One is the inversion. (I don't know what the official name is, though presumably there is one). Thinking things backwards, or in reverse, or upside down. Mutatis mutandis. Slovoj Žižek, for everything that's problematic with him, demonstrates the power of this move all the time.
The second is the thought experiment. My philosophy profs could do these all the time, off the top of their heads, and I aspire to that. One used to sit on the table, swing his legs and say "suppose...."
It's the best way I know to take really abstract and complicated ideas, express them with some pith, and show how they work in a way that gets people to engage with them, try them out, and see how they work. Thought experiments are the hands-on museums of the philosophical world.
One of my favorites is so small it's almost quip size. From Ludwig Wittgenstein: People say it was natural to think the sun revolved around the earth because it looked like the sun revolved around the earth, but how would it have looked if the earth had revolved around the sun?
A good bulk of Wittgenstein's thought is in that.
I'm thinking of this because I've been trying to come up with a thought experiment posing the question about how belief is different in the condition of secularity, when it's a matter of choice (even when what is believed doesn't change).
What I came up with:
Imagine a society of people watching TVs that, to the best of their knowledge, only have one possible channel. They would have no explanation or justification for why they watch what they watch, just taking for granted that this is what it is to watch.
They then find out that one person in this society – the deviant, in sociological terms – has been watching another channel.
Even if everyone chooses to continue to watching what they've always watched (the orthodox channel, as it were), how is watching that channel different?