Exclusive Premises

(also known as: fallacy of exclusive premises)

Description: A standard form categorical syllogism that has two negative premises either in the form of  “no X are Y” or “some X are not Y”.

Logical Forms:

No X are Y.

Some Y are not Z.

Therefore, some Z are not X.


No X are Y.

No Y are Z.

Therefore, no Z are X.

Example #1:

No kangaroos are MMA fighters.

Some MMA fighters are not Mormons.

Therefore, some Mormons are not kangaroos.

Example #2:

No animals are insects.

Some insects are not dogs.

Therefore, some dogs are not animals.

Example #3:

No animals are insects.

No insects are dogs.

Therefore, no dogs are animals.

Explanation: Remember why fallacies are so dangerous: because they appear to be good reasoning.  The conclusion in example #1 makes sense, but it does not follow logically -- it is an invalid argument.  Based on the first two premises, there is no way logically to deduce that conclusion.  Now, look at examples #2 and #3.  We use the same logical form of the argument, committing the same fallacy, but by changing the terms it is much more clear that something went wrong somewhere, and it did.  This kind of argument, the categorical syllogism, cannot have two negative premises and still be valid.

Just because the conclusion appears true, it does not mean the argument is valid (or strong, in the case of an informal argument).

Exception: None.

Tip: Learn to recognize the forms of formal fallacies, and you will easily spot invalid formal arguments.

References: {apa}

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