Steelman
Confusing sufficient and necessary
Also called commutation of conditionals, mistaken reversal, converting a conditional, illicit conversion of a conditional.
Treating “if P then Q” as if it meant “if Q then P”.
What it is
Inferring “If Q, then P” from “If P, then Q”, that is, treating a sufficient condition as if it were also necessary, or a necessary condition as if it were also sufficient.
The pattern
If P then Q. Therefore, if Q then P. (invalid) Valid look-alike (contraposition): If P then Q. Therefore, if not Q then not P.
An example
“Every lottery winner bought a ticket. So if I buy a ticket, I’ll win.”
Buying a ticket is necessary for winning, not sufficient. Almost everyone who buys one loses.
Why it fails
In “if P then Q”, P is sufficient for Q and Q is necessary for P. Those relations only run one way. Buying a ticket is necessary to win the lottery; that doesn’t make it sufficient.
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
- Both directions are independently true, for example in a definition stated as a conditional, where the reverse direction is understood.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Host, on a sports podcast: “The plan for this offseason writes itself: get the defense into the top five, and the title follows. In the last ten years, not one team has won the title without a top-five defense. Not one.”
What’s the flaw?
A top-five defense is something every champion needed, not something that guarantees a title. Several top-five defenses miss out every year, since you still need an offense, health and luck. The host flipped “champions have it” into “having it makes champions”.
A fair reply
“Every champion had a great defense, but so did plenty of teams that went out in the first round.”
Often confused with
- Affirming the consequent
Affirming the consequent is this same reversal used as a step in an argument about a specific case.
- Mistaken negation
Improper transposition negates both parts without swapping them. This one swaps them without negating.
Where the name comes from
Sufficient means enough on its own; necessary means required. “If P then Q” makes P enough for Q and Q required for P, but only that way around. Commutation means trading places, like 2 + 3 becoming 3 + 2, and a conditional is an if-then. So commutation of conditionals, like mistaken reversal, means flipping the two halves. In converting a conditional and illicit conversion of a conditional, converting means turning around and illicit means not allowed.
Aristotle described this confusion in Sophistical Refutations as the “fallacy of the consequent”: people suppose that because rain makes the ground wet, wet ground means it has rained.
Sources
- Commutation of Conditionals, The Fallacy Files
- Logical Reasoning, Law School Admission Council
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of confusing sufficient and necessary, 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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