I think the core idea is much simpler than that. It's the notion that falsifiability is the most powerful tool in our arsenal when we try to conceive of theorie

I think the core idea is much simpler than that. It's the notion that falsifiability is the most powerful tool in our arsenal when we try to conceive of theories that explain a certain state of affairs. The idea you're getting at is that no number of confirming observations can verify a universal generalization -- the reason why we continue to call generally accepted "truths" theories. But we can increase our certainty to the greatest degree possible by trying to test our hypothesis to the greatest degree we can.