*****

**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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