Steelman
Denying the antecedent
Also called inverse error.
If P then Q; P is false; so Q must be false. Invalid.
What it is
Reasoning from “If P, then Q” and “not P” to the conclusion “not Q”. It is the invalid look-alike of modus tollens.
The pattern
If P then Q. Not P. Therefore, not Q. (invalid) Valid look-alike (modus tollens): If P then Q. Not Q. Therefore, not P.
An example
“If you’re a practicing lawyer, you’ve passed a bar exam. Jordan isn’t a practicing lawyer, so Jordan hasn’t passed a bar exam.”
Jordan might have passed the bar and then chosen another career.
Why it fails
P is one way to guarantee Q, not the only way. When P is false, Q can still be true for some other reason.
When it’s not a fallacy
Most lists skip this part. Calling a fair point a fallacy is a mistake too.
It can be fair when
- The speaker clearly means “only if”. “You’ll get dessert if you finish your vegetables” is usually understood as “only if”, and with a biconditional the inference is valid.
- The second premise alone already implies the conclusion.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Town hall. Rosa: “We should raise the minimum wage. People can’t afford groceries.” Glen: “I hear you, but when wages go up, businesses raise their prices to cover it. That happens every time. So keep the wage where it is, and prices stay where they are.” Rosa: “I brought the food bank’s numbers, so let me pass those around.”
What’s the flaw?
Glen’s rule says a raise is one thing that pushes prices up. It doesn’t say it’s the only thing, so holding wages flat doesn’t freeze prices: rent, supply costs and fuel can push them up anyway.
A fair reply
“Prices climb for plenty of other reasons, so keeping wages flat won’t hold them still.”
Often confused with
- Mistaken negation
Improper transposition turns “if P then Q” into the rule “if not P then not Q”. Denying the antecedent applies that mistake to a case.
- Affirming the consequent
Its twin: both run a one-way conditional backwards.
Where the name comes from
The antecedent is the “if” part of an if-then, from the Latin for “going before.” Denying it means saying that part is false, then concluding the “then” part must be false too. It’s also called the inverse error: the inverse puts a “not” in front of both parts, and this move treats that new version as true.
Sources
- Denying the Antecedent, The Fallacy Files
- Fallacies, Bradley Dowden, Internet Encyclopedia of Philosophy
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of denying the antecedent, how to answer it in a real conversation, and practice rounds that mix it with its look-alikes, so you learn the difference, not just the name. Coming soon to iPhone and Android.
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