Alice’s illogical logic

Book two of Fantasy and Science Fiction was the pair of Alice novels: Alice and Wonderland and Through the Looking Glass.  My essay and peer comments are here and again, I generally agree with the comments.  In the essay, I try to make an observation about the logic that Dodgson uses in the books.

The Jabberwocky: I memorized this poem in school at some point and It’s surprising how much I remember… Perhaps my essay caused too much uffish thought.

Namely, I used a construction of logical implication, p \implies q, (I really like WordPress’ inline \LaTeX).  So, in the essay I compare the implication, false implies true (which is a true) statement, with the stories in Alice.  One of the students, who said he was a mathematician disagreed with that comment, and after review, I still think I was right 🙂

Taking the example from this great reference (pages 8-9), the statement, “If pigs can fly, then you can understand the Chebyshev bound,” is true.  Here we have p \implies q where p = “if pigs can fly” and q = “then you can understand the Chebyshev bound.” Which is the case, (F \implies T) = T.

The converse, (as I mention in the essay), is not true, that is: “if you can understand the Chebyshev bound, then pigs can fly.” (q \implies p \neq p \implies q).

I’ll give the reviewer credit in that my argument is not strongly made and is confusing.  With a word limit of 320, it’s a challenge to capture a succinct idea, more so than one may think.  I’m still enjoying the class and as you can tell from the comments, peer reviewers put significant time into the remarks, which I greatly appreciate (even if I disagree).

Unfortunately, I missed my Dracula submission, but I’m nearly finished with Frankenstein and I have some ideas tossing around, so I should be back on track soon!

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