresponds to a name, without which that name could not have meaning. This something is what he calls "a paradigm that is used in connexion with the name in the language game".

So, at 56 and onward, he proceeds to discuss the nature of this "sample". As demonstrated at 55, and earlier, 40-45, this "paradigm" cannot be a object, because it must be in this sense indestructible.

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

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. — Luke

But the point is that the name is more than just a label affixed to the object. The name maintains meaning when the object is destroyed. So the "paradigm" by which the name is taught must be something other than the object. A simple ostensive definition, associating the name with the stones, does not suffice to account for this meaning which the name has, that goes beyond the existence of the stones. Therefore the "paradigm" by which the meaning of the names is taught, must be something other than the stones themselves. I think this is quite explicit at 55.

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.

Yes, because the name is not the object. — Luke

No, it's not because the name is not the object. Consider that even if the name is not the object, but meaning was found in a direct correspondence between name and object, then the name would lose its meaning without object. So, because the name has meaning with or without the existence of the object, meaning is not a direct correspondence between name and object. And since meaning is something other than the direct correspondence of name to object, we must look to something other than the object to understand how we learn meaning. And therefore, this is evidence that we must look at something beyond the object, in order to learn how to use words (meaning is use). Witty says it is by referring to a "paradigm" that we understand how to use the word. This paradigm is not an object because that would imply a direct correspondence between the word and that object.

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

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. Here's what he says again:

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

So Wittgenstein is very explicit. The name has meaning when the object does not exist. The name cannot have meaning without the "paradigm" which he refers to here. Therefore we can quite readily conclude that this "paradigm" cannot be an object, not even an archetypal object, because the name would still have meaning without that archetypal object, and it can't have meaning without the paradigm.

At §56, Wittgenstein challenges the notion that paradigms can be mental rather than public. — Luke

I agree, he claims that paradigms cannot be mental, and argues this at 56 by referring to the failings of memory. However, neither can these paradigms exist as objects, which is argued at 55. This is why I said earlier that I think he must be referring to paradigms of use or something like that.

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.

This is how I understand paradigms also. It seems to me, if one "pulls out" the focus a bit to look at the whole section, the theme is consistently that things are neither this way nor that, but rather a variety of ways united only by the fact that the use serves some function in a game.

So, going right back to the first language game, Wittgenstein says that the paradigm 'might' be a table corresponding words with pictures, but it need not be. It may be simply that the word slab (uttered by a) produces the action of b handing a flat stone and a receiving it evidently to satisfied. Consider later (I'm sorry for the lack of references, I'm following this thread at work and I don't have a copy of the text with the) Wittgenstein mentions how we can tell when a speaker, even of a foreign language, has made an error by their attitude.

The idea behind 'meaning as use', I think, is that words perform something, they make something happen and it is by the evident success of this 'happening' that we check our memory of the meaning from whatever original act gave us cause to think it meant such and such.

We could say that the meaning of a word is maintained by the act of checking for signs of error in its use. All the while you bring the builder an object in response to 'slab!' which he appears satisfied with, you may be content that you have the meaning of 'slab!' in that language game. The moment he rejects what you bring with a frown, you return to the pile and pick a different object, you must have mistaken the meaning of 'slab!'.


It misses the point to put too much emphasis on the original act of definition, this is only what primes us to an idea of what a word can 'do'. It is only when we try that word out and experience first hand what is actually does that we can say we have grasped its meaning.

Yeah, that's thought provoking.

SO, for Kripke as well as for Wittgenstein there is a special role for the stick in Paris. For Kripke the stick is used to baptise a certain length as being one metre. Thereafter that length is fixed by the rigid designator "one metre".

Now the process of checking the length of any item in Metres requires making a comparison between stick and item. For Wittgenstein this creates an issue when it comes to asking if the stick is a metre long; this question becomes for him the same as asking if the stick is as long as itself.

For Kripke, the comparison is not between the stick and itself, but between the stick and the length that has been baptised as "one Metre".

"One Metre" is not a synonym for "the length of the stick in Paris". It makes sense to ask if the length of that stick has changed. But asking if the stick is still a metre long is not the same as asking if the stick is still as long as itself.

So I'm leaning towards agreeing with Kripke that there was something more going on here than Wittgenstein supposed.

Now I want to go and check this against the other points here, such as the discussion of colour swatches.

Let us imagine samples of colours being preserved in Paris like the standard metre. We define: "Sepia" means the colour of the standard sepia which is there kept hermetically sealed. Then it will make no sense to say of this sample either that it is of this colour or that it is not.

(my bolding).

But it does make sense to ask such a question. Perhaps the swatch fades minutely each time a comparison is made; or some chemical reaction in the swatch changes the colour over time; or that the distribution of colour across the swatch is found to be uneven. Such things might happen.

Those who follow Wittgenstein here might say that this is all good; that given "Sepia" means the colour of the standard sepia, then the colour sepia changes over time.

Those who follow Kripke can also say that all is good; but that rather than the colour Sepia changing over time, that "Sepia" rigidly designates the colour in all possible situations, and hence that the swatch ceased to be sepia.

Now you can make your own choice, however it seems to me that Kripke's account is intuitively more appealing.

It makes no sense to say that the standard metre is not one metre long, — Luke

But plainly that is wrong; and that's why the physicists involved went to great lengths to isolate the stick and to maintain its environment. Perhaps one of the reasons that the stick was eventually replaced is that this proved to be an impossible task...

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

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 probably time to continue on... — Luke

Yep.

I don't understand the distinction you're making here, I'd be grateful if you could clarify.

Wittgenstein is obviously not suggesting a method of recording sepia, right? I mean he's not writing a book aimed at colour archivists whom he's hoping might take up his suggestion. He's saying if we were to say that such a sample were the colour 'sepia', then it would make no sense to ask of it "is this Sepia?". So it doesn't matter that, in the real world the colour might fade, that's just a good reason not to store colour paradigms that way, and indeed we don't. The point he's making is not what form the paradigm should take, but that whatever it is it makes no sense to ask questions about its existence or definition.

But maybe I've misunderstood what you're saying?

Well, the "if" is important.

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.

So, as I think @StreetlightX argued, Wittgenstein's point holds; and for our purposes here we can move on; but that subsequent philosophical discussion - Kripke - has shown that there is a muddle in the middle of the discussion of the metre. Wittgenstein claimed that, If A then B, and he was correct; but we now know that not-A.