I think there are two major forms of inconsistency that matter most.
When the parties in a conversation use different definitions for a word, they will just argue in circles. They may both have good points but neither party will understand the other. That’s often fairly easy to resolve, “I can understand your point if we use your definition of X. We can also see how my point stands if we use my definition of X. How about we call them X1 and X2 so we don’t get confused?”
When one party uses different definitions of the word it’s fair to ask them to pick one or to be explicit about when they’re shifting definitions. When someone says, “I believe Y because X is TRUE and I believe Z because X is NOT TRUE,” they’ve introduced a huge logical hole which needs to be addressed.
The second one is definitely a bit trickier.
I think there are two major forms of inconsistency that matter most.
When the parties in a conversation use different definitions for a word, they will just argue in circles. They may both have good points but neither party will understand the other. That’s often fairly easy to resolve, “I can understand your point if we use your definition of X. We can also see how my point stands if we use my definition of X. How about we call them X1 and X2 so we don’t get confused?”
When one party uses different definitions of the word it’s fair to ask them to pick one or to be explicit about when they’re shifting definitions. When someone says, “I believe Y because X is TRUE and I believe Z because X is NOT TRUE,” they’ve introduced a huge logical hole which needs to be addressed.