Rules of Validity
-  Negative Premises and Conclusions  -

4. If Either Premise of a Valid Syllogism Is Negative, the Conclusion Must Be Negative; if the Conclusion Is Negative, One Premise Must Be Negative

If a premise is negative, it tells us that one class (either S or P, depending on which premise it is) is excluded from another class (M). From this information, we might be able to infer that S is excluded from P--if the other rules are satisfied. However, we could never infer that S is included in P.

Conversely, if the conclusion is negative, it says that S is excluded from P. The only information that would justify this conclusion is the information that S is excluded from M (which is included in P) or that S is included in M (which is excluded from P). In either of those cases, we have one negative premise.


Comprehension Questions

1 Is an E proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
2 Is an I proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
3 Is an A proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
4 Is an O proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
5 If the major premise is negative, then the conclusion
a) must be negative
b) can be negative
6 If the conclusion is negative, then one premise
a) must be negative
b) can be negative
7 If the minor premise is negative, then the conclusion
a) must be negative
b) can be negative
8 If one premise is an E proposition, then the conclusion
a) must be negative
b) can be negative
9 If one premise is an O proposition, then the conclusion
a) must be negative
b) can be negative
10 If one of the premises is an A proposition, must the conclusion be and O or an E proposition?
a) yes
b) no
11 If one of the premises is an I proposition, must the conclusion be an O or an E proposition?
a) yes
b) no
12 Does the following syllogism violate the rule that the conclusion must be negative if one of the premises are and that one of the premises must be negative if the conclusion is?

No horned animal is a carnivore
All moose are horned animals


Some moose are not carnivores
a) yes
b) no
13 Does the following syllogism violate the rule that the conclusion must be negative if one of the premises are and that one of the premises must be negative if the conclusion is?

No M is P
All M is S


Some S are P
a) yes
b) no
14 Does the following syllogism violate the rule that the conclusion must be negative if one of the premises are and that one of the premises must be negative if the conclusion is?

All supporters of the nuclear freeze want to preserve peace
No conservatives support nuclear freeze


No conservatives want to preserve peace
a) yes
b) no


The Middle Term | Distributed Terms |
Two Negative Premises | Negative Premises and Conclusions

Rules of Validity

© Copyright 1998, W.W. Norton & Co.