I have recently encountered an interview with you conducted by Krista Tippett, which appeared in her book, Einstein's God. The interview raised quite a few provocative questions in my mind, and I beg for the liberty to share one of them with you:
I know, with something approaching absolute certainty, that, if A > B, and B > C, then A > C. I also know, with the same certainty, that, if I substitute a "<" or an "=" sign for the ">", the same kind of relationship holds. But what is the nature of my knowledge? I have, after all, only examined a very small percentage of the possible a's, b's, and c's in the universe, and none of them very scientifically. So is my knowledge of logical relationships different, in any fundamental way, from mystical insight?
When I was much younger, I was quite impressed for a time by the writings of Ayn Rand, who draws a very sharp dichotomy between rationality and mysticism. But, when I examine the nature of rationality itself, the distinction seems to vanish. I would be quite interested in your thoughts on the matter, and would be most grateful for any guidance you might give to my perplexity.
NB Response: Our knowledge of mathematical truths that can be logically proven is in a sense the only “certain” knowledge and does not depend on an examination of instances, but on the consequences of axioms. And of course if you substitute “is within 1 mile of” for > the deduction does not hold.
However mathematics does show us is that:
a. Not all truths are empirical
b. Not everything that is true can be proven.
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