I agree with your analysis of Yourgrau's assertions. I disagree that he accurately stated Goedel's view.
Surely, ONE non-provable truth would be enough to distinguish oneself from a well-progranned IBM 360(remember those?).
Thanks for posting - I'd never run across this material otherwise.
Surely, ONE non-provable truth would be enough to distinguish oneself from a well-progranned IBM 360(remember those?).
You have to keep in mind that the truth will be non-provable within a specified formal system (of sufficient strength to express integer arithmetic with the operations of addition and multiplication). By augmenting that system with additional axioms, the formerly unprovable truth becomes provable. But (and here's where Gödel's insight really cuts) within the newly augmented system, another unprovable but true proposition will exist; and so on ad infinitum.
Hence, to make the argument that Gödel wanted to make, the argument that Yourgrau summarizes, one must suppose it possible that mathematical truth in its entirety might somehow be graspable, and so the human mind might transcend all formal systems, formal systems which are forever showing themselves to contain true but unprovable propositions.