Inclusive and Exclusive Disjunction
Please observe that the disjunctive syllogism works whether 'or' is considered 'exclusive' or 'inclusive' disjunction. See below for the definitions of these terms.
There are two kinds of logical disjunction:
- inclusive means "and/or" - at least one of them is true, or maybe both.
- exclusive ("xor") means exactly one must be true, but they cannot both be.
The widely used English language concept of or is often ambiguous between these two meanings, but the difference is pivotal in evaluating disjunctive arguments.
This argument:
- Either P or Q.
- Not P.
- Therefore, Q.
is valid and indifferent between both meanings. However, only in the exclusive meaning is the following form valid:
- Either P or Q (exclusive).
- P.
- Therefore, not Q.
With the inclusive meaning you could draw no conclusion from the first two premises of that argument. See affirming a disjunct.
Read more about this topic: Disjunctive Syllogism
Famous quotes containing the words inclusive and/or exclusive:
“We are rarely able to interact only with folks like ourselves, who think as we do. No matter how much some of us deny this reality and long for the safety and familiarity of sameness, inclusive ways of knowing and living offer us the only true way to emancipate ourselves from the divisions that limit our minds and imaginations.”
—bell hooks (b. 1955)
“The exclusive in fashionable life does not see that he excludes himself from enjoyment, in the attempt to appropriate it.”
—Ralph Waldo Emerson (1803–1882)