Chomsky, Math, and Politics

I was recently reading through some of Noam Chomsky's writings on politics, and I came across a comparison he made between different disciplines. He pointed out that when he talked about mathematics, all that people cared about was the content of what he had to say. He is not a professional mathematician, but this does not matter as long as the math checks out. By contrast, when he talked about, say, the Vietnam war, everyone was concerned with his credentials rather than what he had to say, at least in the American media. His explanation was that those disciplines with more intellectual substance don't need credentials, whereas those needing credentials tend to be more concerned with preserving certain power structures in society. I think there is another explanation, however.

I don't wish to discount Chomsky's worries about how the intelligentsia does misuse its position to create facades of expertise, negatively impacting critical discussion of issues. But I equally want to recognize that there is a reason why we expect credentials of people in some fields and not others. When I look at a mathematical proof, all I need to examine is there. I may need to bring in my own knowledge to understand the proof in the first place, but if I can understand it, I can assess it. Other mathematical facts are irrelevant in deciding whether the theorem checks out, so understanding of the steps in this specific proof is all that is required.

When it comes to history or politics, by contrast, there can be many views with their own inner logic, which people take to be determinative of their truth (for example, conspiracy theories, religious apologetics, and the political views of your least favorite party). Looking at whether the argument itself checks out is no longer enough, since external facts can change that picture (technical tangent: David Lewis' book on Counterfactuals comes to mind - could this difference between fields be expressed in terms of modal logic?). Is the history being taught now the same history you learned as a child, for example? And I guarantee that if you have not studied the history of Galileo's contribution to the history of science, you will find it to be much less straightforward than it is made out to be - a couple extra facts about the time make the difference between "Galileo, the destroyer of dark age dogma" and "Galileo, the guy with the interesting idea which nevertheless poorly explained various aspects of the world until Newton posited that mystical, occult force known as gravity."

No matter how certain these sorts of arguments seem on their own, they could be false. Therefore, to know that someone has something worthwhile to say, we need to know more than that their speech makes sense. We need to know that they are the sort of person to know a lot of potentially relevant background information and so able to catch external facts pertinent to the topic. If someone talks about the wars in the Middle East, they need to know something about the history of the area, the differences between the regions and peoples, the root causes for the radical movements, and so on. Otherwise, we get such nonsense as "Saddam Hussein is aiding Osama bin Laden".

Of course, two other things seem to be necessary which complicate the picture. In addition to actually having the information, one needs to have an open mind so that one can readily assess new data and change ones position if necessary - again, the already present internal logic of an historical, religious, political, etc. argument is no sign of its ultimate validity. Also, there needs to be sources for the new information, which is where Chomsky's own point seems to have its place. We need people around who can perturb the system, push back against the recognized system of credentials. No system of credentials could be perfect since the object of study can never be closed off - we never will have knowledge of the specific going-ons in society in the way that we have knowledge of mathematical theorems.