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Nice. I would have liked to have seen more fleshing out of the reasons for his particular assertions and categorizations... such as the necessity of positing causal agents, the grounding of cause-and-effect (why is cause-and-effect a necessary component...
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I assume you say that because "infinity" and "infinitesimals" are only concepts and not actually numbers, or anything that exists in the real world. I'm fine with that. But how is this a problem with calculus? The very definition...
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When it comes down to it, the issue is due to the idea that preference can only be inferred as being demonstrated through action. All else is hot air and speculation, since from an epistemological point of view, we cannot in any reliable way make inferences...
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Mises doesn't rely upon it, all that will be necessary for his argument is that the denial of it is self-contradictory. Whether it's "analytic" or "synthetic" is quite frankly uninteresting. I'd recommend you read Laurence...