Affirming a disjunct

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.File:Wikipedia's W.svg 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.

Cogito ergo sum
Logic and rhetoric
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It is a syllogistic fallacy and a formal fallacy.

Alternate names

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

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.

Error

Affirming a disjunct is fallacious because both options can be true at the same time, making the conclusion invalid.

Examples

Is the bird alive?
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?

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.
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?
P1: Max is a cat or Max is a mammal.
P2: Max is a cat.
C: Therefore, Max is not a mammal.

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?
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?
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

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"

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
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.
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.

gollark: Just do neofetch.
gollark: Oh, you have a pre-ivy thing?
gollark: Well, I don't know what wrong thing your distro names it.
gollark: You might need vulkan-intel.
gollark: `vulkaninfo`

References
  1. Affirming a Disjunct, Fallacy Files
  2. Affirming a disjunct, Iron Chariots
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