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byrnema comments on GroupThink, Theism ... and the Wiki - Less Wrong
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To recap... induction is not a purely deductive principle - since it relies on an axiom known as "The Principle of Uniformity of Nature" - http://en.wikipedia.org/wiki/Principle_of_uniformity which states that the laws of physics are the same from place to place and that the past is a useful guide to the future.
That axiom is not available as a result of any deduction - and attempts to justify it always seem to be circular - i.e. they use induction.
According to http://en.wikipedia.org/wiki/Problem_of_induction#Ancient_origins this problem has been known about for over 2,000 years.
Right. In case anyone thinks this thread is an argument, it's not -- the assumption of induction would need to be added to deduce anything about the empirical world. The definition above didn't say how deductions would be made... You just make assumptions and then keep track of what your conclusions would be given those assumptions (that's deduction). I'm not sure if we could or would start listing the assumptions. I made the mistake of including (1), which is the only explicit assumption, but AndySimpson and ALexU have pointed out that elevating that assumption is empiricism.