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, it should be noted that 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.
C1: B is false.

Accepting the second term and denying the first:

P1: A or B is true.
P2: B is true.
C1: A is false.

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. C1: 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]

Thomas Jefferson! P1: Either Thomas Jefferson or John Adams died on the fourth of July, 1826. P2: Thomas Jefferson died on the fourth of July, 1826. C1: 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. C1: Therefore, Thomas Jefferson did not die on the fourth of July, 1826.[1]

Is Max a mammal?[edit]

P1: Max is a cat or Max is a mammal.
P2: Max is a cat.
C1: Therefore, Max is not a mammal.[2]

The problem here is that "or" is in an inclusive sense, not an exclusive sense. It is possible for something to be both a cat and a mammal.

Fact or theory?[edit]

P1: Evolution is either a theory or a fact. P2: Evolution is a theory. C1: Thus, evolution is not a fact.[3]

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.
C1: Therefore, this celebrity is not very beautiful.[2]

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.
C1: 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.
C1: 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]

See the main article on this topic: Enthymeme

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.
C1: 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]

References[edit]