What is the relationship between critical thinking and problem-solving?
The relationship between critical thinking and problem solving is extremely complex, and is very dependent on the nature of the problem being solved.
The more familiar the problem, the more easily we are likely to solve it without the use of critical thinking.
The the more time and effort is likely to be involved in any particular problem, the more beneficial it is likely to be to put more effort into critical thinking.
The space of possible algorithms (possible ways of doing things) is infinite, so there is always the possibility of coming up with something never before tried; but to counter that is the fact that most non-trivial problems have depths of complexity to them that few people understand well, and therefore demand solutions with aspects across time and space and community that few currently conceive of. So there is always danger in anything that hasn’t had a long history of testing.
To counter that, there is always a danger that the current situation may be different from situations encountered in the past in ways that are critical, and lead to failure of previously reliable systems.
One needs to be conscious of both, and be as critically aware as possible of as many aspects as possible.
Critical thinking involves examining all of the assumptions about the nature of the problem and the nature of the relationships present.
All of our models of reality contain heuristic simplifications that have worked for us, or someone else, in the past. Such history is usually (but not always) a reliable indicator of future functionality.
Sometimes the nature of a problem takes us past a boundary in which our old assumptions worked, and requires us to rethink the way in which consider things to be related.
If the problem is really complex, it may involve us in many such “rethinks” of relationships in many different domains, biological, technological, mathematical, logical, social, cultural, economic, etc.
Sometimes a seemingly trivial problem can start us down a chain of examinations that fundamentally restructure the way we consider the world, and our place in it.
After that has happened a few times, one can be left a very long way from any sort of common understanding, and using systems of understanding that are very uncommon.