I expect that "truth" in this context just mean "opinion what the truth is" which can not be easily verified nor refuted and despite of it both debaters are pretty confident in their opinions. In this case a response can be something like "I would prefer word "opinion" but I hope we understand each other ;-)"
For more accurate response I need some examples. I don't realize coming across this phrase in a discussion.
Can someone help me dissolve this, and give insight into how to proceed with someone who says this?
What are they saying, exactly? That the set of beliefs in their head that they use to make decisions is not the same set of beliefs that you use to make decisions?
Could I say something like "Yes, that's so, but how do you know that your truth matches what is in the real world? Is there some way to know that your truth isn't only true for you, and not actually true for everybody?"
I'm trying to get a feel for what they mean by "true" in this case, since it's obviously not "matching reality."