Affirming the Consequent (Converse Error)
A logical fallacy where the converse of a true conditional statement is assumed to be true. Just because 'If A, then B' is true does not logically justify 'If B, then A'.
THE IDEA
Implications and Converses
Mathematical notation is one of the things that can make mathematics baffling and difficult to learn. However, the notation is there to help us think clearly. Implications and converses demonstrate this. This can be extra confusing in normal language, because of the flexibility of English grammar and where we can put the word “if” in the sentence.
You can have ice cream if you eat your broccoli.
is logically the same as saying
If you eat your broccoli you can have ice cream.
In general we see that “if A is true then B is true” means the same as “B is true if A is true”. This might look like we’ve turned around the flow of logic, but we’ve actually only turned around the grammar.
One advantage of using arrow notation is that the flow of logic is completely clear from the direction of the arrow.
The converse of A → B is B → A.
But also A → B is equivalent to B ← A, as it doesn’t matter which way the arrow is facing on the page, only where it is pointing from and to.
The new statement (the converse, B → A) looks superficially similar to the old one but is logically completely different.
When to use it
Identifying an argument that treats a sufficient condition as necessary, such as assuming that everyone receiving a benefit must meet one particular eligibility rule.
Debugging your own reasoning when developing criteria for a decision.
Evaluating the logic behind rules and policies (e.g., 'If you use a computer, you need a password' does not mean 'If you have a password, you are allowed to use the computer').
FROM THEORY TO EVERYDAY LIFE
In practice
Broccoli and Ice Cream
The text provides the implication: 'If you eat your broccoli, you can have ice cream.' The converse error would be believing: 'If they had ice cream, they must have eaten their broccoli.' This is a fallacy because other reasons for having ice cream exist.
Rain and Clouds
The true implication is: 'If it rains, the ground is wet.' The converse, 'If the ground is wet, it must have rained,' is false. The ground could be wet from a sprinkler, a spilled drink, or a hose.
A MOMENT TO REFLECT
Put it to work.
Suppose a service says premium members receive priority support. Would receiving priority support establish that someone is a premium member? What other explanations might there be?
How does understanding the converse fallacy help when interpreting medical test results (sensitivity vs. specificity)?
Why are the words 'if' and 'only if' so critical in distinguishing an implication from its converse?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- The Art of Logic How to Make Sense in a World that Doesn’t (Eugenia Cheng)