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.