Is It Just Cold?

Before we head off on our weekend of fun in the snow, here are few roughly-drafted thoughts about a writing assessment thing I was helping with recently:

I was struck by the fact that a number of students flat-out rejected van den Haag's claim that the justness of the distribution cannot affect the justness of the punishment. At first, my reaction (shared by my colleagues, resulting in low "critical thinking" scores) was that the students in question had misunderstood the basic distinction between theory and practice, between (in this case) the principle behind a law and the application of that law. After all, if we collapse that distinction, we would be left in the absurd position of saying that because it is in practice impossible to articulate the infinitely long decimal representation of the square root of the number eight, eight is not in fact a number whose square root has a infinitely long decimal representation. If we can't do it, then it must not be correct: surely that reasoning is faulty.

But then I thought of Plato's Theaetetus, which I'm teaching in PHIL 220, and which briefly addresses the nature of the square roots. Not long after that discussion, Socrates and Theaetetus begin an earnest and careful consideration of relativism. Protagoras famously said that a human being is the measure of all things, and Plato's characters try to work out just what that might mean and whether or not we should agree.

I'm no relativist, but sometimes it looks right--for example when it comes to temperature. Is it cold out today? Well, if I say it is, then it is, for me; and if you disagree, then you're also right, relative to you...

And so: what would the relativist, the genuine and committed relativist, have to say about the square root of 8? I can't be sure, but it seems that one account might look like this: if the decimal representation is finite for me, then the decimal representation is in fact finite, since I am the measure. I can of course represent the number as the base of a 8-foot square, or as the diagonal of a 4-foot square (as Socrates does in Plato's Meno), but I cannot represent it as an infinite series of digits, because I cannot represent an infinite series of digits.

If that account works, then it looks like the relativist not only collapses the distinction between theory and practice, but demands such a collapse of all of us. Indeed, in terms of justice the position states that "whatever view a city takes on [matters of justice and injustice] and establishes as its law or convention, is truth and fact for that city" (Theaetetus 172a). Following that reasoning, if a conventional application of a law is unjust, then it seems that the law itself is, for the relativist, also thereby unjust. There is no question of the law being just or unjust independent of its context and application, because justice can only be found in a particular context.

[This is still not quite right... but I think that I'm getting at something. And if not, then I'll at least no longer think I know what I don't know.]

Given this possible explanation of a student's refusal to grant van den Haag the premise that we can evaluate a law or a punishment independent of its application, I grow worried that the CAPE exam is somehow unfairly stacked against the relativist. I am not here endorsing relativism, but it does seem to me that in judging critical thinking they way we (the scorers) have judged it, we have perhaps unjustly made viewing morality as objective a precondition for success in thinking.

Is the demand that students evaluate justice independent of convention and application a demand that students abandon relativism? And is that a demand that a writing assessment ought to be making?