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Unknowns comments on Justifying Induction - Less Wrong
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Since my original point was amended to indicate that my original point about Bayes was overstated, and that the true problem is that Bayes is quite useless without assuming induction is justified (i.e. any observation about the real world or prediction about the future presumes the principle of induction to be justified), I would hardly call this nitpicking. It is my point. Insofar as Bayes' theorem is purely mathematical, it is quite fundamental. I don't dispute that. You can't apply math to the real world without having a real world, and without assuming induction, you can't really have a concept of a real world.
It has occurred to me that the concept of "induction" upon which I rely may be different in nature from that being used by the people arguing with me. This is unsurprisingly causing problems. Induction, as I mean it, is not simply, "the future will be like the past," but, "the correlation between past observations and future observations is nonzero." That is so fundamental I do not think the human mind is capable of not essentially believing it.
If induction means "the correlation between past observations and future observations in nonzero," then not assuming induction could mean one of two things:
1)I might think there is some chance that the correlation is non-zero, and some chance that the correlation is zero. In this case Bayesian reasoning will still work, and confirms that the correlation is non-zero.
2) I might think the correlation is certainly zero. But in this case most people would not describe this as "not assuming induction", but as making a completely unjustified and false assumption instead. It is not negative (not assuming) but positive (assuming something.)