Accused of a fallacy? Suspect a fallacy? Ask Dr. Bo and the community!

Quickly register to comment, ask and respond to questions, and get FREE access to our passive online course on cognitive biases!

one moment please...

Negative Conclusion from Affirmative Premises

(also known as: illicit affirmative)

Description: The conclusion of a standard form categorical syllogism is negative, but both of the premises are positive.  Any valid forms of categorical syllogisms that assert a negative conclusion must have at least one negative premise.

Logical Form:

If A is a subset of B, and B is a subset of C, then A is not a subset of C.

Example #1:

All cats are animals.

Some pets are cats.

Therefore, some pets are not animals.

Explanation: The conclusion might be true -- I had a pet rock growing up, but the argument still does not logically support that.  Think of sets and subsets.  All cats are animals: we have a set of animals and a subset of cats.  “Some” pets are cats: so all we know is that there is a part of our set, “pets” that intersects with the subset, “cats”, but we don’t have the information we need to conclude logically that some pets are not animals.  This argument is invalid, thus as a formal argument, it is fallacious.

Example #2:

All boys are sports fans.

Some bakers are boys.

Therefore, some bakers are not sports fans.

Explanation: The conclusion might be true -- but the argument still does not logically support that for the same reasons in the first example.  This argument is invalid, thus as a formal argument, it is fallacious.

Exception: None.


Goodman, M. F. (1993). First Logic. University Press of America.

Registered User Comments

Become a Logical Fallacy Master. Choose Your Poison.

Logically Fallacious is one of the most comprehensive collections of logical fallacies with all original examples and easy to understand descriptions; perfect for educators, debaters, or anyone who wants to improve his or her reasoning skills.

Get the book, Logically Fallacious by Bo Bennett, PhD by selecting one of the following options:

Not Much of a Reader? No Problem!

Enroll in the Mastering Logical Fallacies Online Course. Over 10 hours of video and interactive learning. Go beyond the book!

Enroll in the Fallacy-A-Day Passive Course. Sit back and learn fallacies the easy way—in just a few minutes per day, via e-mail delivery.

Have a podcast or know someone who does? Putting on a conference? Dr. Bennett is available for interviews and public speaking events. Contact him directly here.

About Archieboy Holdings, LLC. Privacy Policy Other Books Written by Bo
 Copyright 2017, Archieboy Holdings, LLC.