Paradox

"Paradox" comes from Greek roots meaning "beyond belief." When we begin with assumptions that seem quite reasonable and likely, and deduce an unbelievable result from them, we have a paradox. A paradox may be offered as an argument to undercut a proposition that seems, on its face, to be reasonable. The argument is like this: "If we accept your claim, we are led unavoidably to consequences that are unbelievable -- so your claim is just as unbelievable, and must be wrong." This is a powerful undercutting argument that plays a key role in many mathematical proofs. It is not infallible -- it is no better than the reasoning that leads from the assumptions to the unbelievable result, for example -- but has to be taken seriously and can be quite compelling.