What we have to understand that we have to believe into things which can be proved. Now the time has come that Divine itself has to be proved. That God Almighty has to be proved. That Christ as a son of God has to be proved, that His birth as immaculate conception has to be proved. Not by argument, not by reasoning, nor by blind faith but by actualization on your central nervous system.
I proved that I can win the Grand Slams. I proved that I can last four and a half hours and come out on top against one of the strongest guys physically that tennis had probably seen especially on this surface. So they would probably be the things that I would say I have learned tonight: To not doubt myself physically and mentally from now on.
But there are times when men have serious thoughts, and it is at such times, when they begin to think, that they begin to doubt the truth of the Christian religion; and well they may, for it is too fanciful and too full of conjecture, inconsistency, improbability and irrationality, to afford consolation to the thoughtful man. His reason revolts against his creed. He sees that none of its articles are proved, or can be proved.
As records of courts and justice are admissible, it can easily be proved that powerful and malevolent magicians once existed and were a scourge to mankind. The evidence (including confession) upon which certain women were convicted of witchcraft and executed was without a flaw; it is still unimpeachable. The judges' decisions based on it were sound in logic and in law. Nothing in any existing court was ever more thoroughly proved than the charges of witchcraft and sorcery for which so many suffered death. If there were no witches, human testimony and human reason are alike destitute of value.
There is no such thing on earth as an uninteresting subject; the only thing that can exist is an uninterested person. Nothing is more keenly required than a defence of bores. When Byron divided humanity into the bores and bored, he omitted to notice that the higher qualities exist entirely in the bores, the lower qualities in the bored, among whom he counted himself. The bore, by his starry enthusiasm, his solemn happiness, may, in some sense, have proved himself poetical. The bored has certainly proved himself prosaic.
Gilbert K. Chesterton
Though blessed with the enviable properties of a mink coat-graceful, unreasonable, and impractical no matter what she was draped over-she was nevertheless one of those people whose personality proved to be the bane of modern mathematicians. She was neither a flat nor solid shape. She showed no symmetry at all. Trigonometry, Calculus and Statistics all proved useless. Her Pie Chart was a muddle of arbitrary wedges, her Line Graph, the silhouette of the Alps. And just when one listed her under Chaos Theory-Butterfly Effects, Weather Predictions, Fractals, Bifurcation diagrams and whatnot-she showed up as an equilateral triangle, sometimes even a square.
Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.
John D. Barrow