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Examples
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Incompleteness is based on a similar, if more complex, notion that you can't reach every statement with countable means.
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Gödel's result is known as the Incompleteness Theorem.
The Dream of Mind and Machine Rothstein, Edward 1979
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He formulated two theorems, called the Incompleteness theorems, which showed that that very basic approach to Maths (as used by Hilbert, and me ..) is invalid.
internetmonk.com 2009
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Posing the question as "Incompleteness" may not be fair.
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Posing the question as "Incompleteness" may not be fair.
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His notorious Incompleteness Theorem demolished any hope of discovering a foolproof method for yielding mathematical truth—for, in effect, distinguishing signal from noise.
Little Bits Go a Long Way John Horgan 2011
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Incompleteness of my time capsule, its trivialities, the way it
Kronos and Thorns 2010
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The Second Incompleteness Theorem shows that the consistency of arithmetic cannot be proved in arithmetic itself.
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The First Incompleteness Theorem provides a counterexample to completeness by exhibiting an arithmetic statement which is neither provable nor refutable in Peano arithmetic, though true in the standard model.
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Using the Gödel Incompleteness Result for leverage, Roger Penrose has argued that the mechanism for consciousness involves quantum gravitational phenomena, acting through microtubules in neurons.
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