I believe that Gödel’s incompleteness theorems are a gift.
On page 377 of Roger Penrose’s life notes (The Road to Reality: A Complete Guide to the Laws of the Universe) he writes, “There is a common misconception that Gödel’s incompleteness theorems tell us that there are…mathematical truths that are in principle inaccessible to us…whatever rules of proof we have laid down beforehand, if we already accept that those rules are trustworthy (…) and are not too limited, then we are provided with a new means of access to mathematical truths that those particular rules are not powerful enough to derive.”
Using an example of a normal human vision field, what can you see? Can you see the atoms in the buildings around you? How far can you see without your glasses? Our most perceptive sense cannot identify much of what is in front of us. Why can’t this human sense be analogous to a set of axioms that present inaccessible mathematical truths? Why can’t we find a new means to access the additional information in our visual and all sensory fields!
We will see, and continue to see, and ultimately follow Shaddai ‘Elyon’!
