An Introduction to Clearer Thinkingpremise. Neither premise is a universal statement.
(4) Two negatives: Every syllogism must have at least one
affirmative premise. Consider these:
No mothers are men.
Some grandparents are not men.
Therefore ...?
It would be invalid to conclude any relationship between
grandparents and mothers. Neither premise is an affirmative
statement.
(5) Particular switched to universal: If either premise is
a particular, the conclusion must also be a particular. Con
sider:
All natives are citizens at birth.
Some natives are of foreign parentage.
Therefore, all who have foreign parentage are citizens
at birth.
The conclusion is invalid, for it is an “all” statement when
one of the premises was a “some” statement.
(6) Negative switched to affirmative: If either premise is
negative, the conclusion must also be negative. Consider:
No voters are aliens.
Some citizens are voters.
Therefore, some citizens are aliens.
The conclusion is invalid, for it is affirmative although
one of the premises was negative. The conclusion becomes
valid if we convert it to negative: “Some citizens are not
aliens.”
(7) Undistributed switched to distributed: Any term that
is undistributed in a premise must also be undistributed if it
appears in the conclusion. Consider:
Some Texans are Democrats.
No Democrats are Republicans.
Therefore, some Republicans are not Texans.
The conclusion is invalid, for the term Texans is distrib
uted in the conclusion although it was undistributed in the
major premise. The conclusion becomes valid if we convert
it to “some Texans are not Republicans,” leaving the term
Texans in undistributed form.
(i) Enthymeme: An elliptical syllogism. A valid conclu
sion may be drawn although not all the stages of syllogistic