I actually want to come back to §50 for a bit and 'intervene' in the debate that was going on between
@Luke and
@Banno a little earlier. My post on it before was trying to hew closely to the text, but I want to try something a little more free-form to really tease out the significance of the section. Because there's definitely something weird going on with it, and I wanna get at exactly what. Anyway, I want to start with this trilemma by Banno:
is the referent of "One Metre" a length, or is it a stick, or is it a process?
I say it is a length. — Banno
I think this is right, but something is missing. Or it is not the whole story, rather. Surely, the Paris meter is a length... of one meter. But is it
only a length? Or is it also, in addition to a length, something else as well? Well, Wittgenstein would say: it is the means of measuring a meter's length. But here I wonder: can it not be both? And if I were to say this, would I be disagreeing with Wittgenstein? Here's my thesis: I would
not be disagreeing with Wittgenstein, because Witty is approaching the question of the meter rule from a very particular angle, and
outside that angle, it's perfectly possible to agree with Banno that the meter is a length.
So, how to pull this have-my-cake-and-eat-it-too act off? Like this: it can be both, but not at the same time. To wit: note the peculiarity of Witty's discussion of the meter rule, which takes place in the context of names and descriptions, simples and composites. The whole discussion is basically a conditional:
if the Paris meter is the simple by which we measure meter lengths,
then we cannot say of it that it is a meter nor not a meter long. If its
role is that of being the standard by which meters get their measure,
then the question of it's being a meter cannot be sensibly posed. But, as per Witty, roles are anything but fixed, and are themselves context-bound.
So, as
@Ciaran, rightly pointed out, when I'm measuring my shed with my tape measure, I simply don't give a damn about the Paris meter. It doesn't even
have a role in my particular activity of measuring the shed. The Paris meter might as well be just another stick. And if someone, out of the blue were to ask: How long is the Paris meter? One could well reply: a meter long, give or take some minor variation in wear and tear.
But say I start to question if my tape really is a meter long. Maybe I bought the tape from a dodgy store.
Then I invoke the Paris meter and I ask: is my tape of the same length? But now my friend, a committed Cartesian, comes along and opines: but maybe the Paris meter is wrong, and you can't even be sure of that! What can we say to our friend? It's at
this junction, when the Paris meter is playing the role of a standard, that Witty's insight becomes relevant: the 'right' reply to our Cartesian friend is something like: don't be daft, that's not a sensible position to hold.
Another way to put all this is: the Paris meter is just another stupid stick. It 'is' neither a length, nor a process, nor really anything in particular. But, if it has, or is given, a role in a language-game, that role determines what we can and cannot say of it. And in its role as a standard, we can neither say it is or is not a meter long. Outside that role, we can of course say, with no trepidation, that of course it's a meter long. Witty's discussion is explicitly one in which the Paris meter
does occupy that role. To put it yet another way: Witty's pronouncement on the Paris meter is
not a general-purpose statement, and it would be a mistake to treat it as such. It refers to it
only in its capacity (role) as a standard.
To say all this is to keep in mind the 'relativity' of 'words' and 'sentences' in §49, where the same thing can be a word or a sentence "depend[ing] on the situation in which it is uttered or written"; with the caveat that, depending on which role it has, different things may be said of it. And moreover, that something cannot be both
at the same time. One could in fact call this a 'complementarity principle',
a la Bohr on particles and waves - only here we're talking names and descriptions, simples and composites, lengths and standards.
Does this parse things out nicely?