In Enquiry concerning Human Understanding (EHU), §§4.1.20-27, §§4.2.28-33,[17] Hume articulated his view that all human reasoning is of two kinds, Relation of Ideas and Matters of Fact. While the former involves abstract concepts like mathematics where deductive certitude presides, the latter involves empirical experience about which all thought is inductive. Now, since according to Hume, we can know nothing about nature prior to its experience, even a rational man with no experience "could not have inferred from the fluidity and transparency of water that it would suffocate him, or from the light and warmth of fire that it would consume him." (EHU, 4.1.6) Thus, all we can say, think, or predict about nature must come from prior experience, which lays the foundation for the necessity of induction.
Inductive inference says that the past acts as a reliable guide to the future. For example, if in the past the sun has risen in the east and set in the west, then, inductive inference suggests that it will probably rise in the east and set in the west in the future. But how can we justify such an inference, known as the principle of induction? Hume suggested two possible justifications, but rejected both:
1. The first justification states that, as a matter of logical necessity, the future must resemble the past. But, Hume pointed out, we can conceive of a chaotic, erratic world where the future has nothing to do with the past –– or, more tamely, a world just like ours right up until the present, at which point things change completely. So nothing makes the principle of induction logically necessary.
2. The second justification, more modestly, appeals to the past success of induction –– it has worked most often in the past, so it will probably continue to work most often in the future. But, as Hume notes, this justification uses circular reasoning in attempting to justify induction by merely reiterating it, bringing us back where we started.
The noted 20th century theoretician and philosopher Bertrand Russell attempted to reinstate induction as a rational procedure and to restore the credibility of the scientific method. However, all he could say was that induction is an independent logical principle, incapable of being inferred either from experience or from other logical principles, and that without this principle, science is impossible."
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