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Bases Quotes

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Bases Quotes

“In your deliberations, when seeking to determine the military conditions, let them be made the basis of a comparison, in this wise: which of the two generals has the most ability? on which side is Discipline most rigorously enforced? which army is stronger? on which side are the officers and men more highly trained? in which army is there the greater constancy both in reward and punishment?”

“The development of mathematics toward greater precision has led, as is well known, to the formalization of large tracts of it, so that one can prove any theorem using nothing but a few mechanical rules... One might therefore conjecture that these axioms and rules of inference are sufficient to decide any mathematical question that can at all be formally expressed in these systems. It will be shown below that this is not the case, that on the contrary there are in the two systems mentioned relatively simple problems in the theory of integers that cannot be decided on the basis of the axioms.”

“This much I can say with definiteness - namely, that there is no scientific basis for the denial of religion - nor is there in my judgment any excuse for a conflict between science and religion, for their fields are entirely different. Men who know very little of science and men who know very little of religion do indeed get to quarreling, and the onlookers imagine that there is a conflict between science and religion, whereas the conflict is only between two different species of ignorance.”

“During the last two centuries and a half, physical knowledge has been gradually made to rest upon a basis which it had not before. It has become mathematical. The question now is, not whether this or that hypothesis is better or worse to the pure thought, but whether it accords with observed phenomena in those consequences which can be shown necessarily to follow from it, if it be true”