Definitions are hardly a problem just for science (if they are a problem - science seems to doing OK regardless), and I feel they are particularly difficult for those with a strong commitment to the view that ethics must somehow be grounded in something irrefutably true. In fact, I vaguely suspect that Wittgenstein's later position with respect to the rule-following paradox was that seeking such grounding is a doomed pursuit, and he somewhat famously contended that philosophy was not concerned with problems, only linguistic puzzles.

Perhaps rather paradoxically (at least if you see Popper as a champion of science over philosophy), Popper (who, in addition to his work on the philosophy of science, also wrote "The Open Society and its Enemies") felt that Wittgenstein was utterly wrong to deny that there are real philosophical problems.

https://plato.stanford.edu/entries/wittgenstein/#RuleFollPri...

https://ditext.com/wordpress/2019/06/26/puzzles-vs-problems-...