To go into a bit more detail of this likely pipe dream...
One approach could be to have a group of site moderators who make it their mission to, as Paul said, keep their identities as small as possible and simply judge the logic and biases of peoples arguments.
Perhaps their vote is what locks in a statement to be taken as true or false and then everyone has to then play by the rule of accepting their judgment on the matter for future debates.
In a similar way that scientific research builds on the work that was done before it to make progress, standing on the shoulders of giants type stuff, the conversation could be mapped to show these towers of progress grow as people logically move from "if A is true then B must be true..." and so on.
Perhaps the debate branches at points of contention and goes off down different paths.
The idea being that anyone can join in and quickly get up to speed as to where the conversation is up to by looking at the map of statements that have been dealt with so far.
If someone wants to reopen the debate around some statement and attack the foundation of one of these towers and bring it crashing down then they can.
Of course an enormous element of this will be based on the subjective judgment of the moderators. It can't be entirely based on pure logic but if it is useful and leads to new and interesting things then who cares...
Even if it succeeded in removing a lot of the crap around a debate and focus precisely on the points that people differ on so they can be attacked directly I think that would be a useful thing.
My idea for making this somewhat enjoyable and stand a chance of people participating in it would be to make it game like in some way.
Anyway, its all pretty out there stuff I know, but I'll no doubt continue to think about anyway...