@fast,
It is fallacious to think that the meaning a word has now is the meaning it originally had, since meanings change through time. Still, it is seldom that the etymology of a word cannot shed light on its meaning. The etymology of the word "paradox" is from the ancient Greek words "doxa" and "para", which meant "common opinion" and "contrary to" respectively. So, a paradox would be something that was "contrary to common opinion" or, against what we ordinarily believe is true. So, for instance, of of Zeno's paradoxes is that if Achilles and a tortoise engaged in a race, Achilles could not win against the tortoise. That is, of course, contrary to what we ordinarily believe is true. We believe that Achilles would win such a race, hands down. In the present instance, the paradox is known as the Barbershop paradox. It begins by supposing a barber who shaves all, and only, those who do not shave themselves. And it asks the innocent seeming question, does that barber shave himself or not. And quickly (I hope) we see that supposition implies a contradiction, for if the barber were to shave himself that would be contrary to the supposition, and it the barber were not to shave himself, then
that would be contrary to the supposition. It would then follow that such a barber (supposing, of course, there were one) would have both to shave himself and (also) not shave himself. But that, of course is a contradiction. Literally,
no one can perform a contradictory action (not even God). So, in the light of all this, what is the answer to the question, supposing there were such a barber, would he shave himself or not? The only answer there can be is that the supposition is, itself, false. That it is impossible that there should be such a barber, because the supposition of such a barber implies a contradiction, and therefore, the supposition is, itself, a contradiction, since what implies a contradiction is itself a contradiction. So, the paradox is that it would be ordinarily believed (
doxa) that there
could be such a barber, but it turns out, upon analysis, that there
could not be such a barber, and so,
paradoxa, a paradox!
There are several lessons to be drawn from this example. Two of them are: 1. That reason can show that something does not exist. That is something that inspired the epistemology of Rationalism which is the view that thought (what Kant called, "pure reason") that demonstrate that something does not exist, and therefore, it is reasonable to believe that is can demonstrate that something must exist. (But this argument is fallacious). 2. Closer to home, is that we see that a person can hold a self-contradictory belief without realizing that he does. That should make us all more modest.
