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What does it mean to say that we can attribute neither being nor non-being to the elements? One might say: if everything that we call “being” and “non-being” consists in the obtaining and non-obtaining of connections between elements, it makes no sense to speak of the being (non-being) of an element; just as it makes no sense to speak of the destruction of an element, if everything that we call “destruction” lies in the separation of elements. |25| One would like to say, however, that being cannot be attributed to an element, for if it did not exist, one could not even name it, and so one could state nothing at all about it. But let us consider an analogous case. There is one thing of which one can state neither that it is 1 metre long, nor that it is not 1 metre long, and that is the standard metre in Paris. But this is, of course, not to ascribe any remarkable property to it, but only to mark its peculiar role in the game of measuring with a metre-rule. Suppose that samples of colour were preserved in Paris like the standard metre. So we explain that “sepia” means the colour of the standard sepia which is kept there hermetically sealed. Then it will make no sense to state of this sample either that it is of this colour or that it is not. We can put it like this: This sample is an instrument of the language, by means of which we make colour statements. In this game, it is not something that is represented, but is a means of representation. - And the same applies to an element in language-game (48) when we give it a name by uttering the word “R” - in so doing we have given that object a role in our language-game; it is now means of representation. 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 game; something with which comparisons are made. And this may be an important observation; but it is none the less an observation about our language-game - our mode of representation.

Wittgenstein, Philosophical investigations, part 1, paragraph 50.

  1. Does Wittgenstein mean that to say that standard metre is one metre long is just to utter tautology? And therefore there's no use and, consequently, no meaning. Right?

  2. What does “If it did not exist, it could have no name” mean here? I understand that it's not author's position, it's just mentioned by him. But what's the meaning of what he mentioned then?

  3. One would like to say, however, that being cannot be attributed to an element, for if it did not exist, one could not even name it, and so one could state nothing at all about it.

Isn't this a perfect argument on the behalf of being of an element? Why then can't we attribute being to it?

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  • Being "tautology" a technical concept introduced by W itself in the Tractatus, I think taht using it in the title can be misleading. Commented Apr 15 at 13:42
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    @MauroALLEGRANZA The standard metre from Paris is a physical object. And if you say that something is one metre in length, I may check it by using that standard metre. I'll just put standard metre alongside with the thing you claim to be one metre in length. And why it has no meaning to say that SM is one metre long? Because it's gonna be a tautology? Commented Apr 15 at 14:08
  • See C. G. Luckhardt, WITTGENSTEIN: INVESTIGATIONS 50 (1977): "“(T)he establishment of a method of measurement is antecedent to the correctness of incorrectness of a statement of length,”* Wittgenstein says, and so accepting something as the standard meter has logical priority over using it to measure other objects." Commented Apr 15 at 14:19
  • Maybe the issue is: in the language game of measurement it does not make sense to measure the metre of Paris because it is the standard that legislativos what counts as the correct ascription of a measure of one metre to the lengthof a physical pbject. Commented Apr 15 at 15:27
  • The Paris metre is like the axiom of a system: you cannot prove it in the system. Commented Apr 15 at 17:36

3 Answers 3

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Strictly speaking, one may, of course, say of the standard metre rod that it is one metre long. But Wittgenstein's point is that this is quite a different statement from saying that my dog's tail is one metre long. To say of the tail that it is one metre long is to say it is the same length as the standard metre rod. To say of the standard metre rod that it is one metre long does not mean that it is the same length as itself, since that would be a triviality. To say that the standard metre rod is one metre long is instead to say something about the concept and the measurement of length. It is a statement that plays a special role within the language game of stating the lengths of things. This is why Wittgenstein says that the standard is a means of representation in the language game of measuring, not something that is represented in the system.

In context, Wittgenstein is talking about the concept of existence. Suppose we say (as the logical atomists did) that something 'exists' if it is an element, i.e. an atom in the logical sense, or is composed of elements connected together. And we say a thing is destroyed if its simple component parts are disconnected. Then it follows that an element cannot be destroyed since it has no component parts. But it is not some great metaphysical principle that there are indestructable things. To say elements exist becomes merely a statement about our concept of existence. Wittgenstein is pursuing his project of showing that what seem like metaphysical issues are really nothing of the kind and that many/most/all philosophical problems arise from our use or misuse of language.

Famously, Kripke disagrees. He holds that it makes perfect sense to say that the standard metre rod is one metre long. He considers this statement to be an example of a contingent a priori proposition. According to Kripke, it is metaphysically contingent, since the rod might have been a different length from the length it actually is, but it is a priori knowable, since we don't have to measure the length of the rod to know it is one metre long. There has been quite a bit of debate on this issue.

  • Saul Kripke, Naming and Necessity, Oxford, (1980). Especially, pages 54ff.
  • Nathan Salmon "How to Measure the Standard Metre", Proceedings of the Aristotelian Society 88 (1), 193-217 (1988).
  • W. J. Pollock, "Wittgenstein on The Standard Metre", Philosophical Investigations, 27 (2), 148-157 (2004).

(As I expect you are aware, the metre is no longer defined this way. It is now defined in terms of the distance travelled by light in a vacuum in a second.)

