Actually, Godel said "that the axioms [have to]->[can't] be very carefully chosen." The theorem says that any mathematical system that contains the integers cannot be both complete and self-consistent. It is unique in the list of 'impossibility' theorems in that it has a mathematical proof. The others in your list are all contingent on some form of observation.
It's sort of like saying all sets of equations have to be overdetermined or underdetermined or both. Except its really hits at the roots of the mathematical enterprise. They say its announcement hit Bertrand Russell really hard. -Barry On Apr 16, 2013, at 3:49 PM, Owen Densmore <o...@backspaces.net> wrote: > One has to be careful with nearly all the "impossibility" theorems: Arrow's > voting, the speed of light, Godel, Heisenberg, decidability, NoFreeLunch, ... > and so on. > > To tell the truth, Godel .. it seems to me .. says to the practicing > mathematician that the axioms have to be very carefully chosen.
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