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Affirming a disjunct

A formal fallacy in which a positive (affirmative) result for one alternative of an adjunct statement is (mis-)interpreted to imply a negative result for the other option

The following is an example of an affirmation of a disjunction:

It will rain or snow today.
It is raining.

Therefore, it will not snow today.

Even if the premise “It will rain or snow today” holds true, the conclusion does not necessarily so – it is quite possible that there may be both, rain and snow, during the same day (or even at the same time).

Description

In most cases, the underlying error is likely to be a confusion between inclusive and exclusive disjunction (see: ad­junction and contra­valence).

Another possibility is an incorrect application of the Modus tollendo ponens, especially when mixed with the Modus ponendo tollens, can also lead to this fallacy. For comparison, the following table compares the two valid forms with the fallacy:

About the name

This form is similar to the Modus Ponendo Tollens, in which one side of an exclusive disjunct (contravalence) is negated and it follows that the other is affirmative. In this fallacy, the part of the disjunct statement is instead affirmed and it is (incorrectly) assumed that the other side must be negated.

However, the use of the term “disjunction” is somewhat misleading in this context, as this deduction is invalid only for certain kinds of disjunct statements, namely adjunctions (inclusive disjunctions) while it is a valid conclusion for contravalent (exclusive disjunction) statements.

When are such inferences valid?

Affirming a disjunct is a valid conclusion exactly when the premise contains a contravalence (exclusive disjunction) rather than an adjunction (inclusive disjunction). Furthermore, it must be ensured that the set of options is complete, i.e., that there are no other possibilities than the ones put forward.

Example:

For dessert, you can have either an ice cream or a fruit salad.
I’ll have ice cream!

So no fruit salad for you.

By phrasing with “either … or” it is implied that there is an exclusive choice to be made: You can choose either ice cream or fruit salad, but not both! (However, the possibility that one might not want any dessert at all is not considered here).

If the above premises are fulfilled, this is valid inferrence, namely a Modus Ponendo Tollens.

See also

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