Syllogistic Translations

Easier Translations

Syllogistic logic studies arguments whose validity depends on "all," "no," "some," and similar notions. In symbolizing such arguments, we use capital letters for general categories (like "logician") and small letters for specific individuals (like "Gensler").

all A is B
no A is B
some A is B
some A is not B
x is A
x is not A
x is y
x is not y

Important Rules:

Use capital letters for general terms (terms that describe or put in a category)
- Examples: "a cute baby", "charming", "drives a Buick"
Use small letters for singular terms (terms that pick out a specific person or thing)
- Examples: "the world's cutest baby", "this child", "David"

Examples of correct translations:

All babies are cute = all B is C
Will Gensler is a baby = w is B
Will Gensler is the world's cutest baby = w is b

Harder Translations

English has various idiomatic ways to express our wffs. Instead of "all" we can say "any," "each," "every," or "whoever."

all A is B =

A's are B's
Those who are A are B
If a person is A, then she is B
If you're A, then you're B
Only B's are A's
None but B's are A's
No one is A unless she is B
Nothing is A unless it's B
A thing isn't A unless it's B
It's false that some A is not B

no A is B = no B is A =

A's aren't B's
Every (each, any) A is non-B
Whoever (whatever) is A isn't B
Those who are A aren't B
If a person is A, then she isn't B
If you're A, then you aren't B
There isn't a single A that's B
Not any A is B
It's false that there's an A that's B
It's false that some A is B

some A is B = some B is A =

One or more A's are B's
A's are sometimes B's
It's false that no A is B

some A is not B =

One or more A's aren't B's
Not all A's are B's
It's false that all A is B

Examples of correct translations:

Snakes aren't furry = no S is F
Only men are football players = all F is M
Not all steaks are well done = some S is not W

When you translate from English to logic, be careful to use correct WFFs.