How do philosophers approach a problem?
Like suppose a philosopher is asked a question
What is beauty? How should he or she approach it , what should be the starting point of his or her thinking?
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BTW, you already know the starting point, which is asking the question.
Usually, they ask more questions. e.g., Is it the same as appreciation? Is this related to being ugly? Can we answer the question without answering “What is ugly?”. If something is beautiful to me, will it be beautiful to you? Is beauty objective? Can there be a situation when we can call death beautiful? Does beauty lead you to the truth? Is symmetry always beautiful? …
Another philosophical move is to question the assumptions.
Yet another style is to clarify with examples and counterexamples.
As the dialogue begins, we get into reasons and arguments.
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I think philosophers approach problems through conceptual thinking, not through content or context. So asking what is beauty would be philosophically rewritten as " what is this idea of beauty we have? Which also leads to the questions of assumptions we have about this idea etc… ( see reply by GN next)
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This kept me thinking. Can we do conceptual thinking only with other concepts? And never to seek examples from context? Are concepts never grounded in a context?
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Do concepts also need grounding just like symbol-grounding? 
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