And I want to talk about one of the single most convincing arguments against it. It's an argument that doesn't get made all that often, but it's one that I find very telling indeed.
No, it's not "It violates every shred of evidence we have about how the mind works." It's not "Nobody who believes in it has ever proposed a plausible mechanism for how it might work." It's not even "There is not a shred of solid evidence to support it -- every anecdotal report of it is easily explained by confirmation bias etc., and every attempt to rigorously test it using the scientific method has come up with bupkis." Those are all excellent arguments: but I've made them before, and it's not what I want to talk about today.
If telepathy were a real phenomenon, natural selection would have selected for it long ago.
We would all have it. And it would not be a subtle effect, occasionally telling us who's on the phone when it's ringing. It would be obvious. We wouldn't be having debates about whether it's real, any more than we have debates about whether language is real.
Think about it. If telepathy existed -- even to a tiny degree -- it would confer an enormous selective advantage in evolution. Even a tiny amount of telepathy would be far more useful than a tiny amount of camouflage, a tiny amount of a wing for gliding, a tiny amount of language. It would enable you to know, just a little bit quicker than your competitors, that there's a delicious duck with a tasty nest of duck eggs right under that bush... or a ferocious tiger behind that other bush waiting to make you into a meal... or an enemy crouching in the tree branch over your head, waiting to conk you with a stone axe. Even a small amount of telepathy would give you enough of a survival advantage for natural selection to sit up and take notice.
And, need I say, telepathy would confer a ridiculous advantage when it comes to reproduction. If you could know whether the person you're trying to mate with is interested or you're just wasting your time; if you could know what their turn-ons and turn-offs were and work your angle accordingly... you'd be in like Flynn. The ability to know what the opposite sex is thinking, or even to be slightly better at guessing than your competitors, would get your DNA replicated so fast it would make your head spin.
(Yes, I know, all this talk about the opposite sex is assuming heterosexuality, or at least bisexuality. But when you're talking about reproductive strategy in the days before turkey basters, I think that's a fair assumption.)
In the exact same way that slightly improved vision, slightly improved manual dexterity, slightly improved cognitive ability, all gave enough of an advantage for these traits to be selected for, a slight improvement in the ability to know, just know, what other people are thinking, would be a mind-blowingly huge advantage for both survival and reproduction. (Plus it would arguably render language unnecessary, thus freeing up a large amount of expensive real estate in the brain... not to mention eliminating thousands of deaths by choking every year.)
If telepathy were plausible, if it were even possible, if even a tenth of the people who claimed to have it throughout history actually had it in even the slightest degree, we'd all have it by now. At the very least, an awful lot of us would have it. We certainly wouldn't be debating its existence, any more than we debate the existence of eyes or hands or brains.