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.
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