Rules of Validity
-  Two Negative Premises  -

3. No Valid Syllogism Can Have Two Negative Premises

If both premises are negative, they tell us that both the major and the minor term are excluded, wholly or in part, from the middle term. And that does not tell us how the major and minor terms are related to each other.

Example:

Knowing that no chiropractor has sung for the Metropolitan Opera, and that no one who has sung for the Metropolitan Opera has been in Kuala Lumpur, does not tell us that no chiropractors have been in Kuala Lumpur, or that some have, or anything else.


Comprehension Questions

1 Is an A proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
2 Is an O proposition affirmative or negative?
a) It is affirmative.
b) It is negative.
3 Does the following syllogism have two negative premises?

No A are B
Some A are not C


Some C are not B
a) yes
b) no
4 Does the following syllogism have two negative premises?

No one who competes for money is an amateur
No member of the Bush League is an amateur


All members of the Bush League compete for money
a) yes
b) no
5 Does the following syllogism have two negative premises?

Some crimes against property are frauds
All frauds are felonies


Some felonies are crimes against property
a) yes
b) no
6 Does the following syllogism have two negative premises?

Some M are not P
No M are S


Some S are not P
a) yes
b) no
7 Does the following syllogism have two negative premises?

Some P is not M
Some M is not S


Some S is not P
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.