28 July 2006

Mathematicians + Ethics

Last night I said that mathematicians don't get in fistfights over whether a problem is solved. I think the relevant passage shines a light down on ethics. When Wittgenstein says,
Disputes do not break out (among mathematicians, say) over the question whether a rule has been obeyed or not. People don’t come to blows over it, for example. That is part of the framework on which the working of our language is based (for example, in giving descriptions). (240)
He's talking not about rules, but about people. He doesn't see logic as being normative, but from his work in the TLP, I think ethics must be. He calls ethics earlier in the PI an unclearly defined concept (paraphrase, citation missing). But there are certain ways to sharply define ethics: I.e., by figuring out what is not ethics. All the time I was reading OC, certain things came up that I thought could not be ethics. At first I thought acting with certainty would count as a sort of ethical act (along with Professor Benjamin of U. Mich.). But that commits one to a sort of ethical plurality, for people around the world act differently. Merely describing a person's actions as an ethical action is just the same as to say that one is always following a rule, no matter what he does--it's to say nothing. (A 'cold-hearted killer' would act with certainty in killing.)

But in the above quote Wittgenstein gives us an area in which there are no physical disputes. (I take physical violence to be for the most part unethical.) In the domain of mathematics, say--and Wittgenstein's phrasing makes it seem like there are other domains in which people do not get in fistfights--in the domain of math people don't come to blows over whether a rule was followed. People do come to blows in the domains of baseball, basketball, weapons inspecting, international negotiations, marriage, law, poker and innumerable others. Whether or not to use violence against someone else for his failure to act according to your rule. To say that the decision is an ethical decision is to already have an idea of ethics. And regulating blows is not the sole provenance of ethics. So what's going on? It seems like there isn't any more light shed on ethics after all.

If there must already be an ethical structure in place for there to be propositions about ethics, then from where does the ethical structure come? Is it something to which our actions fit? Are ethics and aesthetics the great super-concepts, the status that Wittgenstein denies to logic and cause?