Formal Argument Patterns Using Disjunctive Claims

Introduction
Disjunctions are compound claims which are made up of "disjuncts" The disjuncts are separated by the word "or" or some synonym.

Inclusive and Exclusive "or"

The word "or" is more complex than many first realize. It has two meanings. This isn't always apparent from the context of the sentence, so one must be careful with arguments featuring disjunctive claims.

Exclusive "or"

Example: "Either I will go to Yale or I will go to Stanford." We can see from the context of this sentence that the person is going to one or the other but not both.

Exclusive "or" means, "Either A or B, but not both A and B."

Inclusive "or"

Example: "Either Bob will be at the party or Donna will be at the party." We can see from the context of this sentence that it is possible that both Bob and Donna could show up to the party.

Inclusive "or" means, "Either A or B, or BOTH A and B."

Valid Disjunctive Syllogisms

The inclusive / exclusive aspect of "or" means that there are two disjunctive syllogisms that are valid and two that are invalid (formal fallacies). In this section we will cover the valid forms.

P or Q. It is not the case that P. Therefore, Q.

For instance, "Either I will go to Yale, or I will go to Stanford. I will not go to Yale. Therefore, I will go to Stanford."

P or Q. It is not the case that Q. Therefore, P.

For instance, "Either I will go to Yale, or I will go to Stanford. I will not go to Stanford. Therefore, I will go to Yale."

Notice that in each of the valid forms the second premise denies one of the disjuncts. Valid disjunctive syllogisms always deny one of the disjuncts. Valid DS are limited to these two because of the exclusive / inclusive problem. To learn more about this go to invalid disjunctive syllogisms.

Valid Disjunctive Syllogism Valid Disjunctive Syllogism: