A TANGIBLE STANDARD OF LENGTH

Wittgenstein has puzzled many readers by maintaining that the standard metre bar is neither one metre nor not one metre in length. In a famous passage, he writes:

The standard metre bar surely has some length, and it is odd to say of it – as the paradigm for precisely this one metre unit of measure – that it is not itself of this length. More interesting is Wittgenstein's assertion that the Paris standard metre bar cannot be said to be either one metre or not one metre in length. This suggests that, having been elevated by convention to the status of representing a particular metric unit, the standard metre bar has somehow managed to defy the law of excluded middle. If the standard metre is neither one metre nor not one metre in length, then it would seem not to have any length at all.

What Wittgenstein might have in mind is something like what Gilbert Ryle (1949: 16–23), himself borrowing heavily although not always faithfully from the later Wittgenstein, referred to as a category mistake. There are many such mistakes to beware, including the classic instance of asking to be shown the college after touring all the buildings and grounds.