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 {{wpl|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==
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:
{{syl
|2=A or B is true.
|4=A is true.
|5=C|6=B is false.
}}

Accepting the second term and denying the first:
{{syl
|2=A or B is true.
|4=B is true.
|5=C|6=A is false.
}}
=== Symbolic form ===
{{syl
|2=p .&#8744;. q
|4=p
|5=C|6=&#8756; ~q}}

==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?===
{{syl
|2=The [[bird]] is alive or on the ground.
|4=The bird is on the ground.
|5=C|6=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]]!
{{syl
|2=Either Thomas Jefferson or [[John Adams]] died on the fourth of July, 1826. 
|4=Thomas Jefferson died on the fourth of July, 1826. 
|5=C|6=Therefore, John Adams did not die on the fourth of July, 1826.
}}

John Adams!
{{syl
|2=Either Thomas Jefferson or John Adams died on the fourth of July, 1826. 
|4=John Adams died on the fourth of July, 1826. 
|5=C|6=Therefore, Thomas Jefferson did not die on the fourth of July, 1826.<ref name=FF>[http://www.fallacyfiles.org/afonedis.html Affirming a Disjunct], Fallacy Files</ref>
}}

===Is Max a mammal?===
{{syl
|2=Max is a [[cat]] or Max is a [[mammal]].
|4=Max is a cat.
|5=C|6=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?===
{{syl
|2=[[Evolution]] is either a [[theory]] or a [[fact]].
|4=[[Evolution is only a theory|Evolution is a theory]].
|5=C|6=Thus, evolution is not a fact.<ref>[http://wiki.ironchariots.org/index.php?title=Affirming_a_disjunct Affirming a disjunct], [[Iron Chariots]]</ref>
}}

===Who's on the cover?===
{{syl
|2=To be on the cover of Vogue Magazine, one must be a celebrity or very beautiful.
|4=This month's cover was a celebrity.
|5=C|6=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 [[False dilemma|''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:
{{syl
|2=Amy is alive or dead.
|4=Amy is alive.
|5=C|6=Amy is not dead.
}}

This is a valid conclusion because the "or" is exclusive — only one may be true at a time.
{{syl
|2=The lights are on or off.
|4=The lights are on.
|5=C|6=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:<ref name=FF />
*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===
{{main|Enthymeme}}
Alternately, one can view this fallacy as that of a hidden or suppressed premise.<ref name=FF />

Consider this reformulation of the first form of affirming a disjunct:
{{syl
|2=A or B is true.
|3=P1.5|4=A and B can't both be true.
|5=P2|6=A is true.
|7=C|8=B is false.
}}

This statement is logically valid.

If we have reason to think that such a hidden premise is true (perhaps through [[Fallacy of accent|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==
*[http://www.logicallyfallacious.com/index.php/logical-fallacies/15-affirming-a-disjunct Affirming a Disjunct] — Logically Fallacious
*[http://www.philosophy-index.com/logic/fallacies/affirming-disjunct.php Affirming a disjunct] — Philosophy Index
*[https://logfall.wordpress.com/affirming-a-disjunct/ Affirming a disjunct] — LogFall
*[http://thebiconditional.blogspot.com/2012/11/the-propositional-formal-fallacies_29.html Affirming the Disjunct] — How to Never Be Wrong Again 

==References==
{{reflist}}

{{logfal}}

[[Category:Formal fallacies]]

Categories: Formal fallacies