Affirming a disjunct
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Affirming a disjunct occurs in a deductive argument when it is assumed, because one of multiple possibilities is true, that the other or others are false. It is a misuse use of the law of excluded middle.
However, in select circumstances under the right conditions this is not a fallacy, but a logically valid argument when the law of excluded middle is correctly applied.
It is a syllogistic fallacy and a formal fallacy.
Alternate names[edit]
This one's got an endless stream of boring alternate titles:
- (Fallacy of) Affirming a/the/one disjunct
- (Fallacy of) Affirmation of a/the/one disjunct
- (Fallacy of) Alternative syllogism
- (Fallacy of) Alternative disjunct
- (Fallacy of) Asserting an alternative
- (Fallacy of) A/the/one disjunctive syllogism
- (Fallacy of) Improper disjunctive syllogism
- (Fallacy of) False exclusionary disjunct
Form[edit]
Affirming a disjunct can take two forms:
Accepting the first term and denying the second:
- P1: A or B is true.
- P2: A is true.
- C: B is false.
Accepting the second term and denying the first:
- P1: A or B is true.
- P2: B is true.
- C: A is false.
Symbolic form[edit]
- P1: p .∨. q
- P2: p
- C: ∴ ~q
Error[edit]
Affirming a disjunct is fallacious because both options can be true at the same time, making the conclusion invalid.
Examples[edit]
Is the bird alive?[edit]
- P1: The bird is alive or on the ground.
- P2: The bird is on the ground.
- C: Therefore, it is not alive.
Both disjuncts can be true - a bird can be both alive and on the ground.
Who died on the fourth of July, 1826?[edit]
- P1: Either Thomas Jefferson or John Adams died on the fourth of July, 1826.
- P2: Thomas Jefferson died on the fourth of July, 1826.
- C: Therefore, John Adams did not die on the fourth of July, 1826.
John Adams!
- P1: Either Thomas Jefferson or John Adams died on the fourth of July, 1826.
- P2: John Adams died on the fourth of July, 1826.
- C: Therefore, Thomas Jefferson did not die on the fourth of July, 1826.[1]
Is Max a mammal?[edit]
The problem here is that "or" is in an inclusive sense, not an exclusive sense. A cat is in fact a mammal.
Fact or theory?[edit]
- P1: Evolution is either a theory or a fact.
- P2: Evolution is a theory.
- C: Thus, evolution is not a fact.[2]
Who's on the cover?[edit]
- P1: To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful.
- P2: This month's cover was a celebrity.
- C: Therefore, this celebrity is not very beautiful.
Again, "or" is in an inclusive sense.
Legitimate use[edit]
The only reason this fallacy occurs is because of the lack of clarity in the term "or" and the logical structure of the argument.
Different "or"[edit]
You only fallaciously affirm a disjunct when something is not a dilemma — when both options can be true — but you assert that only one can be true. If something truly is a dilemma, then affirming a disjunct is not fallacious. For example:
- P1: Amy is alive or dead.
- P2: Amy is alive.
- C: Amy is not dead.
This is a valid conclusion because the "or" is exclusive — only one may be true at a time.
- P1: The lights are on or off.
- P2: The lights are on.
- C: The lights are not off.
This is a valid conclusion because the situation is a binary one — there are only two options, of which neither can be true while the other is simultaneously true.
"Or" usually has two meanings in logic:[1]
- Inclusive (or "weak") disjunction (A or B): Implies A, or B, or both. One or both of the disjuncts is true, which is what is meant by the "and/or" of legalese. Affirming a Disjunct is a non-validating form of argument when "or" is inclusive, as it is usually interpreted in propositional logic.
- Exclusive (or "strong") disjunction (A xor B): Implies A, or B, but not both. Exactly one of the disjuncts is true.
Enthymeme[edit]
Alternately, one can view this fallacy as that of a hidden or suppressed premise.[1]
Consider this reformulation of the first form of affirming a disjunct:
- P1: A or B is true.
- P1.5: A and B can't both be true.
- P2: A is true.
C: B is false.
This statement is logically valid.
If we have reason to think that such a hidden premise is true (perhaps through tone of voice, outside knowledge, etc.) then we might assume that an exclusionary premise P1.5 exists. If, alternately, it is possible for both A and B to be true, it should be assumed that no such hidden premise exists.
External links[edit]
- Affirming a Disjunct — Logically Fallacious
- Affirming a disjunct — Philosophy Index
- Affirming a disjunct — LogFall
- Affirming the Disjunct — How to Never Be Wrong Again
References[edit]
- ↑ 1.0 1.1 1.2 Affirming a Disjunct, Fallacy Files
- ↑ Affirming a disjunct, Iron Chariots