(Western) Philosophy from Thales through Aquinas proceeded peaceful and undisturbed over 2000 years. Then Descartes upset the entire endeavor by asking how do we know about the world? By attempting, and failing to answer...he opened up the field of inquiry. Hume's enquiry finished the job, utterly demolishing the pretense of knowledge, and most famously presenting the problem of induction...namely that if you try to justify induction by means of deduction, you cannot. 200 years of failed answers later, Hume seems to have won. But Hume wasn't radical enough.
I assert that philosophy has it 100% backwards. They attempt to justify induction using deduction. In fact, induction is the core process, and decution is a derivation. Outside of mathematics, induction has better predictivity than deduction. Properly, we ought not worry at all about the problem of induction. Induction, instead, is the base.
We should worry about the problem of deduction, and how deduction gets (partially) justified from induction, but almost universally fails in practice.
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Is this controversial? It has occurred to me before, and I'm not all that perceptive about these things.
My wife told me this story about her philosopher ex-boyfriend trying to explain the problem of induction to some factory workers, and, as you can imagine, making little headway. I rephrased it like this:
You know the way in which you know everything you've ever learned? Some guys in tweed jackets have decided that this way of knowing is wrong somehow, and instead you're supposed to think like how they write papers to each other.
Alex,
Measuring from Greece, we have 2700(?) years of philosophy pushing the position that deduction is King. What's the most elegant topic?
Math...and that's pretty indisputable for ~2650 of those 2700 years.
It may be that to the non-mathy, non-philosophically inclined, the induction/deduction inversion is semi-obvious. To the mathematician (who is usually neo-platonic) or the philosopher (steeped in 2500 years of intellectual history)...the question isn't asked.
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