## Saturday, May 25, 2013

### On Troikas 11.5: Spoofing Classical Logic

Once again I am overtaken by writing, and now have another section to interpolate. This really should go just before the "Delta Deduction" section; but I write it now, and include it now.

*****

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:
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:

Some aliens are angels;

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.