Disjunctive Syllogism
A valid argument form that uses an 'either/or' premise and denies one option to conclude the other, but only works if the two options are truly exhaustive.
THE IDEA
DISJUNCTIVE SYLLOGISM
The disjunctive syllogism is perhaps the easiest valid form to remember. This form always has a disjunctive statement—an “either/or” statement—as one of its premises. For example:
Either Bach wrote Mass in B Minor or Wagner wrote it. Wagner did not write Mass in B Minor. Therefore, Bach wrote Mass in B Minor.
In the above, we are presented with two options in the first premise: Bach or Wagner. If these really are the only two choices, and if Wagner did not write Mass in B Minor, then the conclusion follows logically from the premises. If there were other choices that were intentionally left out, then this would be the fallacy of bifurcation.
Validity concerns the inference: if the premises are true, the conclusion must be true. A valid form can contain false premises. Soundness requires both a valid inference and true premises, so a false either-or premise can make a disjunctive syllogism unsound without changing its valid form.
The disjunctive syllogism has the following symbolic form:
Either A or B. Not B (or, not A). Therefore, A (or, B).
From this symbolic form we can clearly see that it does not matter which side of the disjunctive statement is denied. If one option is negated, then the other must be true. Consider these examples.
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Either Holmes solved the crime or Dr. Watson solved the crime. Dr. Watson did not solve the crime. Therefore, Holmes solved the crime.
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Either you go to college or you get a job. You did not get a job. So, you will go to college.
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Truth is either a construct of institutions or it is the correspondence of language to reality. Truth is not a construct of institutions. Therefore, truth is the correspondence of language to reality.
The form is valid. In applying it, check that the disjunction is true and that the rejected option has actually been ruled out.
When to use it
In a logic exercise with two exhaustive possibilities, eliminate one to infer the other; in an actual investigation, check the premise that no other possibility remains.
A binary decision in business (e.g., invest in project A or project B) when resources are limited and the options are mutually exclusive.
Solving a logic puzzle with two possible authors for an anonymous text.
Evaluating a philosophical argument that presents two competing theories and seeks to eliminate one.
FROM THEORY TO EVERYDAY LIFE
In practice
Bach or Wagner
Either Bach wrote Mass in B Minor or Wagner wrote it. Wagner did not write Mass in B Minor. Therefore, Bach wrote Mass in B Minor.
Holmes or Watson
Either Holmes solved the crime or Dr. Watson solved the crime. Dr. Watson did not solve the crime. Therefore, Holmes solved the crime.
College or Job
Either you go to college or you get a job. You did not get a job. So, you will go to college.
Truth Correspondence
Truth is either a construct of institutions or it is the correspondence of language to reality. Truth is not a construct of institutions. Therefore, truth is the correspondence of language to reality.
A MOMENT TO REFLECT
Put it to work.
Can you recall a real argument you've encountered that used a disjunctive syllogism? Were the two options truly exhaustive?
How would you reconstruct a flawed disjunctive syllogism to show that it commits the fallacy of bifurcation?
How could an overlooked alternative make the either-or premise false while leaving the argument’s form valid?
Often confused with
CONTINUE THE CONVERSATION
Source texts
- Informal Logical Fallacies A Brief Guide