Affirming a disjunct

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The logical fallacy of affirming a disjunct also known as the fallacy of the alternative disjunct occurs when a deductive argument takes either of the two following forms:

A or B

Therefore, it is not the case that B

A or B

Therefore, it is not the case that A

The fallacy lies in concluding that one disjunct must be false because the other disjunct is true; in fact they may both be true. A similar form that is valid has the second premise (rather than the conclusion) be a negation. The valid form is known as disjunctive syllogism.

The following argument is a clear case of this fallacy:

It will rain somewhere tomorrow or the sun will shine somewhere tomorrow.

It will rain somewhere tomorrow. (It will rain here according to the weather forecast).

Therefore, it is not the case that the sun will shine somewhere tomorrow.

This inference is obviously invalid. The sun always shines somewhere. Both of the premises are clearly true while the conclusion is clearly false.

The following example is trickier:

Two is an even number or two is an odd number.

Two is an even number.

Therefore, it is not the case that two is an odd number.

This argument seems to be valid because there is another use of the word "or" in ordinary language that would seem more appropriate. If the disjunction is exclusive, that is to say, the "or" implies that only one of the disjuncts is perfectly true, then the argument is valid. However, the meaning of "or" is stipulated in propositional logic in order to avoid equivocation, and this argument is invalid. In this case, the "or" is said to be inclusive, in that it stipulates that one or both of the disjuncts is true. A similar argument that is in fact valid will have the implied assumption explicitly stated, as follows:

Two is an even number or two is an odd number.

Two is an even number.

No number can be both even and odd.

Therefore, it is not the case that two is an odd number.

External links

[Fallacy files: affirming a disjunct]

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Affirming a disjunct

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