search

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

Denying a Conjunct

Description: A formal fallacy in which the first premise states that at least one of the two conjuncts (antecedent and consequent) is false and concludes that the other conjunct must be true.

Logical Forms:

Not both P and Q.

Not P.

Therefore, Q.

 

Not both P and Q.

Not Q.

Therefore, P.

Example #1:

I am not both a moron and an idiot.

I am not a moron.

Therefore, I am an idiot.

Explanation:  I might be an idiot, but the truth of both premises does not guarantee that I am; therefore, this argument is invalid -- technically, the form of this formal argument is invalid.  Being “not both” a moron and an idiot, only means that if I am not one of the two, I am simply not one of the two -- we cannot logically conclude that I am the other.

Example #2:

I am not both a Christian and a Satanist.

I am not a Satanist.

Therefore, I am a Christian.

Explanation:  The truth of both premises does not guarantee that I am a Christian; therefore, this argument is invalid -- the form of this formal argument is invalid.  Being “not both” a Satanist and a Christian, only means that if I am not one of the two, I am simply not one of the two -- we cannot logically conclude that I am the other.

Exception: No exceptions.

Fun Fact: Atheists don’t eat babies.

References:

Kiersky, J. H., & Caste, N. J. (1995). Thinking Critically: Techniques for Logical Reasoning. West Publishing Company.

Questions about this fallacy? Ask our community!

Eat Meat... Or Don't.

Roughly 95% of Americans don’t appear to have an ethical problem with animals being killed for food, yet all of us would have a serious problem with humans being killed for food. What does an animal lack that a human has that justifies killing the animal for food but not the human?

As you start to list properties that the animal lacks to justify eating them, you begin to realize that some humans also lack those properties, yet we don’t eat those humans. Is this logical proof that killing and eating animals for food is immoral? Don’t put away your steak knife just yet.

In Eat Meat… Or Don’t, we examine the moral arguments for and against eating meat with both philosophical and scientific rigor. This book is not about pushing some ideological agenda; it’s ultimately a book about critical thinking.

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