Drawing Categorical Arguments (Episode 55)

Did you know you can check some arguments for fallacies by drawing pictures? Overlapping circles called Venn Diagrams can show whether arguments about categories (like, “All cats are mammals” or “Some scientists are creationists”) are valid. Here’s a crash course on how to do this yourself.

NOTES:
• For Statement Form #3, “Some S are P,” draw the X right in the centre of the overlap between the S and P bubbles, so that the X straddles the border of the third bubble. This shows that it’s not clear which side(s) of the border the “some” individual(s) belong to. If the argument’s conclusion requires that the individuals only be on a certain side of the border, the argument is invalid, because you can’t prove from the diagram which side the individuals belong to.
• Venn Diagrams cannot invalidate arguments where both premises are Forms #1 or #2, and the conclusion is Form #3 or #4. However, you can tell such arguments are invalid by creating absurd examples with the same structure, E.g. “All humans walk on two legs (Form #1). All chickens walk on two legs (Form #1). Therefore, some humans are chickens (Form #3).”

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