Tuesday, September 7, 2021

Trilemmas Define Syllogistics: 10 of 11

 Exercises for the Student

 

Find associated troikas and triads:

 

Some days are bliss;

All bliss is perfect;

No days are perfect.

 

Nobody’s perfect;

You’re somebody;

You’re perfect.

 

Some philosophers are Cretans;

All Cretans are liars;

No philosophers are liars.

 

Only you can prevent forest fires;

Smokey the Bear can prevent forest fires;

You are not Smokey the Bear.

 

Sometimes flattery is stupid;

Stupidity is always boring;

Flattery is never boring.

 

All Scots are canny;

All ghosts are uncanny;

Some Scots are ghosts.

 

Some good deeds are wise;

          Only foolish deeds get punished;

No good deed goes unpunished.

         

Some jokes can save you;

The Book of the SubGenius is no joke;

Only the Book of the SubGenius can save you.

 

All aliens read comic books;

No angels read comic books;

Some aliens are angels.

 

         No soul is pure;

         Only pure souls go to Heaven;

         Some souls go to Heaven.

 

All cats have nine lives;

No vampires have nine lives;

Some cats are vampires.

 

Some men are heroes;

All heroes are immortal;

All men are mortal.

 

Some people are victims;

Victims deserve special treatment;

All people deserve equal treatment.

 

All sages are saints;

All saints are heroes;

Some sages are not heroes.

 

I am a fool;

All fools are crooks;

I am not a crook.

 

X equals Y;

Y equals Z;

X does not equal Z.

 

          Rock  < Paper;           

          Paper < Scissors;                          

          Scissors < Rock.

 

          All elves are fairies, but not all fairies are elves;

          All fairies are genies, but not all genies are fairies;

          All genies are elves, but not all elves are genies.

 

This essay is about advanced Logic;

Any essay about advanced Logic will put you straight to sleep;

This essay will not put you straight to sleep.

 

MacDougal is a true Scotsman;

No true Scotsman would wear such a kilt;

MacDougal wore such a kilt.

 

Unicorns are mythical beasts;

No-one ever saw a mythical beast eating anyone’s rose-bushes;

I saw a unicorn eating Marion Zimmer Bradley’s rose-bushes.

 

Dragons are wise;

Dragons are fierce;

Dragons are not both wise and fierce.

 

Bob is not a genius;

Bob is not an idiot;

Bob is a genius or an idiot.

 

If aliens do not rule Earth, then Bob has no Slack;

If aliens do rule Earth, then Bob has no Slack;

Bob has Slack.

 

If the Hatter is mad, then the Cheshire Cat is there;

If the Hatter is mad, then the Cheshire Cat is not there;

The Hatter is mad.

 

If Alice is ten feet tall, then she fell down a rabbit hole;

If Alice fell down a rabbit hole, then she isn’t ten feet tall;

Alice is ten feet tall.

 

         I love Alice;

         I do not love Bob;

         I love Alice and Bob equally.

 

          Batman is batty;

          Bruce Wayne is not batty;

          Batman is Bruce Wayne.

 

Some frogs are princes;

          Some frogs are not princes;

          All frogs are equally princes.

 

         I opposed the bill on Monday;

         I favored the bill on Tuesday;

         My position on the bill has not changed.

  

         We can’t choose chocolate;

         We can’t choose vanilla;

         We must choose either chocolate or vanilla.

 

         We can’t tell chocolate from vanilla;

         We can’t choose at random;

         We must choose either chocolate or vanilla.

 

         The food is cheap;

         The food is fast;

         The food is good.

 

         He’s honest;

         He’s intelligent;

         He’s an ideologue.

     

         An attorney should keep the client’s secrets;

         An attorney should investigate zealously;

         An attorney should report perjury.

 

         Some art is beautiful;

         All beauty is natural;

         Nature is artless.

        

         God is omniscient;

         If God is omniscient, then there is no free will;

         There is free will.

        

         God is dead;

         If God is dead, then all is permitted;

         Not all is permitted.

        

         Reduce the deficit;

         Increase spending;

         Don’t raise taxes.

        

         Tweedledee is more moral than Tweedledum;

         Only the moral should be President;

         Tweedledum should be President.

        

         No cats are birds;

         Only a bird can land on top of the living-room cabinet;

         My cat Charlie can land on top of the living-room cabinet. 

 

         Life has no meaning within itself;

         Life has no meaning beyond itself;

         Life has meaning.

 

The unexamined life is not worth living;

Life is not examined;

Life is worth living.

 

         There are more saints than sages;

         There are more sages than heroes;

         There are more heroes than saints.

 

         Space is boundless;

         Space is finite;

         Space is flat.

 

         There is a first cause;

         All causes have causes;

         There are no causal loops.

 

         There is a highest reality;

         For every reality, there is a higher reality;

         Two realities cannot be higher than each other. 

 

There’s a set of all sets:

There exists an x, such that for every y,  yϵx;

Every set’s an element:

For every x, there exists a y, such that xϵy;

There are no set loops:

There does not exist an x and a y such that xϵy and yϵx.

 

         1 has property P;

         For any positive integer n, if n has property P then so does n+1;

         Some positive integer N does not have property P.

 

         The function f(x) is real and continuous on the interval [a,b];

         f(x) does not equal zero anywhere on the interval [a,b];

         f(a) and f(b) are of opposite sign.

 

         f(x) is differentiable on the interval [a,b];

         f(a) < f(b) ;

         df/dx is positive nowhere on [a,b].

       

        Anyone in contempt of court shall serve hard time;

           All crooks are liars;

        No bankers shall serve hard time;

       All perjurers are in contempt of court;

       Not all bankers are uncrooked;

       Only perjurers lie.

     

The next fourteen trilemmas spoof 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.

 

Some pillows are soft;

No pokers are soft;

All pillows are pokers.

 

No lobsters are unreasonable;

No reasonable creatures expect impossibilities;

Some lobsters expect impossibilities.

 

         Dolls are never unkind;

Cousins are never kind;

Some cousins are dolls.

 

No frogs are poets;

Some ducks are poets;

All ducks are frogs.

 

All lions are fierce;

Only coffee-drinkers are fierce;

Some lions do not drink coffee.

 

No bridges are made of sugar;

Some bridges are picturesque;

Anything picturesque is made of sugar.

 

Some epicures are ungenerous;

Any uncle of mine is generous;

Any epicure is an uncle of mine.

 

Some of these boys work hard;

All who work hard are anxious to learn;

None of these boys are anxious to learn.

 

No hedge-hogs can read;

Only those who can read are well-educated;

Some hedge-hogs are well-educated.

 

A prudent man shuns hyenas;

No banker is imprudent;

Some bankers do not shun hyenas.

 

All wasps are unfriendly;

All puppies are friendly;

Some wasps are puppies.

 

Sugar is sweet;

Salt is not sweet;

Salt is sugar.

 

No ducks waltz;

All officers waltz;

Some ducks are officers.

 

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