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:
- Not all crabs live in water.
- All crabs do not live in water.
- Movie stars are all rich.
- If anybody hits me, I will
hate them. - If anything is broken, it does
not work. - Somebody loves you.
- Somebody does not love you.
- Nobody loves me but my mother.
- Anybody who is Mormon
believes in God. - My friends are the only ones
who care. - Only seniors may take this
course. - Our pit bull is a good pet.
- Everything that is cheap is
no good. - Some things that are expensive
are no good. - Some things that are cheap are
good. - Some things that are not cheap
are good. - Some things that are cheap are
not good. - Some things that are not cheap
are not good. - Not all cars have four wheels.
- There are couples without
children. - There are no people who hate
chocolate. - There are people who hate
chocolate. - Nothing that is purple is an apple.
- Nothing that is not white is snow.
- There aren’t any runners who are
slow. - 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.
97364_ch07_ptg01_151-176.indd 159 15/11/13 10:29 AM
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