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At 09:32 AM 07/05/01 -0400, Simon St.Laurent wrote: >I was driving home from the hardware store yesterday when I heard a report >on NPR about Godel's Incompleteness Theorem. It concluded with a discussion >of the Semantic Web, with the interviewee making claims that the Semantic >Web would run into sizable issues with Incompleteness. To one who remembers what understanding the Goedel proof used to feel like, this sounds deeply suspect. In the same way, the mathematically illiterate often like to claim that this or that ordinary visible effect is the result of the uncertainty principle - or worse, that there's a deep parallel between Goedel/uncertainty and some piece of politicosociomythotrophic theory. Even Hofstadter skated close to the edge, but was entertaining enough to get away with it. Goedel shows that in a formal system enough rich enough to build conventional mathematical logic on [most people have no idea what real mathematical logic looks or smells like], the set of true assertions is larger than the set of provable ones. Given the *extreme* mathematical contortions he had to go through in establishing this, I'd be surprised if this were notable among the obstacles facing the construction of the semantic web. -T
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