If Socrates was born, Socrates became either when Socrates existed not or when Socrates already existed; but if he shall be said to have become when he already existed, he will have become twice; and if when he did not exist, Socrates was both existent and non-existent at the same time — existent through having become, non-existent by hypothesis. And if Socrates died, he died either when he lived or when he died. Now he did not die when he lived, since he would have been at once both alive and dead; nor yet when he died, since he would have been dead twice. Therefore Socrates did not die. And by applying this argument in turn to each of the things said to become or perish it is possible to abolish becoming and perishing.

— Sextus Empiricus

He was prettily and fantastically troubled, who, having used to put his trust in dreams, one night dreamed that all dreams were vain; for he considered, if so, then this was vain, and then dreams might be true for all this: but if they might be true, then this dream might be so upon equal reason: and then dreams were vain, because this dream which told him so was true; and so round again.

— Jeremy Taylor (1613–1667), “The Deceitfulness of the Heart”

“If the northern hemisphere were land, and all the southern hemisphere water, ought we to call the northern hemisphere an island, or the southern hemisphere a lake?” — Augustus De Morgan

In this conundrum by Mitsunobu Matsuyama, when four congruent quadrilaterals are rotated about their centers, their area seems to increase. What has become of the red square?

The answer is that each side of the large square is slightly shorter after the rotation. If θ is the angle between two opposing sides in each quadrilateral, then the ratio of the areas of the two large squares is sec² θ, about 0.8 percent when θ is 5°.

OHIO reads the same sideways.

We have a strong intuition that it’s wrong to punish someone for a crime he hasn’t committed, but is this always the case? Algy, an Alaskan motorist, and Ben, a traffic policeman, both know reliably that Algy intends to speed on a remote, unpatrolled, but radar-surveyed highway at 10:31 tomorrow morning. They also know that, if this happens, police won’t be able to reach the scene of the offense until several hours after it’s been committed.

Algy radios Ben with an offer: If Ben issues a ticket for this crime before it occurs, Algy will pay the fine. If Ben doesn’t issue the ticket until after the offense has occurred, then Algy will flee the country to avoid paying the fine. Ben thinks about this, then issues the ticket now, writing in tomorrow’s date. He delivers the ticket to Algy’s address, where Algy’s wife gives him Algy’s check for the fine, which Ben cashes immediately. At 10:31 tomorrow, Algy exceeds the speed limit as described.

University of Hong Kong philosopher Christopher New writes, “If this example is valid, it suggests that there may be room in our moral thought for the notion of prepunishment [punishment before an offense is committed], and that it may be only epistemic, rather than moral, constraints that prevent us from practising it.”

(Christopher New, “Time and Punishment,” Analysis 52:1 [January 1992], 35-40.)