Commutation of Conditionals
Reversing a conditional without justification: inferring that if Q then P solely from the premise that if P then Q. This is related to affirming the consequent.
THE IDEA
Commutation of Conditionals
(also known as: the fallacy of the consequent, converting a conditional)
Description: Switching the antecedent and the consequent in a logical argument.
Logical Form:
- If P, then Q.
- Therefore, if Q, then P.
Example #1:
- Premise: If someone has a PhD, then they are smart.
- Conclusion: Therefore, if someone is smart, then they have a PhD.
- Explanation: There are many smart people without PhDs. The premise does not guarantee the conclusion.
Example #2:
- Premise: For this logical example, suppose that everyone with herpes has a rash.
- Conclusion: Therefore, if someone has a rash, then they have herpes.
- Explanation: Other conditions can cause a rash, so a rash alone does not establish herpes. The assumed premise is not a general medical rule.
Exception: If P and Q are logically equivalent (i.e., P if and only if Q), then the commutation is valid. For example, "If a triangle is equilateral, then it is equiangular" and vice versa.
When to use it
Evaluating causal claims in medical studies (e.g., 'If treatment then recovery' does not mean 'If recovery then treatment').
Analyzing advertising slogans that imply a correlation is a one-way condition (e.g., 'If you use our product, you'll be happy' does not mean 'If you are happy, you use our product').
Debunking common superstitions or conspiracy theories that reverse cause and effect.
Teaching critical thinking to students by highlighting the fallacy in everyday reasoning.
FROM THEORY TO EVERYDAY LIFE
In practice
The PhD and Smartness Fallacy
Premise: If someone has a PhD, then they are smart. Conclusion: Therefore, if someone is smart, then they have a PhD. Explanation: This is invalid because many smart people lack PhDs.
The Rash and Herpes Fallacy
Premise: For this logical example, suppose that everyone with herpes has a rash. Conclusion: Therefore, if someone has a rash, then they have herpes. Explanation: A rash can have other causes, so it does not establish herpes. The premise is an assumption for the argument, not a general medical rule.
A MOMENT TO REFLECT
Put it to work.
Can you think of a real-world argument where someone mistakenly swaps the antecedent and consequent? How would you point out the error?
Why is it important to distinguish between a conditional and its converse in scientific reasoning? Provide an example.
Under what conditions would swapping the antecedent and consequent be logically valid? Give an example.
CONTINUE THE CONVERSATION
Source texts
- Logically Fallacious - The Ultimate Collection of Over 300 Logical Fallacies