Ever tried to define, what cannot be defined?
Ever tried to win an argument and can't be won?
How in the world does one do those things?
My answer to this typically, has been that you need to go into another medium. First you have to verify that you have a clear path, clear and appropriate words and logic.
In using words, try instead using something non-verbal. Or non-spoken, such as song or even, just melody.
Perhaps, visuals would be better. When you are trying to explain something in physics and you hit a wall, try going into a metaphor, then pull back once again, into the hard science lexicon. Sometimes you just need to get someone in the general realm of what you are trying to show them, in order for them to see, what you are saying.
Things go by context, in general. Ever seen someone in a new location, and not recognized them, because you've never seen them outside, say, your dentist office? If they walked up and said, hi, I'm your dentist, you'd recognize them immediately. But if you stand off to the side and see them, you wonder, where do I know them from? You just need a small clue, and bang, you have their identity nailed down.
What IS the purpose of Art? The visual, the musical, or other forms. I think it is exactly that at times, to define the undefinable.
Consider Robert M. Pirsig's Classical and Romantic dichotomy from his Zen and the Art of Motorcycle Maintenance, a book that has affected probably, millions over the years since its original 1974 publish date. I have taken that book on motorcycle rides several times, reading it to completion before returning home a few days later. Its a journey into your mind and life through that of a very interesting character, based upon Pirsig's own life.
When ever I run into a topic I have trouble defining or explaining to someone, I try to find a quantifiable separation in the idiom, or the topic, genre, or what have you, at the time. Like the classical vs romantic notion, or specific and general which is a great one. I find that many disagreements seem to spawn from one person taking one orientation and another, taking an opposing orientation, without either realizing it.
Have you ever been in an argument with someone, only to find, perhaps hours or days later, that you were both arguing on the same side of some point or another? Frustrating, yes? But, hopefully, perhaps, you both did learn something out if it and so it wasn't a total waste of time.
I took a Logic class during my University days and my Professor said he was going to teach us something we'd find very useful and cathartic; wherein, we would never have to lose certain arguments, ever again. And he was right.
He asked if we had ever lost an argument with someone, and not a bickering fight, but a discussion, where each party takes an opposing view and both submit their points of view until a rational meeting of the minds is achieved, and although you KNEW you were right, you just couldn't see where you lost your case along the way?
I had that happen with my mother so many times I can't count, and I never could figure out how she could be so wrong, but I couldn't convince her of it, nor could I see where I had failed in winning a winning argument.
The Professor's explanation was that somewhere along the line, the other person had simply switched or jumped the forms of logic they were using, and therefore, it became an unwinnable argument for you; since basically, you were arguing against well, insanity.
Once you realize that can happen, the next time you had an argument with that person, and they tried it again, through their lack of understanding, when they jumped the forms of logic they were using, you simply need to have them back up and point that out to them. Once they see the mistake, you can literally watch their argument crumble before their eyes. And you walk away, the winner, with your argument being fully supported and rational.
Of course, you have to start with a rational argument to begin with, otherwise, you have two insane people arguing over an unwinnable point and you still won't win that argument.
My point in all this is, when you have trouble defining the undefinable, or you cannot win, the winable, you need to pay attention to what is going on. Sometimes, you have to either switch your tact, or see where the inconsistency is. Then, you should be able to find a way to your goal.
Just remember that "winning" an argument, is not a goal one should really bother about. So much of the troubles in life are about just that, competition in areas where there should be no actual competition, but a team effort at finding the "truth" in an argument. Something positive for both or all involved, for that is the only truly important element in communication.
Sometimes, we forget that, and then everyone is the loser.