Right Reasoning, pt. V, Reductio Ad Absurdum

We come now to a favorite of mine, the...

V. Reductio ad absurdum

A. Formally stated:

1. In order to prove P,
2. Presuppose, for argument’s sake, its contrary, not-P.
3. Argue that, in presupposing not-P, we’d have to conclude Q.
4. Demonstrate the absurdity and/or inviability of Q.
5. Conclude, P must be true.

B. 1. Illustrated from a pro-abortion argument:

i. In order to prove that, (P) women do not have the right to destroy the life within them,

ii. presuppose the opposite that, (not-P) women do have the right to destroy the life within them, since “women have a right over their own bodies” and that that “tissue” within them “is their own body.”

iii. However, if we presuppose this (not-P), then we must conclude that (Q) a. the aborted “tissue” (i.e., the child) has identical DNA to the woman, and b. that approximately half of women who have abortions also have penises (because approximately half of those aborted are boys).

iv. But both of these conclusions (Q) are utterly absurd.

v. Therefore, (P) it is not the case that women have the right to destroy the life within them.

B. 2. Illustrated from Scripture (Matt 12:24—26):

i. (P-assumed: I [Jesus] do not cast out demons by Beelzebul).

ii. Assume though that, (not-P) Satan casts out Satan

iii. If (not-P) Satan casts out Satan, then (Q) his kingdom is divided, ruined and cannot continue.

iv. But, since demonic activity is continuing, clearly (Q) is absurd.

v. Therefore, (P) I do not cast out demons by the power of Beelzebul.

B. 3. Again, Illustrated from Scripture (Matt 22:41ff):

i. (P-assumed: I [Jesus] am the Christ, more than merely David’s son)

ii. Assume (not-P), that I am merely David’s physical descendent (the Pharisees’ answer, see v. 42).

iii. If (not-P), then (Q) Jesus could not be David’s “Lord” (especially in first century near Eastern culture!!).

iv. But since David, writing “in the Spirit,” in Psalm 110:1, calls him “Lord,” (Q) is absurd.

v. Therefore, (P) I am the Christ, more than merely David’s son.

(NOTE: “And no one was able to answer him a word, nor from that day did anyone dare to ask him any more question” v. 46.)

Douglas Groothuis comments on this passage in this way:

“Jesus’ point was not to deny the Christ’s ancestral lineage to David, since Jesus himself is called ‘the son of David’ in the Gospels (Matthew 1:1), and since Jesus accepts the title without rebuke (Matthew 20:30—31). Rather, Jesus is denying that the Christ is merely the son of David; he is also Lord, and was so at the time of David. By using this reductio ad absurdum argument, Jesus attempts to expand his audience’s understanding of who the Christ is and that he himself is the Christ” (On Jesus, 34).

C. Fallacy factor:

Because the reductio is an indirect or negative argument, it is not as susceptible to particular fallacies. In essence, however, its just an expanded modus tollens. And since the modus tollens is subject to both informal fallacies and the formal fallacy of denying the antecedent, review those pitfalls there.