The Language of Argument

1 5 9

C a t e g o r i c a l P r o p o s i t i o n s

Contradictories

Once we understand A, E, I, and O propositions by themselves, the next step

is to ask how they are related to each other. From their diagrams, some re-

lationships are immediately evident. Consider the Venn diagrams for the E

and I propositional forms:

5. Not all crabs live in water.


6. All crabs do not live in water.


7. Movie stars are all rich.


8. If anybody hits me, I will
   hate them.


9. If anything is broken, it does
   not work.


10. Somebody loves you.


11. Somebody does not love you.


12. Nobody loves me but my mother.


13. Anybody who is Mormon
    believes in God.


14. My friends are the only ones
    who care.


15. Only seniors may take this
    course.


16. Our pit bull is a good pet.


17. Everything that is cheap is
    no good.


18. Some things that are expensive
    are no good.


19. Some things that are cheap are
    good.


20. Some things that are not cheap
    are good.


21. Some things that are cheap are
    not good.


22. Some things that are not cheap
    are not good.


23. Not all cars have four wheels.


24. There are couples without
    children.


25. There are no people who hate
    chocolate.


26. There are people who hate
    chocolate.


27. Nothing that is purple is an apple.


28. Nothing that is not white is snow.


29. There aren’t any runners who are
    slow.


30. Flamingos aren’t friendly.

The first diagram has shading in the very same region that contains an as-

terisk in the second diagram. This makes it obvious that an E proposition

and the corresponding I proposition (that is, the I proposition that has the

same subject and predicate terms as the E proposition) cannot both be true.

For an E proposition to be true, there must be nothing in the central region.

S P S P

E: No S is P. I: Some S is P.

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