Sunday, September 17, 2006

Measure and Measured

Kripke, quoting Wittgenstein's Philosophical Investigations:

He says, 'There is one thing of which one can say neither that it is one meter long nor that it is not one meter long, and that is the standard meter 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 meter rule.' This seems to be a very 'extraordinary property', actually, for any stick to have. I think he must be wrong. If the stick is a stick, for example, 39.37 inches long (I assume we have some different standard for inches), why isn't it one meter long?

[Kripke, Naming and Necessity. Harvard (Cambridge: 1980) p. 54]

What Kripke is missing, I think, is that, whatever our standard for inches, what makes 39.37 inches a meter is simply its being measured as such by the standard meter. I take it that what Wittgenstein has in mind is that the standard meter, insofar as it is the standard, is never measured to be a meter; it's what measures things as a meter, and so, insfoar as meter is a unit of measure for length, it never applies to the standard meter.

Of course we no longer use a platinum-iridium standard for meters. The standard was changed in 1960 to 1,650,763.73 wavelengths of the orange-red light produced in a vacuum by burning krypton-86, and again in 1984 to the distance traversed by light in a vacuum in 1/299,792,458 seconds as measured by a cesium-133 atomic clock. Now it's the case that the platinum-iridium standard is one meter long, because it is no longer the standard, no longer the measure but the measured.

Of course, Wittgenstein's claim in the first place can only be made if we make some controversial assumptions about what it is to measure. For instance, if I take 'meter' to mean anything that can be measured exactly by the standard measure or anything equivalent to it, the standard meter would, in fact, be one meter long, because it can be measured by a meter stick equivalent to itself. But the claim does make sense, and the property Wittgenstein is talking about is really not extraordinary at all.