Friday, June 7, 2013

Carrollian Trilemmas

        Carrollian Trilemmas

            A trilemma is a triple of propositions, any two of which can be true but not all three. Any trilemma implies this deductive principle; from any two, derive the negation of the third. For instance, consider this “Some-All-None trilemma”, a.k.a. “Anti-syllogism”:

Some days are bliss;
All bliss is perfect;
No days are perfect;
            Deny one!

            It implies these deduction rules:
From all bliss is perfect; no days are perfect: 
   Deduce no days are bliss.
From  no days are perfect; some days are bliss:
   Deduce some bliss is imperfect.
From  some days are bliss; all bliss is perfect:
   Deduce some days are perfect.

Exercise for the student: find deduction rules from these trilemmas:

All beauty is natural;
Some art is beautiful;
Anything natural is artless.

Equal men cannot be free;
Unequal men cannot be free;
Some men are free.

Some jokes can save you;
The Book of the SubGenius is not a joke;
Only the Book of the SubGenius can save you.

Here are ten trilemmas that I derived from syllogisms in Lewis Carroll’s book, “Symbolic Logic and Game of Logic”:

All dowagers are well-bred;
All thistles are ill-bred;
Some dowagers are thistles.

No frogs are poetical;
Some ducks are poetical;
Only frogs are ducks.

Some pillows are soft;
No pokers are soft;
All pillows are pokers.

All eagles can fly;
Some pigs can't fly;
Only eagles are pigs.

Oysters are fossils;
No fossil can be crossed in love;
An oyster can be crossed in love.

Some epicures are ungenerous;
Any uncle of mine is generous;
Any epicure is an uncle of mine.

Every lion is fierce;
Only coffee-drinkers are fierce;
Some lions do not drink coffee.

Some of these boys work hard;
All who work hard are anxious to learn;
None of these boys are anxious to learn.

A prudent man shuns hyenas;
No banker is imprudent;
Some bankers do not shun hyenas.

No ducks waltz;
All officers waltz;
Some officers are ducks.

No comments:

Post a Comment