“Yes, sir,” said Just Alice.
“And you helped to get his master to renounce any claim on him by means of, well, of a sort of trick, I suppose,” said Roderick.
“I guess you could call it that,” said Just Alice, “but—”
“Then, by your own admission, you basically cheated an honest man out of something that belonged to him,” said Roderick. “We require the highest standards of honesty and ethical conduct in our profession.” He scowled at Just Alice. “I vote no.”
“That’s bad,” whispered Oswald.
“These things can be complicated,” said Walter of Uskborough. “Under the circumstances—” He waved King Julian’s letter of recommendation in the air.
“Impertinence!” snapped Old Henry. “No, wait, I meant influence.” He pointed at the letter. “Influence!”
“—I vote yes.”
“So it’s down to me,” said Alfred the Gray. He sat and considered it for a long moment. “It’s a goblin’s puzzle. There’s just no arguing with that,” he said at last, and he shrugged. “By a vote of three to two, an extraordinary is awarded to the girl known as Just Alice. Young lady, if you can find a sage to take you on, you may apprentice yourself to him.”
“Thank you,” said Just Alice, bowing her head a little. She turned and rushed over to Hero and Oswald. They both rose to meet her. “Outside, quickly, before someone changes his mind,” she whispered.
The three of them slipped out of the Great Hall. Once they were out in the bustling streets of Roggenheim, Oswald gave her a big hug. “Congratulations, my dear,” said Oswald.
“Thank you, Papa,” she said.
Hero hugged her as well. “You were great up there,” he said.
“Of course I was,” she said, but she smiled a little. “Luckily, enough of them saw that.”
“Don’t think I missed Alfred’s little dig,” said Oswald. “ ‘If you can find a sage’? Really.”
“Are you still going to let me be your apprentice?” said Just Alice.
“Of course I will,” said Oswald. “I didn’t mean—”
“Then it doesn’t matter what he said,” said Just Alice.
Oswald nodded. “Quite right. Quite right.”
“The tide is still with us,” said Hero. “If we are quick, we can sail for Farnham today.” He took Just Alice by the hand and led her down the street.
“Come on, Papa, come on,” called Just Alice over her shoulder as she and Hero hurried, hand in hand, toward the ship that would take them all home.
Dear Reader,
Now that you’ve read The Goblin’s Puzzle, you know that a lot of the story has to do with logical puzzles, errors and fallacies. (And if you haven’t read the book, why have you skipped to the end to read the afterword first? Is there something wrong with you?) Anyway, by the end of the book, most of the logical twists and turns have been explained. But there’s still that business with the boy convincing Ludwig he is “no one.”
I’d like to take a moment to explain just how wrong the boy was and why, but first you need to know a few things about logic. Logic is the study of how we prove things. In logic, you have premises and conclusions. A premise is an idea we assume to be true. When you put a couple of premises together, they might lead you to discover something new: a conclusion. Taken together, the premises and conclusion add up to an argument, but not the kind you have with your little brother (and stop picking on him). A famous example goes like this:
All men are mortal. Socrates is a man. Therefore, Socrates is mortal.
“All men are mortal” and “Socrates is a man” are your premises. If they are true, then your conclusion—“Socrates is mortal”—must also be true. That’s the case here, so the argument is valid. (Socrates, by the way, was an ancient Greek philosopher who was famous for asking awkward questions. Eventually, everyone got sick of this and he was executed. So he was definitely mortal. And if you like asking awkward questions, let that be a lesson to you.)
When the conclusion is true because the premises are true, the argument is valid. The premises prove the conclusion. Our “Socrates is mortal” argument, for example, is valid. But be careful. It is not enough that your premises and conclusion all happen to be true. The premises must cause your conclusion to be true. Consider, for a moment, a slightly different argument:
All men are mortal. Socrates is mortal. Therefore, Socrates is a man.
That might sound good, but it isn’t valid. To see why, try substituting “my dog Scout” for “Socrates.” You get: “All men are mortal.” True. “My dog Scout is mortal.” Also true. (Sorry, boy.) “Therefore, my dog Scout is a man.” Oops. The argument is invalid because it embraces a fallacy—an error in logical reasoning. In this case, the argument makes the mistake of suggesting that because all men are mortal, all mortal creatures must be men. This particular fallacy is called mistaking the part for the whole.
