How to solve Lewis Carroll's 'No wise young pigs' problem?

Question

In 'Symbolic Logic' Carroll invites a deduction from 9 premises :

1. All, who neither dance on tight ropes nor eat penny-buns, are old.

2. Pigs that are liable to giddiness are treated with respect.

3. A wise balloonist takes an umbrella with him.

4. No one ought to lunch in public who looks ridiculous and eats penny- buns.

5. Young creatures who go up in balloons are liable to giddiness.

6. Fat creatures who look ridiculous may lunch in public if they do not dance on tight-ropes.

7. No wise creatures dance on tight-ropes if they are liable to giddiness.

8. A pig looks ridiculous carrying an umbrella.

9. All, who do not dance on tight-ropes and who are treated with respect, are fat.

Therefore, no wise young pigs...

I can't get a handle on this. Can anyone help ? I'm not sure whether Lewis makes an unacknowledged assumption that all pigs are fat creatures. If so, that would amount to a missing premise that damages deductive validity. Or am I all at sea ?

Answer 1

This has been majorly edited:

Answer: No wise young pigs are balloonsists.

First off, I will assume that for all x, if x is old, then x is not young.

D = dances on tight ropes

E = eats penny-buns

L = eats lunch in public

Y = is young

G = liable to giddiness

T = treated with respect

U = has umbrella

W = is wise

B = is ballonist

R = looks ridiculous

F = is fat

P = is pig

1. ~D & ~E -> ~Y

2. P & G -> T

3. W & B -> U

4. R & E -> ~L

5. Y & B  -> G

6. F & R & ~D -> L

7. W & G -> ~D

8. P & U -> R

9. ~D & T -> F

Now remember A -> B is the same as ~A v B. Also ~(A & B) is the same as ~A v ~B. We will rewrite the nine statements.

1. D v E v ~Y

2. ~P v ~G v T

3. ~W v ~B v U

4. ~R v ~E v ~L

5. ~Y v ~B v G

6. ~F v ~R v D v L

7. ~W v ~G v ~D

8. ~P v ~U v R

9. D v ~T v F

Also note that if A v ~C and B v C then A v B.

So essentially, many things cancel out. ie D and ~D (lines 6 and 7) E and ~E (lines 1 and 4) etc etc.

The following do not cancel out: ~Y ~P ~W ~B

Therefore, no wise young pigs are balloonsists.

Jon: I think my original reason was incorrect. I wanted to first start by assuming that a wise young pig was a balloonist. From this we can get:

From 5, he is also liable to giddiness.

From 7, he therefore doesn't dance on tight-rope.

From 2, he is treated with respect.

From 1, I was hoping to come to the conclusion that he must eat penny-buns, but I believe that is incorrect. (my head hurts currently, and I don't want to reason if this is correct or not - someone want to figure it out for me?)

But from there, I was hoping he was fat (from 9)

At this point we from 3, he takes an umbrella and from 8, he looks ridiculous.

Then 4 and 6 would contradict.

In any case, I like my new method better =P

Answer 2

They don't dance on tight ropes from 7.

7. No wise creatures (this includes wise young pigs) dance on tight-ropes if they are liable to giddiness.

How do we know that wise young pigs are liable to giddiness?

From 5. Young creatures (including wise young pigs) who go up in balloons are liable to giddiness.

So wise young pigs who go up in balloons are liable to giddiness.

What about wise young pigs who do not go up in balloons?

We don't know. How do we find out? Take them up in a balloon.

Then they are young creatures up in a balloon, so they also are liable to giddiness.

Farful, I don't think that all young pigs eat penny-buns.

EDIT:

I changed my mind. Farful,  you're right. Assume some wise young pigs go up in balloons. Follow it through to the contradiction.

(These young pigs would eat penny-buns.)