Sunday, September 8, 2013

"Suppose we take a set of Lego blocks, and the things we can construct with them, as the domain of a very simple science. We can list all possible ways of attaching two blocks together, and then use that list to describe how to attach a third, a fourth, and so on, recursively. Eventually we have descriptions of an immense set of objects – walls, bridges, houses, and of course many objects that have no meaning for us at all. Now suppose, further, that before we start testing this theory of Lego objects, a mischievous daemon introduces an identical, slight, imperceptible curvature in the shape of each block. We will have no knowledge of it because it is so slight as to unmeasurable in individual blocks. The first objects we build will be in accord with the theory that we developed for perfectly rectangular blocks, but as they grow, we may find that many objects can’t be completed because the members become warped in various ways, as a result of an accumulating curvature. On the other hand, we find that some objects, like gently curving walls, can be extended indefinitely, occasionally producing, among other things, cylindrical towers of some large but invariable diameter. This development is not predicted by the theory because the curvature of individual blocks is imperceptible in individual blocks and is not represented in the combining rules of our theory.

Cylindrical tower-forming is, in a simple way, an emergent property of the daemonized Lego block physics. Since the curvature of individual blocks is imperceptible, we cannot be sure of its existence, and we cannot legitimately build it into the ground level rules of combination, but empirically we see that as objects grow larger, the ground level theory breaks down and something else increasingly determines the objects’ shapes. It appears to us that somehow the Lego blocks were meant for building cylindrical towers, but we do not and cannot know exactly what the cause is, although we can postulate that it has to do with some elementary property of the Lego blocks. Blocks builders will say something like “As structures get very large, the blocks seem to want to form coherent curved surfaces; when the direction of curvature remains constant, we get towers.” The attribution of intentionality is, of course, not testable, but also not disprovable, since the underlying, non-intentional theory does not account for it.

[...]

It appears that Nagel sees a sort of Lego-block teleology as present in the material which has furnished the basis for evolution on our planet, and sees this teleology as indeed having produced learning or discovery algorithms in humans that can converge on objective truths of certain kinds."

That's definitely an interesting interpretation of Nagel's philosophical position. Mulling over it...