Jainism

[Belacqua]

Okay, well, the sort I was talking of has nothing to do with theism. I was merely talking of the logical system that says that there can be true contradictions.

Depending on your view of infinity, the coincidentia oppositorum could be non-theistic. 

The point being that, to me, Jainst logic, while impressive by religious standards, is a system of logic that appears to be incoherent and it seems to think that something can both be or not be. i.e. that seems like saying that there are true contradictions.

I don't think it's incoherent at all. It says that things may appear to be true from one viewpoint and not true from another. 

You haven't explained to me yet whether the Jains hold all viewpoints to be true, even the contradictory ones, or whether they rule out some according to their own metaphysics. I'm assuming that since they are mind/body dualists they wouldn't accept a monist's viewpoint as true. They might lay out a structure detailing where a monist's viewpoint accords with theirs and where it doesn't. 

But if they're structuring ideas and looking at logical compatibility, that's different from saying that a viewpoint is true or not. Just as a syllogism can be valid but not sound. 

If like the Christians, they hold that God (or the Brahman, or whatever it is Jains hold to) is infinite, then they might well think that both A and not-A can be true. 

As for saying "impressive by religious standards," that indicates to me that you haven't studied much religious thought. A lot of it is extremely impressive. And if you want to jettison things that had their origin in religious thought, you're going to end up throwing out a lot of stuff atheists still believe -- e.g. "action at a distance," which the very religious Newton renamed "gravity." 

Don't assume that just because a thinker is religious that he's dumb or sloppy.