Disjunctive syllogism
A disjunctive syllogism is one valid, simple argument form:- Either P or Q.
- Not P.
- Therefore, Q.
- ¬
Roughly, we are told that it has to be one or the other that is true; then we are told that it is not the one that is true; so we infer that it has to be the other that is true. The reason this is called "disjunctive syllogism" is that, first, it is a syllogism--a three-step argument--and second, it contains a disjunction, which means simply an "or" statement. "Either P or Q" is a disjunction; P and Q are called the statement's disjuncts.
Here is an example:
- Either I will choose soup or I will choose salad.
- I will not choose soup.
- Therefore, I will choose salad.
- Either the Browns win or the Bengals win.
- The Browns do not win.
- Therefore, the Bengals win.
It should be noted with importance that there are two kinds of logical disjunction:
- inclusive means "and/or" where at least one term must be true or they can both be true.
- exclusive ("xor") means one must be true and the other must be false. Both terms cannot be true and both cannot be false.
This argument:
- Either P or Q.
- Not P.
- Therefore, Q.
- Either P or Q (exclusive).
- P.
- Therefore, not Q.
Other forms of syllogism: hypothetical syllogism, categorical syllogism.