search

Become an active member of our fallacy-discussing community (or just become a lurker!)

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.

Fun Fact: I taught my pet rock how to play dead. It was its only trick.

References:

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

Questions about this fallacy? Ask our community!

Reason: Books I & II

This book is based on the first five years of The Dr. Bo Show, where Bo takes a critical thinking-, reason-, and science-based approach to issues that matter with the goal of educating and entertaining. Every chapter in the book explores a different aspect of reason by using a real-world issue or example.

Part one is about how science works even when the public thinks it doesn't. Part two will certainly ruffle some feathers by offering a reason- and science-based perspective on issues where political correctness has gone awry. Part three provides some data-driven advice for your health and well-being. Part four looks at human behavior and how we can better navigate our social worlds. In part five we put on our skeptical goggles and critically examine a few commonly-held beliefs. In the final section, we look at a few ways how we all can make the world a better place.

Get 20% off this book and all Bo's books*. Use the promotion code: websiteusers

* This is for the author's bookstore only. Applies to autographed hardcover, audiobook, and ebook.

Get the Book