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Gödel
1. Someone introduces Gödel to a UTM, a machine that is supposed to be a Universal Truth Machine, capable of correctly answering any question at all.
2. Gödel asks for the program and the circuit design of the UTM. The program may be complicated, but it can only be finitely long. Call the program P(UTM) for Program of the Universal Truth Machine.
3. Smiling a little, Gödel writes out the following sentence: “The machine constructed on the basis of the program P(UTM) will never say that this sentence is true.” Call this sentence G for Gödel. Note that G is equivalent to: “UTM will never say G is true.”
4. Now Gödel laughs his high laugh and asks UTM whether G is true or not.
5. If UTM says G is true, then “UTM will never say G is true” is false. If “UTM will never say G is true” is false, then G is false (since G = “UTM will never say G is true”). So if UTM says G is true, then G is in fact false, and UTM has made a false statement. So UTM will never say that G is true, since UTM makes only true statements.
6. We have established that UTM will never say G is true. So “UTM will never say G is true” is in fact a true statement. So G is true (since G = “UTM will never say G is true”).
7. “I know a truth that UTM can never utter,” Gödel says. “I know that G is true. UTM is not truly universal.”
./\.
1. london was awesome. random highlights:
seeing jimi hendrix’s and john lennon’s old houses
catching up with old friends
good coffee
brick lane
sunday up market
full english breakfast!
seeing hipsters (trendy mutherfuckers)
shoreditch
good times with jamie ruth
british museum
pavement / the clean
soho in general.
2. here’s a bunch of cool flash from a german book I saw at good times:
2. here’s a botanical drawing of some banksias i’ve nicked from some other blog because i think it looks cool.
3. how about this: i’ll be seeing the following bands in the space of a week. excited:
– heavy trash
– dead meadow
– the clean
– dinosaur jr.
– pavement