Science And Religion, the Rational And the Superrational : An Address Delivered May 4, 1914 Before the Phi Beta Kappa Alumni in New York

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One of them is the infinite domain of the uncharted.
Another is time. Another is human knowl- edge, a variable that increases with time, but whose present value or amount is finite.
Finally, there is the rate of the growth of knowledge. This, too, is finite, and I assume that it will continue to be so, the abstract SCIENCE AND EELIGION 88 possibility that the speed of advancing science may at length become infinite being too improbable for serious consideration. I fancy your thought leaps ahead
... of my speech, anticipating alike the reasoning and the conclusion. The infinite realm of the uncharted is to shrink as knowledge grows.
Present knowledge is finite. Its rate of growth is finite and will remain so. It fol- lows that after the lapse of any finite length of time, however long, the amount of then accumulated knowledge, though it may be immense, yet will be finite. How much of the uncharted will remain.? The answer is. An amount precisely as great as before, just as if, beginning with the number one, we sup- pose wiped out from the endless series of cardinal numbers any succession of integers, however finitely long, the multitude remain- ing will be exactly as numerous as before, for the first one not wiped out may be marked 1, the second 2, and so on forever.


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