LSAT Logic in Alice in Wonderland

Lewis Carroll wrote Alice in Wonderland and Through the Looking Glass, but he was also a logician. This post will examine just a few aspects of formal logic he raised in his work.

Alice in Wonderland
On Wikipedia.
Free ebook.

"[Y]ou should say what you mean,' the March Hare went on.
'I do,' Alice hastily replied; 'at least — at least I mean what I say — that's the same thing, you know.'
'Not the same thing a bit!' said the Hatter. 'You might just as well say that "I see what I eat" is the same thing as "I eat what I see"!'
'You might just as well say,' added the March Hare, 'that "I like what I get" is the same thing as "I get what I like"!'
'You might just as well say,' added the Dormouse, who seemed to be talking in his sleep, 'that "I breathe when I sleep" is the same thing as "I sleep when I breathe"!'"

In the excerpt above, Alice makes the fallacy of mistaken reversal / converse (equating "X then Y" with "Y then X").

"at least I mean what I say" (from Carroll) = "whatever I say, I mean" (my translation)

Mapped out in the "if/then" structure, this becomes "If I say it, then I mean it" = say -> mean.

This is not equivalent to "say what you mean," (from Carroll) = "whatever I mean, I say" (my translation)

Mapped out in the "if/then" structure, it becomes "If I mean it, then I say it" = mean -> say.

In the excerpt above, the Hatter, March Hare, and Dormouse all point out the absurd results of this logical fallacy by switching the X and Y as Alice does.

"I say what I mean and I mean what I say" is overused in everyday life (perhaps as a result of "Alice in Wonderland"). For this reason, I'll demonstrate the mistaken reversal / converse with another example.

Example
The statement "I buy what I break" fits the classic china shop rule "If you break it, you buy it."

In "if/then" structure, this statement would read, "If I break it, then I will buy it." This means breaking it is a sufficient condition for buying it, but not the ONLY (or necessary) condition for buying it.

The mistaken reversal would be "If I buy it, then I broke it," which suggests breaking something is the ONLY condition under which you would buy something.

The bottom line: Despite Alice's seemingly normal behavior as our guide through Wonderland, the Tea Party's attendees have a better understanding of logic than Alice (in this example).

Word Ladder
Aside from writing children's books, Lewis Carroll invented a logic puzzle called the Word Ladder. In a Word Ladder, one word becomes another through several intermediate steps.

PrepTest 10, Section 2, Game 3 is a perfect example of a "Word Ladder."

In this game's setup, "'words' (real or nonsensical) consist of any combination of at least four letters of the English alphabet...[and] any 'sentence' consists of exactly five words." You create each new word when you delete, add, or replace one letter with another.

Although I can't publish the LSAT logic game's actual text here, a sentence in a word ladder might go something like:

clock -> click -> lick -> lice -> slice

In my made-up example, all 5 words happen to be real words, but word ladders don't always require this.

I'm fairly certain PrepTest 10 is the only one to contain a word ladder. However, this is no guarantee a word ladder won't come up again.