Lesson on Deductive Arguments
Categorical Syllogism

Kids argue over the silliest things.

One kid says,
"All dogs are mammals."

The other kid says,
"All cats are mammals."

So the one kid arrives at the conclusion that,
"All cats are dogs."

But the other kid says,
"I don't think so!"

Sure you know which kid is correct, but let's check the validity of this deductive argument by using Categorical Logic and Venn Diagrams.

Steps to the solution:

  1. Follow the Cyber Dog link (above) to analyze the statement
    "All dogs are mammals."
  2. Follow the Cyber Cat link (above) to analyze the statement
    "All cats are mammals."
  3. Put steps 1 and 2 together to get the solution.

Try some more examples of deducing the validity of conclusions drawn from given premises using Categorical Logic and Venn Diagrams.

Exercise for you.

Use Venn Diagrams to analyze the following:

Some reformers are fanatics, so some idealists are fanatics, since all reformers are idealists.

Written by:
CJ Kentler, V.S. Manoranjan in the Department of Mathematics, and
Joseph Keim Campbell in the Department of Philosophy
Washington State University
Pullman, Wa. 99164
© 1997, 1998