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Spoofing Classical Logic
There
are nineteen syllogisms of classical logic. For each one there is a counter-troika
spoofing it. These are the syllogisms and their counter-troikas:
1:AAA
Every
M is P; every S is M; therefore every S is P
Contra
1:AAA
Moe: Some M is not P; every S is M; some S is not P
Larry: Every M is P; some S is not M; some S is not
P
Curly: Every M is P; every S is M; every S is P
So by 2/3: every M is P; every S is M; some S is not P.
Exercise for the student: expand this troika:
All
brainiacs wear glasses;
All
scientists are brainiacs;
Some
scientists don’t wear glasses.
1:EAE
No
M is P; every S is M; therefore no S is P
Contra
1:EAE
Moe: Some M is P; every S is M; some S is P
Larry: No M is P; some S is not M; some S is P
Curly: No M is P; every S is M; no S is P
So by 2/3: No M is P; every S is M; some S is P
Exercise for the student: expand this troika:
No
beggar is honest;
All
televangelists are beggars;
Some
televangelists are honest.
1:AII
Every
M is P; some S is M; therefore some S is P
Contra
1:AII
Moe: some M is not P; some S is M; no S is P
Larry: Every M is P; no S is M; no S is P
Curly: Every M is P; some S is M; some S is P
So by 2/3: Every
M is P; some S is M; no S is P
Exercise for the student: expand this troika:
All
men are beasts;
Some
saints are men;
No
saints are beasts.
1:EIO
No
M is P; some S is M; therefore some S is not P
Contra
1:EIO
Moe: Some M is P; some S is M; every S is P
Larry: No M is P; no S is M; every S is P
Curly: No M is P; some S is M; some S is not P
So by 2/3: No
M is P; some S is M; every S is P
Exercise for the student: expand this troika:
The
only good writer is a dead writer;
Some
Americans are good writers;
Every
American is alive.
2:EAE
No
P is M; every S is M; therefore no S is P
Contra
2:EAE
Moe: Some P is M; every S is M; some S is P
Larry: No P is M; some S is not M; some S is P
Curly: No P is M; every S is M; no S is P
So by 2/3: No
P is M; every S is M; some S is P
Exercise for the student: expand this troika:
Teachers
are never enthusiastic;
You
are always enthusiastic;
You
are sometimes a teacher.
2:AEE
Every
P is M; no S is M; therefore no S is P
Contra
2:AEE
Moe: Some P is not M; no S is M; some S is P
Larry: Every P is M; some S is M; some S is P
Curly: Every P is M; no S is M; no S is P
So by 2/3: Every
P is M; no S is M; some S is P
Exercise for the student: expand this troika:
Every
dog has his day;
No
skinflint has his day;
Some
skinflints are dogs.
2:EIO
No
P is M; some S is M; therefore some S is not P
Contra
2:EIO
Moe: Some P is M; some S is M; every S is P
Larry: No P is M; no S is M; every S is P
Curly: No P is M; some S is M; some S is not P
So by 2/3: No
P is M; some S is M; every S is P
Exercise for the student: expand this troika:
No
president is a moron;
Some
illiterates are morons;
Every
illiterate is president.
2:AOO
Every
P is M; some S is not M; therefore some S is not P
Contra
2:AOO
Moe: Some P is not M; some S is not M; every S is P
Larry: Every P is M; every S is M; every S is P
Curly: Every P is M; some S is not M; some S is not
P
So by 2/3: Every
P is M; some S is not M; every S is P
Exercise for the student: expand this troika:
Every
good book is readable;
Some
classics are unreadable;
All
classics are good books.
3:AII
Every
M is P; some M is S; therefore some S is P
Contra
3:AII
Moe: Some M is not P; some M is S; no S is P
Larry: Every M is P; no M is S; no S is P
Curly: Every M is P; some M is S; some S is P
So by 2/3: Every
M is P; some M is S; no S is P
Exercise for the student: expand this troika:
Every
weekend I play golf;
Some
weekends I’m with my father;
I
never play golf with my father.
3:EIO
No
M is P; some M is S; therefore some S is not P
Contra
3:EIO
Moe: Some M is P; some M is S; every S is P
Larry: No M is P; no M is S; every S is P
Curly: No M is P; some M is S; some S is not P
So by 2/3: No
M is P; some M is S; every S is P
Exercise for the student: expand this troika:
No
man is an island;
Some
men float;
Everything
afloat is an island.
