What does it mean to explore the "ill-defined"?

We think it means something tantamount to “engaging with concepts or problems that lack clear margins or precise definitions.” Okay… But what does it mean to “engage” with them? Is it to think about them? To talk about them? To take them “seriously”? To “wrestle” with them?

Firstly, recognize this: the world is replete with intractable anomalies, so much…