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DEDUCTION: Part 3 -
Page a
Figures
and Moods of
The Categorical Syllogism
by Jonathan Dolhenty, Ph.D.
The Third
Figure
The middle term (M) is the subject of both
premises.
The rule for the Third Figure is: The minor
premise must be affirmative and the conclusion must
be particular.
Explanation of
the Rule
First Part: The minor premise must be
affirmative.
If the minor premise is negative, the major
premise would have to be affirmative. This is
because the premises cannot consist of two negative
propositions, according to General Rule Number
6.
In that case, however, the major term (P), which
is the predicate of the major premise, would be a
particular term, since it is the predicate of an
affirmative proposition.
According to General Rule Number 7, a negative
minor premise would necessitate a negative
conclusion. That would make its predicate, which is
the major term (P), a universal term. This would
result in an illicit major, a violation of
General Rule Number 2.
This will occur every time the minor premise is
negative. So the minor premise can never be
negative and to avoid an illicit major, the
minor premise must be affirmative.
Second Part: The conclusion must be
particular.
The minor term (S) will always be a particular
term in the premise since, according to the first
part of this rule, the minor premise must be
affirmative. In this minor premise the minor term
(S) is the predicate. The predicate of an
affirmative sentence is always particular.
The minor term (S) is the subject of the
conclusion. It must also be a particular term in
the conclusion. Otherwise General Rule Number 2
would be violated and we would have an illicit
minor. Therefore, the conclusion must be
particular.
The Valid Moods
of the Third Figure
When we consider the moods which are valid for
the syllogisms of the Third Figure, we find that
six of the eight possible legitimate combinations
are valid and two are invalid. Here are the
diagrams:
|
Moods of
the Third Figure
|
|
A
|
uM
|
+
|
pP
|
|
A
|
uM
|
+
|
pS
|
|
|
pS
|
+
|
pP
|
|
|
Valid
|
|
|
A
|
uM
|
+
|
pP
|
|
E
|
uM
|
-
|
uS
|
|
|
uS
|
-
|
uP
|
|
|
Illicit
Major
|
|
|
A
|
uM
|
+
|
pP
|
|
I
|
pS
|
+
|
pS
|
|
|
pS
|
+
|
pP
|
|
|
Valid
|
|
|
A
|
uM
|
+
|
pP
|
|
O
|
pM
|
-
|
uS
|
|
|
uS
|
-
|
uP
|
|
|
Illicit
Major
|
|
|
E
|
uM
|
-
|
uP
|
|
A
|
uM
|
+
|
pS
|
|
|
pS
|
-
|
uP
|
|
|
Valid
|
|
|
E
|
uM
|
-
|
uP
|
|
I
|
pM
|
+
|
pS
|
|
|
pS
|
-
|
uP
|
|
|
Valid
|
|
|
I
|
pM
|
+
|
pP
|
|
A
|
uM
|
+
|
pS
|
|
|
pS
|
+
|
pP
|
|
|
Valid
|
|
|
O
|
pM
|
-
|
uP
|
|
A
|
uM
|
+
|
pS
|
|
|
pS
|
-
|
uP
|
|
|
Valid
|
|
Clearly, there are six valid moods for the Third
Figure: A A, A I, E A, E I, I A, and O A. Each one
follows the rule that the minor premise must be
affirmative and the conclusion must be
particular.
The A E and A O moods are invalid because of an
illicit major brought into the conclusion. They
violate the first part of the rule: The minor
premise must be affirmative.
Study the following arguments which illustrate
the valid moods:
|
A
|
All birds have wings.
|
|
A
|
All birds are bipeds.
|
|
|
Therefore, Some bipeds have
wings.
|
|
A
|
All geniuses think they are
wise.
|
|
I
|
Some geniuses are foolish
people.
|
|
|
Therefore, Some foolish people think
they are wise.
|
|
E
|
No misers are generous.
|
|
A
|
All misers are people who abuse
their riches.
|
|
|
Therefore, Some people who abuse
their riches are not generous.
|
|
E
|
No animals are immortal.
|
|
I
|
Some animals are dogs.
|
|
|
Therefore, Some dogs are not
immortal.
|
|
I
|
Some Communists are
revolutionary.
|
|
A
|
All Communists are radicals.
|
|
|
Therefore, Some radicals are
revolutionary.
|
|
O
|
Some criminals are
teenagers.
|
|
A
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All criminals break the law.
|
|
|
Therefore, Some who break the law
are teenagers.
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2-b of Figures and Moods of the Syllogism
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