Disjunctive Syllogism

3.Disjunctive Syllogism – A syllogism whose major premise is a disjunctive proposition.

a.It is a strict disjunctive if only one among the alternatives enumerated in

the major premise is true. For the disjunctive syllogism in the strict sense

the following rules are applicable:

Rule 1: If the minor premise posits one or more members of the

major premise, the conclusion must sublate each of the other

members.

It is either A or B. It is either A or B or C.

But it is A. But it is A.

Therefore it is not B. Therefore it is neither B nor C.

Rule 2: If the minor premise sublates one or more of the members

of the major premise, the conclusion posits the remaining

members, one of which must be true.

It is either A or B. It is either A or B or C.

But it is not A. But it is not A.

Therefore it is B. Therefore it is either B or C.

b.It is a broad disjunctive if at least one alternative among those

enumerated in the major premise is true but more may be true. In a

disjunctive syllogism in the broad sense, the major premise is a

disjunctive proposition in the broad sense. There is only one valid

procedure: to sublate one (or more – but not all) of the members in the

minor and posit the remaining member or (members) in the conclusion.

If more than one member remains, the conclusion itself must be a

disjunctive proposition in the broad sense.

It is either A or B or C or D – at least one of them

But it is neither A nor B;

Therefore it is either C or D – at least one of them.