I like to think dialectically. I define dialectical thinking as looking to opposing sides of an issue, and seeking to find an answer that integrates the truths in both sides, while freeing itself of the falsehoods of both sides.
Dialectical thinking is premised on two philosophical positions:
1) All people are at least partially rational -- that is to say, any honestly held belief ascribed to by any reasonable number of people must have, at its center, at least a kernal of Truth.
2) Reality is consistent -- that is to say, if two people disagree on an issue, then their disagreement is necessarily the result of error on the part of one or both of them.
Consequently, when I look at debates, I approach them with the premise that there is most likely truth and falsehood on both sides -- and I dive into the issues, to figure out what they are. I then synthesize a new, creative answer that (to the best of my ability anyway) distills the good from the bad.
For example: Creationism and evolutionism. The kernal of truth in creationism is that life, and the universe, show attributes that we commonly associate with design, and that design-free theories of origins are riddled with errors and outright lies. The kernal of truth in evolutionism is that supernaturalism is philosophically indefensible (as for anything to interact with the physical universe, it must do so through causal mechanisms, making "supernaturalism" fundamentally meaningless), and dogmatism of religious creationists is profoundly irrational -- that is to say, placing utter faith in the text of a book (without critically evaluating its credibility) pretty much embodies superstitious thinking.
So I take both of those truths, and I integrate them. Eliminate the supernaturalism from creationism, and you have the hypothesis that life was designed by natural agent(s), by natural means. Eliminate the dogmatism from creationism, and you have hypotheses of historical creation based on historical sources, which are tentatively accepted, just as any historical document might be, with a critical eye toward the possibility of their being some combination of history, fiction, and error.
On the evolutionist side. eliminate the a priori rejection of the above hypothesis, and intelligent design becomes a vastly more reasonable explanation for the origin of life than naturalistic abiogenesis -- as we have seen the mechanisms of genetic engineering, but have not seen how the ooze came alive.
Or take abortion. The kernal of truth in the pro-life side is that the organism in the womb is biologically distinct from its mother -- with separate DNA, separate sensations, and organs of its own. The kernal of truth in the pro-choice side is that the organism in the womb is not social -- and that in some cases, babies are conceived in circumstances which are very difficult for the mother (and baby) to thrive.
Put those together, and what do you get? In this case, not so much an answer as two fundamentally unanswered questions -- what makes us human, and when do humans have a right to life? Are we human based on our genetics, or on our independence? Do humans acquire a right to life when they interact with the world, or when they become human?
I don't think we have solid answers to these questions yet -- but dialectical thinking at least gets the questions asked. Only then can we try to develop the tools to find the answers.
The result of dialectical thinking, in my experience, is an almost extraordinary capacity to anger both sides of a debate. Yet I cannot help but do it, because it is a natural outgrowth of the two philosophical premises which started this article -- premises in which I am a passionate believer.