You can solve a problem by playing by the rules, which means finding the solution. There is always a clear solution to a rule-based problem. Algebra is like this, and so is grammar, and all competitive games.
Another way of solving a problem is to reframe it. Looking at it from a different angle, recontextualising, forgetting about the rules altogether. Not that no rules apply, but that other rules might apply.
One of the big challenges in late medieval thought was to reconcile Aristotle with Christian theology. Many answers were given, which advanced the fields of both philosophy and theology, giving rise to new ideas about language, cognition, and the theory of the mind. But from a strictly medieval perspective, which was one of solving a problem according to its own rules, the solutions were nevertheless inadequate, always falling short of the expectations.
At least until the whole problem was reframed. Or until European thought developed a capacity for reframing its problems. What if the question had been wrong all along? What if reconciling the two paradigms was not the best way to go about? Enter the Renaissance, whether in philosophy, art, political science or simply science.
Paradigm shifts presuppose the reframing of the entire framework. The answer is not merely different, but it leads to a new understanding of the frame itself. Which leads to a new reframing, spawning new ideas and new perspectives.