Denying a Conjunct
The invalid inference that if two statements cannot both be true and one is false, the other must be true. Both statements could be false.
THE IDEA
Description
A formal fallacy that starts with the premise that two statements cannot both be true. It then denies one statement and concludes that the other must be true, overlooking the possibility that both are false.
Logical Form
¬(A ∧ B), ¬A ∴ B (invalid) ¬(A ∧ B), ¬B ∴ A (invalid)
Examples
Example #1:
"It is not true that I am both a moron and an idiot. I am not a moron. Therefore, I am an idiot." This argument is invalid. Being “not both” a moron and an idiot allows either one or both descriptions to be false. Denying one does not establish the other.
Example #2:
"It is not true that I am both a Satanist and a Christian. I am not a Satanist. Therefore, I am a Christian." This argument is invalid for the same reason: being “not both” does not allow us to infer the truth of the remaining conjunct.
Exception
None.
When to use it
Evaluating logical arguments that use 'not both' statements in philosophy or debate.
Analyzing everyday reasoning where someone incorrectly concludes a specific option based on the negation of a conjunction.
Teaching formal logic courses to illustrate common formal fallacies.
Detecting flawed reasoning in legal or scientific arguments that involve binary alternatives.
FROM THEORY TO EVERYDAY LIFE
In practice
The Moron and Idiot Fallacy
Premise 1: It is not true that I am both a moron and an idiot. Premise 2: I am not a moron. Conclusion: Therefore, I am an idiot. This is a fallacy because excluding one conjunct does not force the other to be true.
The Religion Fallacy
Premise 1: It is not true that I am both a Satanist and a Christian. Premise 2: I am not a Satanist. Conclusion: Therefore, I am a Christian. This is invalid because the premises do not guarantee the conclusion; the person could follow another religion or none.
A MOMENT TO REFLECT
Put it to work.
Can you think of a situation where you might have mistakenly concluded that because one of two possibilities is false, the other must be true?
Why is it fallacious to assume that when two things cannot both be true, excluding one forces the other?
How can you avoid committing the Denying a Conjunct fallacy in your own reasoning?
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies