Thursday, 31 July 2008

Bourbaki

I have been thinking about Bourbaki and how right and wrong he was. His wrongness cannot, of course, have anything to do with the fact that he didn't exist. Some people claim the same for Homer, or the authors of the Bible and Koran.

Let us then praise Nicolas Bourbaki, so much more real than other mathematicans (except perhaps Paul Erdos). How right he was to set out to construct axiomatically everything which we could say that we knew. An admirable concept.

Why then, was it indirectly corrupted into structuralism and the doctrine that the truth was relative?

It is one thing to say that the truth is unknowable; that our grasp of it is always relative (Which is no more than quantum dynamics has shown). But the 20th Century Continental philosophers who came to believe that the truth itself was relative always somehow believed that their grasp of it was absolute. In every instance, these thoughts landed people in the camps.

The search for structure is a fine thing. But structure is not – as Bourbaki might have realized – realized by confining it to set theory. It is probably not even category theory, or string theory, or M theory. These are signposts on the way. They are what we have in order to approximate a description of what is real.

To complain that one cannot identify the physical change in the communion wafer is to make a category mistake, just as it would be to say that a novel or a symphony or a cricket match makes a factual error