Logic: Categorical Syllogisms

I. Categorical Syllogisms

Deals with "all", "some", and "none." Use capital letters to refer to general terms (dogs, people, brown), and lowercase letters to refer to particular individuals (this dog, Rex, Bob). Always use the word "is" to connect subject and predicate.

II. Example Translation

1. All dogs are mammals
2. Rex is a dog
3. Therefore, Rex is a mammal

Translates to:

1. All D is M
2. r is D (note the individual Rex is converted to a lowercase letter)
3. Therefore, r is M

III. Testing For Validity

Use the "star test" to see if the argument is logically valid. Star all distributed terms in the premises, and all undistributed terms in the conclusion. A distributed term is one that either immediately follows "All", or both terms if they follow "No". Example:

1. All D* is M (star the term immediately following "All")
2. No B* is D* (star both terms following "No")
3. Therefore, no B is M (only star undistributed terms in the conclusion)

The argument is logically valid if all capital letter terms are starred once and only once, and there is only one starred term in the right-hand "column." In the example above, the D is starred twice, and the M isn't starred at all. So the argument is logically invalid and the conclusion. Another example:

1. No B* is X*
2. All U* is B
3. Therefore, no U is X

Each capital letter is starred once and only once, and there is one star in the right hand "column" (the X). This argument is logically valid. Plug in true premises, and you have a sound argument.