[hist-analytic] Kripke and the Meter Stick

Baynesr at comcast.net Baynesr at comcast.net
Wed Oct 14 09:43:46 EDT 2009

I am skeptical of Kripke's conclusions, on the meter stick as discussed by Wittgenstein (PI 50).  The focus of my remarks is, Naming and Necessity pp. 54-56). I sometimes type out stuff as I think, since I am my only audience "in lecture." But I thought that since I will be discussing this issue in the book, I would post a couple of things I've thought about but not, as yet, included in the book, because I need to work them out a bit more. So I thought I'd throw this at the list. Run it up the flag pole so to speak and see what the crowd does if anything. These are not conclusions; they are attempts at probing an issue before laying out my real conclusions, probably, elsewhere (the book). 

This is all getting set up to discuss Aune on related topics. This may substitute for discussion of his treatment of the meter stick example. 

We can't treat the identity 'The length of this stick = 39.37 inches' like just any other identity, especially if we take ‘the length of this stick’ as rigidly designating the length of this stick, now, here, etc. If we did, then 'The length of this stick = 39.37 inches' would be a necessary truth. Now there is the appearance of contingency; the stick it seems might have been a different length. But if this is the case, then I must account for the appearance of contingency. Keep in mind that the situation is one where I have two edges, clearly, in sight; two bodies that are rigid, at least relative to one another. I confess that I cannot imagine two such edges being congruent without the length of this stick being 39.37 inches, unless I am mistaken as to how many inches the foot-rule is from which we get the figure 39.37 inches. Part of the problem is that 'the length of this stick' refers to what Russell called a 'magnitude' and not a 'quantity'. But, now, let's ask: with respect to the necessity of identity does the requirement of explaining the appearance of contingency apply to both quantities and magnitudes or do we restrict this to quantities only? But in this case, the relevant identity is not between quantities (the two sticks) but, rather, magnitudes. Thus 'this stick is a meter long' is not an identity statement. 

When we say 'This stick is one meter long', we appear to be talking about a quantity, not a magnitude. This is not an identity but a predication. If we should say 'One meter is the length of this stick' then we seem to be talking about magnitudes. The relevant identity is an identity between two magnitudes, not two quantities, as in the case say of the identity ‘Pain = C-fibers firing’: a quantity cannot be identical with a magnitude. So if we are comparing magnitudes how can we possibly imagine this magnitude being 39.37 inches not being a meter? I can no more say that there is an epistemic counterpart of ‘the length of this stick’ which is not 39.37 inches than I can say there is an epistemic counterpart of being the length of this stick, the one I’ve set beside the foot-rule, which is not 39.37 inches. By contrast, I can imagine an epistemic counterpart of water which is not H2O! 

There is no contingent property available to me that I can use to pick out the length of this stick unless it is the contingent property or some other stick having the same length. But then our dilemma is recreated with this other stick. If we take ‘meter’ to be a magnitude, then on Kripke’s view it cannot be 39.37 inches long, since I cannot explain the appearance of contingency of this identity. Essential is the idea of congruence. If two bodies are rigid, relative to one another, and they are congruent, then I cannot imagine an epistemic counterpart where congruency does not obtain. Therefore, I cannot explain the appearance of contingency; therefore the identity fails. Let’s consider the problem from a, slightly, different angle. 

Suppose someone lays down the foot-rule and comes up with 39.37 inches and declares: "Witgenstein is wrong! Kant is wrong! As anyone can plainly see, this stick measures 39.37 inches and, so, we can attribute being a meter to this stick in Paris. Wittgenstein rises from the grave, saying "Just wait one moment young man! How can you say that this other stick is 39.37 inches long? Without pause the answer is: "Well I measured it against the standard foot-rule in Kookamonga and that what it shows." The ghost of Wittgenstein continues: "What justifies me in saying that that stick in Kookamonga is a foot long, and besides, you’ve been moving that stick around an awful lot; so, how can you say it is the length you say it is?" Answer: "I dunno." If ‘the length of the meter stick in Paris’ designates a particular length, a magnitude, we still have a problem: length is relative to the operation of measurement using a standard rigid body. Length is conceptually dependent on measurement, even conceptually. Fixing reference to one length seems to be a hold over from pre-Relativity days. I can hear the groans; but that, I’m afraid, was what Wittgenstein was talking about, viz. whether we can assert of something that it is such and such, absolutely. In the case of the meter stick’s being a meter we cannot make the attribution, let alone that it is absolute; the same holds for any elements which we take to be ultimate constituents of the world. We can no more attribute existence to these fundamental entities than we can attribute length to the meter stick in Paris. Kripke ignores the point. It’s old fashioned. Take another illustration. 

Suppose someone draws a line and calls it "the standard straight line." Someone says I can neither say that it is straight, nor that it is not. Someone runs up with a stick and lays it alongside what up to now is the standard stick. He declares, "Yes, this stick is straight. It is congruent with this stick, so I can say it is straight. You see I compared it to this other standard. Now here we are not speaking of metric properties, but the principle holds. If you don’t believe it, think of how one would in fact deal with the case of the standard straight line. There are no standard straight lines; there are no standard rigid bodies. It make no sense, and I wish to emphasize this, to say this body, the one I’m using as a metric in defining ‘length’, is rigid. There is no length "out there" waiting to be designated. 

Steve Bayne 

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