How to solve the problem of induction
Solving the problem of induction.
Are we justified to infer the universal from the particular? If all the swans that we see are white, are we justified to believe that all swans are white? That is the problem of induction. (Many philosophers consider it. –As Nassim Taleb said, the problem of induction is not David Hume’s problem, but Sextus Empiricus’.)
How to solve it?
If a swan cannot be different than white and we know it and, given our question, all the swans that we see are white, then we are justified to infer the truth that all swans are white (induction) (And the truth is absolute.); otherwise, we are not justified –but if we assume that all swans are white and see a single black swan, we will falsify the assumption and also discover the truth that not all swans are white (For Nassim Taleb, we can discover the truth by falsification. –And the truth that we discover by falsification is absolute.); that is Popperian falsification; and once our assumption is falsified, it will always be falsified (induction by falsification). As we can see, they are either all the same or not; but no matter how they are, we can generalize without mistake.
We can make two mistakes here: One is to believe that they are not all the same when they are all the same and the other is to believe that they are all the same when they are not all the same. (Those who study errors may be familiar with them.)
As in this case, proceed in all the cases.
The problem of induction is solved.
Another case from science.
Just as not all swans are white, given that black swans do exist (Nassim Taleb.), not all planets orbit the Sun in the same direction as the Sun’s rotation, given that retrograde planets do exist (As I discovered in a scientific paper.).
And two cases from Judaism.
There is a justified induction in The Book of Genesis: As a man dies, all will.
Another justified induction in The Tanack, that is, the Hebrew Bible: For the Ecclesiastes, as one thing is a vanity, all things are vanities; and what justifies his induction is this: He searched out by wisdom everything that exists under the sky.
How to solve the problem of induction is no longer a known unknown. A solution: You must know all the particulars and see if there is a unity in diversity, like Solomon in The Ecclesiastes (as a thing is a vanity, all things are vanities). Another solution: You must know if all the particulars cannot not have something in common, like Moses in The Torah (as Adam and Eve are mortals, we are all mortals). And another solution: Once falsified, always falsified –any given scientific theory; here, Popperian falsifiability solves the problem of induction. What you see are different solutions to different problems of induction in different domains (sometimes the domain is not religious).
Post Scriptum: Solving the problem of induction is a progress in reasoning, rather than in knowledge.
Addition: For many philosophers, such as David Hume, causality is an induction problem. If you solve the problem of induction, causality is known.
Either similar causes produce similar effects all the time or not. In either case, you can generalize. (The former: “There is no smoke without fire.” And the latter: Iatrogenic disease as absolute truth discovered by falsification.)
