I call upon You, Lord, God of Abraham and God of Isaac and God of Jacob and Israel, You who are the Father of our Lord Jesus Christ, the God who, through the abundance of your mercy, was well-pleased towards us so that we may know You, who made heaven and earth, who rules over all, You who are the one and the true God, above whom there is no other God; You who, by our Lord Jesus Christ gave us the gift of the Holy Spirit, give to every one who reads this writing to know You, that You alone are God, to be strengthened in You, and to avoid every heretical and godless and impious teaching.

St Irenaeus of Lyons, Against the Heresies 3:6:4

Saturday, February 6, 2010

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.


  1. All of these arguments are helpful. There was a time when I was searching for a book which listed and succinctly described logical arguments, fallacies, and formal logic. This series of posts helps greatly with the arguments.

  2. Thanks for the kind words, Steve. I'm blessed that someone has found them helpful. I think that you'll enjoy the final entry, which I'm just about to post; it's on the transcendental argument. And you know how important our understanding of it is.

    Thanks for reading.