We need science. We need empirical evidence. We can't just use mathematical reasoning to deduce the nature of the world.
It was while I was studying philosophy that I came to understand. . . that it is no sign of moral or spiritual strength to believe that for which one has no evidence, neither a priori evidence as in math, nor a posteriori evidence as in science. . . . It's a violation almost immoral in its transgressiveness to shirk the responsibilities of rationality.
When you ask why did some particular question occur to a scientist or philosopher for the first time, or why did this particular approach seem natural, then your questions concern the context of discovery. When you ask whether the argument the philosopher puts forth to answer that question is sound, or whether the evidence justifies the scientific theory proposed, then you've entered the context of justification. Considerations of history, sociology, anthropology, and psychology are relevant to the context of discovery, but not to justification.
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