invincible ignorance

Occasionally one comes across someone who is simply unable to grasp the concept that you're explaining to them. It isn't often that this is a trained computer repairperson.

The people fixing B's computer had said they would move her hard drive to a new box. But it turned out that they cloned the hard drive instead. A problem had turned up with the new drive, and I wondered whether this was also true of the old drive.

Another worker in the shop, overhearing this conversation, undertook to interject himself into the conversation. He explained at some length that if there's a problem with the old drive, it will automatically reproduce itself in the clone. If true, that raises the question of why bother to clone the thing at all, but I didn't raise that. I merely said that that was very interesting but it didn't address my question.

So what is your question, he said. I said, could there be a problem with the new drive that didn't come from the old drive.

He said that was merely the same question in different words. I said no, it's the inverse of the first question. I tried several ways to explain it, and finally he said I was just using circular logic.

That's when I lost my temper, and, having goaded me into this, he then shrugged and went back to work. It occurred to me to draw a Venn diagram of problems with the old drive, problems with the new drive, and problems with both, but when I showed it to him, he crumpled it up and threw it away without looking at it. Invincible in his ignorance.

It occurred to me later that there was a simpler way of explaining the difference. If problems with the old drive are A, and problems with the new drive are B, then he was telling me that
If A, Then B.
And I was asking if it was also true that
If B, Then A.
Those are fundamentally different statements, a basic concept in elementary logic, so it's really disturbing to find someone who thinks there's no difference between them, and accuses you of circular logic when you try to explain it. Invincible ignorance.