Right Reasoning, pt. II, Modus Tollens

To continue our series in valid forms of argument...

II. Modus Tollens (Latin, lit. “The mode of taking”):

A. Formally stated:

1. If P is the case, the Q is also the case;
2. Not-Q,
3. Therefore, not-P

B. 1. Illustrated from ethics:

(Here I cite Gregory Koukl and Francis Beckwith’s Relativism: Feet Firmly Planted in Mid-Air, 1999, 65.)

“In like fashion [to B. F. Skinner’s conclusions in Beyond Freedom and Dignity], relativists must remove the words praise and blame from their vocabularies. But if the notions of praise and blame are valid, then relativism must be false.”

The line of reasoning is modus tollens.

i. If (P) moral relativism is the case, then (Q) the words praise and blame are unintelligible.

ii. But, (not-Q) the words praise and blame are valid moral categories (even presupposed by relativists!).

iii. Therefore, (not-P) relativism is not the case.

B. 2. Illustrated from Scripture (1 John 2:19, speaking of the antichrist heretics):

“They went out from us, but they were not of us; for if they had been of us, they would have continued with us. But they went out, that it might become plain that they all are not of us.”

Again, modus tollens.

i. If (P) they had been of us, then (Q) they would have continued with us.

ii. But (not-Q) they did not continue with us.

iii. Therefore, (not-P) they were not of us.

B. 3. Illustrated from Sir Arthur Conan Doyle’s Sherlock Holmes, “The Adventure of Silver Blaze” (since Sherlock Holmes is Beaner new favorite movie!):

“A dog was kept in the stalls, and yet, though someone had been in and fetched out a horse, the dog had not barked. Obviously the visitor was someone whom the dog knew well...”

i. If (P) the horse thief was a stranger, then (Q) the dog would have barked, since the dog always barks at strangers.

ii. But (not-Q) the dog never barked.

iii. Therefore, (not-P) the horse thief was not a stranger.

C. The fallacy factor:

As with the modus ponens, discussed in pt. I of the Right Reasoning series, the modus tollens is susceptible to a formal logical fallacy, namely the fallacy of 'denying the antecedent.' (Remember, in the case of an “If...then” conditional statement, the “If” clause is the antecedent, and the “then” clause is the consequent.)

Obviously, the fallacious attempt at a modus tollens would formally follow like this:

1. If P, then Q;
2. Not-P,
3. Therefore, not-Q.

However, the conclusion, though perhaps true, doesn’t follow from the premises. This too is an invalid line of inference.

Consider this.

1. If (P) the doctrine of the perseverance of the saints (i.e., that the elect will persevere in their faith to the end) is true, then (Q) no Christian would denounce the faith.

2. However, (not-Q) some once-professed Christians do denounce the faith.

3. Therefore, (not-P) the doctrine of the perseverance of the saints is not true.

It is amazing how many Arminians believe this to be a reasonable argument!

D. This last argument is valid, yet unsound: (see section D of Right Reasoning, pt I).