A matter of definitions

One thing that has been bothering me lately is defining terms used for philosophical discussion. (Those who know me, know that I am working on an essay dealing with freedom and its relation to rights.)

I come largely from a math background where it seems that we define terms, and then use the definitions to create proofs. But, it doesn't seem like it would be appropriate to just define a term according to what I think it should be and then use those definitions to analyze the terms. Especially if those terms already have a common meaning throughout society.

Another approach is the dialectic. But, it seems to me that the dialectic relies heavily upon one's native language. So, when defining terms used for discussion, what is the most helpful approach at arriving at what is the truth?

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Please solve the math problem above and type in the result. e.g. for 1+1, type 2.
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