How long is the standard meter?

Question

In the Philosophical Investigations §50, Wittgenstein writes:

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. – But this is, of course, not to ascribe any extraordinary property to it, but only to mark its peculiar role in the language-game of measuring with a metre-rule.

Suppose a child looks at the standard metre, not knowing what it was, points at it and asks his father how long it is, what should his father answer?

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EDIT - a note about the paper by Pollock, referenced by @JosephWeissman in the comments:

In the paper Pollock criticizes Kripke:

Kripke certainly does not seem to understand how a standard is chosen for a measuring system when he suggests that the person who chose the standard for the metric system already knew what a metre was before he had chosen the standard for the system.
...
As Kripke puts it in Naming and Necessity, the person who performs such a ceremony is:

using this definition not to give the meaning of what he called the ‘meter’, but to fix the reference. (For such an abstract thing as a unit of length, the notion of reference may be unclear. But let’s suppose it’s clear enough for the present purposes). He uses it to fix a reference. There is a certain length which he wants to mark out. He marks it out by an accidental property, namely that there is a stick of that length

But it seems to me that Kripke correctly describes how the standard metre of Paris was created according to the Wikipedia:

While Méchain and Delambre were completing their survey, the commission had ordered a series of platinum bars to be made based on the provisional metre. When the final result was known, the bar whose length was closest to the meridional definition of the metre was selected and placed in the National Archives on 22 June 1799 as a permanent record of the result. This standard metre bar became known as the mètre des Archives.

Namely, the French committee chose the platinum bar which was accidentally closest to the length computed by the surveyors.

Answer 1

There has been a fair bit of discussion of this statement from Wittgenstein. Kripke in Naming and Necessity famously disagrees entirely and offers "the standard metre in Paris is 1 metre long" as an example of an aprioi contingent statement. A priori because we don't have to measure it to know it is 1 metre long, but contingent because that particular rod could have had a different length from the one it actually has.

I'm not an expert on Wittgenstein so I wouldn't presume to interpret him, but he may be making the point that to say (1) the standard metre is one metre long; is quite a different kind of statement from saying (2) a piece of wood in my hand is one metre long. (2) ultimately means that the piece of wood is the same length as the standard metre, while (1) cannot simply mean that the standard metre is the same length as itself, because that is vacuous. Rather, (1) is part of a language game of measuring and has a special status in that game.

As to what the father should say to his son, I don't see any problem with the father giving the answer: it is one metre long - that is how the metre is defined.

(Incidentally, although the metre was defined that way at the time Wittgenstein and Kripke were writing, it isn't any longer; it is now defined in terms of the speed of light.)

Answer 2

The answer, unfortunately, belongs more in Parenting SE than in Philosophy SE. The real question is what the father wishes to do with the situation the child has created. If the child does not need any more questions in their life, the answer may be "it is 1 meter long," and be done with it.

The deeper line of reasoning that Wittgenstein is engaging in may be approached with "It is 1 meter long. In fact, the meter is defined such that this object is exactly 1 meter long." This may go over the child's head, or it may open up a line of questioning about why a meter needs a definition in the first place. It may even open up a line of questions regarding how humans attempt to capture their environment in their minds using such tools to measure it.

Or, you can get so totally petrified with trying to figure out the best answer that you belt out, "This object is approximately one meter long. As of 1983, the metre is defined to be the length of the path travelled by light in vacuum during a time interval of 1/299792458 of a second. A second is defined to be 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom." and pray to the deity of your preference that the child doesn't ask you what a Caesium atom is today.

Answer 3

Wittgenstein states, "one can say neither that it is one metre long, nor that it is not one metre long". The first condition denies something while the second permits something. Each activity needs to be considered separately to make the sense that Wittgenstein had in mind.

What was he denying? He was denying that the role of the standard metre is something in need of being measured. How would we check (in Wittgenstein's time) whether the standard metre were actually a meter long? There was nothing one could appeal to, because whatever the standard metre is it tells us what a meter measures as. Under this condition the standard metre is not an empirical thing, not subject to testing or doubt in much the same way that Wittgenstein considers Moore's propositions in his later writings collected in On Certainty. The mistake is to think of them as empirical (open to question or discovery) rather than the actual framing of the language game.

What he is allowing in the second condition is that the standard metre still is a physical thing, and a meter stick measured by it can be turned into that which measures the standard metre. It is a question of what is measuring what at what time. Not to verify that the standard metre is a meter long (nothing in Wittgenstein's time could offer that), but, for instance, to make marks on it that show a quarter meter, a half meter, and so forth. We can measure the standard meter not as if we were in any doubts as to how long it actually is, but because other empirical operations are possible. Because it still is something physical.

Wittgenstein's idea is that we get trapped looking at the thing itself as if it could reveal itself to us. As if mysterious properties might yet be disclosed. What we instead ought to focus on, for him, is the actual use a thing has in our lives. The standard metre was at that time a thing whose role was so specific, that Wittgenstein felt he could clearly show us the difference between taking something as an empirical question, where doubt and testing would live, and taking something as quite other. In On Certainty he explores this more fully, making the same points but with more familiar examples. His obsession in those later years was to bring some clarity to an issue we still stumble around, that a thing that counts as a measure needs to be considered as having an entirely different role from things we expect to measure.

From On Certainty:

96. It might be imagined that some propositions, of the form of empirical propositions, were hardened and functioned as channels for such empirical propositions as were not hardened but fluid; and that this relation altered with time, in that fluid propositions hardened, and hard ones became fluid.

97. The mythology may change back into a state of flux, the river-bed of thoughts may shift. But I distinguish between the movement of the waters on the river-bed and the shift of the bed itself; though there is not a sharp division of the one from the other.

98. But if someone were to say "So logic too is an empirical science" he would be wrong. Yet this is right: the same proposition may get treated at one time as something to test by experience, at another as a rule of testing.

99. And the bank of that river consists partly of hard rock, subject to no alteration or only to an imperceptible one, partly of sand, which now in one place now in another gets washed away, or deposited.

100. The truths which Moore says he knows, are such as, roughly speaking, all of us know, if he knows them.

The ancient Greek fable of Procrustes might have helped remove our confusion. This was a story where an innkeeper guaranteed that his customers would perfectly fit his beds. But rather than the bed changing shape to fit the customer the customer was stretched out or hacked up become the right size. It simply matters what we take to be the measure and what we take to be the thing measured.

Answer 4

Wittgenstein's point is that every standard is at some level strictly conventional: we agree that it is so, explicitly or implicitly, and by agreeing make it so. We cannot talk about the measurement of the standard without falling into self-reference.

When a father answers this question, he would (obviously) say that the meter bar is one meter long. But we as philosophers should notice that he is engaged in a different language game when he does it. This is not a 'measure the length of...' language game, it is a 'share the convention of...' language game. By telling his son this bar is one meter long, the father is inducting his child into the convention of 'meter'.

Answer 5

You have to start somewhere.

The question makes sense ONLY if there is an agreed standard for measuring, and an agreed sample representing that standard in practice. The metre ruler (or for that matter a distance based on the speed of light) can't measure itself.