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 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
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:

Accepting the second term and denying the first:

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

Is the bird 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!

John Adams!

Is Max a mammal?
The problem here is that "or" is in an inclusive sense, not an exclusive sense. A cat is in fact a mammal.

Who's on the cover?
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:

This is a valid conclusion because the "or" is exclusive — only one may be true at a time.

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:
 * 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
Alternately, one can view this fallacy as that of a hidden or suppressed premise.

Consider this reformulation of the first form of affirming a disjunct:

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.