Taken from "The Demon Haunted World" by Carl Sagan:
"A fire-breathing dragon lives in my garage."
Suppose I seriously make such an assertion to you. Surely you'd want to check it out, see for yourself. There have been innumerable stories of dragons over the centuries, but no real evidence. What an opportunity!
"Show me", you say, and I lead you to my garage. You look inside and see a ladder, empty paint cans, an old tricycle - but no dragon
"Where's the dragon?", you ask.
"Oh, she's right here", I reply, waving vaguely. "I neglected to mention that she's an invisible dragon".
You propose spreading flour on the floor of the garage to capture the dragon's footprints. "Good idea", I say, "but this dragon floats in the air". Then you'll use an infrared sensor to detect the invisible fire. "Good idea, but the invisible fire is also heatless", I say. You'll spray-paint the dragon and make her visible. "Good idea, except she's an incorporeal (bodyless) dragon and the paint won't stick!"
And so on. I counter every physical test you propose with a special explanation of why it won't work.
Now what is the difference between an invisible, incorporeal, floating dragon who spits heatless fire and no dragon at all? If there's no way to disprove my contention, no conceivable experiment that would count against it, what does it mean to say that my dragon exists? You're inability to invalidate my hypothesis is not at all the same thing as proving it true. Claims that cannot be tested, assertions immune to disproof are veridically worthless, whatever value they may have in inspiring us or in exciting our sense of wonder. What I'm asking you to do comes down to believing, in the absence of evidence, on my say-so.
The only thing you've really learned from my insistence that there's a dragon in my garage is that something funny is going on inside my head. You'd wonder, if no physical tests apply, what convinced me. The possibility that it was a dream or hallucination would certainly enter your mind. But then why am I taking it so seriously? Maybe I need help. At the least, maybe I've seriously underestimated human fallibility.