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Logic in Alice in Wonderland

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Nicole Kim

on 18 June 2013

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Transcript of Logic in Alice in Wonderland

Logic Review
Now onto some trickier passages
IX: The Mock Turtle's Story
Logic in Alice in Wonderland
`Oh, I know!' exclaimed Alice, who had not attended to this last remark, `it's a vegetable. It doesn't look like one, but it is.'

`I quite agree with you,' said the Duchess; `and the moral of that is--"Be what you would seem to be"--or if you'd like it put more simply--"Never imagine yourself not to be otherwise than what it might appear to others that what you were or might have been was not otherwise than what you had been would have appeared to them to be otherwise."'

by:Jenan Abu-Hakmeh
Lauren Beglin
Nicole Kim

"I: Down the Rabbit Hole"
"If it makes me grow larger, I can reach the key, and if it makes me grow smaller, I can creep under the door, so either way I’ll get into the garden, and I don’t care which happens!"
`But I don't want to go among mad people,' Alice remarked.

`Oh, you can't help that,' said the Cat: `we're all mad here. I'm mad. You're mad.'

`How do you know I'm mad?' said Alice.

`You must be,' said the Cat, `or you wouldn't have come here.'

Alice didn't think that proved it at all; however, she went on, 'And how do you know that you're mad?'

'To begin with,' said the Cat, 'a dog's not mad. You grant that?'

'I suppose so,' said Alice.

'Well, then,' the Cat went on, 'you see, a dog growls when it's angry, and wags its tail when it's pleased. Now I growl when I'm pleased, and wag my tail when I'm angry. Therefore, I'm mad.'
Mad people/ places/ things
If you are in Wonderland (p), then you are mad (q): p --> q

I am in Wonderland (p), therefore I am mad (q).
Alice is in Wonderland (p), therefore she is mad (q).

Alice says she is not mad: ~q
If she is not mad, then she would not be in Wonderland: ~q --> ~p

Given that Alice is in Wonderland: p
Therefore Alice is mad: q

p --> q given
p given
q modus ponens

*The Cheshire Cat has a logically valid argument.
*He and Alice are in Wonderland, and Wonderland is within the circle of mad people/places/things.

Wonderland
Works Cited
Carroll, Lewis, and Helen Oxenbury. Alice's Adventures in Wonderland. Cambridge, MA: Candlewick, 2003. Print.
'But I'm NOT a serpent, I tell you!' said Alice. 'I'm a -- I'm a --'

'Well! WHAT are you?' said the Pigeon. 'I can see you're trying to invent something!'

'I -- I'm a little girl,' said Alice, rather doubtfully, as she remembered the number of changes she had gone through that day.

'A likely story indeed!' said the Pigeon in a tone of the deepest contempt. 'I've seen a good many little girls in my time, but never ONE with such a neck as that! No, no! You're a serpent; and there's no use denying it. I suppose you'll be telling me next that you never tasted an egg!'

'I HAVE tasted eggs, certainly,' said Alice, who was a very truthful child; 'but little girls eat eggs quite as much as serpents do, you know.'

'I don't believe it,' said the Pigeon; 'but if they do, why then they're a kind of serpent, that's all I can say.'


VI: Pig and Pepper
Be what you would seem to be
(p)
> This can be written as “Be what you appear to others”

Never imagine yourself not to be otherwise than what it might appear to that what you were
or
might have been was not otherwise than what you had been would have appeared to them to be otherwise.
> After “or” is a repetition of the first half of the sentence, so let’s just look at the first part.

Never (~) imagine yourself not to be otherwise (~) than what it might appear to that what you were (p):
~(~p)

p is logically equivalent to ~(~p)

* Example of double negation
*Therefore the second statement is a valid expression of the original expression.
If you are a serpent (p), then you have tasted eggs (q): p --> q
Alice has tasted eggs, therefore she is a serpent: q --> p

p --> q given
q given
p converse error

*This exhibits the converse error
* The pigeon presents an invalid argument
> Alice is clearly not a serpent!
Now let's break down some passages from Alice in Wonderland!
V: Advice from a Caterpillar

If an animal growls when it’s angry (p) and wags its tail when it’s pleased (q), then it is sane (r): p^q --> r
The cat does not growl when it’s angry and does not wag its tail when pleased, therefore, it is not sane: ~ (p^q) --> ~ r

p^q --> r given
~(p^q) given
~r inverse error

*The cat has an invalid argument
*This is an example of inverse error.

Thank you
for watching and participating!!

Now it's your turn to try!
If it makes me grow larger (p), then I can reach the key (q): p --> q
If I can reach the key (q), then I can get into the garden (r): q --> r
(p --> q) ^ (q --> r); therefore p --> r

If it makes me grow smaller (s), then I can creep under the door (t): s --> t
If I can creep under the door (t), then I can get into the garden (r): t --> r
(s --> t) ^ (t --> r); therefore, s --> r

p --> q given
q --> r given
p --> r hypothetical syllogism
s --> t given
t --> r given
s --> r hypothetical syllogism
(p V s) --> r disjunctive addition

*This is a valid argument
*Alice is correct in saying that if either happens,
she will get into the garden.

Double Negation:
(~(~p)
is equivalent to
p

Disjunctive Addition:
p
q
p V q


If - then:
If p, then q
p --> q

Modus Ponens:
p --> q
p
Therefore q

Modus Tollens
p --> q
~q
Therefore ~p
Converse Error:
p --> q
is not equivalent to
q --> p

Inverse Error:
p --> q
is not equivalent to ~p --> ~q

Hypothetical Syllogism:
p --> q
q --> r
Therefore p --> r

Some Logic Rules!
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