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Hume suggested two possible justifications but he rejected both.
1) The first justification states that we can imagine a world in the future which has nothing to do with our past. So the principle of induction is not that logically necessary.
2) The second justification states that whatever worked in the past can work in the future as well...
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But Hume also mentions that this just takes us around in circles. And does not leave room for development of thought and mind.
The Story of Philosophy
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