3:IAI
Some
M is P; every M is S; therefore some S is P
Contra
3:IAI
Moe: No M is P; every M is S; no S is P
Larry: Some M is P; some M is not S; no S is P
Curly: Some M is P; every M is S; some S is P
So by 2/3: Some
M is P; every M is S; no S is P
Exercise for the student: expand this troika:
Some
days I’m happy;
Every
day I have the blues;
I’m
never happy on the days I have the blues.
3:OAO
Some
M is not P; every M is S; therefore some S is not P
Contra
3:OAO
Moe: Every M is P; every M is S; every S is P
Larry: Some M is not P; some M is not S; every S is
P
Curly: Some M is not P; every M is S; some S is not
P
So by 2/3: Some
M is not P; every M is S; every S is P
Exercise for the student: expand this troika:
Some
women are not pretty;
Every
woman is lovely;
Every
lovely is pretty.
3:AAI
Every
M is P; every M is S; therefore some S is P
Contra
3:AAI
Moe: Some M is not P; every M is S; no S is P
Larry: Every M is P; some M is not S; no S is P
Curly: Every M is P; every M is S; some S is P
So by 2/3: Every
M is P; every M is S; no S is P
Exercise for the student: expand this troika:
Every
sex act is nasty;
Every
sex act is sacred;
Nothing
sacred is nasty.
3:EAO
No
M is P; every M is S; therefore some S is not P
Contra
3:EAO
Moe: Some M is P; every M is S; every S is P
Larry: No M is P; some M is not S; every S is P
Curly: No M is P; every M is S; some S is not P
So by 2/3: No
M is P; every M is S; every S is P
Exercise for the student: expand this troika:
No
parents love war;
Every
parent is a producer;
Every
producer loves war.
4:AEE
Every
P is M; no M is S; therefore no S is P
Contra
4:AEE
Moe: Some P is not M; no M is S; some S is P
Larry: Every P is M; some M is S; some S is P
Curly: Every P is M; no M is S; no S is P
So by 2/3: Every
P is M; no M is S; some S is P
Exercise for the student: expand this troika:
Everything
that he likes is esoteric;
Nothing
esoteric is on TV;
There’s
something on TV that he likes.
4:EIO
No
P is M; some M is S; therefore some S is not P
Contra
4:EIO
Moe: Some P is M; some M is S; every S is P
Larry: No P is M; no M is S; every S is P
Curly: No P is M; some M is S; some S is not P
So by 2/3: No
P is M; some M is S; every S is P
Exercise for the student: expand this troika:
No
criminal is kind;
Some
kind people are poor;
All
poor people are criminals.
4:IAI
Some
P is M; every M is S; therefore some S is P
Contra
4:IAI
Moe: No P is M; every M is S; no S is P
Larry: Some P is M; some M is not S; no S is P
Curly: Some P is M; every M is S; some S is P
So by 2/3: Some
P is M; every M is S; no S is P
Exercise for the student: expand this troika:
Some
important truths are obvious;
Everything
obvious is dull;
Nothing
dull is important.
4:AAI
Every
P is M; every M is S; therefore some S is P
Contra
4:AAI
Moe: Some P is not M; every M is S; no S is P
Larry: Every P is M; some M is not S; no S is P
Curly: Every P is M; every M is S; some S is P
So by 2/3: Every
P is M; every M is S; no S is P
Exercise for the student: expand this troika:
Every
person is an object;
Every
object is a pattern in Hilbert space;
No
pattern in Hilbert space is a person.
4:EAO
No
P is M; every M is S; therefore some S is not P
Contra
4:EAO
Moe: Some P is M; every M is S; every S is P
Larry: No P is M; some M is not S; every S is P
Curly: No P is M; every M is S; some S is not P
So by 2/3: No
P is M; every M is S; every S is P
Exercise for the student: expand this troika:
Nothing
I can explain takes long to read;
Anything
that takes long to read is profound;
Anything
profound, I can explain.
Note that in each case,
Curly repeats the classic syllogism, but he is overruled in the third term!
And a
word of thanks to Rudy Rucker, from whose book “Mind Tools” I cribbed the
nineteen syllogisms here spoofed.
Exercise
for the student: expand these troikas:
All
aliens read comic books;
Some
aliens are angels;
No
angels read comic books.
All
cats have nine lives;
No
vampires have nine lives;
Some
cats are vampires.
All Scots are
canny;
All ghosts are
uncanny;
Some Scots are
ghosts.
No
cowards are men;
All
mortals are cowards;
All
men are mortal.
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