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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