Monday, January 19, 2009

Gödelizing Gödel (and random thoughts)

It strikes me that Gödel's incompleteness theorem bears a bit of a resemblance to the types of skepticism I keep criticizing, insofar as it makes a universal statement about formal systems which seems to limit or hinder their power. Yet I wonder--could it be that to make this kind of statement successfully requires an implicit perspective subject to the same critique the incoimpletness theorem makes in the first place?

This is an idle thought, and it does not seem to me that Gödel's theorem could be undermined or subverted by its own conclusion, and nor am I qualified to investigate much further.

Analogously, that might have implications for the halting problem.

Just wondering.

And on a completely (?) unrelated note, I feel obliged to mention how Jorge Luis Borges' story "Funes the Memorious" features a man with complete eidetic/photographic memory, who experiences and recalls the "sensory manifold" in toto, rather than as we do in bits and pieces. (Here roughly meaning Kant's "sensory manifold", or whatever modern analogy there is). As a consequence, the man sees little point in abstraction and in fact has difficulty recognizing the similarities behind different species of dogs, or even different objects seen from different angles. I'm reminded next (through reading Gregory Chaitin) of information theory and Kolmogorov Complexity, where we judge the complexity of algorithms or objects based on the smallest instruction set necessary to recreate them.


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