Shadows of the Mind: A Search for the Missing Science of Consciousness
Description: Shadows of the Mind: A Search for the Missing Science of Consciousness presents Roger Penrose's investigation into the relationship between the mind and physical laws, focusing on the challenges of understanding consciousness through current scientific frameworks
ISBN: 0198539789
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I just meant undecidable propositions.
> Do you have an example
Maybe check out the conclusion on p.76 of this book[1] by Penrose (and the argument supporting it that begins on p.72.): "Human mathematicians are not using a knowably sound algorithm in order to ascertain mathematical truth".
His example is our knowledge that a certain computation will not halt, and the impossibility of constructing an algorithm that can prove that fact.
More flippantly, you know that you can examine the soundness of your own reasoning, but no algorithm can reach conclusions about its own correctness.
[1]http://www.amazon.com/dp/0198539789