Thomas Edison offered this burlesque on perpetual motion. “There will always be a nine opposed to a six,” explains Sam Loyd, “and as nine weighs more than six, it will make the wheel revolve rapidly, as well as your head when you understand it thoroughly.”
A contronym is a word with two contrary meanings, such as cleave or sanction (more here).
The word contronym itself has no double meaning. Is it a contronym?
“Not until I came along!” writes Charles Melton in Word Ways. “I declare that it is a contronym for the simple reason that it isn’t! It is both a self-opposite and not a self-opposite. QED.”
A logic exercise by Lewis Carroll. What conclusion is implied by these premises?
If Brown hopes to throw a six in a game of dice and succeeds, we wouldn’t say he threw the six intentionally. If Brown puts his last cartridge into a six-chambered revolver, spins the chamber as he aims it at Smith, his archenemy, pulls the trigger, and kills Smith, we’d say he killed him intentionally. Does that make sense? In both cases Brown hoped for a certain result, in both cases the probability of that result was the same. If Brown didn’t intentionally throw a six, why did he intentionally shoot Smith?
— Leo Katz, Bad Acts and Guilty Minds, 1987
Bonus poser: In what sport does only the winning team travel backward?
You say you know your brother.
Yet when your brother is hooded you are unable to identify him.
Therefore you both do and do not know your brother.
— Eubulides
Some of the figures (particularly the holy ones) in El Greco paintings seem unnaturally tall and thin. An ophthalmologist surmised that the painter had a defect of vision that caused him to see people this way.
The zoologist Sir Peter Medawar pointed out that we can reject this conjecture on purely logical grounds. What was his insight?
‘What I am saying cannot be proved.’
Suppose this statement can be proved. Then what it says must be true. But it says it cannot be proved. If we assume it can be proved, we prove it cannot be proved. So our supposition that it was provable is wrong. With that road closed to us, let’s try the only other one available — let’s suppose it cannot be proved. Since that is precisely what it says, then it is true after all. And this ends our proof of the above statement!
— Gary Hayden and Michael Picard, This Book Does Not Exist, 2009
A letter from Lewis Carroll to 14-year-old Wilton Rix:
Honoured Sir,
Understanding you to be a distinguished algebraist (i.e. distinguished from other algebraists by different face, different height, etc.), I beg to submit to you a difficulty which distresses me much.
If x and y are each equal to ‘1,’ it is plain that 2 × (x2 – y2) = 0, and also that 5 × (x – y) = 0.
Hence 2 × (x2 – y2) = 5 × (x – y).
Now divide each side of this equation by (x – y).
Then 2 × (x + y) = 5.
But (x + y) = (1 + 1), i.e. = 2.
So that 2 × 2 = 5.
Ever since this painful fact has been forced upon me, I have not slept more than 8 hours a night, and have not been able to eat more than 3 meals a day.
I trust you will pity me and will kindly explain the difficulty to
Your obliged, Lewis Carroll