Now, let’s take a look at the boy’s argument in chapter 11:
No one has no name. I have no name. Therefore, I am no one.
Just Alice shows us that the boy is mistaking the part for the whole. But there is something even more wrong with the boy’s argument. In fact, the boy piles several different fallacies on top of each other. Another of his fallacies—as Just Alice points out—is reification. Reification is the fallacy of treating something abstract or intangible as if it were a solid object.
Love is more precious than gold. You should keep precious things in a safe. Therefore, you should keep love in a safe.
In the same way, the boy uses the phrase “no one” as if there were such a person. That’s reification.
But there’s at least one more fallacy that the boy uses—equivocation. Equivocation is when you use the same word or phrase to mean different things at different times. A good example of equivocation is:
The water is full of man-eating sharks. Brenda is not a man. Therefore, it should be safe for Brenda to take a dip.
The first time we use the word “man”—“man-eating sharks”—we use it to mean human beings. (A bit sexist, but there it is.) The second time—“Brenda is not a man”—we use it to mean males. And so it is in the boy’s argument to the dragon. The first time the boy uses “no one,” he means “There is no such person.” That’s how he gets the dragon to agree with the statement. But the second time he uses “no one,” he means—well, it’s not exactly clear what he means, but he seems to mean that there is a particular person “no one,” kind of like there is a particular dragon “Ludwig.”
(If, by the way, you are unusually clever, you might have noticed that our man-eating-shark argument also used the fallacy of mistaking the part for the whole. After all, my dog Scout is not a man by any definition, but I suspect he would be no better off swimming with those man-eating sharks than poor Brenda. Fallacies, it turns out, are a bit like man-eating sharks. They’ll sneak up on you if you let them.)
To see what’s really wrong with the boy’s argument, try rephrasing the first premise. If you think about it, “No one has no name” really means the same thing as “Everyone has a name.” Swap those two out, and the boy’s argument becomes:
Everyone has a name. I have no name. Therefore—
Uh-oh.
Remember that a valid argument is one where the conclusion must be true when both of the premises are true. In this case, the two premises contradict each other. They cannot both be true at the same time. The boy cannot use these two premises to construct any valid argument.
But, I hear you cry, the boy did free Ludwig. If his argument was invalid, how could he do that?
Well, even when an argument is invalid, the conclusion can still turn out to be true. Think back to “All men are mortal. Socrates is mortal. Therefore, Socrates is a man.” The argument is invalid, but Socrates really is a man. The conclusion is still true. In fact, arguing that a conclusion is false because the argument that supports that conclusion is invalid is itself a logical fallacy. It is called, some
what imaginatively, the fallacy fallacy.
But all of this does not quite answer the question of how the boy was able to free Ludwig. How does he have this power? Where does it come from? I’m afraid I’m going to leave that to you to work out on your own. I can’t do everything for you. Well, maybe I can, but I’m not going to. After all, where would the fun be in that?
Your friend,
Andrew S. Chilton
I owe a great debt to the many, many people whose help made this book possible. Thanks first to the thaumaturges: Pam Howell, my agent, and Katherine Harrison, my editor. In addition, this book would almost certainly never have been published without the indispensable help of John Claude Bemis and Dante W. Harper. Then there are all those who gave me so much advice, encouragement and help along the way, always, it seemed, at just the right moment. These include Greg and Karen Wilson, Matt Stiegler, Patty Skuster, Chris Quinn, Joan Petit, Kami Patterson, James McDonald, Chris Marthinson, Chris Lee, Mike Jones, Jack Hott, Kerry-Anne Harris, Paul Hamilton, Jody Grant, Joe Gomez, Erin Galli, Preston Dunlop, Jennifer Drolet, Helen Cox, Mark Chilton, Ted Blaszak, David Auerbach, Miriam Angress and Fatima Alejos-Gonzalez. Doubtless, there are many more who are slipping my mind. To them, I can only say, “Oops.”
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