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A. It should be mentioned that this "Induction Problem" ("Why would things work in the future as in the past, more probably than in some other way") (or actually the criticism of the Induction Hypothesis) is due to the Scottish Enlightenment philosopher and liberal David Hume. http://en.wikipedia.org/wiki/David_Hume#Problem_of_induction
B. Why do our brains trust in Occam's Razor or in induction (that things work in the future as in the past, ...)? Because the universe behaved that way in the past, so most brains working in another way were eliminated in natural selection. So our belief is not a piece of evidence, just a repetition of the fact (?) that IN THE PAST Occam's Razor worked, i.e., that the "natural laws" etc. did not change (terribly much).
Yet I believe in the Induction Hypothesis, although I cannot give a rational justification. Perhaps just because by making no assumptions I could make no conclusions, so I want to make one, and Induction hypothesis is the most appealing one to my brains.
Without assuming something you cannot conclude anything, you cannot know anything (not even that something would be more probably than something else).
Similarly, TO HAVE ANY REASON TO DO ANYTHING, EVER, I think that I have to make the following three assumptions (or something "less plausible"), and that more or less everyone does make them more or less always:
- Something matters. (E.g., at least in one situation, there is an alternative that is more right/good/ethical than some other alternative. Why would it be so? Because there is a god who says so? But why would that make it truely matter?)
- I can affect it. (E.g., the world and particularly I am not fully deterministic).
- By trying to do what is right, I more likely do something in that direction than something in the opposite direction. (E.g., I can somehow conclude something about what is more likely to be right than something else.)
Unless I make all those three assumptions (or something else, more complex and less plausible, I think), there is no point for me to do anything.
So before even starting to think of something, I should assume that I am in one of those possible universes where those three assumptions hold true. (Unless it is more probable that I'm in one where the opposite is true - in that case I should try to avoid what I believe being right...)
I prefer to make the induction hypothesis too, because, otherwise "3." above remains terribly weak. So do the others seem to do too. As also everyone seems to always make the hypotheses 1. - 3. (and the Induction Hypothesis), more or less consciously, the hypotheses 1. - 3. could be taken as the axioms of ethics.
Moreover, they must even be strengthened: one should make some kind of assumption on how to get info on a. what is right (the "most difficult part"; this cannot be directly concluded from 1. - 3. but they are of some help) (I refer to answers such as pleasure (utilitarism), liberty (libertarism), following the ten commandments, doing what feels right, "nothing else matters except that the purpose of life is to kick stones as many times as possible" or something else) b. how to affect it (in b. the Induction Hypothesis makes "most of the work" - if I believe in it, I can think of how to kick stones and how to keep myself alive in order to do that for a long time).