παράδοξον, in philosophy, is a proposition seemingly absurd, as being contrary to received opinions, but yet true in fact.

The vulgar and illiterate take almost every thing, even the most important, upon the authority of others, without ever examining it themselves. But although this implicit confidence is seldom attended with any bad consequences in the common affairs of life, it has nevertheless, in other things, been much abused; and in political and religious matters it has produced fatal effects. On the other hand, knowing that learned men, in order to avoid this weakness, have fallen into the contrary extreme, some of them believe every thing to be unreasonable or impossible that appears so to their first apprehension; not adverting to the narrow limits of the human understanding, and the infinite variety of objects, with their mutual operations, combinations, and affections, which may be presented to it.

It must be owned that credulity has produced more mischief in the world than incredulity ever has done, or ever will do; because the influences of the latter extend only to such as have some share of literature, or affect the reputation of knowledge. And since the human mind is not necessarily impelled, without evidence, either to belief or unbelief, but may suspend its assent to or dissent from any proposition, till after a thorough examination, it is to be wished that men of learning, especially philosophers, would not hastily, and from the first appearances, determine themselves with respect to the truth or falsehood, possibility or impossibility, of things.

A person who has made but little progress in the mathematics, though in other respects learned and judicious, would be apt to pronounce it impossible that two lines, which were nowhere two inches asunder, may continually approach towards each other, and yet never meet, though continued to infinity; and yet the truth of this proposition may be easily demonstrated. In fact, no science abounds more with paradoxes than geometry.