How many ways can words be wrong? (Part I)

“Saying “Words are arbitrary; I can define a word any way I like” makes around as much sense as driving a car over thin ice with the accelerator floored and saying, “Looking at this steering wheel, I can’t see why one radial angle is special – so I can turn the steering wheel any way I like.”

If you’re trying to go anywhere, or even just trying to survive, you had better start paying attention to the three or six dozen optimality criteria that control how you use words, definitions, categories, classes, boundaries, labels, and concepts.”


Nowadays it seems I’m always short on time, so I’ve decided to blog through Eliezer Yudkowsky’s classic “37 ways that words can be wrong” series of posts one entry (or a few) at a time, from which I got the quote up top. It’s best if you just refer to the series directly for unadulterated content, but here goes nothing.

When might it be justified to say a word has been used “wrongly”?

1. A word fails to connect to reality in the first place. 

Eliezer has a nice story he adapted from Raymond Smullyan (of “the hardest logic puzzle ever” fame, as well as “To Mock a Mockingbird” and “What is the name of this book?” which I was incidentally reading when the car I was in crashed into a tree in Yosemite and nearly killed me, and probably my favorite living logician – oh heck I have to talk about this, this and this) on this called “The Parable of the Dagger“, which I’ll reproduce below in full because I’m running late for class:

Once upon a time, there was a court jester who dabbled in logic.

The jester presented the king with two boxes.  Upon the first box was inscribed:

“Either this box contains an angry frog, or the box with a false inscription contains an angry frog, but not both.”

On the second box was inscribed:

“Either this box contains gold and the box with a false inscription contains an angry frog, or this box contains an angry frog and the box with a true inscription contains gold.”

And the jester said to the king:  “One box contains an angry frog, the other box gold; and one, and only one, of the inscriptions is true.”

The king opened the wrong box, and was savaged by an angry frog.

“You see,” the jester said, “let us hypothesize that the first inscription is the true one.  Then suppose the first box contains gold.  Then the other box would have an angry frog, while the box with a true inscription would contain gold, which would make the second statement true as well.  Now hypothesize that the first inscription is false, and that the first box contains gold.  Then the second inscription would be—”

The king ordered the jester thrown in the dungeons.

A day later, the jester was brought before the king in chains, and shown two boxes.

“One box contains a key,” said the king, “to unlock your chains; and if you find the key you are free.  But the other box contains a dagger for your heart, if you fail.”

And the first box was inscribed:

“Either both inscriptions are true, or both inscriptions are false.”

And the second box was inscribed:

“This box contains the key.”

The jester reasoned thusly:  “Suppose the first inscription is true.  Then the second inscription must also be true.  Now suppose the first inscription is false.  Then again the second inscription must be true. So the second box must contain the key, if the first inscription is true, and also if the first inscription is false.  Therefore, the second box must logically contain the key.”

The jester opened the second box, and found a dagger.

“How?!” cried the jester in horror, as he was dragged away.  “It’s logically impossible!”

“It is entirely possible,” replied the king.  “I merely wrote those inscriptions on two boxes, and then I put the dagger in the second one.”

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