The Language of Argument

1 7 2

C H A P T E R 7 ■ C a t e g o r i c a l L o g i c

fathers, because we were not given information saying whether anything

falls into the category of fathers or not. For the same reason, we had to put

an asterisk on the boundary of the circle for golfers when diagramming

“Some fathers are doctors.” The upshot was that we did not indicate that

anything exists in the region of overlap between fathers and golfers. But this

is what the conclusion demands, so the form of this syllogism is not valid.

Here is an invalid syllogism with negative premises:

No babies are golfers.

No fathers are babies.

∴ No fathers are golfers.

Fathers Golfers Fathers

Premises: Conclusion:

Golfers

Babies

Again, we see that the form of this syllogism is not valid, because the entire

area of overlap between the circles is shaded in the diagram for the conclu-

sion, but part of that area is not shaded in the diagram for the premises.

The method of Venn diagrams is adequate for deciding the validity or in-

validity of all possible forms of categorical syllogism. To master this method,

all you need is a little practice.

Using Venn diagrams, test the following syllogistic forms for validity:

1. All M is P.
   All M is S.
   ∴ All S is P.


2. All P is M.
   All M is S.
   ∴ All S is P.


3. All M is P.
   Some M is S.
   ∴ Some S is P.


4. All P is M.
   Some M is S.
   ∴ Some S is P.


5. All P is M.
   Some S is M.
   ∴ Some S is P.


6. All P is M
   Some S is not M.
   ∴ Some S is not P.

Exercise VII

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