Why do we say that induction is stronger than deduction?
It depends, because induction is stronger than deduction in several ways.
Formal strength lies in part in what sort of problem the method can work on. Induction can work on stuff that deduction can't even begin to work on.
Strength of output lies in how well the outcomes tolerate contradiction. An inductive conclusion can withstand quite a bit of contradiction. Deductive outcomes cannot withstand any contradiction at all.
These two are related, though.
An inductive outcome can be formed from input that contains contradictions. And when the outcome encounters a contradiction, this is simply added to the Body of Evidence, with all the other contradictions that in the end didn't manage to prevent conclusion.
Of course, given enough such evidence, a better outcome or set of outcomes can be produced.
But with deduction, if you hit even a single contradiction, your entire effort was wasted - the conclusion is now worthless.
This strength of induction was predicted already by Hume, who described what we now call inductive reasoning as:
- infallible in its operations
- discovers itself at the first appearance of life and thought
- independent of all the laboured deductions of the understanding
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