Steelman
Denying a conjunct
Also called fallacy of the disjunctive syllogism (misapplied).
Not both P and Q; not P; so Q. Invalid, since both could be false.
What it is
Reasoning from “Not both P and Q” and “not P” to “Q”. Ruling out that both are true doesn’t mean at least one is.
The pattern
Not both P and Q. Not P. Therefore, Q. (invalid) Valid look-alike: Not both P and Q. P. Therefore, not Q.
An example
“You can’t be at the party and at the library at the same time. You’re not at the party, so you must be at the library.”
You could be at home, at work, or anywhere else.
Why it fails
“Not both” allows three possibilities: only P, only Q, or neither. Eliminating P still leaves “neither”.
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
- There’s an extra premise that one of the two must be true (“P or Q”). Then the inference is valid.
Try one
A question from the app. The wrong answers are its usual look-alikes.
Fan theory thread for a murder-mystery show. Ollie: “The show made it clear Marcus couldn’t have been at the gala and on the yacht at nine; the timeline won’t allow both. And the bartender swore he never showed up, so he wasn’t at the gala. He was on the yacht at nine, then, right where the body turned up. Episode six is going to be wild.”
What’s the flaw?
“Not both” leaves room for neither. Ruling out the gala doesn’t put Marcus on the yacht; he could have been anywhere else that night.
A fair reply
“Missing the gala doesn’t put him on the yacht; he could’ve been anywhere.”
Often confused with
- False dilemma
A false dilemma asserts that only two options exist. Denying a conjunct never asserts it; it silently assumes it.
- Affirming a disjunct
Affirming a disjunct starts from “P or Q” and wrongly rules one out.
Where the name comes from
A conjunct is one part of an “and” statement, from a Latin word for “joined together.” The argument says “not both,” denies one conjunct, then decides the other must be true. The disjunctive syllogism is a valid step: “it’s this or that; not this; so that.” The rarer name, fallacy of the disjunctive syllogism (misapplied), says that step is being used on “not both,” where it doesn’t work.
Sources
- Denying a Conjunct, The Fallacy Files
In the app
Practice spotting it on arguments that sound real.
Steelman has more examples of denying a conjunct, 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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