Wednesday, 29 March 2006

The Local Meme, Part II

Plato was an aristocrat: the idea that you could know everything, that you sat, imperial, having information delivered to you, was completely natural. Perhaps if epistemology had started on a different track, it would not now be so challenged by finding that this model isn't the way nature seems to work. For now at least, it seems that the Platonic observer is far too distant from the world. Instead, we have to leave our chairs to find out about reality, and whatever we do changes things. Is that really so unnatural, so dissatisfying?

In mathematics, isn't the idea that you select a meta-mathematics for the task at hand completely reasonable? You don't try to do the plumbing with just a hammer and nails, after all. And the axiom of choice is no more or less than a tool to be chosen or ignored, as the task at hand requires. It is no more `true' than a hammer is: asking for the global truth of mathematical foundations increasingly seems to be a category error.

So, gentle reader, celebrate the triumph of local truth, of good enough for the here and now. Global truth is not just a dangerous ontological abstraction, it doesn't even make sense.


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