The major purpose of reigning in the use of the word ‘problem’ is to clear a path to the thesis that the world is good and, beyond this, beautiful. The minor purpose is to return the concept ‘problem’ to its proper linguistic settings.
Certain concepts are ‘at home’ in certain linguistic contexts. Yet for social, historical, metaphysical, and political reasons, some can be extended beyond their proper bounds and, as a result, distend our understanding. I believe the concept of problem represents one such ‘colonization.’
Concerning the minor purpose, then, when one knows in what contexts the concept ‘problem’ is at home and, indeed, unproblematic, then one can rest assured in employing it. Here are some perfectly legitimate uses of the concept problem:
The problem with Lucy is that she has a loose tongue after she has had a few too many drinks.
(In saying this, one is implying either that her loose tongue is something that one should be mindful of [be careful, e.g., not to pour her one too many], or else that it may be something to point out to Lucy once she is sober.
Being mindful of X or pointing out Y are perfectly fine and natural things to do.)
The problem with Joshua Tree is that it doesn’t have a food coop.
(In this case, one is noticing what might make a place a better place to live, yet one is also willing to accept it as it is. Indeed, one may be absolutely content with the totality of a thing despite its small blemish. Another case: it may be perfectly fine main dish that one is enjoying even if it would be better if it had a little of this or that or a little extra something.
This line of thought strikes me as aesthetic.)
The problem with your posture is that it is slumped over.
(The implication is that this is a question of habit. A bad habit such as sitting slumped over in your chair can be corrected. It is as if one were speaking of poor penmanship.
Here, we are speaking of minor corrections, revisions, and modifications.)
John completed the math problem set his mathematics teacher assigned to him.
(There are some activities in which a problem can be solved by virtue of following a set of procedures, a process of reasoning, or certain algorithms.)
After two weeks of working on his project, Chris Sharma finally sent his boulder problem.
(This is rather like dance with an aim. A problem that is sent honors the time, commitment, puzzlement, trials, and the rock with which one was always interacting.)
In the Topics, Aristotle writes, ‘The difference between a problem and a proposition is a difference in the turn of the phrase.’ A definition such as ‘man is rational, bipedal mammal’ can be turned into a question: Is man a rational, bipedal mammal?
(Unproblematically, assertions can be transformed into questions.)