Negating Antecedent and Consequent
Negating both sides of a conditional does not produce its contrapositive unless their order is also reversed. From if p then q, the valid contrapositive is if not q then not p; if not p then not q does not follow.
THE IDEA
Negating Antecedent and Consequent
Also known as improper transposition.
A conditional has the form: if p, then q. Its valid contrapositive reverses and negates the parts: if not q, then not p. Simply negating them gives an invalid inference: if not p, then not q. The consequent might occur for another reason.
Example #1
The source discusses the premise that if Barry Manilow sings love songs, he is gay. That premise is not established by the type of songs he sings. Even granting it for the sake of examining the form, it would not follow that if he does not sing love songs, he is not gay. The contrapositive would instead say that if he is not gay, he does not sing love songs. Validity concerns whether the conclusion follows when the premises are true; it does not establish that those premises are true.
Example #2
The source’s second example makes a conditional connection between Tom holding that belief and being an idiot. Negating the belief would not establish that Tom is not an idiot: the original conditional leaves other possible reasons open. The invalid step is again negating both parts without reversing their order.
When to use it
Identifying flawed reasoning in debates or political arguments that incorrectly use negation.
Evaluating the logical validity of arguments in academic or professional writing.
Teaching formal logic to students by contrasting valid and invalid forms of transposition.
Analyzing everyday reasoning to avoid committing this fallacy.
FROM THEORY TO EVERYDAY LIFE
In practice
Example #1
The source’s conditional links Barry Manilow singing love songs with being gay. Even if that unsupported premise were granted, it would not follow that not singing love songs means he is not gay. Negating both parts without reversing them is invalid.
Example #2
Suppose Tom holding a particular belief is offered as a sufficient reason to call him an idiot. Tom not holding that belief would not exclude other reasons. The negative conclusion therefore does not follow from the conditional.
A MOMENT TO REFLECT
Put it to work.
Think of an argument you've heard that negated both parts without switching the antecedent and consequent. Why does it fail?
How can you distinguish between a valid modus tollens and this fallacy?
Create an original example of this fallacy from a real-world debate or discussion.
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies