Monday, January 16, 2017

Logic in Wonderland

I know what you're thinking: "Logic? In a place filled with food that makes you shrink and bunny rabbits that talk, not to mention power-crazed card-queens and floating, invisible cats? That Wonderland? Pfft. You must be mad."

And to that I say, we're all mad here, sir. But really, hear me out before going off with my head.

I refer specifically to the events at the tea party. I know, I know: "The tea party? The mad tea party with a capital 'M', where time stood still and the maddest of characters sat around having tea forever and asking riddles with no answers and speaking of drawings of muchness. That tea party?"

To which I say, yes indeed, that tea party. And if you were stuck in a crazy world that made no sense, reliving the same hour over and over, having nothing but tea (I hate tea), I dare say you'd go mad too! So let's try not to be quite so judgmental.

But I promised to reveal a lesson in logic, which Lewis Carrol, being a logician, decided to sneak into his fairy story. So here it is.

Here's part of the exchange that took place at the table with unlimited tea:


"Then you should say what you mean" ~ the March Hare.

"... I mean what I say–that’s the same thing, you know.’ ~Alice


Let's find out if Alice is right.

Let A represent the statement: "I mean."
And B represent the statement: "I say."

Then, the first quote, which can be re-written as:

"If I mean something, I say it",

becomes: A => B.

Whereas, the second quote, which can be re-written as:

"I say something only if I mean it", 

becomes: B => A, 

which is really the converse of "A=>B" and therefore does not necessarily follow (check the truth tables for yourself).

In fact, as the Hatter said, it would be rather like saying, "“I see what I eat” is the same thing as “I eat what I see”!", which is quite absurd (unless you're Jughead maybe) and an apt example showing that the converse of an implication need not hold.

And there you go! A lesson in logic from a beloved children's story that tickles my brain to this day.

Stay curiouser! 

(Tips hat to Lewis Carroll's ghost, saying, "I see what you did there, Mr. Carroll.")


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