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Many antinomies (paradoxes,) such as that one - a variation on wossname's 'All Cretans are liars ...' - have an oscillating first order Truth Value with the TV changing depending on the step: On True Then False Then True & etc XOR On False Then True Then False & etc.  Since they are infinitely oscillating there is no resolution possible.  

By moving to the Second Order, on the other hand, the True/False OR False/True oscillation is, sometimes, capable of resolution.

But that, very often, takes you outside the original axiomatic system.

She believed in nothing; only her skepticism kept her from being an atheist. -- Jean-Paul Sartre

by ATinNM on Thu Jan 3rd, 2008 at 05:27:32 AM EST
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