Tuesday 15 November 2011

The metre

Wittgenstein, in Philosophical Investigations, part 1, section 50, commented that we could not say that the standard metre bar in Paris was one metre long, nor that it was not one metre long. He went on to explain that this was not to ascribe some strange property to the metre bar, but only to note its peculiar role in the language game of measurement with the metre standard. Much has been written about the problem since. A good starting-point is the paper by W J Pollock, "Wittgenstein on The Standard Metre", Philosophical Investigations, 27:2, April 2004, available here:


Moving on to the modern definition of a metre as a certain fraction of the distance travelled by light in a second, we can reproduce the problem. One thing of which we cannot say either that it is, or that it is not, a metre is the distance travelled by any instance of a beam of light in vacuo in 1/299 792 458 of a second.

The philosophical analysis may be a bit different because the demonstrative referent (the referent of "that" in "that is what we mean by a metre") is not a physical object but a reproducible phenomenon, and one that is integrated with our physical theory. The words "any instance of" are included in order to separate examples from the theory, and get us as close as we can to actual metal bars. Our theory guarantees that it does not matter which instance we take.

1 comment:

  1. "Much has been written about the problem since." What problem? Wittgenstein uses the example in the course of an exposition many pages long as to how the language-game of meaning works. It's pretty plain that we cannot say that the standard metre is a metre in length; in exactly the same way that I cannot say that I am as tall as myself. It conveys no information, neither does it make any point worth making. His example on the other hand makes a point worth making, within its context.

    Personally I've always found Wittgenstein's own remarks many times clearer than any of the comments on his remarks. I can't help feeling that when people feel the need to explain what he said (or express "what he meant to say") they are insulting the man, because he is always clear.

    On the other hand, I'm always grateful to those who annotate his remarks with why they think he said them - for example as counterarguments to what he wrote earlier in the Tractatus.