The problem of induction concerns inductive reasoning and therefore is of extreme importance to the scientific materialist's worldview. If you cannot deductively solve the problem of induction, then the scientific method has no basis. Inductive reasoning is the ability to generalize from specific events to the formulation of laws. The problem, as laid out by Hume, is as follows:
All observed Fs have also been Gs,
a is an F,
do not imply
a is a G.
It is false that “instances of which we have had no experience must resemble those of which we have had experience” (EHU, 89).
So what justifies or grounds our ability to reason inductively? How do you know every electron behaves like the ones we've observed? How do you know that the electrons you've observed behave the same way when you're not observing them? How do you know gravity exists on other planets? What allows us to generalize from our observations here to the events on other planets millions of years ago?
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