Paradoxymoron

Vanessa tries to explain the difference between a paradox and an oxymoron. Xeno's paradox is mentioned.

The Tortoise challenged Achilles to a race, claiming that he would win as long as Achilles gave him a small head start. Achilles laughed at this, for of course he was a mighty warrior and swift of foot, whereas the Tortoise was heavy and slow.“How big a head start do you need?” he asked the Tortoise with a smile.“Ten meters,” the latter replied.Achilles laughed louder than ever. “You will surely lose, my friend, in that case,” he told the Tortoise, “but let us race, if you wish it.”“On the contrary,” said the Tortoise, “I will win, and I can prove it to you by a simple argument.”“Go on then,” Achilles replied, with less confidence than he felt before. He knew he was the superior athlete, but he also knew the Tortoise had the sharper wits, and he had lost many a bewildering argument with him before this.“Suppose,” began the Tortoise, “that you give me a 10-meter head start. Would you say that you could cover that 10 meters between us very quickly?”“Very quickly,” Achilles affirmed.“And in that time, how far should I have gone, do you think?”“Perhaps a meter – no more,” said Achilles after a moment's thought.“Very well,” replied the Tortoise, “so now there is a meter between us. And you would catch up that distance very quickly?”“Very quickly indeed!”“And yet, in that time I shall have gone a little way farther, so that now you must catch that distance up, yes?”
“Ye-es,” said Achilles slowly.“And while you are doing so, I shall have gone a little way farther, so that you must then catch up the new distance,” the Tortoise continued smoothly.Achilles said nothing.“And so you see, in each moment you must be catching up the distance between us, and yet I – at the same time – will be adding a new distance, however small, for you to catch up again.”“Indeed, it must be so,” said Achilles wearily.“And so you can never catch up,” the Tortoise concluded sympathetically.“You are right, as always,” said Achilles sadly – and conceded the race.

That was by Lewis Carrol. It's a paradox because ... well, because ... um, hey look! Alice falling through a hole in the earth!

In Carroll's day there was considerable popular speculation about what would happen if one fell through a hole that went straight through the center of the earth. Plutarch had asked the question and many famous thinkers, including Francis Bacon and Voltaire, had argued about it. Galileo (Dialogo dei Massimi Sistemi, Giornata Seconda, Florence edition of 1842, Vol. 1, pages 251–52), gave the correct answer: the object would fall with increasing speed but decreasing acceleration until it reached the center of the earth, at which spot its acceleration would be zero. Thereafter it would slow down in speed, with increasing deceleration, until it reached the opening at the other end. Then it would fall back again. By ignoring air resistance and the coriolis force resulting from the earth's rotation (unless the hole ran from pole to pole), the object would oscillate back and forth forever. Air resistance of course would eventually bring it to rest at the earth's center. The interested reader should consult "A Hole through the Earth," by the French astronomer Camille Flammarion, in The Strand Magazine, Vol. 38 (1909), page 348, if only to look at the lurid illustrations.

Now I'm not sure whether that is illustrative of Xeno's paradox, or of paradoxes in general, but that's certainly interesting. Though I think that Alice might get a bit bored in the end.

Anyway, to get back to the point - the difference between a paradox and an oxymoron. 'Paradox' is a term for an apparent contradiction, while an oxymoron is a contradiction in terms. Simple.