Xeno's paradox is a simple one. It's solved by the physics law x(t)=vt (assuming no acceleration) and the application of a geometric series.
Statistical decision theory also supercedes many philosophical problems.
A number of lesswrong articles, typically addressing the nature of categories and how to reason based on them, also move into this territory and browsing lesswrong is probably worthwhile if you are interested.
>A number of lesswrong articles, typically addressing the nature of categories and how to reason based on them, also move into this territory and browsing lesswrong is probably worthwhile if you are interested.
To summarize, for those who don't want to archive-dive LW:
Analytic philosophy has traditionally held that concepts/categories are logical: defined by a conjunction or disjunction of predicates in a formal language. Or at least, it holds that they ought to be once we stop being silly and think clearly.
Most everything we've ever learned in machine-learning and cognitive science instead tell us that concepts/categories are statistical, and that formal logic is therefore not only a brittle framework for real-world reasoning but thoroughly incapable of describing where its own constituent objects come from in the mind.
were statistics and controlled studies discovered in the domain of philosophy? Or were those discovered by mathemeticians, which simply replaced philosophy.
This is a false dichotomy. Frege was a mathematician and wrote philosophy attempting to explain what a number was. Questions about which domain this effort ought to be bucketed in don't have an answer.
In addition to the math and statistics described by others here, a better understanding of biology has helped solve some problems in ethics. For example the beginning and end of personhood; the beginning is not before the fusing of gametes, and as the brain is the seat of consciousness, someone's "soul" does not lie in their heart or liver, loss of brain function is therefore the end of personhood.
Statistical decision theory also supercedes many philosophical problems.
A number of lesswrong articles, typically addressing the nature of categories and how to reason based on them, also move into this territory and browsing lesswrong is probably worthwhile if you are interested.