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    What you have said - that it is different to say that the international prototype meter is 1m long, than to say that a a dog's tail is 1m long - is defensible, but not what Wittgenstein said. What he said was that we cannot say that the international prototype meter is 1m long.
    – causative
    Commented Apr 15 at 17:32
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    Note that using the current definition of the metre one could reformulate Wittgenstein's argument by replacing "what is the length of the standard metre rod?" by "what is the speed of light?"
    – armand
    Commented Apr 16 at 0:42
  • @armand Yes, and of course light does have a speed.
    – causative
    Commented Apr 16 at 6:46
  • @causative yes. But it's not the point. The point is that Wittgenstein argues it's meaningless (as he uses the word, ie it produces no new information about the world) to say "light crosses 300.000.000 meter per second" when precisely a meter is defined as "the distance light crosses in 1/300.000.000 second", just like it's meaningless to say "the rod is one meter long" when a meter is defined as "the length of the rod".
    – armand
    Commented Apr 16 at 6:58
  • @armand Neither are meaningless. Also Wittgenstein didn't use the word "meaningless," he said it could not be said that the rod has a length of 1m. But it can be said the rod has a length of 1m, and it can be said that light crosses 299,792,458 m in a second. These facts are not only meaningful, they are centrally important, if you're a physicist.
    – causative
    Commented Apr 16 at 7:16
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There is one thing of which one can state neither that it is 1 metre long, nor that it is not 1 metre long, and that is the standard metre in Paris.

Wittgenstein is referring to the international prototype meter, which was a physical object that looks like this:

enter image description here

Prior to 1960 (when Wittgenstein was writing) the international prototype meter was defined to be exactly one meter long. The same would be said of the standard kilogram. The standard meter was a real, physical, existing object, which Wittgenstein emphasizes by saying it is in Paris, so of course it had a length that you could measure, and that length was 1m.

Wittgenstein's notion of an "element" here is very vague and confused. He is trying to use the standard meter to justify his claim that "elements" can't be said to exist or not exist, but certainly the standard meter physically existed.

There could be things that we might decline to say exist or don't exist. Does the number 1 exist? Arguably, it's not meaningful to say the number 1 does or doesn't exist. (It is also arguable that 1 does exist, and it is also arguable that 1 doesn't exist). But there's no question about the standard meter in Paris; it physically existed and had a definite length.

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    Wittgenstein is rather saying something quite obvious: if to measure length is to compare to the standard meter, we cannot measure the standard meter, as what would we compare it with? As simple as that: <<only to mark its peculiar role in the game of measuring with a metre-rule.>> Commented Apr 15 at 15:26
  • @JulioDiEgidio You compare it with itself, and find the ratio is 1:1, therefore it is 1 meter. The same with the standard kilogram. (Though note this was only true in Wittgenstein's time; the definitions have moved on since then.) This isn't controversial unless you're really drinking the Wittgenstein kool-aid. Any (macroscopic) physical object has a measurable length.
    – causative
    Commented Apr 15 at 16:15
  • I don't know why this is necessary, but suppose you wanted the length of the standard meter plus a penny laid down beside it. That would be easily measurable, about 1019.05 mm. Suppose you wanted the length of the standard meter plus a grain of sand next to it. Again no problem, maybe 1000.5 mm. So, why would you throw a NaN error when you take away the grain of sand?
    – causative
    Commented Apr 15 at 16:48
  • Actually, from a philosophical standpoint, the rod is likely not to match itself if high-tech mensuration occurs. Subtle differences in temperature will results in subtle differences in length. One can aim for "standard conditions", but such a target is an engineering challenge that ultimately has a precision. Macroscopic physical objects have a measurable length, but the measurement is never exact or capable of being perfectly replicated. All measurements are approximate.
    – J D
    Commented Apr 15 at 17:54
  • @Julio Di Egidio " if to measure length is to compare to the standard meter, we cannot measure the standard meter, as what would we compare it with?" The standard meter is indeed a normative fiction to establish an engineering convention, and does not exist in the sense of apples or rocks.
    – J D
    Commented Apr 15 at 17:55
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One would like to say, however, that being cannot be attributed to an element, for if it did not exist, one could not even name it... “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.

I've bolded the mistakes that I think your question makes, while trying to show what the paragraph is saying (which is well captured in the above quote).


Wittgenstein claims that existential claims about primary elements are nonsensical

Wittgenstein can infer that if something did not exist it could not be named; being and non-being make no sense for elements, not being and non-being itself.

"X exists" is meant simply to say: "X" has a meaning... we quite readily say that a particular colour exists; and that is as much as to say that something exists that has that colour

Paragraph 58


The aim the analogy is to show that a nonsensical existential status does not mean elements are simple indestructible parts of reality. A metre rule cannot be used to measure itself but can still be used in a game: being (a metre long) can be nonsense (which is nothing "remarkable... but its peculiar role").

Whether or not the metre rule is tautologously a metre (these are different games) primary elements do not tautologously exist (else, however little it says about the world, we could assume it as we assume the the laws of logic): rather, they are "means of representation"

Similarly, if in a given language it makes no sense to say that X exists or does not, this doesn’t mean that X has any magic powers: it is just that ‘X’ plays a certain role in that language: they are the things whose names in that language have no further explanation (e.g. names for the kings on a chess board in a language for describing the disposition of the pieces). ‘What looks as if it had to exist, is part of the language’

tl;dr

'X exists' and 'X does not exist' makes sense, but 'primary elements exist' doesn't, which is why what doesn't exist cannot be named, but a name doesn't mean that thing exists.

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    IDK why this is at -1, as it seems to be the correct answer, to me
    – andrós
    Commented Apr 16 at 9:17
  • what do i know? makes sense from the little i know
    – andrós
    Commented Apr 18 at 15:02

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