Right Reasoning, pt. VI, The Disjunctive Syllogism

A crucial form of argument for presuppositional apologetics...

VI. The Disjunctive Syllogism

A. 1. Formally stated:

i. Either P or Q
ii. not-Q
iii. Therefore, P

A. 2. Defined:

The disjunctive syllogism “is an argument in which the leading premise is a disjunction, the other premise being a denial of one of the alternatives, concluding to the remaining alternative” (The Cambridge Dictionary of Philosophy, “Syllogism,” 894—96).

B. 1. Illustrated from life:

i. Either we’re having a (P) baby boy or a (Q) baby girl.

ii. The sonogram proved that we’re (not-P) not having a baby boy,

iii. therefore, (Q) we’re having a baby girl!

B. 2. a. Illustrated from the abortion debate:

i. Either that which is in the womb is (P) a human being or (Q) it is not.

ii. It is not the case that (not-Q) it is not a human being,

iii. therefore, (P) that which is in the womb is a human being.

B. 2. b. Again, Illustrated from the abortion debate:

i. The moral status and value of a human being is based on either (P) their essential being (what they are) or (Q) their social function (what they can do).

ii. The moral status and value of human beings (not-Q) are not based on social function (what they can do).

iii. Therefore, (P) the moral status and value of human beings are based on their essential being (what they are).

C. Fallacy factor:

Informally speaking, one risks setting up a false dilemma, which is defined here. And there’s also something to be said about the “or,” which elucidates whether or not one is constructing a false dilemma.

With a disjunctive syllogism the “or” may be either inclusive (making it a weak disjunctive) or exclusive (making it a strong disjunctive). The “or” may be inclusive and true provided not both alternatives (i.e., disjuncts) are false. For example, “Either I am typing this while on Mars or I am typing this on Jupiter,” obviously fails to meet the criterion. A more subtle example might be, “Either the Bible is the words of God or the words of men.” Neither alternative is true, as they stand. The orthodox view of inspiration holds to a careful admixture of these otherwise polarized concepts. Thus, both alternatives are false, as far as they go.

The “or” may be exclusive when exactly one alternative is true and exactly one false. “Either is will pass philosophy class or I will fail” would be an instance of an exclusive or strong disjunction.

You can see how this subtlety, which may seem tedious at first glance, is crucial for establishing the right argument.