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Reason is universal because no attempted challenge to its results can avoid appealing to reason in the end-by claiming, for example, that what was presented as an argument is really a rationalization. This can undermine our confidence in the original method or practice only by giving us reasons to believe something else, so that finally we have to think about the arguments to make up our minds.
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It seems to me that, as it is usually presented, the current orthodoxy about the cosmic order is the product of governing assumptions that are unsupported, and that it flies in the face of common sense.