## Wednesday, October 31, 2012

### Metric Standard

A somewhat odd claim by John Danaher, in the course of discussing Adams's divine command theory and an analogy using metric standard:

Particularist Predicates: The criterion for the application of a particularist predicate is determined by reference to one or more concrete individuals. An example might be the criterion for the application of the term “metre”. Whether it makes sense to say that a particular length is one metre long depends on whether it is isomorphic to the standard metre-stick which is kept in Paris.

Now, as it happens, the account of “metre-hood” offered here is historically inaccurate. It was not the case that a particular platinum-iridium bar was chosen to be standard against which all other purported metre-lengths would be judged. Rather, it was the case that a particular platinum-iridium bar was chosen because it most closely approximated the length of one metre (which was a measurement that was already being used). But this doesn’t matter. Suppose it was the other way round, then we would have an idea of what a particularist criterion for predicate application might involve.

I'm not sure what Danaher means by this. Prior to 1791, there were several different things called the 'meter'; in 1791 the French Academy of Sciences decided to standardize the meter by establishing that half the longitudinal meridian running through Paris, from the North Pole to the Equator, was ten million meters. But this required actually measuring that distance; the Academy of Sciences then established the prototype meter on the basis of the provisional results of an expedition to determine this length. This prototype meter, originally an iron bar, was then the standard meter. As it happens, the expedition did quite a good job, but the calculations for the meter did not get the earth's spheroidal deviation from a sphere exactly right -- because it spins, the earth is a little flattened on the ends, and this obviously has to be taken into account. So there was a very slight disparity, a fraction of a millimeter between the prototype meter and one ten-millionth of the half-meridian. However, it was the prototype meter bar that defined the meter -- it's why you have a prototype meter in the first place. Later platiniridium bars were put in place, it is true, to standardize the meter already in existence by allowing more precise definition under a wider range of circumstances; but it is precisely the case that once they were the prototype meter, anything one meter long was so entirely because it was isomorphic to the new prototype meter bar, to a relevant degree of precision. The prototype meter was then later replaced by wavelength definitions, and now by electromagnetic propagation definitions. But precisely the point of all of this has always been to to choose a standard "against which all other purported metre-length would be judged"; and it is even the case that when new standards have been put forward, they had first to be judged as a meter, to a given degree of precision, by the prior prototype. (You want to keep as a meter anything that already counted as a meter, to the extent practically possible, to avoid throwing measurements into confusion.) Thus it all goes back to a prototype meter bar that was, in fact, chosen to be a standard.

In any case, it is odd to bring up history here, since obviously the question is determination of reference, and history is related to determination of reference as etymology is related to meaning -- it's certainly relevant, but it is not constitutive. How reference is determined now necessarily has a history but it is not this history that determines how the reference is determined in cases of measurement -- it's comparison to the standard, and in the case of measurement this standard has to be something concretely identifiable. And it is clearly this, not originally historical choice, that is the governing feature in the account given of how the references of "particularist predicates" are determined.