What makes a problem a problem is not that a large amount of search is required for its solution, but that a large amount would be required if a requisite level of intelligence were not applied. ~ Allen Newell and Herbert Simon
Here's how to look at problems: Problems are guidelines, not stop signs! ~ Robert H. Schuller
A problem is a doubtful or difficult matter requiring a solution, or something hard to understand, accomplish or deal with.
A problem never exists in isolation; it is surrounded by other problems in space and time. The more of the context of a problem that a scientist can comprehend, the greater are his chances of finding a truly adequate solution.
After 25 years of buying and supervising a great variety of businesses, Charlie and I have not learned how to solve difficult business problems. What we have learned is to avoid them. To the extent we have been successful, it is because we concentrated on identifying one-foot hurdles that we could step over because we acquired any ability to clear seven-footers.
It is only insofar as some sort of order arises as a result of individual action but without being designed by any individual that a problem is raised.
Friedrich Hayek, The Counter-Revolution of Science : Studies on the Abuse of Reason (1979)
To think out a problem is not unlike drawing a caricature. You have to exaggerate the salient point and leave out that which is not typical. "To illustrate a principle," says Bagehot, "you must exaggerate much and you must omit much." As to the quantity of absolute truth in a thought: it seems to me the more comprehensive and unobjectionable a thought becomes, the more clumsy and unexciting it gets. I like half-truths of a certain kind — they are interesting and they stimulate.